MAYBE Problem: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(U101(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U101(tt(),V1,V2)) -> U102#(isNaturalKind(V1),V1,V2) active#(U102(tt(),V1,V2)) -> isLNatKind#(V2) active#(U102(tt(),V1,V2)) -> U103#(isLNatKind(V2),V1,V2) active#(U103(tt(),V1,V2)) -> isLNatKind#(V2) active#(U103(tt(),V1,V2)) -> U104#(isLNatKind(V2),V1,V2) active#(U104(tt(),V1,V2)) -> isNatural#(V1) active#(U104(tt(),V1,V2)) -> U105#(isNatural(V1),V2) active#(U105(tt(),V2)) -> isLNat#(V2) active#(U105(tt(),V2)) -> U106#(isLNat(V2)) active#(U11(tt(),N,XS)) -> isNaturalKind#(N) active#(U11(tt(),N,XS)) -> U12#(isNaturalKind(N),N,XS) active#(U111(tt(),V2)) -> isLNatKind#(V2) active#(U111(tt(),V2)) -> U112#(isLNatKind(V2)) active#(U12(tt(),N,XS)) -> isLNat#(XS) active#(U12(tt(),N,XS)) -> U13#(isLNat(XS),N,XS) active#(U121(tt(),V2)) -> isLNatKind#(V2) active#(U121(tt(),V2)) -> U122#(isLNatKind(V2)) active#(U13(tt(),N,XS)) -> isLNatKind#(XS) active#(U13(tt(),N,XS)) -> U14#(isLNatKind(XS),N,XS) active#(U14(tt(),N,XS)) -> splitAt#(N,XS) active#(U14(tt(),N,XS)) -> snd#(splitAt(N,XS)) active#(U171(tt(),V2)) -> isLNatKind#(V2) active#(U171(tt(),V2)) -> U172#(isLNatKind(V2)) active#(U181(tt(),V1)) -> isLNatKind#(V1) active#(U181(tt(),V1)) -> U182#(isLNatKind(V1),V1) active#(U182(tt(),V1)) -> isLNat#(V1) active#(U182(tt(),V1)) -> U183#(isLNat(V1)) active#(U191(tt(),V1)) -> isNaturalKind#(V1) active#(U191(tt(),V1)) -> U192#(isNaturalKind(V1),V1) active#(U192(tt(),V1)) -> isNatural#(V1) active#(U192(tt(),V1)) -> U193#(isNatural(V1)) active#(U201(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U201(tt(),V1,V2)) -> U202#(isNaturalKind(V1),V1,V2) active#(U202(tt(),V1,V2)) -> isLNatKind#(V2) active#(U202(tt(),V1,V2)) -> U203#(isLNatKind(V2),V1,V2) active#(U203(tt(),V1,V2)) -> isLNatKind#(V2) active#(U203(tt(),V1,V2)) -> U204#(isLNatKind(V2),V1,V2) active#(U204(tt(),V1,V2)) -> isNatural#(V1) active#(U204(tt(),V1,V2)) -> U205#(isNatural(V1),V2) active#(U205(tt(),V2)) -> isLNat#(V2) active#(U205(tt(),V2)) -> U206#(isLNat(V2)) active#(U21(tt(),X,Y)) -> isLNatKind#(X) active#(U21(tt(),X,Y)) -> U22#(isLNatKind(X),X,Y) active#(U22(tt(),X,Y)) -> isLNat#(Y) active#(U22(tt(),X,Y)) -> U23#(isLNat(Y),X,Y) active#(U23(tt(),X,Y)) -> isLNatKind#(Y) active#(U23(tt(),X,Y)) -> U24#(isLNatKind(Y),X) active#(U231(tt(),V2)) -> isLNatKind#(V2) active#(U231(tt(),V2)) -> U232#(isLNatKind(V2)) active#(U241(tt(),V1,V2)) -> isLNatKind#(V1) active#(U241(tt(),V1,V2)) -> U242#(isLNatKind(V1),V1,V2) active#(U242(tt(),V1,V2)) -> isLNatKind#(V2) active#(U242(tt(),V1,V2)) -> U243#(isLNatKind(V2),V1,V2) active#(U243(tt(),V1,V2)) -> isLNatKind#(V2) active#(U243(tt(),V1,V2)) -> U244#(isLNatKind(V2),V1,V2) active#(U244(tt(),V1,V2)) -> isLNat#(V1) active#(U244(tt(),V1,V2)) -> U245#(isLNat(V1),V2) active#(U245(tt(),V2)) -> isLNat#(V2) active#(U245(tt(),V2)) -> U246#(isLNat(V2)) active#(U251(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U251(tt(),V1,V2)) -> U252#(isNaturalKind(V1),V1,V2) active#(U252(tt(),V1,V2)) -> isLNatKind#(V2) active#(U252(tt(),V1,V2)) -> U253#(isLNatKind(V2),V1,V2) active#(U253(tt(),V1,V2)) -> isLNatKind#(V2) active#(U253(tt(),V1,V2)) -> U254#(isLNatKind(V2),V1,V2) active#(U254(tt(),V1,V2)) -> isNatural#(V1) active#(U254(tt(),V1,V2)) -> U255#(isNatural(V1),V2) active#(U255(tt(),V2)) -> isLNat#(V2) active#(U255(tt(),V2)) -> U256#(isLNat(V2)) active#(U261(tt(),V2)) -> isLNatKind#(V2) active#(U261(tt(),V2)) -> U262#(isLNatKind(V2)) active#(U271(tt(),V2)) -> isLNatKind#(V2) active#(U271(tt(),V2)) -> U272#(isLNatKind(V2)) active#(U281(tt(),N)) -> isNaturalKind#(N) active#(U281(tt(),N)) -> U282#(isNaturalKind(N),N) active#(U282(tt(),N)) -> s#(N) active#(U282(tt(),N)) -> natsFrom#(s(N)) active#(U282(tt(),N)) -> cons#(N,natsFrom(s(N))) active#(U291(tt(),N,XS)) -> isNaturalKind#(N) active#(U291(tt(),N,XS)) -> U292#(isNaturalKind(N),N,XS) active#(U292(tt(),N,XS)) -> isLNat#(XS) active#(U292(tt(),N,XS)) -> U293#(isLNat(XS),N,XS) active#(U293(tt(),N,XS)) -> isLNatKind#(XS) active#(U293(tt(),N,XS)) -> U294#(isLNatKind(XS),N,XS) active#(U294(tt(),N,XS)) -> afterNth#(N,XS) active#(U294(tt(),N,XS)) -> head#(afterNth(N,XS)) active#(U301(tt(),X,Y)) -> isLNatKind#(X) active#(U301(tt(),X,Y)) -> U302#(isLNatKind(X),Y) active#(U302(tt(),Y)) -> isLNat#(Y) active#(U302(tt(),Y)) -> U303#(isLNat(Y),Y) active#(U303(tt(),Y)) -> isLNatKind#(Y) active#(U303(tt(),Y)) -> U304#(isLNatKind(Y),Y) active#(U31(tt(),N,XS)) -> isNaturalKind#(N) active#(U31(tt(),N,XS)) -> U32#(isNaturalKind(N),N,XS) active#(U311(tt(),XS)) -> isLNatKind#(XS) active#(U311(tt(),XS)) -> U312#(isLNatKind(XS),XS) active#(U312(tt(),XS)) -> pair#(nil(),XS) active#(U32(tt(),N,XS)) -> isLNat#(XS) active#(U32(tt(),N,XS)) -> U33#(isLNat(XS),N,XS) active#(U321(tt(),N,X,XS)) -> isNaturalKind#(N) active#(U321(tt(),N,X,XS)) -> U322#(isNaturalKind(N),N,X,XS) active#(U322(tt(),N,X,XS)) -> isNatural#(X) active#(U322(tt(),N,X,XS)) -> U323#(isNatural(X),N,X,XS) active#(U323(tt(),N,X,XS)) -> isNaturalKind#(X) active#(U323(tt(),N,X,XS)) -> U324#(isNaturalKind(X),N,X,XS) active#(U324(tt(),N,X,XS)) -> isLNat#(XS) active#(U324(tt(),N,X,XS)) -> U325#(isLNat(XS),N,X,XS) active#(U325(tt(),N,X,XS)) -> isLNatKind#(XS) active#(U325(tt(),N,X,XS)) -> U326#(isLNatKind(XS),N,X,XS) active#(U326(tt(),N,X,XS)) -> splitAt#(N,XS) active#(U326(tt(),N,X,XS)) -> U327#(splitAt(N,XS),X) active#(U327(pair(YS,ZS),X)) -> cons#(X,YS) active#(U327(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS) active#(U33(tt(),N,XS)) -> isLNatKind#(XS) active#(U33(tt(),N,XS)) -> U34#(isLNatKind(XS),N) active#(U331(tt(),N,XS)) -> isNaturalKind#(N) active#(U331(tt(),N,XS)) -> U332#(isNaturalKind(N),XS) active#(U332(tt(),XS)) -> isLNat#(XS) active#(U332(tt(),XS)) -> U333#(isLNat(XS),XS) active#(U333(tt(),XS)) -> isLNatKind#(XS) active#(U333(tt(),XS)) -> U334#(isLNatKind(XS),XS) active#(U341(tt(),N,XS)) -> isNaturalKind#(N) active#(U341(tt(),N,XS)) -> U342#(isNaturalKind(N),N,XS) active#(U342(tt(),N,XS)) -> isLNat#(XS) active#(U342(tt(),N,XS)) -> U343#(isLNat(XS),N,XS) active#(U343(tt(),N,XS)) -> isLNatKind#(XS) active#(U343(tt(),N,XS)) -> U344#(isLNatKind(XS),N,XS) active#(U344(tt(),N,XS)) -> splitAt#(N,XS) active#(U344(tt(),N,XS)) -> fst#(splitAt(N,XS)) active#(U41(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNaturalKind(V1),V1,V2) active#(U42(tt(),V1,V2)) -> isLNatKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isLNatKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> isLNatKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isLNatKind(V2),V1,V2) active#(U44(tt(),V1,V2)) -> isNatural#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNatural(V1),V2) active#(U45(tt(),V2)) -> isLNat#(V2) active#(U45(tt(),V2)) -> U46#(isLNat(V2)) active#(U51(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNaturalKind(V1),V1,V2) active#(U52(tt(),V1,V2)) -> isLNatKind#(V2) active#(U52(tt(),V1,V2)) -> U53#(isLNatKind(V2),V1,V2) active#(U53(tt(),V1,V2)) -> isLNatKind#(V2) active#(U53(tt(),V1,V2)) -> U54#(isLNatKind(V2),V1,V2) active#(U54(tt(),V1,V2)) -> isNatural#(V1) active#(U54(tt(),V1,V2)) -> U55#(isNatural(V1),V2) active#(U55(tt(),V2)) -> isLNat#(V2) active#(U55(tt(),V2)) -> U56#(isLNat(V2)) active#(U61(tt(),V1)) -> isPLNatKind#(V1) active#(U61(tt(),V1)) -> U62#(isPLNatKind(V1),V1) active#(U62(tt(),V1)) -> isPLNat#(V1) active#(U62(tt(),V1)) -> U63#(isPLNat(V1)) active#(U71(tt(),V1)) -> isNaturalKind#(V1) active#(U71(tt(),V1)) -> U72#(isNaturalKind(V1),V1) active#(U72(tt(),V1)) -> isNatural#(V1) active#(U72(tt(),V1)) -> U73#(isNatural(V1)) active#(U81(tt(),V1)) -> isPLNatKind#(V1) active#(U81(tt(),V1)) -> U82#(isPLNatKind(V1),V1) active#(U82(tt(),V1)) -> isPLNat#(V1) active#(U82(tt(),V1)) -> U83#(isPLNat(V1)) active#(U91(tt(),V1)) -> isLNatKind#(V1) active#(U91(tt(),V1)) -> U92#(isLNatKind(V1),V1) active#(U92(tt(),V1)) -> isLNat#(V1) active#(U92(tt(),V1)) -> U93#(isLNat(V1)) active#(afterNth(N,XS)) -> isNatural#(N) active#(afterNth(N,XS)) -> U11#(isNatural(N),N,XS) active#(fst(pair(X,Y))) -> isLNat#(X) active#(fst(pair(X,Y))) -> U21#(isLNat(X),X,Y) active#(head(cons(N,XS))) -> isNatural#(N) active#(head(cons(N,XS))) -> U31#(isNatural(N),N,XS) active#(isLNat(afterNth(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(afterNth(V1,V2))) -> U41#(isNaturalKind(V1),V1,V2) active#(isLNat(cons(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(cons(V1,V2))) -> U51#(isNaturalKind(V1),V1,V2) active#(isLNat(fst(V1))) -> isPLNatKind#(V1) active#(isLNat(fst(V1))) -> U61#(isPLNatKind(V1),V1) active#(isLNat(natsFrom(V1))) -> isNaturalKind#(V1) active#(isLNat(natsFrom(V1))) -> U71#(isNaturalKind(V1),V1) active#(isLNat(snd(V1))) -> isPLNatKind#(V1) active#(isLNat(snd(V1))) -> U81#(isPLNatKind(V1),V1) active#(isLNat(tail(V1))) -> isLNatKind#(V1) active#(isLNat(tail(V1))) -> U91#(isLNatKind(V1),V1) active#(isLNat(take(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(take(V1,V2))) -> U101#(isNaturalKind(V1),V1,V2) active#(isLNatKind(afterNth(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(afterNth(V1,V2))) -> U111#(isNaturalKind(V1),V2) active#(isLNatKind(cons(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(cons(V1,V2))) -> U121#(isNaturalKind(V1),V2) active#(isLNatKind(fst(V1))) -> isPLNatKind#(V1) active#(isLNatKind(fst(V1))) -> U131#(isPLNatKind(V1)) active#(isLNatKind(natsFrom(V1))) -> isNaturalKind#(V1) active#(isLNatKind(natsFrom(V1))) -> U141#(isNaturalKind(V1)) active#(isLNatKind(snd(V1))) -> isPLNatKind#(V1) active#(isLNatKind(snd(V1))) -> U151#(isPLNatKind(V1)) active#(isLNatKind(tail(V1))) -> isLNatKind#(V1) active#(isLNatKind(tail(V1))) -> U161#(isLNatKind(V1)) active#(isLNatKind(take(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(take(V1,V2))) -> U171#(isNaturalKind(V1),V2) active#(isNatural(head(V1))) -> isLNatKind#(V1) active#(isNatural(head(V1))) -> U181#(isLNatKind(V1),V1) active#(isNatural(s(V1))) -> isNaturalKind#(V1) active#(isNatural(s(V1))) -> U191#(isNaturalKind(V1),V1) active#(isNatural(sel(V1,V2))) -> isNaturalKind#(V1) active#(isNatural(sel(V1,V2))) -> U201#(isNaturalKind(V1),V1,V2) active#(isNaturalKind(head(V1))) -> isLNatKind#(V1) active#(isNaturalKind(head(V1))) -> U211#(isLNatKind(V1)) active#(isNaturalKind(s(V1))) -> isNaturalKind#(V1) active#(isNaturalKind(s(V1))) -> U221#(isNaturalKind(V1)) active#(isNaturalKind(sel(V1,V2))) -> isNaturalKind#(V1) active#(isNaturalKind(sel(V1,V2))) -> U231#(isNaturalKind(V1),V2) active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V1) active#(isPLNat(pair(V1,V2))) -> U241#(isLNatKind(V1),V1,V2) active#(isPLNat(splitAt(V1,V2))) -> isNaturalKind#(V1) active#(isPLNat(splitAt(V1,V2))) -> U251#(isNaturalKind(V1),V1,V2) active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V1) active#(isPLNatKind(pair(V1,V2))) -> U261#(isLNatKind(V1),V2) active#(isPLNatKind(splitAt(V1,V2))) -> isNaturalKind#(V1) active#(isPLNatKind(splitAt(V1,V2))) -> U271#(isNaturalKind(V1),V2) active#(natsFrom(N)) -> isNatural#(N) active#(natsFrom(N)) -> U281#(isNatural(N),N) active#(sel(N,XS)) -> isNatural#(N) active#(sel(N,XS)) -> U291#(isNatural(N),N,XS) active#(snd(pair(X,Y))) -> isLNat#(X) active#(snd(pair(X,Y))) -> U301#(isLNat(X),X,Y) active#(splitAt(0(),XS)) -> isLNat#(XS) active#(splitAt(0(),XS)) -> U311#(isLNat(XS),XS) active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N) active#(splitAt(s(N),cons(X,XS))) -> U321#(isNatural(N),N,X,XS) active#(tail(cons(N,XS))) -> isNatural#(N) active#(tail(cons(N,XS))) -> U331#(isNatural(N),N,XS) active#(take(N,XS)) -> isNatural#(N) active#(take(N,XS)) -> U341#(isNatural(N),N,XS) active#(U101(X1,X2,X3)) -> active#(X1) active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3) active#(U102(X1,X2,X3)) -> active#(X1) active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3) active#(U103(X1,X2,X3)) -> active#(X1) active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3) active#(U104(X1,X2,X3)) -> active#(X1) active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3) active#(U105(X1,X2)) -> active#(X1) active#(U105(X1,X2)) -> U105#(active(X1),X2) active#(U106(X)) -> active#(X) active#(U106(X)) -> U106#(active(X)) active#(U11(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U111(X1,X2)) -> active#(X1) active#(U111(X1,X2)) -> U111#(active(X1),X2) active#(U112(X)) -> active#(X) active#(U112(X)) -> U112#(active(X)) active#(U13(X1,X2,X3)) -> active#(X1) active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3) active#(U121(X1,X2)) -> active#(X1) active#(U121(X1,X2)) -> U121#(active(X1),X2) active#(U122(X)) -> active#(X) active#(U122(X)) -> U122#(active(X)) active#(U14(X1,X2,X3)) -> active#(X1) active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3) active#(U131(X)) -> active#(X) active#(U131(X)) -> U131#(active(X)) active#(snd(X)) -> active#(X) active#(snd(X)) -> snd#(active(X)) active#(splitAt(X1,X2)) -> active#(X1) active#(splitAt(X1,X2)) -> splitAt#(active(X1),X2) active#(splitAt(X1,X2)) -> active#(X2) active#(splitAt(X1,X2)) -> splitAt#(X1,active(X2)) active#(U141(X)) -> active#(X) active#(U141(X)) -> U141#(active(X)) active#(U151(X)) -> active#(X) active#(U151(X)) -> U151#(active(X)) active#(U161(X)) -> active#(X) active#(U161(X)) -> U161#(active(X)) active#(U171(X1,X2)) -> active#(X1) active#(U171(X1,X2)) -> U171#(active(X1),X2) active#(U172(X)) -> active#(X) active#(U172(X)) -> U172#(active(X)) active#(U181(X1,X2)) -> active#(X1) active#(U181(X1,X2)) -> U181#(active(X1),X2) active#(U182(X1,X2)) -> active#(X1) active#(U182(X1,X2)) -> U182#(active(X1),X2) active#(U183(X)) -> active#(X) active#(U183(X)) -> U183#(active(X)) active#(U191(X1,X2)) -> active#(X1) active#(U191(X1,X2)) -> U191#(active(X1),X2) active#(U192(X1,X2)) -> active#(X1) active#(U192(X1,X2)) -> U192#(active(X1),X2) active#(U193(X)) -> active#(X) active#(U193(X)) -> U193#(active(X)) active#(U201(X1,X2,X3)) -> active#(X1) active#(U201(X1,X2,X3)) -> U201#(active(X1),X2,X3) active#(U202(X1,X2,X3)) -> active#(X1) active#(U202(X1,X2,X3)) -> U202#(active(X1),X2,X3) active#(U203(X1,X2,X3)) -> active#(X1) active#(U203(X1,X2,X3)) -> U203#(active(X1),X2,X3) active#(U204(X1,X2,X3)) -> active#(X1) active#(U204(X1,X2,X3)) -> U204#(active(X1),X2,X3) active#(U205(X1,X2)) -> active#(X1) active#(U205(X1,X2)) -> U205#(active(X1),X2) active#(U206(X)) -> active#(X) active#(U206(X)) -> U206#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U211(X)) -> active#(X) active#(U211(X)) -> U211#(active(X)) active#(U23(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> U23#(active(X1),X2,X3) active#(U221(X)) -> active#(X) active#(U221(X)) -> U221#(active(X)) active#(U24(X1,X2)) -> active#(X1) active#(U24(X1,X2)) -> U24#(active(X1),X2) active#(U231(X1,X2)) -> active#(X1) active#(U231(X1,X2)) -> U231#(active(X1),X2) active#(U232(X)) -> active#(X) active#(U232(X)) -> U232#(active(X)) active#(U241(X1,X2,X3)) -> active#(X1) active#(U241(X1,X2,X3)) -> U241#(active(X1),X2,X3) active#(U242(X1,X2,X3)) -> active#(X1) active#(U242(X1,X2,X3)) -> U242#(active(X1),X2,X3) active#(U243(X1,X2,X3)) -> active#(X1) active#(U243(X1,X2,X3)) -> U243#(active(X1),X2,X3) active#(U244(X1,X2,X3)) -> active#(X1) active#(U244(X1,X2,X3)) -> U244#(active(X1),X2,X3) active#(U245(X1,X2)) -> active#(X1) active#(U245(X1,X2)) -> U245#(active(X1),X2) active#(U246(X)) -> active#(X) active#(U246(X)) -> U246#(active(X)) active#(U251(X1,X2,X3)) -> active#(X1) active#(U251(X1,X2,X3)) -> U251#(active(X1),X2,X3) active#(U252(X1,X2,X3)) -> active#(X1) active#(U252(X1,X2,X3)) -> U252#(active(X1),X2,X3) active#(U253(X1,X2,X3)) -> active#(X1) active#(U253(X1,X2,X3)) -> U253#(active(X1),X2,X3) active#(U254(X1,X2,X3)) -> active#(X1) active#(U254(X1,X2,X3)) -> U254#(active(X1),X2,X3) active#(U255(X1,X2)) -> active#(X1) active#(U255(X1,X2)) -> U255#(active(X1),X2) active#(U256(X)) -> active#(X) active#(U256(X)) -> U256#(active(X)) active#(U261(X1,X2)) -> active#(X1) active#(U261(X1,X2)) -> U261#(active(X1),X2) active#(U262(X)) -> active#(X) active#(U262(X)) -> U262#(active(X)) active#(U271(X1,X2)) -> active#(X1) active#(U271(X1,X2)) -> U271#(active(X1),X2) active#(U272(X)) -> active#(X) active#(U272(X)) -> U272#(active(X)) active#(U281(X1,X2)) -> active#(X1) active#(U281(X1,X2)) -> U281#(active(X1),X2) active#(U282(X1,X2)) -> active#(X1) active#(U282(X1,X2)) -> U282#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(natsFrom(X)) -> active#(X) active#(natsFrom(X)) -> natsFrom#(active(X)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(U291(X1,X2,X3)) -> active#(X1) active#(U291(X1,X2,X3)) -> U291#(active(X1),X2,X3) active#(U292(X1,X2,X3)) -> active#(X1) active#(U292(X1,X2,X3)) -> U292#(active(X1),X2,X3) active#(U293(X1,X2,X3)) -> active#(X1) active#(U293(X1,X2,X3)) -> U293#(active(X1),X2,X3) active#(U294(X1,X2,X3)) -> active#(X1) active#(U294(X1,X2,X3)) -> U294#(active(X1),X2,X3) active#(head(X)) -> active#(X) active#(head(X)) -> head#(active(X)) active#(afterNth(X1,X2)) -> active#(X1) active#(afterNth(X1,X2)) -> afterNth#(active(X1),X2) active#(afterNth(X1,X2)) -> active#(X2) active#(afterNth(X1,X2)) -> afterNth#(X1,active(X2)) active#(U301(X1,X2,X3)) -> active#(X1) active#(U301(X1,X2,X3)) -> U301#(active(X1),X2,X3) active#(U302(X1,X2)) -> active#(X1) active#(U302(X1,X2)) -> U302#(active(X1),X2) active#(U303(X1,X2)) -> active#(X1) active#(U303(X1,X2)) -> U303#(active(X1),X2) active#(U304(X1,X2)) -> active#(X1) active#(U304(X1,X2)) -> U304#(active(X1),X2) active#(U31(X1,X2,X3)) -> active#(X1) active#(U31(X1,X2,X3)) -> U31#(active(X1),X2,X3) active#(U32(X1,X2,X3)) -> active#(X1) active#(U32(X1,X2,X3)) -> U32#(active(X1),X2,X3) active#(U311(X1,X2)) -> active#(X1) active#(U311(X1,X2)) -> U311#(active(X1),X2) active#(U312(X1,X2)) -> active#(X1) active#(U312(X1,X2)) -> U312#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(U33(X1,X2,X3)) -> active#(X1) active#(U33(X1,X2,X3)) -> U33#(active(X1),X2,X3) active#(U321(X1,X2,X3,X4)) -> active#(X1) active#(U321(X1,X2,X3,X4)) -> U321#(active(X1),X2,X3,X4) active#(U322(X1,X2,X3,X4)) -> active#(X1) active#(U322(X1,X2,X3,X4)) -> U322#(active(X1),X2,X3,X4) active#(U323(X1,X2,X3,X4)) -> active#(X1) active#(U323(X1,X2,X3,X4)) -> U323#(active(X1),X2,X3,X4) active#(U324(X1,X2,X3,X4)) -> active#(X1) active#(U324(X1,X2,X3,X4)) -> U324#(active(X1),X2,X3,X4) active#(U325(X1,X2,X3,X4)) -> active#(X1) active#(U325(X1,X2,X3,X4)) -> U325#(active(X1),X2,X3,X4) active#(U326(X1,X2,X3,X4)) -> active#(X1) active#(U326(X1,X2,X3,X4)) -> U326#(active(X1),X2,X3,X4) active#(U327(X1,X2)) -> active#(X1) active#(U327(X1,X2)) -> U327#(active(X1),X2) active#(U34(X1,X2)) -> active#(X1) active#(U34(X1,X2)) -> U34#(active(X1),X2) active#(U331(X1,X2,X3)) -> active#(X1) active#(U331(X1,X2,X3)) -> U331#(active(X1),X2,X3) active#(U332(X1,X2)) -> active#(X1) active#(U332(X1,X2)) -> U332#(active(X1),X2) active#(U333(X1,X2)) -> active#(X1) active#(U333(X1,X2)) -> U333#(active(X1),X2) active#(U334(X1,X2)) -> active#(X1) active#(U334(X1,X2)) -> U334#(active(X1),X2) active#(U341(X1,X2,X3)) -> active#(X1) active#(U341(X1,X2,X3)) -> U341#(active(X1),X2,X3) active#(U342(X1,X2,X3)) -> active#(X1) active#(U342(X1,X2,X3)) -> U342#(active(X1),X2,X3) active#(U343(X1,X2,X3)) -> active#(X1) active#(U343(X1,X2,X3)) -> U343#(active(X1),X2,X3) active#(U344(X1,X2,X3)) -> active#(X1) active#(U344(X1,X2,X3)) -> U344#(active(X1),X2,X3) active#(fst(X)) -> active#(X) active#(fst(X)) -> fst#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3) active#(U43(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3) active#(U44(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3) active#(U45(X1,X2)) -> active#(X1) active#(U45(X1,X2)) -> U45#(active(X1),X2) active#(U46(X)) -> active#(X) active#(U46(X)) -> U46#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> U52#(active(X1),X2,X3) active#(U53(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> U53#(active(X1),X2,X3) active#(U54(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> U54#(active(X1),X2,X3) active#(U55(X1,X2)) -> active#(X1) active#(U55(X1,X2)) -> U55#(active(X1),X2) active#(U56(X)) -> active#(X) active#(U56(X)) -> U56#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> U62#(active(X1),X2) active#(U63(X)) -> active#(X) active#(U63(X)) -> U63#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X1,X2)) -> active#(X1) active#(U72(X1,X2)) -> U72#(active(X1),X2) active#(U73(X)) -> active#(X) active#(U73(X)) -> U73#(active(X)) active#(U81(X1,X2)) -> active#(X1) active#(U81(X1,X2)) -> U81#(active(X1),X2) active#(U82(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> U82#(active(X1),X2) active#(U83(X)) -> active#(X) active#(U83(X)) -> U83#(active(X)) active#(U91(X1,X2)) -> active#(X1) active#(U91(X1,X2)) -> U91#(active(X1),X2) active#(U92(X1,X2)) -> active#(X1) active#(U92(X1,X2)) -> U92#(active(X1),X2) active#(U93(X)) -> active#(X) active#(U93(X)) -> U93#(active(X)) active#(tail(X)) -> active#(X) active#(tail(X)) -> tail#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U105#(mark(X1),X2) -> U105#(X1,X2) U106#(mark(X)) -> U106#(X) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U111#(mark(X1),X2) -> U111#(X1,X2) U112#(mark(X)) -> U112#(X) U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U121#(mark(X1),X2) -> U121#(X1,X2) U122#(mark(X)) -> U122#(X) U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U131#(mark(X)) -> U131#(X) snd#(mark(X)) -> snd#(X) splitAt#(mark(X1),X2) -> splitAt#(X1,X2) splitAt#(X1,mark(X2)) -> splitAt#(X1,X2) U141#(mark(X)) -> U141#(X) U151#(mark(X)) -> U151#(X) U161#(mark(X)) -> U161#(X) U171#(mark(X1),X2) -> U171#(X1,X2) U172#(mark(X)) -> U172#(X) U181#(mark(X1),X2) -> U181#(X1,X2) U182#(mark(X1),X2) -> U182#(X1,X2) U183#(mark(X)) -> U183#(X) U191#(mark(X1),X2) -> U191#(X1,X2) U192#(mark(X1),X2) -> U192#(X1,X2) U193#(mark(X)) -> U193#(X) U201#(mark(X1),X2,X3) -> U201#(X1,X2,X3) U202#(mark(X1),X2,X3) -> U202#(X1,X2,X3) U203#(mark(X1),X2,X3) -> U203#(X1,X2,X3) U204#(mark(X1),X2,X3) -> U204#(X1,X2,X3) U205#(mark(X1),X2) -> U205#(X1,X2) U206#(mark(X)) -> U206#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U211#(mark(X)) -> U211#(X) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U221#(mark(X)) -> U221#(X) U24#(mark(X1),X2) -> U24#(X1,X2) U231#(mark(X1),X2) -> U231#(X1,X2) U232#(mark(X)) -> U232#(X) U241#(mark(X1),X2,X3) -> U241#(X1,X2,X3) U242#(mark(X1),X2,X3) -> U242#(X1,X2,X3) U243#(mark(X1),X2,X3) -> U243#(X1,X2,X3) U244#(mark(X1),X2,X3) -> U244#(X1,X2,X3) U245#(mark(X1),X2) -> U245#(X1,X2) U246#(mark(X)) -> U246#(X) U251#(mark(X1),X2,X3) -> U251#(X1,X2,X3) U252#(mark(X1),X2,X3) -> U252#(X1,X2,X3) U253#(mark(X1),X2,X3) -> U253#(X1,X2,X3) U254#(mark(X1),X2,X3) -> U254#(X1,X2,X3) U255#(mark(X1),X2) -> U255#(X1,X2) U256#(mark(X)) -> U256#(X) U261#(mark(X1),X2) -> U261#(X1,X2) U262#(mark(X)) -> U262#(X) U271#(mark(X1),X2) -> U271#(X1,X2) U272#(mark(X)) -> U272#(X) U281#(mark(X1),X2) -> U281#(X1,X2) U282#(mark(X1),X2) -> U282#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) natsFrom#(mark(X)) -> natsFrom#(X) s#(mark(X)) -> s#(X) U291#(mark(X1),X2,X3) -> U291#(X1,X2,X3) U292#(mark(X1),X2,X3) -> U292#(X1,X2,X3) U293#(mark(X1),X2,X3) -> U293#(X1,X2,X3) U294#(mark(X1),X2,X3) -> U294#(X1,X2,X3) head#(mark(X)) -> head#(X) afterNth#(mark(X1),X2) -> afterNth#(X1,X2) afterNth#(X1,mark(X2)) -> afterNth#(X1,X2) U301#(mark(X1),X2,X3) -> U301#(X1,X2,X3) U302#(mark(X1),X2) -> U302#(X1,X2) U303#(mark(X1),X2) -> U303#(X1,X2) U304#(mark(X1),X2) -> U304#(X1,X2) U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U311#(mark(X1),X2) -> U311#(X1,X2) U312#(mark(X1),X2) -> U312#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U321#(mark(X1),X2,X3,X4) -> U321#(X1,X2,X3,X4) U322#(mark(X1),X2,X3,X4) -> U322#(X1,X2,X3,X4) U323#(mark(X1),X2,X3,X4) -> U323#(X1,X2,X3,X4) U324#(mark(X1),X2,X3,X4) -> U324#(X1,X2,X3,X4) U325#(mark(X1),X2,X3,X4) -> U325#(X1,X2,X3,X4) U326#(mark(X1),X2,X3,X4) -> U326#(X1,X2,X3,X4) U327#(mark(X1),X2) -> U327#(X1,X2) U34#(mark(X1),X2) -> U34#(X1,X2) U331#(mark(X1),X2,X3) -> U331#(X1,X2,X3) U332#(mark(X1),X2) -> U332#(X1,X2) U333#(mark(X1),X2) -> U333#(X1,X2) U334#(mark(X1),X2) -> U334#(X1,X2) U341#(mark(X1),X2,X3) -> U341#(X1,X2,X3) U342#(mark(X1),X2,X3) -> U342#(X1,X2,X3) U343#(mark(X1),X2,X3) -> U343#(X1,X2,X3) U344#(mark(X1),X2,X3) -> U344#(X1,X2,X3) fst#(mark(X)) -> fst#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U55#(mark(X1),X2) -> U55#(X1,X2) U56#(mark(X)) -> U56#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U63#(mark(X)) -> U63#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U73#(mark(X)) -> U73#(X) U81#(mark(X1),X2) -> U81#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U83#(mark(X)) -> U83#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U92#(mark(X1),X2) -> U92#(X1,X2) U93#(mark(X)) -> U93#(X) tail#(mark(X)) -> tail#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(U101(X1,X2,X3)) -> proper#(X3) proper#(U101(X1,X2,X3)) -> proper#(X2) proper#(U101(X1,X2,X3)) -> proper#(X1) proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3)) proper#(U102(X1,X2,X3)) -> proper#(X3) proper#(U102(X1,X2,X3)) -> proper#(X2) proper#(U102(X1,X2,X3)) -> proper#(X1) proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3)) proper#(isNaturalKind(X)) -> proper#(X) proper#(isNaturalKind(X)) -> isNaturalKind#(proper(X)) proper#(U103(X1,X2,X3)) -> proper#(X3) proper#(U103(X1,X2,X3)) -> proper#(X2) proper#(U103(X1,X2,X3)) -> proper#(X1) proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3)) proper#(isLNatKind(X)) -> proper#(X) proper#(isLNatKind(X)) -> isLNatKind#(proper(X)) proper#(U104(X1,X2,X3)) -> proper#(X3) proper#(U104(X1,X2,X3)) -> proper#(X2) proper#(U104(X1,X2,X3)) -> proper#(X1) proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3)) proper#(U105(X1,X2)) -> proper#(X2) proper#(U105(X1,X2)) -> proper#(X1) proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2)) proper#(isNatural(X)) -> proper#(X) proper#(isNatural(X)) -> isNatural#(proper(X)) proper#(U106(X)) -> proper#(X) proper#(U106(X)) -> U106#(proper(X)) proper#(isLNat(X)) -> proper#(X) proper#(isLNat(X)) -> isLNat#(proper(X)) proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U111(X1,X2)) -> proper#(X2) proper#(U111(X1,X2)) -> proper#(X1) proper#(U111(X1,X2)) -> U111#(proper(X1),proper(X2)) proper#(U112(X)) -> proper#(X) proper#(U112(X)) -> U112#(proper(X)) proper#(U13(X1,X2,X3)) -> proper#(X3) proper#(U13(X1,X2,X3)) -> proper#(X2) proper#(U13(X1,X2,X3)) -> proper#(X1) proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3)) proper#(U121(X1,X2)) -> proper#(X2) proper#(U121(X1,X2)) -> proper#(X1) proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2)) proper#(U122(X)) -> proper#(X) proper#(U122(X)) -> U122#(proper(X)) proper#(U14(X1,X2,X3)) -> proper#(X3) proper#(U14(X1,X2,X3)) -> proper#(X2) proper#(U14(X1,X2,X3)) -> proper#(X1) proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3)) proper#(U131(X)) -> proper#(X) proper#(U131(X)) -> U131#(proper(X)) proper#(snd(X)) -> proper#(X) proper#(snd(X)) -> snd#(proper(X)) proper#(splitAt(X1,X2)) -> proper#(X2) proper#(splitAt(X1,X2)) -> proper#(X1) proper#(splitAt(X1,X2)) -> splitAt#(proper(X1),proper(X2)) proper#(U141(X)) -> proper#(X) proper#(U141(X)) -> U141#(proper(X)) proper#(U151(X)) -> proper#(X) proper#(U151(X)) -> U151#(proper(X)) proper#(U161(X)) -> proper#(X) proper#(U161(X)) -> U161#(proper(X)) proper#(U171(X1,X2)) -> proper#(X2) proper#(U171(X1,X2)) -> proper#(X1) proper#(U171(X1,X2)) -> U171#(proper(X1),proper(X2)) proper#(U172(X)) -> proper#(X) proper#(U172(X)) -> U172#(proper(X)) proper#(U181(X1,X2)) -> proper#(X2) proper#(U181(X1,X2)) -> proper#(X1) proper#(U181(X1,X2)) -> U181#(proper(X1),proper(X2)) proper#(U182(X1,X2)) -> proper#(X2) proper#(U182(X1,X2)) -> proper#(X1) proper#(U182(X1,X2)) -> U182#(proper(X1),proper(X2)) proper#(U183(X)) -> proper#(X) proper#(U183(X)) -> U183#(proper(X)) proper#(U191(X1,X2)) -> proper#(X2) proper#(U191(X1,X2)) -> proper#(X1) proper#(U191(X1,X2)) -> U191#(proper(X1),proper(X2)) proper#(U192(X1,X2)) -> proper#(X2) proper#(U192(X1,X2)) -> proper#(X1) proper#(U192(X1,X2)) -> U192#(proper(X1),proper(X2)) proper#(U193(X)) -> proper#(X) proper#(U193(X)) -> U193#(proper(X)) proper#(U201(X1,X2,X3)) -> proper#(X3) proper#(U201(X1,X2,X3)) -> proper#(X2) proper#(U201(X1,X2,X3)) -> proper#(X1) proper#(U201(X1,X2,X3)) -> U201#(proper(X1),proper(X2),proper(X3)) proper#(U202(X1,X2,X3)) -> proper#(X3) proper#(U202(X1,X2,X3)) -> proper#(X2) proper#(U202(X1,X2,X3)) -> proper#(X1) proper#(U202(X1,X2,X3)) -> U202#(proper(X1),proper(X2),proper(X3)) proper#(U203(X1,X2,X3)) -> proper#(X3) proper#(U203(X1,X2,X3)) -> proper#(X2) proper#(U203(X1,X2,X3)) -> proper#(X1) proper#(U203(X1,X2,X3)) -> U203#(proper(X1),proper(X2),proper(X3)) proper#(U204(X1,X2,X3)) -> proper#(X3) proper#(U204(X1,X2,X3)) -> proper#(X2) proper#(U204(X1,X2,X3)) -> proper#(X1) proper#(U204(X1,X2,X3)) -> U204#(proper(X1),proper(X2),proper(X3)) proper#(U205(X1,X2)) -> proper#(X2) proper#(U205(X1,X2)) -> proper#(X1) proper#(U205(X1,X2)) -> U205#(proper(X1),proper(X2)) proper#(U206(X)) -> proper#(X) proper#(U206(X)) -> U206#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U211(X)) -> proper#(X) proper#(U211(X)) -> U211#(proper(X)) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U23(X1,X2,X3)) -> U23#(proper(X1),proper(X2),proper(X3)) proper#(U221(X)) -> proper#(X) proper#(U221(X)) -> U221#(proper(X)) proper#(U24(X1,X2)) -> proper#(X2) proper#(U24(X1,X2)) -> proper#(X1) proper#(U24(X1,X2)) -> U24#(proper(X1),proper(X2)) proper#(U231(X1,X2)) -> proper#(X2) proper#(U231(X1,X2)) -> proper#(X1) proper#(U231(X1,X2)) -> U231#(proper(X1),proper(X2)) proper#(U232(X)) -> proper#(X) proper#(U232(X)) -> U232#(proper(X)) proper#(U241(X1,X2,X3)) -> proper#(X3) proper#(U241(X1,X2,X3)) -> proper#(X2) proper#(U241(X1,X2,X3)) -> proper#(X1) proper#(U241(X1,X2,X3)) -> U241#(proper(X1),proper(X2),proper(X3)) proper#(U242(X1,X2,X3)) -> proper#(X3) proper#(U242(X1,X2,X3)) -> proper#(X2) proper#(U242(X1,X2,X3)) -> proper#(X1) proper#(U242(X1,X2,X3)) -> U242#(proper(X1),proper(X2),proper(X3)) proper#(U243(X1,X2,X3)) -> proper#(X3) proper#(U243(X1,X2,X3)) -> proper#(X2) proper#(U243(X1,X2,X3)) -> proper#(X1) proper#(U243(X1,X2,X3)) -> U243#(proper(X1),proper(X2),proper(X3)) proper#(U244(X1,X2,X3)) -> proper#(X3) proper#(U244(X1,X2,X3)) -> proper#(X2) proper#(U244(X1,X2,X3)) -> proper#(X1) proper#(U244(X1,X2,X3)) -> U244#(proper(X1),proper(X2),proper(X3)) proper#(U245(X1,X2)) -> proper#(X2) proper#(U245(X1,X2)) -> proper#(X1) proper#(U245(X1,X2)) -> U245#(proper(X1),proper(X2)) proper#(U246(X)) -> proper#(X) proper#(U246(X)) -> U246#(proper(X)) proper#(U251(X1,X2,X3)) -> proper#(X3) proper#(U251(X1,X2,X3)) -> proper#(X2) proper#(U251(X1,X2,X3)) -> proper#(X1) proper#(U251(X1,X2,X3)) -> U251#(proper(X1),proper(X2),proper(X3)) proper#(U252(X1,X2,X3)) -> proper#(X3) proper#(U252(X1,X2,X3)) -> proper#(X2) proper#(U252(X1,X2,X3)) -> proper#(X1) proper#(U252(X1,X2,X3)) -> U252#(proper(X1),proper(X2),proper(X3)) proper#(U253(X1,X2,X3)) -> proper#(X3) proper#(U253(X1,X2,X3)) -> proper#(X2) proper#(U253(X1,X2,X3)) -> proper#(X1) proper#(U253(X1,X2,X3)) -> U253#(proper(X1),proper(X2),proper(X3)) proper#(U254(X1,X2,X3)) -> proper#(X3) proper#(U254(X1,X2,X3)) -> proper#(X2) proper#(U254(X1,X2,X3)) -> proper#(X1) proper#(U254(X1,X2,X3)) -> U254#(proper(X1),proper(X2),proper(X3)) proper#(U255(X1,X2)) -> proper#(X2) proper#(U255(X1,X2)) -> proper#(X1) proper#(U255(X1,X2)) -> U255#(proper(X1),proper(X2)) proper#(U256(X)) -> proper#(X) proper#(U256(X)) -> U256#(proper(X)) proper#(U261(X1,X2)) -> proper#(X2) proper#(U261(X1,X2)) -> proper#(X1) proper#(U261(X1,X2)) -> U261#(proper(X1),proper(X2)) proper#(U262(X)) -> proper#(X) proper#(U262(X)) -> U262#(proper(X)) proper#(U271(X1,X2)) -> proper#(X2) proper#(U271(X1,X2)) -> proper#(X1) proper#(U271(X1,X2)) -> U271#(proper(X1),proper(X2)) proper#(U272(X)) -> proper#(X) proper#(U272(X)) -> U272#(proper(X)) proper#(U281(X1,X2)) -> proper#(X2) proper#(U281(X1,X2)) -> proper#(X1) proper#(U281(X1,X2)) -> U281#(proper(X1),proper(X2)) proper#(U282(X1,X2)) -> proper#(X2) proper#(U282(X1,X2)) -> proper#(X1) proper#(U282(X1,X2)) -> U282#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(natsFrom(X)) -> proper#(X) proper#(natsFrom(X)) -> natsFrom#(proper(X)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(U291(X1,X2,X3)) -> proper#(X3) proper#(U291(X1,X2,X3)) -> proper#(X2) proper#(U291(X1,X2,X3)) -> proper#(X1) proper#(U291(X1,X2,X3)) -> U291#(proper(X1),proper(X2),proper(X3)) proper#(U292(X1,X2,X3)) -> proper#(X3) proper#(U292(X1,X2,X3)) -> proper#(X2) proper#(U292(X1,X2,X3)) -> proper#(X1) proper#(U292(X1,X2,X3)) -> U292#(proper(X1),proper(X2),proper(X3)) proper#(U293(X1,X2,X3)) -> proper#(X3) proper#(U293(X1,X2,X3)) -> proper#(X2) proper#(U293(X1,X2,X3)) -> proper#(X1) proper#(U293(X1,X2,X3)) -> U293#(proper(X1),proper(X2),proper(X3)) proper#(U294(X1,X2,X3)) -> proper#(X3) proper#(U294(X1,X2,X3)) -> proper#(X2) proper#(U294(X1,X2,X3)) -> proper#(X1) proper#(U294(X1,X2,X3)) -> U294#(proper(X1),proper(X2),proper(X3)) proper#(head(X)) -> proper#(X) proper#(head(X)) -> head#(proper(X)) proper#(afterNth(X1,X2)) -> proper#(X2) proper#(afterNth(X1,X2)) -> proper#(X1) proper#(afterNth(X1,X2)) -> afterNth#(proper(X1),proper(X2)) proper#(U301(X1,X2,X3)) -> proper#(X3) proper#(U301(X1,X2,X3)) -> proper#(X2) proper#(U301(X1,X2,X3)) -> proper#(X1) proper#(U301(X1,X2,X3)) -> U301#(proper(X1),proper(X2),proper(X3)) proper#(U302(X1,X2)) -> proper#(X2) proper#(U302(X1,X2)) -> proper#(X1) proper#(U302(X1,X2)) -> U302#(proper(X1),proper(X2)) proper#(U303(X1,X2)) -> proper#(X2) proper#(U303(X1,X2)) -> proper#(X1) proper#(U303(X1,X2)) -> U303#(proper(X1),proper(X2)) proper#(U304(X1,X2)) -> proper#(X2) proper#(U304(X1,X2)) -> proper#(X1) proper#(U304(X1,X2)) -> U304#(proper(X1),proper(X2)) proper#(U31(X1,X2,X3)) -> proper#(X3) proper#(U31(X1,X2,X3)) -> proper#(X2) proper#(U31(X1,X2,X3)) -> proper#(X1) proper#(U31(X1,X2,X3)) -> U31#(proper(X1),proper(X2),proper(X3)) proper#(U32(X1,X2,X3)) -> proper#(X3) proper#(U32(X1,X2,X3)) -> proper#(X2) proper#(U32(X1,X2,X3)) -> proper#(X1) proper#(U32(X1,X2,X3)) -> U32#(proper(X1),proper(X2),proper(X3)) proper#(U311(X1,X2)) -> proper#(X2) proper#(U311(X1,X2)) -> proper#(X1) proper#(U311(X1,X2)) -> U311#(proper(X1),proper(X2)) proper#(U312(X1,X2)) -> proper#(X2) proper#(U312(X1,X2)) -> proper#(X1) proper#(U312(X1,X2)) -> U312#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(U33(X1,X2,X3)) -> proper#(X3) proper#(U33(X1,X2,X3)) -> proper#(X2) proper#(U33(X1,X2,X3)) -> proper#(X1) proper#(U33(X1,X2,X3)) -> U33#(proper(X1),proper(X2),proper(X3)) proper#(U321(X1,X2,X3,X4)) -> proper#(X4) proper#(U321(X1,X2,X3,X4)) -> proper#(X3) proper#(U321(X1,X2,X3,X4)) -> proper#(X2) proper#(U321(X1,X2,X3,X4)) -> proper#(X1) proper#(U321(X1,X2,X3,X4)) -> U321#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U322(X1,X2,X3,X4)) -> proper#(X4) proper#(U322(X1,X2,X3,X4)) -> proper#(X3) proper#(U322(X1,X2,X3,X4)) -> proper#(X2) proper#(U322(X1,X2,X3,X4)) -> proper#(X1) proper#(U322(X1,X2,X3,X4)) -> U322#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U323(X1,X2,X3,X4)) -> proper#(X4) proper#(U323(X1,X2,X3,X4)) -> proper#(X3) proper#(U323(X1,X2,X3,X4)) -> proper#(X2) proper#(U323(X1,X2,X3,X4)) -> proper#(X1) proper#(U323(X1,X2,X3,X4)) -> U323#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U324(X1,X2,X3,X4)) -> proper#(X4) proper#(U324(X1,X2,X3,X4)) -> proper#(X3) proper#(U324(X1,X2,X3,X4)) -> proper#(X2) proper#(U324(X1,X2,X3,X4)) -> proper#(X1) proper#(U324(X1,X2,X3,X4)) -> U324#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U325(X1,X2,X3,X4)) -> proper#(X4) proper#(U325(X1,X2,X3,X4)) -> proper#(X3) proper#(U325(X1,X2,X3,X4)) -> proper#(X2) proper#(U325(X1,X2,X3,X4)) -> proper#(X1) proper#(U325(X1,X2,X3,X4)) -> U325#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U326(X1,X2,X3,X4)) -> proper#(X4) proper#(U326(X1,X2,X3,X4)) -> proper#(X3) proper#(U326(X1,X2,X3,X4)) -> proper#(X2) proper#(U326(X1,X2,X3,X4)) -> proper#(X1) proper#(U326(X1,X2,X3,X4)) -> U326#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U327(X1,X2)) -> proper#(X2) proper#(U327(X1,X2)) -> proper#(X1) proper#(U327(X1,X2)) -> U327#(proper(X1),proper(X2)) proper#(U34(X1,X2)) -> proper#(X2) proper#(U34(X1,X2)) -> proper#(X1) proper#(U34(X1,X2)) -> U34#(proper(X1),proper(X2)) proper#(U331(X1,X2,X3)) -> proper#(X3) proper#(U331(X1,X2,X3)) -> proper#(X2) proper#(U331(X1,X2,X3)) -> proper#(X1) proper#(U331(X1,X2,X3)) -> U331#(proper(X1),proper(X2),proper(X3)) proper#(U332(X1,X2)) -> proper#(X2) proper#(U332(X1,X2)) -> proper#(X1) proper#(U332(X1,X2)) -> U332#(proper(X1),proper(X2)) proper#(U333(X1,X2)) -> proper#(X2) proper#(U333(X1,X2)) -> proper#(X1) proper#(U333(X1,X2)) -> U333#(proper(X1),proper(X2)) proper#(U334(X1,X2)) -> proper#(X2) proper#(U334(X1,X2)) -> proper#(X1) proper#(U334(X1,X2)) -> U334#(proper(X1),proper(X2)) proper#(U341(X1,X2,X3)) -> proper#(X3) proper#(U341(X1,X2,X3)) -> proper#(X2) proper#(U341(X1,X2,X3)) -> proper#(X1) proper#(U341(X1,X2,X3)) -> U341#(proper(X1),proper(X2),proper(X3)) proper#(U342(X1,X2,X3)) -> proper#(X3) proper#(U342(X1,X2,X3)) -> proper#(X2) proper#(U342(X1,X2,X3)) -> proper#(X1) proper#(U342(X1,X2,X3)) -> U342#(proper(X1),proper(X2),proper(X3)) proper#(U343(X1,X2,X3)) -> proper#(X3) proper#(U343(X1,X2,X3)) -> proper#(X2) proper#(U343(X1,X2,X3)) -> proper#(X1) proper#(U343(X1,X2,X3)) -> U343#(proper(X1),proper(X2),proper(X3)) proper#(U344(X1,X2,X3)) -> proper#(X3) proper#(U344(X1,X2,X3)) -> proper#(X2) proper#(U344(X1,X2,X3)) -> proper#(X1) proper#(U344(X1,X2,X3)) -> U344#(proper(X1),proper(X2),proper(X3)) proper#(fst(X)) -> proper#(X) proper#(fst(X)) -> fst#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3)) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3)) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3)) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2)) proper#(U46(X)) -> proper#(X) proper#(U46(X)) -> U46#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> U52#(proper(X1),proper(X2),proper(X3)) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> U53#(proper(X1),proper(X2),proper(X3)) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> U54#(proper(X1),proper(X2),proper(X3)) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U55(X1,X2)) -> U55#(proper(X1),proper(X2)) proper#(U56(X)) -> proper#(X) proper#(U56(X)) -> U56#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> U62#(proper(X1),proper(X2)) proper#(isPLNatKind(X)) -> proper#(X) proper#(isPLNatKind(X)) -> isPLNatKind#(proper(X)) proper#(U63(X)) -> proper#(X) proper#(U63(X)) -> U63#(proper(X)) proper#(isPLNat(X)) -> proper#(X) proper#(isPLNat(X)) -> isPLNat#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U72(X1,X2)) -> U72#(proper(X1),proper(X2)) proper#(U73(X)) -> proper#(X) proper#(U73(X)) -> U73#(proper(X)) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U81(X1,X2)) -> U81#(proper(X1),proper(X2)) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> U82#(proper(X1),proper(X2)) proper#(U83(X)) -> proper#(X) proper#(U83(X)) -> U83#(proper(X)) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U91(X1,X2)) -> U91#(proper(X1),proper(X2)) proper#(U92(X1,X2)) -> proper#(X2) proper#(U92(X1,X2)) -> proper#(X1) proper#(U92(X1,X2)) -> U92#(proper(X1),proper(X2)) proper#(U93(X)) -> proper#(X) proper#(U93(X)) -> U93#(proper(X)) proper#(tail(X)) -> proper#(X) proper#(tail(X)) -> tail#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3) U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3) isNaturalKind#(ok(X)) -> isNaturalKind#(X) U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3) isLNatKind#(ok(X)) -> isLNatKind#(X) U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3) U105#(ok(X1),ok(X2)) -> U105#(X1,X2) isNatural#(ok(X)) -> isNatural#(X) U106#(ok(X)) -> U106#(X) isLNat#(ok(X)) -> isLNat#(X) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) U111#(ok(X1),ok(X2)) -> U111#(X1,X2) U112#(ok(X)) -> U112#(X) U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3) U121#(ok(X1),ok(X2)) -> U121#(X1,X2) U122#(ok(X)) -> U122#(X) U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3) U131#(ok(X)) -> U131#(X) snd#(ok(X)) -> snd#(X) splitAt#(ok(X1),ok(X2)) -> splitAt#(X1,X2) U141#(ok(X)) -> U141#(X) U151#(ok(X)) -> U151#(X) U161#(ok(X)) -> U161#(X) U171#(ok(X1),ok(X2)) -> U171#(X1,X2) U172#(ok(X)) -> U172#(X) U181#(ok(X1),ok(X2)) -> U181#(X1,X2) U182#(ok(X1),ok(X2)) -> U182#(X1,X2) U183#(ok(X)) -> U183#(X) U191#(ok(X1),ok(X2)) -> U191#(X1,X2) U192#(ok(X1),ok(X2)) -> U192#(X1,X2) U193#(ok(X)) -> U193#(X) U201#(ok(X1),ok(X2),ok(X3)) -> U201#(X1,X2,X3) U202#(ok(X1),ok(X2),ok(X3)) -> U202#(X1,X2,X3) U203#(ok(X1),ok(X2),ok(X3)) -> U203#(X1,X2,X3) U204#(ok(X1),ok(X2),ok(X3)) -> U204#(X1,X2,X3) U205#(ok(X1),ok(X2)) -> U205#(X1,X2) U206#(ok(X)) -> U206#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U211#(ok(X)) -> U211#(X) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) U221#(ok(X)) -> U221#(X) U24#(ok(X1),ok(X2)) -> U24#(X1,X2) U231#(ok(X1),ok(X2)) -> U231#(X1,X2) U232#(ok(X)) -> U232#(X) U241#(ok(X1),ok(X2),ok(X3)) -> U241#(X1,X2,X3) U242#(ok(X1),ok(X2),ok(X3)) -> U242#(X1,X2,X3) U243#(ok(X1),ok(X2),ok(X3)) -> U243#(X1,X2,X3) U244#(ok(X1),ok(X2),ok(X3)) -> U244#(X1,X2,X3) U245#(ok(X1),ok(X2)) -> U245#(X1,X2) U246#(ok(X)) -> U246#(X) U251#(ok(X1),ok(X2),ok(X3)) -> U251#(X1,X2,X3) U252#(ok(X1),ok(X2),ok(X3)) -> U252#(X1,X2,X3) U253#(ok(X1),ok(X2),ok(X3)) -> U253#(X1,X2,X3) U254#(ok(X1),ok(X2),ok(X3)) -> U254#(X1,X2,X3) U255#(ok(X1),ok(X2)) -> U255#(X1,X2) U256#(ok(X)) -> U256#(X) U261#(ok(X1),ok(X2)) -> U261#(X1,X2) U262#(ok(X)) -> U262#(X) U271#(ok(X1),ok(X2)) -> U271#(X1,X2) U272#(ok(X)) -> U272#(X) U281#(ok(X1),ok(X2)) -> U281#(X1,X2) U282#(ok(X1),ok(X2)) -> U282#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) natsFrom#(ok(X)) -> natsFrom#(X) s#(ok(X)) -> s#(X) U291#(ok(X1),ok(X2),ok(X3)) -> U291#(X1,X2,X3) U292#(ok(X1),ok(X2),ok(X3)) -> U292#(X1,X2,X3) U293#(ok(X1),ok(X2),ok(X3)) -> U293#(X1,X2,X3) U294#(ok(X1),ok(X2),ok(X3)) -> U294#(X1,X2,X3) head#(ok(X)) -> head#(X) afterNth#(ok(X1),ok(X2)) -> afterNth#(X1,X2) U301#(ok(X1),ok(X2),ok(X3)) -> U301#(X1,X2,X3) U302#(ok(X1),ok(X2)) -> U302#(X1,X2) U303#(ok(X1),ok(X2)) -> U303#(X1,X2) U304#(ok(X1),ok(X2)) -> U304#(X1,X2) U31#(ok(X1),ok(X2),ok(X3)) -> U31#(X1,X2,X3) U32#(ok(X1),ok(X2),ok(X3)) -> U32#(X1,X2,X3) U311#(ok(X1),ok(X2)) -> U311#(X1,X2) U312#(ok(X1),ok(X2)) -> U312#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) U33#(ok(X1),ok(X2),ok(X3)) -> U33#(X1,X2,X3) U321#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U321#(X1,X2,X3,X4) U322#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U322#(X1,X2,X3,X4) U323#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U323#(X1,X2,X3,X4) U324#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U324#(X1,X2,X3,X4) U325#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U325#(X1,X2,X3,X4) U326#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U326#(X1,X2,X3,X4) U327#(ok(X1),ok(X2)) -> U327#(X1,X2) U34#(ok(X1),ok(X2)) -> U34#(X1,X2) U331#(ok(X1),ok(X2),ok(X3)) -> U331#(X1,X2,X3) U332#(ok(X1),ok(X2)) -> U332#(X1,X2) U333#(ok(X1),ok(X2)) -> U333#(X1,X2) U334#(ok(X1),ok(X2)) -> U334#(X1,X2) U341#(ok(X1),ok(X2),ok(X3)) -> U341#(X1,X2,X3) U342#(ok(X1),ok(X2),ok(X3)) -> U342#(X1,X2,X3) U343#(ok(X1),ok(X2),ok(X3)) -> U343#(X1,X2,X3) U344#(ok(X1),ok(X2),ok(X3)) -> U344#(X1,X2,X3) fst#(ok(X)) -> fst#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) U46#(ok(X)) -> U46#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) U56#(ok(X)) -> U56#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) isPLNatKind#(ok(X)) -> isPLNatKind#(X) U63#(ok(X)) -> U63#(X) isPLNat#(ok(X)) -> isPLNat#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) U73#(ok(X)) -> U73#(X) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) U83#(ok(X)) -> U83#(X) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) U92#(ok(X1),ok(X2)) -> U92#(X1,X2) U93#(ok(X)) -> U93#(X) tail#(ok(X)) -> tail#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(U101(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U101(tt(),V1,V2)) -> U102#(isNaturalKind(V1),V1,V2) active#(U102(tt(),V1,V2)) -> isLNatKind#(V2) active#(U102(tt(),V1,V2)) -> U103#(isLNatKind(V2),V1,V2) active#(U103(tt(),V1,V2)) -> isLNatKind#(V2) active#(U103(tt(),V1,V2)) -> U104#(isLNatKind(V2),V1,V2) active#(U104(tt(),V1,V2)) -> isNatural#(V1) active#(U104(tt(),V1,V2)) -> U105#(isNatural(V1),V2) active#(U105(tt(),V2)) -> isLNat#(V2) active#(U105(tt(),V2)) -> U106#(isLNat(V2)) active#(U11(tt(),N,XS)) -> isNaturalKind#(N) active#(U11(tt(),N,XS)) -> U12#(isNaturalKind(N),N,XS) active#(U111(tt(),V2)) -> isLNatKind#(V2) active#(U111(tt(),V2)) -> U112#(isLNatKind(V2)) active#(U12(tt(),N,XS)) -> isLNat#(XS) active#(U12(tt(),N,XS)) -> U13#(isLNat(XS),N,XS) active#(U121(tt(),V2)) -> isLNatKind#(V2) active#(U121(tt(),V2)) -> U122#(isLNatKind(V2)) active#(U13(tt(),N,XS)) -> isLNatKind#(XS) active#(U13(tt(),N,XS)) -> U14#(isLNatKind(XS),N,XS) active#(U14(tt(),N,XS)) -> splitAt#(N,XS) active#(U14(tt(),N,XS)) -> snd#(splitAt(N,XS)) active#(U171(tt(),V2)) -> isLNatKind#(V2) active#(U171(tt(),V2)) -> U172#(isLNatKind(V2)) active#(U181(tt(),V1)) -> isLNatKind#(V1) active#(U181(tt(),V1)) -> U182#(isLNatKind(V1),V1) active#(U182(tt(),V1)) -> isLNat#(V1) active#(U182(tt(),V1)) -> U183#(isLNat(V1)) active#(U191(tt(),V1)) -> isNaturalKind#(V1) active#(U191(tt(),V1)) -> U192#(isNaturalKind(V1),V1) active#(U192(tt(),V1)) -> isNatural#(V1) active#(U192(tt(),V1)) -> U193#(isNatural(V1)) active#(U201(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U201(tt(),V1,V2)) -> U202#(isNaturalKind(V1),V1,V2) active#(U202(tt(),V1,V2)) -> isLNatKind#(V2) active#(U202(tt(),V1,V2)) -> U203#(isLNatKind(V2),V1,V2) active#(U203(tt(),V1,V2)) -> isLNatKind#(V2) active#(U203(tt(),V1,V2)) -> U204#(isLNatKind(V2),V1,V2) active#(U204(tt(),V1,V2)) -> isNatural#(V1) active#(U204(tt(),V1,V2)) -> U205#(isNatural(V1),V2) active#(U205(tt(),V2)) -> isLNat#(V2) active#(U205(tt(),V2)) -> U206#(isLNat(V2)) active#(U21(tt(),X,Y)) -> isLNatKind#(X) active#(U21(tt(),X,Y)) -> U22#(isLNatKind(X),X,Y) active#(U22(tt(),X,Y)) -> isLNat#(Y) active#(U22(tt(),X,Y)) -> U23#(isLNat(Y),X,Y) active#(U23(tt(),X,Y)) -> isLNatKind#(Y) active#(U23(tt(),X,Y)) -> U24#(isLNatKind(Y),X) active#(U231(tt(),V2)) -> isLNatKind#(V2) active#(U231(tt(),V2)) -> U232#(isLNatKind(V2)) active#(U241(tt(),V1,V2)) -> isLNatKind#(V1) active#(U241(tt(),V1,V2)) -> U242#(isLNatKind(V1),V1,V2) active#(U242(tt(),V1,V2)) -> isLNatKind#(V2) active#(U242(tt(),V1,V2)) -> U243#(isLNatKind(V2),V1,V2) active#(U243(tt(),V1,V2)) -> isLNatKind#(V2) active#(U243(tt(),V1,V2)) -> U244#(isLNatKind(V2),V1,V2) active#(U244(tt(),V1,V2)) -> isLNat#(V1) active#(U244(tt(),V1,V2)) -> U245#(isLNat(V1),V2) active#(U245(tt(),V2)) -> isLNat#(V2) active#(U245(tt(),V2)) -> U246#(isLNat(V2)) active#(U251(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U251(tt(),V1,V2)) -> U252#(isNaturalKind(V1),V1,V2) active#(U252(tt(),V1,V2)) -> isLNatKind#(V2) active#(U252(tt(),V1,V2)) -> U253#(isLNatKind(V2),V1,V2) active#(U253(tt(),V1,V2)) -> isLNatKind#(V2) active#(U253(tt(),V1,V2)) -> U254#(isLNatKind(V2),V1,V2) active#(U254(tt(),V1,V2)) -> isNatural#(V1) active#(U254(tt(),V1,V2)) -> U255#(isNatural(V1),V2) active#(U255(tt(),V2)) -> isLNat#(V2) active#(U255(tt(),V2)) -> U256#(isLNat(V2)) active#(U261(tt(),V2)) -> isLNatKind#(V2) active#(U261(tt(),V2)) -> U262#(isLNatKind(V2)) active#(U271(tt(),V2)) -> isLNatKind#(V2) active#(U271(tt(),V2)) -> U272#(isLNatKind(V2)) active#(U281(tt(),N)) -> isNaturalKind#(N) active#(U281(tt(),N)) -> U282#(isNaturalKind(N),N) active#(U282(tt(),N)) -> s#(N) active#(U282(tt(),N)) -> natsFrom#(s(N)) active#(U282(tt(),N)) -> cons#(N,natsFrom(s(N))) active#(U291(tt(),N,XS)) -> isNaturalKind#(N) active#(U291(tt(),N,XS)) -> U292#(isNaturalKind(N),N,XS) active#(U292(tt(),N,XS)) -> isLNat#(XS) active#(U292(tt(),N,XS)) -> U293#(isLNat(XS),N,XS) active#(U293(tt(),N,XS)) -> isLNatKind#(XS) active#(U293(tt(),N,XS)) -> U294#(isLNatKind(XS),N,XS) active#(U294(tt(),N,XS)) -> afterNth#(N,XS) active#(U294(tt(),N,XS)) -> head#(afterNth(N,XS)) active#(U301(tt(),X,Y)) -> isLNatKind#(X) active#(U301(tt(),X,Y)) -> U302#(isLNatKind(X),Y) active#(U302(tt(),Y)) -> isLNat#(Y) active#(U302(tt(),Y)) -> U303#(isLNat(Y),Y) active#(U303(tt(),Y)) -> isLNatKind#(Y) active#(U303(tt(),Y)) -> U304#(isLNatKind(Y),Y) active#(U31(tt(),N,XS)) -> isNaturalKind#(N) active#(U31(tt(),N,XS)) -> U32#(isNaturalKind(N),N,XS) active#(U311(tt(),XS)) -> isLNatKind#(XS) active#(U311(tt(),XS)) -> U312#(isLNatKind(XS),XS) active#(U312(tt(),XS)) -> pair#(nil(),XS) active#(U32(tt(),N,XS)) -> isLNat#(XS) active#(U32(tt(),N,XS)) -> U33#(isLNat(XS),N,XS) active#(U321(tt(),N,X,XS)) -> isNaturalKind#(N) active#(U321(tt(),N,X,XS)) -> U322#(isNaturalKind(N),N,X,XS) active#(U322(tt(),N,X,XS)) -> isNatural#(X) active#(U322(tt(),N,X,XS)) -> U323#(isNatural(X),N,X,XS) active#(U323(tt(),N,X,XS)) -> isNaturalKind#(X) active#(U323(tt(),N,X,XS)) -> U324#(isNaturalKind(X),N,X,XS) active#(U324(tt(),N,X,XS)) -> isLNat#(XS) active#(U324(tt(),N,X,XS)) -> U325#(isLNat(XS),N,X,XS) active#(U325(tt(),N,X,XS)) -> isLNatKind#(XS) active#(U325(tt(),N,X,XS)) -> U326#(isLNatKind(XS),N,X,XS) active#(U326(tt(),N,X,XS)) -> splitAt#(N,XS) active#(U326(tt(),N,X,XS)) -> U327#(splitAt(N,XS),X) active#(U327(pair(YS,ZS),X)) -> cons#(X,YS) active#(U327(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS) active#(U33(tt(),N,XS)) -> isLNatKind#(XS) active#(U33(tt(),N,XS)) -> U34#(isLNatKind(XS),N) active#(U331(tt(),N,XS)) -> isNaturalKind#(N) active#(U331(tt(),N,XS)) -> U332#(isNaturalKind(N),XS) active#(U332(tt(),XS)) -> isLNat#(XS) active#(U332(tt(),XS)) -> U333#(isLNat(XS),XS) active#(U333(tt(),XS)) -> isLNatKind#(XS) active#(U333(tt(),XS)) -> U334#(isLNatKind(XS),XS) active#(U341(tt(),N,XS)) -> isNaturalKind#(N) active#(U341(tt(),N,XS)) -> U342#(isNaturalKind(N),N,XS) active#(U342(tt(),N,XS)) -> isLNat#(XS) active#(U342(tt(),N,XS)) -> U343#(isLNat(XS),N,XS) active#(U343(tt(),N,XS)) -> isLNatKind#(XS) active#(U343(tt(),N,XS)) -> U344#(isLNatKind(XS),N,XS) active#(U344(tt(),N,XS)) -> splitAt#(N,XS) active#(U344(tt(),N,XS)) -> fst#(splitAt(N,XS)) active#(U41(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNaturalKind(V1),V1,V2) active#(U42(tt(),V1,V2)) -> isLNatKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isLNatKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> isLNatKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isLNatKind(V2),V1,V2) active#(U44(tt(),V1,V2)) -> isNatural#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNatural(V1),V2) active#(U45(tt(),V2)) -> isLNat#(V2) active#(U45(tt(),V2)) -> U46#(isLNat(V2)) active#(U51(tt(),V1,V2)) -> isNaturalKind#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNaturalKind(V1),V1,V2) active#(U52(tt(),V1,V2)) -> isLNatKind#(V2) active#(U52(tt(),V1,V2)) -> U53#(isLNatKind(V2),V1,V2) active#(U53(tt(),V1,V2)) -> isLNatKind#(V2) active#(U53(tt(),V1,V2)) -> U54#(isLNatKind(V2),V1,V2) active#(U54(tt(),V1,V2)) -> isNatural#(V1) active#(U54(tt(),V1,V2)) -> U55#(isNatural(V1),V2) active#(U55(tt(),V2)) -> isLNat#(V2) active#(U55(tt(),V2)) -> U56#(isLNat(V2)) active#(U61(tt(),V1)) -> isPLNatKind#(V1) active#(U61(tt(),V1)) -> U62#(isPLNatKind(V1),V1) active#(U62(tt(),V1)) -> isPLNat#(V1) active#(U62(tt(),V1)) -> U63#(isPLNat(V1)) active#(U71(tt(),V1)) -> isNaturalKind#(V1) active#(U71(tt(),V1)) -> U72#(isNaturalKind(V1),V1) active#(U72(tt(),V1)) -> isNatural#(V1) active#(U72(tt(),V1)) -> U73#(isNatural(V1)) active#(U81(tt(),V1)) -> isPLNatKind#(V1) active#(U81(tt(),V1)) -> U82#(isPLNatKind(V1),V1) active#(U82(tt(),V1)) -> isPLNat#(V1) active#(U82(tt(),V1)) -> U83#(isPLNat(V1)) active#(U91(tt(),V1)) -> isLNatKind#(V1) active#(U91(tt(),V1)) -> U92#(isLNatKind(V1),V1) active#(U92(tt(),V1)) -> isLNat#(V1) active#(U92(tt(),V1)) -> U93#(isLNat(V1)) active#(afterNth(N,XS)) -> isNatural#(N) active#(afterNth(N,XS)) -> U11#(isNatural(N),N,XS) active#(fst(pair(X,Y))) -> isLNat#(X) active#(fst(pair(X,Y))) -> U21#(isLNat(X),X,Y) active#(head(cons(N,XS))) -> isNatural#(N) active#(head(cons(N,XS))) -> U31#(isNatural(N),N,XS) active#(isLNat(afterNth(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(afterNth(V1,V2))) -> U41#(isNaturalKind(V1),V1,V2) active#(isLNat(cons(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(cons(V1,V2))) -> U51#(isNaturalKind(V1),V1,V2) active#(isLNat(fst(V1))) -> isPLNatKind#(V1) active#(isLNat(fst(V1))) -> U61#(isPLNatKind(V1),V1) active#(isLNat(natsFrom(V1))) -> isNaturalKind#(V1) active#(isLNat(natsFrom(V1))) -> U71#(isNaturalKind(V1),V1) active#(isLNat(snd(V1))) -> isPLNatKind#(V1) active#(isLNat(snd(V1))) -> U81#(isPLNatKind(V1),V1) active#(isLNat(tail(V1))) -> isLNatKind#(V1) active#(isLNat(tail(V1))) -> U91#(isLNatKind(V1),V1) active#(isLNat(take(V1,V2))) -> isNaturalKind#(V1) active#(isLNat(take(V1,V2))) -> U101#(isNaturalKind(V1),V1,V2) active#(isLNatKind(afterNth(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(afterNth(V1,V2))) -> U111#(isNaturalKind(V1),V2) active#(isLNatKind(cons(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(cons(V1,V2))) -> U121#(isNaturalKind(V1),V2) active#(isLNatKind(fst(V1))) -> isPLNatKind#(V1) active#(isLNatKind(fst(V1))) -> U131#(isPLNatKind(V1)) active#(isLNatKind(natsFrom(V1))) -> isNaturalKind#(V1) active#(isLNatKind(natsFrom(V1))) -> U141#(isNaturalKind(V1)) active#(isLNatKind(snd(V1))) -> isPLNatKind#(V1) active#(isLNatKind(snd(V1))) -> U151#(isPLNatKind(V1)) active#(isLNatKind(tail(V1))) -> isLNatKind#(V1) active#(isLNatKind(tail(V1))) -> U161#(isLNatKind(V1)) active#(isLNatKind(take(V1,V2))) -> isNaturalKind#(V1) active#(isLNatKind(take(V1,V2))) -> U171#(isNaturalKind(V1),V2) active#(isNatural(head(V1))) -> isLNatKind#(V1) active#(isNatural(head(V1))) -> U181#(isLNatKind(V1),V1) active#(isNatural(s(V1))) -> isNaturalKind#(V1) active#(isNatural(s(V1))) -> U191#(isNaturalKind(V1),V1) active#(isNatural(sel(V1,V2))) -> isNaturalKind#(V1) active#(isNatural(sel(V1,V2))) -> U201#(isNaturalKind(V1),V1,V2) active#(isNaturalKind(head(V1))) -> isLNatKind#(V1) active#(isNaturalKind(head(V1))) -> U211#(isLNatKind(V1)) active#(isNaturalKind(s(V1))) -> isNaturalKind#(V1) active#(isNaturalKind(s(V1))) -> U221#(isNaturalKind(V1)) active#(isNaturalKind(sel(V1,V2))) -> isNaturalKind#(V1) active#(isNaturalKind(sel(V1,V2))) -> U231#(isNaturalKind(V1),V2) active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V1) active#(isPLNat(pair(V1,V2))) -> U241#(isLNatKind(V1),V1,V2) active#(isPLNat(splitAt(V1,V2))) -> isNaturalKind#(V1) active#(isPLNat(splitAt(V1,V2))) -> U251#(isNaturalKind(V1),V1,V2) active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V1) active#(isPLNatKind(pair(V1,V2))) -> U261#(isLNatKind(V1),V2) active#(isPLNatKind(splitAt(V1,V2))) -> isNaturalKind#(V1) active#(isPLNatKind(splitAt(V1,V2))) -> U271#(isNaturalKind(V1),V2) active#(natsFrom(N)) -> isNatural#(N) active#(natsFrom(N)) -> U281#(isNatural(N),N) active#(sel(N,XS)) -> isNatural#(N) active#(sel(N,XS)) -> U291#(isNatural(N),N,XS) active#(snd(pair(X,Y))) -> isLNat#(X) active#(snd(pair(X,Y))) -> U301#(isLNat(X),X,Y) active#(splitAt(0(),XS)) -> isLNat#(XS) active#(splitAt(0(),XS)) -> U311#(isLNat(XS),XS) active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N) active#(splitAt(s(N),cons(X,XS))) -> U321#(isNatural(N),N,X,XS) active#(tail(cons(N,XS))) -> isNatural#(N) active#(tail(cons(N,XS))) -> U331#(isNatural(N),N,XS) active#(take(N,XS)) -> isNatural#(N) active#(take(N,XS)) -> U341#(isNatural(N),N,XS) active#(U101(X1,X2,X3)) -> active#(X1) active#(U101(X1,X2,X3)) -> U101#(active(X1),X2,X3) active#(U102(X1,X2,X3)) -> active#(X1) active#(U102(X1,X2,X3)) -> U102#(active(X1),X2,X3) active#(U103(X1,X2,X3)) -> active#(X1) active#(U103(X1,X2,X3)) -> U103#(active(X1),X2,X3) active#(U104(X1,X2,X3)) -> active#(X1) active#(U104(X1,X2,X3)) -> U104#(active(X1),X2,X3) active#(U105(X1,X2)) -> active#(X1) active#(U105(X1,X2)) -> U105#(active(X1),X2) active#(U106(X)) -> active#(X) active#(U106(X)) -> U106#(active(X)) active#(U11(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U111(X1,X2)) -> active#(X1) active#(U111(X1,X2)) -> U111#(active(X1),X2) active#(U112(X)) -> active#(X) active#(U112(X)) -> U112#(active(X)) active#(U13(X1,X2,X3)) -> active#(X1) active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3) active#(U121(X1,X2)) -> active#(X1) active#(U121(X1,X2)) -> U121#(active(X1),X2) active#(U122(X)) -> active#(X) active#(U122(X)) -> U122#(active(X)) active#(U14(X1,X2,X3)) -> active#(X1) active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3) active#(U131(X)) -> active#(X) active#(U131(X)) -> U131#(active(X)) active#(snd(X)) -> active#(X) active#(snd(X)) -> snd#(active(X)) active#(splitAt(X1,X2)) -> active#(X1) active#(splitAt(X1,X2)) -> splitAt#(active(X1),X2) active#(splitAt(X1,X2)) -> active#(X2) active#(splitAt(X1,X2)) -> splitAt#(X1,active(X2)) active#(U141(X)) -> active#(X) active#(U141(X)) -> U141#(active(X)) active#(U151(X)) -> active#(X) active#(U151(X)) -> U151#(active(X)) active#(U161(X)) -> active#(X) active#(U161(X)) -> U161#(active(X)) active#(U171(X1,X2)) -> active#(X1) active#(U171(X1,X2)) -> U171#(active(X1),X2) active#(U172(X)) -> active#(X) active#(U172(X)) -> U172#(active(X)) active#(U181(X1,X2)) -> active#(X1) active#(U181(X1,X2)) -> U181#(active(X1),X2) active#(U182(X1,X2)) -> active#(X1) active#(U182(X1,X2)) -> U182#(active(X1),X2) active#(U183(X)) -> active#(X) active#(U183(X)) -> U183#(active(X)) active#(U191(X1,X2)) -> active#(X1) active#(U191(X1,X2)) -> U191#(active(X1),X2) active#(U192(X1,X2)) -> active#(X1) active#(U192(X1,X2)) -> U192#(active(X1),X2) active#(U193(X)) -> active#(X) active#(U193(X)) -> U193#(active(X)) active#(U201(X1,X2,X3)) -> active#(X1) active#(U201(X1,X2,X3)) -> U201#(active(X1),X2,X3) active#(U202(X1,X2,X3)) -> active#(X1) active#(U202(X1,X2,X3)) -> U202#(active(X1),X2,X3) active#(U203(X1,X2,X3)) -> active#(X1) active#(U203(X1,X2,X3)) -> U203#(active(X1),X2,X3) active#(U204(X1,X2,X3)) -> active#(X1) active#(U204(X1,X2,X3)) -> U204#(active(X1),X2,X3) active#(U205(X1,X2)) -> active#(X1) active#(U205(X1,X2)) -> U205#(active(X1),X2) active#(U206(X)) -> active#(X) active#(U206(X)) -> U206#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U211(X)) -> active#(X) active#(U211(X)) -> U211#(active(X)) active#(U23(X1,X2,X3)) -> active#(X1) active#(U23(X1,X2,X3)) -> U23#(active(X1),X2,X3) active#(U221(X)) -> active#(X) active#(U221(X)) -> U221#(active(X)) active#(U24(X1,X2)) -> active#(X1) active#(U24(X1,X2)) -> U24#(active(X1),X2) active#(U231(X1,X2)) -> active#(X1) active#(U231(X1,X2)) -> U231#(active(X1),X2) active#(U232(X)) -> active#(X) active#(U232(X)) -> U232#(active(X)) active#(U241(X1,X2,X3)) -> active#(X1) active#(U241(X1,X2,X3)) -> U241#(active(X1),X2,X3) active#(U242(X1,X2,X3)) -> active#(X1) active#(U242(X1,X2,X3)) -> U242#(active(X1),X2,X3) active#(U243(X1,X2,X3)) -> active#(X1) active#(U243(X1,X2,X3)) -> U243#(active(X1),X2,X3) active#(U244(X1,X2,X3)) -> active#(X1) active#(U244(X1,X2,X3)) -> U244#(active(X1),X2,X3) active#(U245(X1,X2)) -> active#(X1) active#(U245(X1,X2)) -> U245#(active(X1),X2) active#(U246(X)) -> active#(X) active#(U246(X)) -> U246#(active(X)) active#(U251(X1,X2,X3)) -> active#(X1) active#(U251(X1,X2,X3)) -> U251#(active(X1),X2,X3) active#(U252(X1,X2,X3)) -> active#(X1) active#(U252(X1,X2,X3)) -> U252#(active(X1),X2,X3) active#(U253(X1,X2,X3)) -> active#(X1) active#(U253(X1,X2,X3)) -> U253#(active(X1),X2,X3) active#(U254(X1,X2,X3)) -> active#(X1) active#(U254(X1,X2,X3)) -> U254#(active(X1),X2,X3) active#(U255(X1,X2)) -> active#(X1) active#(U255(X1,X2)) -> U255#(active(X1),X2) active#(U256(X)) -> active#(X) active#(U256(X)) -> U256#(active(X)) active#(U261(X1,X2)) -> active#(X1) active#(U261(X1,X2)) -> U261#(active(X1),X2) active#(U262(X)) -> active#(X) active#(U262(X)) -> U262#(active(X)) active#(U271(X1,X2)) -> active#(X1) active#(U271(X1,X2)) -> U271#(active(X1),X2) active#(U272(X)) -> active#(X) active#(U272(X)) -> U272#(active(X)) active#(U281(X1,X2)) -> active#(X1) active#(U281(X1,X2)) -> U281#(active(X1),X2) active#(U282(X1,X2)) -> active#(X1) active#(U282(X1,X2)) -> U282#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(natsFrom(X)) -> active#(X) active#(natsFrom(X)) -> natsFrom#(active(X)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(U291(X1,X2,X3)) -> active#(X1) active#(U291(X1,X2,X3)) -> U291#(active(X1),X2,X3) active#(U292(X1,X2,X3)) -> active#(X1) active#(U292(X1,X2,X3)) -> U292#(active(X1),X2,X3) active#(U293(X1,X2,X3)) -> active#(X1) active#(U293(X1,X2,X3)) -> U293#(active(X1),X2,X3) active#(U294(X1,X2,X3)) -> active#(X1) active#(U294(X1,X2,X3)) -> U294#(active(X1),X2,X3) active#(head(X)) -> active#(X) active#(head(X)) -> head#(active(X)) active#(afterNth(X1,X2)) -> active#(X1) active#(afterNth(X1,X2)) -> afterNth#(active(X1),X2) active#(afterNth(X1,X2)) -> active#(X2) active#(afterNth(X1,X2)) -> afterNth#(X1,active(X2)) active#(U301(X1,X2,X3)) -> active#(X1) active#(U301(X1,X2,X3)) -> U301#(active(X1),X2,X3) active#(U302(X1,X2)) -> active#(X1) active#(U302(X1,X2)) -> U302#(active(X1),X2) active#(U303(X1,X2)) -> active#(X1) active#(U303(X1,X2)) -> U303#(active(X1),X2) active#(U304(X1,X2)) -> active#(X1) active#(U304(X1,X2)) -> U304#(active(X1),X2) active#(U31(X1,X2,X3)) -> active#(X1) active#(U31(X1,X2,X3)) -> U31#(active(X1),X2,X3) active#(U32(X1,X2,X3)) -> active#(X1) active#(U32(X1,X2,X3)) -> U32#(active(X1),X2,X3) active#(U311(X1,X2)) -> active#(X1) active#(U311(X1,X2)) -> U311#(active(X1),X2) active#(U312(X1,X2)) -> active#(X1) active#(U312(X1,X2)) -> U312#(active(X1),X2) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> pair#(active(X1),X2) active#(pair(X1,X2)) -> active#(X2) active#(pair(X1,X2)) -> pair#(X1,active(X2)) active#(U33(X1,X2,X3)) -> active#(X1) active#(U33(X1,X2,X3)) -> U33#(active(X1),X2,X3) active#(U321(X1,X2,X3,X4)) -> active#(X1) active#(U321(X1,X2,X3,X4)) -> U321#(active(X1),X2,X3,X4) active#(U322(X1,X2,X3,X4)) -> active#(X1) active#(U322(X1,X2,X3,X4)) -> U322#(active(X1),X2,X3,X4) active#(U323(X1,X2,X3,X4)) -> active#(X1) active#(U323(X1,X2,X3,X4)) -> U323#(active(X1),X2,X3,X4) active#(U324(X1,X2,X3,X4)) -> active#(X1) active#(U324(X1,X2,X3,X4)) -> U324#(active(X1),X2,X3,X4) active#(U325(X1,X2,X3,X4)) -> active#(X1) active#(U325(X1,X2,X3,X4)) -> U325#(active(X1),X2,X3,X4) active#(U326(X1,X2,X3,X4)) -> active#(X1) active#(U326(X1,X2,X3,X4)) -> U326#(active(X1),X2,X3,X4) active#(U327(X1,X2)) -> active#(X1) active#(U327(X1,X2)) -> U327#(active(X1),X2) active#(U34(X1,X2)) -> active#(X1) active#(U34(X1,X2)) -> U34#(active(X1),X2) active#(U331(X1,X2,X3)) -> active#(X1) active#(U331(X1,X2,X3)) -> U331#(active(X1),X2,X3) active#(U332(X1,X2)) -> active#(X1) active#(U332(X1,X2)) -> U332#(active(X1),X2) active#(U333(X1,X2)) -> active#(X1) active#(U333(X1,X2)) -> U333#(active(X1),X2) active#(U334(X1,X2)) -> active#(X1) active#(U334(X1,X2)) -> U334#(active(X1),X2) active#(U341(X1,X2,X3)) -> active#(X1) active#(U341(X1,X2,X3)) -> U341#(active(X1),X2,X3) active#(U342(X1,X2,X3)) -> active#(X1) active#(U342(X1,X2,X3)) -> U342#(active(X1),X2,X3) active#(U343(X1,X2,X3)) -> active#(X1) active#(U343(X1,X2,X3)) -> U343#(active(X1),X2,X3) active#(U344(X1,X2,X3)) -> active#(X1) active#(U344(X1,X2,X3)) -> U344#(active(X1),X2,X3) active#(fst(X)) -> active#(X) active#(fst(X)) -> fst#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3) active#(U43(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3) active#(U44(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3) active#(U45(X1,X2)) -> active#(X1) active#(U45(X1,X2)) -> U45#(active(X1),X2) active#(U46(X)) -> active#(X) active#(U46(X)) -> U46#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> U52#(active(X1),X2,X3) active#(U53(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> U53#(active(X1),X2,X3) active#(U54(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> U54#(active(X1),X2,X3) active#(U55(X1,X2)) -> active#(X1) active#(U55(X1,X2)) -> U55#(active(X1),X2) active#(U56(X)) -> active#(X) active#(U56(X)) -> U56#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> U62#(active(X1),X2) active#(U63(X)) -> active#(X) active#(U63(X)) -> U63#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X1,X2)) -> active#(X1) active#(U72(X1,X2)) -> U72#(active(X1),X2) active#(U73(X)) -> active#(X) active#(U73(X)) -> U73#(active(X)) active#(U81(X1,X2)) -> active#(X1) active#(U81(X1,X2)) -> U81#(active(X1),X2) active#(U82(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> U82#(active(X1),X2) active#(U83(X)) -> active#(X) active#(U83(X)) -> U83#(active(X)) active#(U91(X1,X2)) -> active#(X1) active#(U91(X1,X2)) -> U91#(active(X1),X2) active#(U92(X1,X2)) -> active#(X1) active#(U92(X1,X2)) -> U92#(active(X1),X2) active#(U93(X)) -> active#(X) active#(U93(X)) -> U93#(active(X)) active#(tail(X)) -> active#(X) active#(tail(X)) -> tail#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U105#(mark(X1),X2) -> U105#(X1,X2) U106#(mark(X)) -> U106#(X) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U111#(mark(X1),X2) -> U111#(X1,X2) U112#(mark(X)) -> U112#(X) U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U121#(mark(X1),X2) -> U121#(X1,X2) U122#(mark(X)) -> U122#(X) U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U131#(mark(X)) -> U131#(X) snd#(mark(X)) -> snd#(X) splitAt#(mark(X1),X2) -> splitAt#(X1,X2) splitAt#(X1,mark(X2)) -> splitAt#(X1,X2) U141#(mark(X)) -> U141#(X) U151#(mark(X)) -> U151#(X) U161#(mark(X)) -> U161#(X) U171#(mark(X1),X2) -> U171#(X1,X2) U172#(mark(X)) -> U172#(X) U181#(mark(X1),X2) -> U181#(X1,X2) U182#(mark(X1),X2) -> U182#(X1,X2) U183#(mark(X)) -> U183#(X) U191#(mark(X1),X2) -> U191#(X1,X2) U192#(mark(X1),X2) -> U192#(X1,X2) U193#(mark(X)) -> U193#(X) U201#(mark(X1),X2,X3) -> U201#(X1,X2,X3) U202#(mark(X1),X2,X3) -> U202#(X1,X2,X3) U203#(mark(X1),X2,X3) -> U203#(X1,X2,X3) U204#(mark(X1),X2,X3) -> U204#(X1,X2,X3) U205#(mark(X1),X2) -> U205#(X1,X2) U206#(mark(X)) -> U206#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U211#(mark(X)) -> U211#(X) U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U221#(mark(X)) -> U221#(X) U24#(mark(X1),X2) -> U24#(X1,X2) U231#(mark(X1),X2) -> U231#(X1,X2) U232#(mark(X)) -> U232#(X) U241#(mark(X1),X2,X3) -> U241#(X1,X2,X3) U242#(mark(X1),X2,X3) -> U242#(X1,X2,X3) U243#(mark(X1),X2,X3) -> U243#(X1,X2,X3) U244#(mark(X1),X2,X3) -> U244#(X1,X2,X3) U245#(mark(X1),X2) -> U245#(X1,X2) U246#(mark(X)) -> U246#(X) U251#(mark(X1),X2,X3) -> U251#(X1,X2,X3) U252#(mark(X1),X2,X3) -> U252#(X1,X2,X3) U253#(mark(X1),X2,X3) -> U253#(X1,X2,X3) U254#(mark(X1),X2,X3) -> U254#(X1,X2,X3) U255#(mark(X1),X2) -> U255#(X1,X2) U256#(mark(X)) -> U256#(X) U261#(mark(X1),X2) -> U261#(X1,X2) U262#(mark(X)) -> U262#(X) U271#(mark(X1),X2) -> U271#(X1,X2) U272#(mark(X)) -> U272#(X) U281#(mark(X1),X2) -> U281#(X1,X2) U282#(mark(X1),X2) -> U282#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) natsFrom#(mark(X)) -> natsFrom#(X) s#(mark(X)) -> s#(X) U291#(mark(X1),X2,X3) -> U291#(X1,X2,X3) U292#(mark(X1),X2,X3) -> U292#(X1,X2,X3) U293#(mark(X1),X2,X3) -> U293#(X1,X2,X3) U294#(mark(X1),X2,X3) -> U294#(X1,X2,X3) head#(mark(X)) -> head#(X) afterNth#(mark(X1),X2) -> afterNth#(X1,X2) afterNth#(X1,mark(X2)) -> afterNth#(X1,X2) U301#(mark(X1),X2,X3) -> U301#(X1,X2,X3) U302#(mark(X1),X2) -> U302#(X1,X2) U303#(mark(X1),X2) -> U303#(X1,X2) U304#(mark(X1),X2) -> U304#(X1,X2) U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U311#(mark(X1),X2) -> U311#(X1,X2) U312#(mark(X1),X2) -> U312#(X1,X2) pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U321#(mark(X1),X2,X3,X4) -> U321#(X1,X2,X3,X4) U322#(mark(X1),X2,X3,X4) -> U322#(X1,X2,X3,X4) U323#(mark(X1),X2,X3,X4) -> U323#(X1,X2,X3,X4) U324#(mark(X1),X2,X3,X4) -> U324#(X1,X2,X3,X4) U325#(mark(X1),X2,X3,X4) -> U325#(X1,X2,X3,X4) U326#(mark(X1),X2,X3,X4) -> U326#(X1,X2,X3,X4) U327#(mark(X1),X2) -> U327#(X1,X2) U34#(mark(X1),X2) -> U34#(X1,X2) U331#(mark(X1),X2,X3) -> U331#(X1,X2,X3) U332#(mark(X1),X2) -> U332#(X1,X2) U333#(mark(X1),X2) -> U333#(X1,X2) U334#(mark(X1),X2) -> U334#(X1,X2) U341#(mark(X1),X2,X3) -> U341#(X1,X2,X3) U342#(mark(X1),X2,X3) -> U342#(X1,X2,X3) U343#(mark(X1),X2,X3) -> U343#(X1,X2,X3) U344#(mark(X1),X2,X3) -> U344#(X1,X2,X3) fst#(mark(X)) -> fst#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U55#(mark(X1),X2) -> U55#(X1,X2) U56#(mark(X)) -> U56#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X1),X2) -> U62#(X1,X2) U63#(mark(X)) -> U63#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U73#(mark(X)) -> U73#(X) U81#(mark(X1),X2) -> U81#(X1,X2) U82#(mark(X1),X2) -> U82#(X1,X2) U83#(mark(X)) -> U83#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U92#(mark(X1),X2) -> U92#(X1,X2) U93#(mark(X)) -> U93#(X) tail#(mark(X)) -> tail#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(U101(X1,X2,X3)) -> proper#(X3) proper#(U101(X1,X2,X3)) -> proper#(X2) proper#(U101(X1,X2,X3)) -> proper#(X1) proper#(U101(X1,X2,X3)) -> U101#(proper(X1),proper(X2),proper(X3)) proper#(U102(X1,X2,X3)) -> proper#(X3) proper#(U102(X1,X2,X3)) -> proper#(X2) proper#(U102(X1,X2,X3)) -> proper#(X1) proper#(U102(X1,X2,X3)) -> U102#(proper(X1),proper(X2),proper(X3)) proper#(isNaturalKind(X)) -> proper#(X) proper#(isNaturalKind(X)) -> isNaturalKind#(proper(X)) proper#(U103(X1,X2,X3)) -> proper#(X3) proper#(U103(X1,X2,X3)) -> proper#(X2) proper#(U103(X1,X2,X3)) -> proper#(X1) proper#(U103(X1,X2,X3)) -> U103#(proper(X1),proper(X2),proper(X3)) proper#(isLNatKind(X)) -> proper#(X) proper#(isLNatKind(X)) -> isLNatKind#(proper(X)) proper#(U104(X1,X2,X3)) -> proper#(X3) proper#(U104(X1,X2,X3)) -> proper#(X2) proper#(U104(X1,X2,X3)) -> proper#(X1) proper#(U104(X1,X2,X3)) -> U104#(proper(X1),proper(X2),proper(X3)) proper#(U105(X1,X2)) -> proper#(X2) proper#(U105(X1,X2)) -> proper#(X1) proper#(U105(X1,X2)) -> U105#(proper(X1),proper(X2)) proper#(isNatural(X)) -> proper#(X) proper#(isNatural(X)) -> isNatural#(proper(X)) proper#(U106(X)) -> proper#(X) proper#(U106(X)) -> U106#(proper(X)) proper#(isLNat(X)) -> proper#(X) proper#(isLNat(X)) -> isLNat#(proper(X)) proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U111(X1,X2)) -> proper#(X2) proper#(U111(X1,X2)) -> proper#(X1) proper#(U111(X1,X2)) -> U111#(proper(X1),proper(X2)) proper#(U112(X)) -> proper#(X) proper#(U112(X)) -> U112#(proper(X)) proper#(U13(X1,X2,X3)) -> proper#(X3) proper#(U13(X1,X2,X3)) -> proper#(X2) proper#(U13(X1,X2,X3)) -> proper#(X1) proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3)) proper#(U121(X1,X2)) -> proper#(X2) proper#(U121(X1,X2)) -> proper#(X1) proper#(U121(X1,X2)) -> U121#(proper(X1),proper(X2)) proper#(U122(X)) -> proper#(X) proper#(U122(X)) -> U122#(proper(X)) proper#(U14(X1,X2,X3)) -> proper#(X3) proper#(U14(X1,X2,X3)) -> proper#(X2) proper#(U14(X1,X2,X3)) -> proper#(X1) proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3)) proper#(U131(X)) -> proper#(X) proper#(U131(X)) -> U131#(proper(X)) proper#(snd(X)) -> proper#(X) proper#(snd(X)) -> snd#(proper(X)) proper#(splitAt(X1,X2)) -> proper#(X2) proper#(splitAt(X1,X2)) -> proper#(X1) proper#(splitAt(X1,X2)) -> splitAt#(proper(X1),proper(X2)) proper#(U141(X)) -> proper#(X) proper#(U141(X)) -> U141#(proper(X)) proper#(U151(X)) -> proper#(X) proper#(U151(X)) -> U151#(proper(X)) proper#(U161(X)) -> proper#(X) proper#(U161(X)) -> U161#(proper(X)) proper#(U171(X1,X2)) -> proper#(X2) proper#(U171(X1,X2)) -> proper#(X1) proper#(U171(X1,X2)) -> U171#(proper(X1),proper(X2)) proper#(U172(X)) -> proper#(X) proper#(U172(X)) -> U172#(proper(X)) proper#(U181(X1,X2)) -> proper#(X2) proper#(U181(X1,X2)) -> proper#(X1) proper#(U181(X1,X2)) -> U181#(proper(X1),proper(X2)) proper#(U182(X1,X2)) -> proper#(X2) proper#(U182(X1,X2)) -> proper#(X1) proper#(U182(X1,X2)) -> U182#(proper(X1),proper(X2)) proper#(U183(X)) -> proper#(X) proper#(U183(X)) -> U183#(proper(X)) proper#(U191(X1,X2)) -> proper#(X2) proper#(U191(X1,X2)) -> proper#(X1) proper#(U191(X1,X2)) -> U191#(proper(X1),proper(X2)) proper#(U192(X1,X2)) -> proper#(X2) proper#(U192(X1,X2)) -> proper#(X1) proper#(U192(X1,X2)) -> U192#(proper(X1),proper(X2)) proper#(U193(X)) -> proper#(X) proper#(U193(X)) -> U193#(proper(X)) proper#(U201(X1,X2,X3)) -> proper#(X3) proper#(U201(X1,X2,X3)) -> proper#(X2) proper#(U201(X1,X2,X3)) -> proper#(X1) proper#(U201(X1,X2,X3)) -> U201#(proper(X1),proper(X2),proper(X3)) proper#(U202(X1,X2,X3)) -> proper#(X3) proper#(U202(X1,X2,X3)) -> proper#(X2) proper#(U202(X1,X2,X3)) -> proper#(X1) proper#(U202(X1,X2,X3)) -> U202#(proper(X1),proper(X2),proper(X3)) proper#(U203(X1,X2,X3)) -> proper#(X3) proper#(U203(X1,X2,X3)) -> proper#(X2) proper#(U203(X1,X2,X3)) -> proper#(X1) proper#(U203(X1,X2,X3)) -> U203#(proper(X1),proper(X2),proper(X3)) proper#(U204(X1,X2,X3)) -> proper#(X3) proper#(U204(X1,X2,X3)) -> proper#(X2) proper#(U204(X1,X2,X3)) -> proper#(X1) proper#(U204(X1,X2,X3)) -> U204#(proper(X1),proper(X2),proper(X3)) proper#(U205(X1,X2)) -> proper#(X2) proper#(U205(X1,X2)) -> proper#(X1) proper#(U205(X1,X2)) -> U205#(proper(X1),proper(X2)) proper#(U206(X)) -> proper#(X) proper#(U206(X)) -> U206#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U211(X)) -> proper#(X) proper#(U211(X)) -> U211#(proper(X)) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U23(X1,X2,X3)) -> U23#(proper(X1),proper(X2),proper(X3)) proper#(U221(X)) -> proper#(X) proper#(U221(X)) -> U221#(proper(X)) proper#(U24(X1,X2)) -> proper#(X2) proper#(U24(X1,X2)) -> proper#(X1) proper#(U24(X1,X2)) -> U24#(proper(X1),proper(X2)) proper#(U231(X1,X2)) -> proper#(X2) proper#(U231(X1,X2)) -> proper#(X1) proper#(U231(X1,X2)) -> U231#(proper(X1),proper(X2)) proper#(U232(X)) -> proper#(X) proper#(U232(X)) -> U232#(proper(X)) proper#(U241(X1,X2,X3)) -> proper#(X3) proper#(U241(X1,X2,X3)) -> proper#(X2) proper#(U241(X1,X2,X3)) -> proper#(X1) proper#(U241(X1,X2,X3)) -> U241#(proper(X1),proper(X2),proper(X3)) proper#(U242(X1,X2,X3)) -> proper#(X3) proper#(U242(X1,X2,X3)) -> proper#(X2) proper#(U242(X1,X2,X3)) -> proper#(X1) proper#(U242(X1,X2,X3)) -> U242#(proper(X1),proper(X2),proper(X3)) proper#(U243(X1,X2,X3)) -> proper#(X3) proper#(U243(X1,X2,X3)) -> proper#(X2) proper#(U243(X1,X2,X3)) -> proper#(X1) proper#(U243(X1,X2,X3)) -> U243#(proper(X1),proper(X2),proper(X3)) proper#(U244(X1,X2,X3)) -> proper#(X3) proper#(U244(X1,X2,X3)) -> proper#(X2) proper#(U244(X1,X2,X3)) -> proper#(X1) proper#(U244(X1,X2,X3)) -> U244#(proper(X1),proper(X2),proper(X3)) proper#(U245(X1,X2)) -> proper#(X2) proper#(U245(X1,X2)) -> proper#(X1) proper#(U245(X1,X2)) -> U245#(proper(X1),proper(X2)) proper#(U246(X)) -> proper#(X) proper#(U246(X)) -> U246#(proper(X)) proper#(U251(X1,X2,X3)) -> proper#(X3) proper#(U251(X1,X2,X3)) -> proper#(X2) proper#(U251(X1,X2,X3)) -> proper#(X1) proper#(U251(X1,X2,X3)) -> U251#(proper(X1),proper(X2),proper(X3)) proper#(U252(X1,X2,X3)) -> proper#(X3) proper#(U252(X1,X2,X3)) -> proper#(X2) proper#(U252(X1,X2,X3)) -> proper#(X1) proper#(U252(X1,X2,X3)) -> U252#(proper(X1),proper(X2),proper(X3)) proper#(U253(X1,X2,X3)) -> proper#(X3) proper#(U253(X1,X2,X3)) -> proper#(X2) proper#(U253(X1,X2,X3)) -> proper#(X1) proper#(U253(X1,X2,X3)) -> U253#(proper(X1),proper(X2),proper(X3)) proper#(U254(X1,X2,X3)) -> proper#(X3) proper#(U254(X1,X2,X3)) -> proper#(X2) proper#(U254(X1,X2,X3)) -> proper#(X1) proper#(U254(X1,X2,X3)) -> U254#(proper(X1),proper(X2),proper(X3)) proper#(U255(X1,X2)) -> proper#(X2) proper#(U255(X1,X2)) -> proper#(X1) proper#(U255(X1,X2)) -> U255#(proper(X1),proper(X2)) proper#(U256(X)) -> proper#(X) proper#(U256(X)) -> U256#(proper(X)) proper#(U261(X1,X2)) -> proper#(X2) proper#(U261(X1,X2)) -> proper#(X1) proper#(U261(X1,X2)) -> U261#(proper(X1),proper(X2)) proper#(U262(X)) -> proper#(X) proper#(U262(X)) -> U262#(proper(X)) proper#(U271(X1,X2)) -> proper#(X2) proper#(U271(X1,X2)) -> proper#(X1) proper#(U271(X1,X2)) -> U271#(proper(X1),proper(X2)) proper#(U272(X)) -> proper#(X) proper#(U272(X)) -> U272#(proper(X)) proper#(U281(X1,X2)) -> proper#(X2) proper#(U281(X1,X2)) -> proper#(X1) proper#(U281(X1,X2)) -> U281#(proper(X1),proper(X2)) proper#(U282(X1,X2)) -> proper#(X2) proper#(U282(X1,X2)) -> proper#(X1) proper#(U282(X1,X2)) -> U282#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(natsFrom(X)) -> proper#(X) proper#(natsFrom(X)) -> natsFrom#(proper(X)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(U291(X1,X2,X3)) -> proper#(X3) proper#(U291(X1,X2,X3)) -> proper#(X2) proper#(U291(X1,X2,X3)) -> proper#(X1) proper#(U291(X1,X2,X3)) -> U291#(proper(X1),proper(X2),proper(X3)) proper#(U292(X1,X2,X3)) -> proper#(X3) proper#(U292(X1,X2,X3)) -> proper#(X2) proper#(U292(X1,X2,X3)) -> proper#(X1) proper#(U292(X1,X2,X3)) -> U292#(proper(X1),proper(X2),proper(X3)) proper#(U293(X1,X2,X3)) -> proper#(X3) proper#(U293(X1,X2,X3)) -> proper#(X2) proper#(U293(X1,X2,X3)) -> proper#(X1) proper#(U293(X1,X2,X3)) -> U293#(proper(X1),proper(X2),proper(X3)) proper#(U294(X1,X2,X3)) -> proper#(X3) proper#(U294(X1,X2,X3)) -> proper#(X2) proper#(U294(X1,X2,X3)) -> proper#(X1) proper#(U294(X1,X2,X3)) -> U294#(proper(X1),proper(X2),proper(X3)) proper#(head(X)) -> proper#(X) proper#(head(X)) -> head#(proper(X)) proper#(afterNth(X1,X2)) -> proper#(X2) proper#(afterNth(X1,X2)) -> proper#(X1) proper#(afterNth(X1,X2)) -> afterNth#(proper(X1),proper(X2)) proper#(U301(X1,X2,X3)) -> proper#(X3) proper#(U301(X1,X2,X3)) -> proper#(X2) proper#(U301(X1,X2,X3)) -> proper#(X1) proper#(U301(X1,X2,X3)) -> U301#(proper(X1),proper(X2),proper(X3)) proper#(U302(X1,X2)) -> proper#(X2) proper#(U302(X1,X2)) -> proper#(X1) proper#(U302(X1,X2)) -> U302#(proper(X1),proper(X2)) proper#(U303(X1,X2)) -> proper#(X2) proper#(U303(X1,X2)) -> proper#(X1) proper#(U303(X1,X2)) -> U303#(proper(X1),proper(X2)) proper#(U304(X1,X2)) -> proper#(X2) proper#(U304(X1,X2)) -> proper#(X1) proper#(U304(X1,X2)) -> U304#(proper(X1),proper(X2)) proper#(U31(X1,X2,X3)) -> proper#(X3) proper#(U31(X1,X2,X3)) -> proper#(X2) proper#(U31(X1,X2,X3)) -> proper#(X1) proper#(U31(X1,X2,X3)) -> U31#(proper(X1),proper(X2),proper(X3)) proper#(U32(X1,X2,X3)) -> proper#(X3) proper#(U32(X1,X2,X3)) -> proper#(X2) proper#(U32(X1,X2,X3)) -> proper#(X1) proper#(U32(X1,X2,X3)) -> U32#(proper(X1),proper(X2),proper(X3)) proper#(U311(X1,X2)) -> proper#(X2) proper#(U311(X1,X2)) -> proper#(X1) proper#(U311(X1,X2)) -> U311#(proper(X1),proper(X2)) proper#(U312(X1,X2)) -> proper#(X2) proper#(U312(X1,X2)) -> proper#(X1) proper#(U312(X1,X2)) -> U312#(proper(X1),proper(X2)) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> pair#(proper(X1),proper(X2)) proper#(U33(X1,X2,X3)) -> proper#(X3) proper#(U33(X1,X2,X3)) -> proper#(X2) proper#(U33(X1,X2,X3)) -> proper#(X1) proper#(U33(X1,X2,X3)) -> U33#(proper(X1),proper(X2),proper(X3)) proper#(U321(X1,X2,X3,X4)) -> proper#(X4) proper#(U321(X1,X2,X3,X4)) -> proper#(X3) proper#(U321(X1,X2,X3,X4)) -> proper#(X2) proper#(U321(X1,X2,X3,X4)) -> proper#(X1) proper#(U321(X1,X2,X3,X4)) -> U321#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U322(X1,X2,X3,X4)) -> proper#(X4) proper#(U322(X1,X2,X3,X4)) -> proper#(X3) proper#(U322(X1,X2,X3,X4)) -> proper#(X2) proper#(U322(X1,X2,X3,X4)) -> proper#(X1) proper#(U322(X1,X2,X3,X4)) -> U322#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U323(X1,X2,X3,X4)) -> proper#(X4) proper#(U323(X1,X2,X3,X4)) -> proper#(X3) proper#(U323(X1,X2,X3,X4)) -> proper#(X2) proper#(U323(X1,X2,X3,X4)) -> proper#(X1) proper#(U323(X1,X2,X3,X4)) -> U323#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U324(X1,X2,X3,X4)) -> proper#(X4) proper#(U324(X1,X2,X3,X4)) -> proper#(X3) proper#(U324(X1,X2,X3,X4)) -> proper#(X2) proper#(U324(X1,X2,X3,X4)) -> proper#(X1) proper#(U324(X1,X2,X3,X4)) -> U324#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U325(X1,X2,X3,X4)) -> proper#(X4) proper#(U325(X1,X2,X3,X4)) -> proper#(X3) proper#(U325(X1,X2,X3,X4)) -> proper#(X2) proper#(U325(X1,X2,X3,X4)) -> proper#(X1) proper#(U325(X1,X2,X3,X4)) -> U325#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U326(X1,X2,X3,X4)) -> proper#(X4) proper#(U326(X1,X2,X3,X4)) -> proper#(X3) proper#(U326(X1,X2,X3,X4)) -> proper#(X2) proper#(U326(X1,X2,X3,X4)) -> proper#(X1) proper#(U326(X1,X2,X3,X4)) -> U326#(proper(X1),proper(X2),proper(X3),proper(X4)) proper#(U327(X1,X2)) -> proper#(X2) proper#(U327(X1,X2)) -> proper#(X1) proper#(U327(X1,X2)) -> U327#(proper(X1),proper(X2)) proper#(U34(X1,X2)) -> proper#(X2) proper#(U34(X1,X2)) -> proper#(X1) proper#(U34(X1,X2)) -> U34#(proper(X1),proper(X2)) proper#(U331(X1,X2,X3)) -> proper#(X3) proper#(U331(X1,X2,X3)) -> proper#(X2) proper#(U331(X1,X2,X3)) -> proper#(X1) proper#(U331(X1,X2,X3)) -> U331#(proper(X1),proper(X2),proper(X3)) proper#(U332(X1,X2)) -> proper#(X2) proper#(U332(X1,X2)) -> proper#(X1) proper#(U332(X1,X2)) -> U332#(proper(X1),proper(X2)) proper#(U333(X1,X2)) -> proper#(X2) proper#(U333(X1,X2)) -> proper#(X1) proper#(U333(X1,X2)) -> U333#(proper(X1),proper(X2)) proper#(U334(X1,X2)) -> proper#(X2) proper#(U334(X1,X2)) -> proper#(X1) proper#(U334(X1,X2)) -> U334#(proper(X1),proper(X2)) proper#(U341(X1,X2,X3)) -> proper#(X3) proper#(U341(X1,X2,X3)) -> proper#(X2) proper#(U341(X1,X2,X3)) -> proper#(X1) proper#(U341(X1,X2,X3)) -> U341#(proper(X1),proper(X2),proper(X3)) proper#(U342(X1,X2,X3)) -> proper#(X3) proper#(U342(X1,X2,X3)) -> proper#(X2) proper#(U342(X1,X2,X3)) -> proper#(X1) proper#(U342(X1,X2,X3)) -> U342#(proper(X1),proper(X2),proper(X3)) proper#(U343(X1,X2,X3)) -> proper#(X3) proper#(U343(X1,X2,X3)) -> proper#(X2) proper#(U343(X1,X2,X3)) -> proper#(X1) proper#(U343(X1,X2,X3)) -> U343#(proper(X1),proper(X2),proper(X3)) proper#(U344(X1,X2,X3)) -> proper#(X3) proper#(U344(X1,X2,X3)) -> proper#(X2) proper#(U344(X1,X2,X3)) -> proper#(X1) proper#(U344(X1,X2,X3)) -> U344#(proper(X1),proper(X2),proper(X3)) proper#(fst(X)) -> proper#(X) proper#(fst(X)) -> fst#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3)) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3)) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3)) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2)) proper#(U46(X)) -> proper#(X) proper#(U46(X)) -> U46#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> U52#(proper(X1),proper(X2),proper(X3)) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> U53#(proper(X1),proper(X2),proper(X3)) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> U54#(proper(X1),proper(X2),proper(X3)) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U55(X1,X2)) -> U55#(proper(X1),proper(X2)) proper#(U56(X)) -> proper#(X) proper#(U56(X)) -> U56#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> U62#(proper(X1),proper(X2)) proper#(isPLNatKind(X)) -> proper#(X) proper#(isPLNatKind(X)) -> isPLNatKind#(proper(X)) proper#(U63(X)) -> proper#(X) proper#(U63(X)) -> U63#(proper(X)) proper#(isPLNat(X)) -> proper#(X) proper#(isPLNat(X)) -> isPLNat#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U72(X1,X2)) -> U72#(proper(X1),proper(X2)) proper#(U73(X)) -> proper#(X) proper#(U73(X)) -> U73#(proper(X)) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U81(X1,X2)) -> U81#(proper(X1),proper(X2)) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> U82#(proper(X1),proper(X2)) proper#(U83(X)) -> proper#(X) proper#(U83(X)) -> U83#(proper(X)) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U91(X1,X2)) -> U91#(proper(X1),proper(X2)) proper#(U92(X1,X2)) -> proper#(X2) proper#(U92(X1,X2)) -> proper#(X1) proper#(U92(X1,X2)) -> U92#(proper(X1),proper(X2)) proper#(U93(X)) -> proper#(X) proper#(U93(X)) -> U93#(proper(X)) proper#(tail(X)) -> proper#(X) proper#(tail(X)) -> tail#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3) U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3) isNaturalKind#(ok(X)) -> isNaturalKind#(X) U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3) isLNatKind#(ok(X)) -> isLNatKind#(X) U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3) U105#(ok(X1),ok(X2)) -> U105#(X1,X2) isNatural#(ok(X)) -> isNatural#(X) U106#(ok(X)) -> U106#(X) isLNat#(ok(X)) -> isLNat#(X) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) U111#(ok(X1),ok(X2)) -> U111#(X1,X2) U112#(ok(X)) -> U112#(X) U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3) U121#(ok(X1),ok(X2)) -> U121#(X1,X2) U122#(ok(X)) -> U122#(X) U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3) U131#(ok(X)) -> U131#(X) snd#(ok(X)) -> snd#(X) splitAt#(ok(X1),ok(X2)) -> splitAt#(X1,X2) U141#(ok(X)) -> U141#(X) U151#(ok(X)) -> U151#(X) U161#(ok(X)) -> U161#(X) U171#(ok(X1),ok(X2)) -> U171#(X1,X2) U172#(ok(X)) -> U172#(X) U181#(ok(X1),ok(X2)) -> U181#(X1,X2) U182#(ok(X1),ok(X2)) -> U182#(X1,X2) U183#(ok(X)) -> U183#(X) U191#(ok(X1),ok(X2)) -> U191#(X1,X2) U192#(ok(X1),ok(X2)) -> U192#(X1,X2) U193#(ok(X)) -> U193#(X) U201#(ok(X1),ok(X2),ok(X3)) -> U201#(X1,X2,X3) U202#(ok(X1),ok(X2),ok(X3)) -> U202#(X1,X2,X3) U203#(ok(X1),ok(X2),ok(X3)) -> U203#(X1,X2,X3) U204#(ok(X1),ok(X2),ok(X3)) -> U204#(X1,X2,X3) U205#(ok(X1),ok(X2)) -> U205#(X1,X2) U206#(ok(X)) -> U206#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U211#(ok(X)) -> U211#(X) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) U221#(ok(X)) -> U221#(X) U24#(ok(X1),ok(X2)) -> U24#(X1,X2) U231#(ok(X1),ok(X2)) -> U231#(X1,X2) U232#(ok(X)) -> U232#(X) U241#(ok(X1),ok(X2),ok(X3)) -> U241#(X1,X2,X3) U242#(ok(X1),ok(X2),ok(X3)) -> U242#(X1,X2,X3) U243#(ok(X1),ok(X2),ok(X3)) -> U243#(X1,X2,X3) U244#(ok(X1),ok(X2),ok(X3)) -> U244#(X1,X2,X3) U245#(ok(X1),ok(X2)) -> U245#(X1,X2) U246#(ok(X)) -> U246#(X) U251#(ok(X1),ok(X2),ok(X3)) -> U251#(X1,X2,X3) U252#(ok(X1),ok(X2),ok(X3)) -> U252#(X1,X2,X3) U253#(ok(X1),ok(X2),ok(X3)) -> U253#(X1,X2,X3) U254#(ok(X1),ok(X2),ok(X3)) -> U254#(X1,X2,X3) U255#(ok(X1),ok(X2)) -> U255#(X1,X2) U256#(ok(X)) -> U256#(X) U261#(ok(X1),ok(X2)) -> U261#(X1,X2) U262#(ok(X)) -> U262#(X) U271#(ok(X1),ok(X2)) -> U271#(X1,X2) U272#(ok(X)) -> U272#(X) U281#(ok(X1),ok(X2)) -> U281#(X1,X2) U282#(ok(X1),ok(X2)) -> U282#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) natsFrom#(ok(X)) -> natsFrom#(X) s#(ok(X)) -> s#(X) U291#(ok(X1),ok(X2),ok(X3)) -> U291#(X1,X2,X3) U292#(ok(X1),ok(X2),ok(X3)) -> U292#(X1,X2,X3) U293#(ok(X1),ok(X2),ok(X3)) -> U293#(X1,X2,X3) U294#(ok(X1),ok(X2),ok(X3)) -> U294#(X1,X2,X3) head#(ok(X)) -> head#(X) afterNth#(ok(X1),ok(X2)) -> afterNth#(X1,X2) U301#(ok(X1),ok(X2),ok(X3)) -> U301#(X1,X2,X3) U302#(ok(X1),ok(X2)) -> U302#(X1,X2) U303#(ok(X1),ok(X2)) -> U303#(X1,X2) U304#(ok(X1),ok(X2)) -> U304#(X1,X2) U31#(ok(X1),ok(X2),ok(X3)) -> U31#(X1,X2,X3) U32#(ok(X1),ok(X2),ok(X3)) -> U32#(X1,X2,X3) U311#(ok(X1),ok(X2)) -> U311#(X1,X2) U312#(ok(X1),ok(X2)) -> U312#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) U33#(ok(X1),ok(X2),ok(X3)) -> U33#(X1,X2,X3) U321#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U321#(X1,X2,X3,X4) U322#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U322#(X1,X2,X3,X4) U323#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U323#(X1,X2,X3,X4) U324#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U324#(X1,X2,X3,X4) U325#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U325#(X1,X2,X3,X4) U326#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U326#(X1,X2,X3,X4) U327#(ok(X1),ok(X2)) -> U327#(X1,X2) U34#(ok(X1),ok(X2)) -> U34#(X1,X2) U331#(ok(X1),ok(X2),ok(X3)) -> U331#(X1,X2,X3) U332#(ok(X1),ok(X2)) -> U332#(X1,X2) U333#(ok(X1),ok(X2)) -> U333#(X1,X2) U334#(ok(X1),ok(X2)) -> U334#(X1,X2) U341#(ok(X1),ok(X2),ok(X3)) -> U341#(X1,X2,X3) U342#(ok(X1),ok(X2),ok(X3)) -> U342#(X1,X2,X3) U343#(ok(X1),ok(X2),ok(X3)) -> U343#(X1,X2,X3) U344#(ok(X1),ok(X2),ok(X3)) -> U344#(X1,X2,X3) fst#(ok(X)) -> fst#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) U46#(ok(X)) -> U46#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) U56#(ok(X)) -> U56#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) isPLNatKind#(ok(X)) -> isPLNatKind#(X) U63#(ok(X)) -> U63#(X) isPLNat#(ok(X)) -> isPLNat#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) U73#(ok(X)) -> U73#(X) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) U83#(ok(X)) -> U83#(X) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) U92#(ok(X1),ok(X2)) -> U92#(X1,X2) U93#(ok(X)) -> U93#(X) tail#(ok(X)) -> tail#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: ... SCC Processor: #sccs: 132 #rules: 665 #arcs: 178181/1340964 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(U101(X1,X2,X3)) -> active#(X1) active#(U102(X1,X2,X3)) -> active#(X1) active#(U103(X1,X2,X3)) -> active#(X1) active#(U104(X1,X2,X3)) -> active#(X1) active#(U105(X1,X2)) -> active#(X1) active#(U106(X)) -> active#(X) active#(U11(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) active#(U111(X1,X2)) -> active#(X1) active#(U112(X)) -> active#(X) active#(U13(X1,X2,X3)) -> active#(X1) active#(U121(X1,X2)) -> active#(X1) active#(U122(X)) -> active#(X) active#(U14(X1,X2,X3)) -> active#(X1) active#(U131(X)) -> active#(X) active#(snd(X)) -> active#(X) active#(splitAt(X1,X2)) -> active#(X1) active#(splitAt(X1,X2)) -> active#(X2) active#(U141(X)) -> active#(X) active#(U151(X)) -> active#(X) active#(U161(X)) -> active#(X) active#(U171(X1,X2)) -> active#(X1) active#(U172(X)) -> active#(X) active#(U181(X1,X2)) -> active#(X1) active#(U182(X1,X2)) -> active#(X1) active#(U183(X)) -> active#(X) active#(U191(X1,X2)) -> active#(X1) active#(U192(X1,X2)) -> active#(X1) active#(U193(X)) -> active#(X) active#(U201(X1,X2,X3)) -> active#(X1) active#(U202(X1,X2,X3)) -> active#(X1) active#(U203(X1,X2,X3)) -> active#(X1) active#(U204(X1,X2,X3)) -> active#(X1) active#(U205(X1,X2)) -> active#(X1) active#(U206(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(U211(X)) -> active#(X) active#(U23(X1,X2,X3)) -> active#(X1) active#(U221(X)) -> active#(X) active#(U24(X1,X2)) -> active#(X1) active#(U231(X1,X2)) -> active#(X1) active#(U232(X)) -> active#(X) active#(U241(X1,X2,X3)) -> active#(X1) active#(U242(X1,X2,X3)) -> active#(X1) active#(U243(X1,X2,X3)) -> active#(X1) active#(U244(X1,X2,X3)) -> active#(X1) active#(U245(X1,X2)) -> active#(X1) active#(U246(X)) -> active#(X) active#(U251(X1,X2,X3)) -> active#(X1) active#(U252(X1,X2,X3)) -> active#(X1) active#(U253(X1,X2,X3)) -> active#(X1) active#(U254(X1,X2,X3)) -> active#(X1) active#(U255(X1,X2)) -> active#(X1) active#(U256(X)) -> active#(X) active#(U261(X1,X2)) -> active#(X1) active#(U262(X)) -> active#(X) active#(U271(X1,X2)) -> active#(X1) active#(U272(X)) -> active#(X) active#(U281(X1,X2)) -> active#(X1) active#(U282(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) active#(natsFrom(X)) -> active#(X) active#(s(X)) -> active#(X) active#(U291(X1,X2,X3)) -> active#(X1) active#(U292(X1,X2,X3)) -> active#(X1) active#(U293(X1,X2,X3)) -> active#(X1) active#(U294(X1,X2,X3)) -> active#(X1) active#(head(X)) -> active#(X) active#(afterNth(X1,X2)) -> active#(X1) active#(afterNth(X1,X2)) -> active#(X2) active#(U301(X1,X2,X3)) -> active#(X1) active#(U302(X1,X2)) -> active#(X1) active#(U303(X1,X2)) -> active#(X1) active#(U304(X1,X2)) -> active#(X1) active#(U31(X1,X2,X3)) -> active#(X1) active#(U32(X1,X2,X3)) -> active#(X1) active#(U311(X1,X2)) -> active#(X1) active#(U312(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X1) active#(pair(X1,X2)) -> active#(X2) active#(U33(X1,X2,X3)) -> active#(X1) active#(U321(X1,X2,X3,X4)) -> active#(X1) active#(U322(X1,X2,X3,X4)) -> active#(X1) active#(U323(X1,X2,X3,X4)) -> active#(X1) active#(U324(X1,X2,X3,X4)) -> active#(X1) active#(U325(X1,X2,X3,X4)) -> active#(X1) active#(U326(X1,X2,X3,X4)) -> active#(X1) active#(U327(X1,X2)) -> active#(X1) active#(U34(X1,X2)) -> active#(X1) active#(U331(X1,X2,X3)) -> active#(X1) active#(U332(X1,X2)) -> active#(X1) active#(U333(X1,X2)) -> active#(X1) active#(U334(X1,X2)) -> active#(X1) active#(U341(X1,X2,X3)) -> active#(X1) active#(U342(X1,X2,X3)) -> active#(X1) active#(U343(X1,X2,X3)) -> active#(X1) active#(U344(X1,X2,X3)) -> active#(X1) active#(fst(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2,X3)) -> active#(X1) active#(U43(X1,X2,X3)) -> active#(X1) active#(U44(X1,X2,X3)) -> active#(X1) active#(U45(X1,X2)) -> active#(X1) active#(U46(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2,X3)) -> active#(X1) active#(U53(X1,X2,X3)) -> active#(X1) active#(U54(X1,X2,X3)) -> active#(X1) active#(U55(X1,X2)) -> active#(X1) active#(U56(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X1,X2)) -> active#(X1) active#(U63(X)) -> active#(X) active#(U71(X1,X2)) -> active#(X1) active#(U72(X1,X2)) -> active#(X1) active#(U73(X)) -> active#(X) active#(U81(X1,X2)) -> active#(X1) active#(U82(X1,X2)) -> active#(X1) active#(U83(X)) -> active#(X) active#(U91(X1,X2)) -> active#(X1) active#(U92(X1,X2)) -> active#(X1) active#(U93(X)) -> active#(X) active#(tail(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: proper#(U101(X1,X2,X3)) -> proper#(X3) proper#(U101(X1,X2,X3)) -> proper#(X2) proper#(U101(X1,X2,X3)) -> proper#(X1) proper#(U102(X1,X2,X3)) -> proper#(X3) proper#(U102(X1,X2,X3)) -> proper#(X2) proper#(U102(X1,X2,X3)) -> proper#(X1) proper#(isNaturalKind(X)) -> proper#(X) proper#(U103(X1,X2,X3)) -> proper#(X3) proper#(U103(X1,X2,X3)) -> proper#(X2) proper#(U103(X1,X2,X3)) -> proper#(X1) proper#(isLNatKind(X)) -> proper#(X) proper#(U104(X1,X2,X3)) -> proper#(X3) proper#(U104(X1,X2,X3)) -> proper#(X2) proper#(U104(X1,X2,X3)) -> proper#(X1) proper#(U105(X1,X2)) -> proper#(X2) proper#(U105(X1,X2)) -> proper#(X1) proper#(isNatural(X)) -> proper#(X) proper#(U106(X)) -> proper#(X) proper#(isLNat(X)) -> proper#(X) proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U111(X1,X2)) -> proper#(X2) proper#(U111(X1,X2)) -> proper#(X1) proper#(U112(X)) -> proper#(X) proper#(U13(X1,X2,X3)) -> proper#(X3) proper#(U13(X1,X2,X3)) -> proper#(X2) proper#(U13(X1,X2,X3)) -> proper#(X1) proper#(U121(X1,X2)) -> proper#(X2) proper#(U121(X1,X2)) -> proper#(X1) proper#(U122(X)) -> proper#(X) proper#(U14(X1,X2,X3)) -> proper#(X3) proper#(U14(X1,X2,X3)) -> proper#(X2) proper#(U14(X1,X2,X3)) -> proper#(X1) proper#(U131(X)) -> proper#(X) proper#(snd(X)) -> proper#(X) proper#(splitAt(X1,X2)) -> proper#(X2) proper#(splitAt(X1,X2)) -> proper#(X1) proper#(U141(X)) -> proper#(X) proper#(U151(X)) -> proper#(X) proper#(U161(X)) -> proper#(X) proper#(U171(X1,X2)) -> proper#(X2) proper#(U171(X1,X2)) -> proper#(X1) proper#(U172(X)) -> proper#(X) proper#(U181(X1,X2)) -> proper#(X2) proper#(U181(X1,X2)) -> proper#(X1) proper#(U182(X1,X2)) -> proper#(X2) proper#(U182(X1,X2)) -> proper#(X1) proper#(U183(X)) -> proper#(X) proper#(U191(X1,X2)) -> proper#(X2) proper#(U191(X1,X2)) -> proper#(X1) proper#(U192(X1,X2)) -> proper#(X2) proper#(U192(X1,X2)) -> proper#(X1) proper#(U193(X)) -> proper#(X) proper#(U201(X1,X2,X3)) -> proper#(X3) proper#(U201(X1,X2,X3)) -> proper#(X2) proper#(U201(X1,X2,X3)) -> proper#(X1) proper#(U202(X1,X2,X3)) -> proper#(X3) proper#(U202(X1,X2,X3)) -> proper#(X2) proper#(U202(X1,X2,X3)) -> proper#(X1) proper#(U203(X1,X2,X3)) -> proper#(X3) proper#(U203(X1,X2,X3)) -> proper#(X2) proper#(U203(X1,X2,X3)) -> proper#(X1) proper#(U204(X1,X2,X3)) -> proper#(X3) proper#(U204(X1,X2,X3)) -> proper#(X2) proper#(U204(X1,X2,X3)) -> proper#(X1) proper#(U205(X1,X2)) -> proper#(X2) proper#(U205(X1,X2)) -> proper#(X1) proper#(U206(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U211(X)) -> proper#(X) proper#(U23(X1,X2,X3)) -> proper#(X3) proper#(U23(X1,X2,X3)) -> proper#(X2) proper#(U23(X1,X2,X3)) -> proper#(X1) proper#(U221(X)) -> proper#(X) proper#(U24(X1,X2)) -> proper#(X2) proper#(U24(X1,X2)) -> proper#(X1) proper#(U231(X1,X2)) -> proper#(X2) proper#(U231(X1,X2)) -> proper#(X1) proper#(U232(X)) -> proper#(X) proper#(U241(X1,X2,X3)) -> proper#(X3) proper#(U241(X1,X2,X3)) -> proper#(X2) proper#(U241(X1,X2,X3)) -> proper#(X1) proper#(U242(X1,X2,X3)) -> proper#(X3) proper#(U242(X1,X2,X3)) -> proper#(X2) proper#(U242(X1,X2,X3)) -> proper#(X1) proper#(U243(X1,X2,X3)) -> proper#(X3) proper#(U243(X1,X2,X3)) -> proper#(X2) proper#(U243(X1,X2,X3)) -> proper#(X1) proper#(U244(X1,X2,X3)) -> proper#(X3) proper#(U244(X1,X2,X3)) -> proper#(X2) proper#(U244(X1,X2,X3)) -> proper#(X1) proper#(U245(X1,X2)) -> proper#(X2) proper#(U245(X1,X2)) -> proper#(X1) proper#(U246(X)) -> proper#(X) proper#(U251(X1,X2,X3)) -> proper#(X3) proper#(U251(X1,X2,X3)) -> proper#(X2) proper#(U251(X1,X2,X3)) -> proper#(X1) proper#(U252(X1,X2,X3)) -> proper#(X3) proper#(U252(X1,X2,X3)) -> proper#(X2) proper#(U252(X1,X2,X3)) -> proper#(X1) proper#(U253(X1,X2,X3)) -> proper#(X3) proper#(U253(X1,X2,X3)) -> proper#(X2) proper#(U253(X1,X2,X3)) -> proper#(X1) proper#(U254(X1,X2,X3)) -> proper#(X3) proper#(U254(X1,X2,X3)) -> proper#(X2) proper#(U254(X1,X2,X3)) -> proper#(X1) proper#(U255(X1,X2)) -> proper#(X2) proper#(U255(X1,X2)) -> proper#(X1) proper#(U256(X)) -> proper#(X) proper#(U261(X1,X2)) -> proper#(X2) proper#(U261(X1,X2)) -> proper#(X1) proper#(U262(X)) -> proper#(X) proper#(U271(X1,X2)) -> proper#(X2) proper#(U271(X1,X2)) -> proper#(X1) proper#(U272(X)) -> proper#(X) proper#(U281(X1,X2)) -> proper#(X2) proper#(U281(X1,X2)) -> proper#(X1) proper#(U282(X1,X2)) -> proper#(X2) proper#(U282(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(natsFrom(X)) -> proper#(X) proper#(s(X)) -> proper#(X) proper#(U291(X1,X2,X3)) -> proper#(X3) proper#(U291(X1,X2,X3)) -> proper#(X2) proper#(U291(X1,X2,X3)) -> proper#(X1) proper#(U292(X1,X2,X3)) -> proper#(X3) proper#(U292(X1,X2,X3)) -> proper#(X2) proper#(U292(X1,X2,X3)) -> proper#(X1) proper#(U293(X1,X2,X3)) -> proper#(X3) proper#(U293(X1,X2,X3)) -> proper#(X2) proper#(U293(X1,X2,X3)) -> proper#(X1) proper#(U294(X1,X2,X3)) -> proper#(X3) proper#(U294(X1,X2,X3)) -> proper#(X2) proper#(U294(X1,X2,X3)) -> proper#(X1) proper#(head(X)) -> proper#(X) proper#(afterNth(X1,X2)) -> proper#(X2) proper#(afterNth(X1,X2)) -> proper#(X1) proper#(U301(X1,X2,X3)) -> proper#(X3) proper#(U301(X1,X2,X3)) -> proper#(X2) proper#(U301(X1,X2,X3)) -> proper#(X1) proper#(U302(X1,X2)) -> proper#(X2) proper#(U302(X1,X2)) -> proper#(X1) proper#(U303(X1,X2)) -> proper#(X2) proper#(U303(X1,X2)) -> proper#(X1) proper#(U304(X1,X2)) -> proper#(X2) proper#(U304(X1,X2)) -> proper#(X1) proper#(U31(X1,X2,X3)) -> proper#(X3) proper#(U31(X1,X2,X3)) -> proper#(X2) proper#(U31(X1,X2,X3)) -> proper#(X1) proper#(U32(X1,X2,X3)) -> proper#(X3) proper#(U32(X1,X2,X3)) -> proper#(X2) proper#(U32(X1,X2,X3)) -> proper#(X1) proper#(U311(X1,X2)) -> proper#(X2) proper#(U311(X1,X2)) -> proper#(X1) proper#(U312(X1,X2)) -> proper#(X2) proper#(U312(X1,X2)) -> proper#(X1) proper#(pair(X1,X2)) -> proper#(X2) proper#(pair(X1,X2)) -> proper#(X1) proper#(U33(X1,X2,X3)) -> proper#(X3) proper#(U33(X1,X2,X3)) -> proper#(X2) proper#(U33(X1,X2,X3)) -> proper#(X1) proper#(U321(X1,X2,X3,X4)) -> proper#(X4) proper#(U321(X1,X2,X3,X4)) -> proper#(X3) proper#(U321(X1,X2,X3,X4)) -> proper#(X2) proper#(U321(X1,X2,X3,X4)) -> proper#(X1) proper#(U322(X1,X2,X3,X4)) -> proper#(X4) proper#(U322(X1,X2,X3,X4)) -> proper#(X3) proper#(U322(X1,X2,X3,X4)) -> proper#(X2) proper#(U322(X1,X2,X3,X4)) -> proper#(X1) proper#(U323(X1,X2,X3,X4)) -> proper#(X4) proper#(U323(X1,X2,X3,X4)) -> proper#(X3) proper#(U323(X1,X2,X3,X4)) -> proper#(X2) proper#(U323(X1,X2,X3,X4)) -> proper#(X1) proper#(U324(X1,X2,X3,X4)) -> proper#(X4) proper#(U324(X1,X2,X3,X4)) -> proper#(X3) proper#(U324(X1,X2,X3,X4)) -> proper#(X2) proper#(U324(X1,X2,X3,X4)) -> proper#(X1) proper#(U325(X1,X2,X3,X4)) -> proper#(X4) proper#(U325(X1,X2,X3,X4)) -> proper#(X3) proper#(U325(X1,X2,X3,X4)) -> proper#(X2) proper#(U325(X1,X2,X3,X4)) -> proper#(X1) proper#(U326(X1,X2,X3,X4)) -> proper#(X4) proper#(U326(X1,X2,X3,X4)) -> proper#(X3) proper#(U326(X1,X2,X3,X4)) -> proper#(X2) proper#(U326(X1,X2,X3,X4)) -> proper#(X1) proper#(U327(X1,X2)) -> proper#(X2) proper#(U327(X1,X2)) -> proper#(X1) proper#(U34(X1,X2)) -> proper#(X2) proper#(U34(X1,X2)) -> proper#(X1) proper#(U331(X1,X2,X3)) -> proper#(X3) proper#(U331(X1,X2,X3)) -> proper#(X2) proper#(U331(X1,X2,X3)) -> proper#(X1) proper#(U332(X1,X2)) -> proper#(X2) proper#(U332(X1,X2)) -> proper#(X1) proper#(U333(X1,X2)) -> proper#(X2) proper#(U333(X1,X2)) -> proper#(X1) proper#(U334(X1,X2)) -> proper#(X2) proper#(U334(X1,X2)) -> proper#(X1) proper#(U341(X1,X2,X3)) -> proper#(X3) proper#(U341(X1,X2,X3)) -> proper#(X2) proper#(U341(X1,X2,X3)) -> proper#(X1) proper#(U342(X1,X2,X3)) -> proper#(X3) proper#(U342(X1,X2,X3)) -> proper#(X2) proper#(U342(X1,X2,X3)) -> proper#(X1) proper#(U343(X1,X2,X3)) -> proper#(X3) proper#(U343(X1,X2,X3)) -> proper#(X2) proper#(U343(X1,X2,X3)) -> proper#(X1) proper#(U344(X1,X2,X3)) -> proper#(X3) proper#(U344(X1,X2,X3)) -> proper#(X2) proper#(U344(X1,X2,X3)) -> proper#(X1) proper#(fst(X)) -> proper#(X) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2,X3)) -> proper#(X3) proper#(U42(X1,X2,X3)) -> proper#(X2) proper#(U42(X1,X2,X3)) -> proper#(X1) proper#(U43(X1,X2,X3)) -> proper#(X3) proper#(U43(X1,X2,X3)) -> proper#(X2) proper#(U43(X1,X2,X3)) -> proper#(X1) proper#(U44(X1,X2,X3)) -> proper#(X3) proper#(U44(X1,X2,X3)) -> proper#(X2) proper#(U44(X1,X2,X3)) -> proper#(X1) proper#(U45(X1,X2)) -> proper#(X2) proper#(U45(X1,X2)) -> proper#(X1) proper#(U46(X)) -> proper#(X) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2,X3)) -> proper#(X3) proper#(U52(X1,X2,X3)) -> proper#(X2) proper#(U52(X1,X2,X3)) -> proper#(X1) proper#(U53(X1,X2,X3)) -> proper#(X3) proper#(U53(X1,X2,X3)) -> proper#(X2) proper#(U53(X1,X2,X3)) -> proper#(X1) proper#(U54(X1,X2,X3)) -> proper#(X3) proper#(U54(X1,X2,X3)) -> proper#(X2) proper#(U54(X1,X2,X3)) -> proper#(X1) proper#(U55(X1,X2)) -> proper#(X2) proper#(U55(X1,X2)) -> proper#(X1) proper#(U56(X)) -> proper#(X) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U62(X1,X2)) -> proper#(X2) proper#(U62(X1,X2)) -> proper#(X1) proper#(isPLNatKind(X)) -> proper#(X) proper#(U63(X)) -> proper#(X) proper#(isPLNat(X)) -> proper#(X) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U72(X1,X2)) -> proper#(X2) proper#(U72(X1,X2)) -> proper#(X1) proper#(U73(X)) -> proper#(X) proper#(U81(X1,X2)) -> proper#(X2) proper#(U81(X1,X2)) -> proper#(X1) proper#(U82(X1,X2)) -> proper#(X2) proper#(U82(X1,X2)) -> proper#(X1) proper#(U83(X)) -> proper#(X) proper#(U91(X1,X2)) -> proper#(X2) proper#(U91(X1,X2)) -> proper#(X1) proper#(U92(X1,X2)) -> proper#(X2) proper#(U92(X1,X2)) -> proper#(X1) proper#(U93(X)) -> proper#(X) proper#(tail(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: tail#(mark(X)) -> tail#(X) tail#(ok(X)) -> tail#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U93#(mark(X)) -> U93#(X) U93#(ok(X)) -> U93#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U92#(mark(X1),X2) -> U92#(X1,X2) U92#(ok(X1),ok(X2)) -> U92#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U91#(mark(X1),X2) -> U91#(X1,X2) U91#(ok(X1),ok(X2)) -> U91#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U83#(mark(X)) -> U83#(X) U83#(ok(X)) -> U83#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U82#(mark(X1),X2) -> U82#(X1,X2) U82#(ok(X1),ok(X2)) -> U82#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U81#(mark(X1),X2) -> U81#(X1,X2) U81#(ok(X1),ok(X2)) -> U81#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U73#(mark(X)) -> U73#(X) U73#(ok(X)) -> U73#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U72#(mark(X1),X2) -> U72#(X1,X2) U72#(ok(X1),ok(X2)) -> U72#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isPLNat#(ok(X)) -> isPLNat#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U63#(mark(X)) -> U63#(X) U63#(ok(X)) -> U63#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isPLNatKind#(ok(X)) -> isPLNatKind#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U62#(mark(X1),X2) -> U62#(X1,X2) U62#(ok(X1),ok(X2)) -> U62#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U56#(mark(X)) -> U56#(X) U56#(ok(X)) -> U56#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U55#(mark(X1),X2) -> U55#(X1,X2) U55#(ok(X1),ok(X2)) -> U55#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3) U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3) U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3) U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U46#(mark(X)) -> U46#(X) U46#(ok(X)) -> U46#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U45#(mark(X1),X2) -> U45#(X1,X2) U45#(ok(X1),ok(X2)) -> U45#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: fst#(mark(X)) -> fst#(X) fst#(ok(X)) -> fst#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U344#(mark(X1),X2,X3) -> U344#(X1,X2,X3) U344#(ok(X1),ok(X2),ok(X3)) -> U344#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U343#(mark(X1),X2,X3) -> U343#(X1,X2,X3) U343#(ok(X1),ok(X2),ok(X3)) -> U343#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U342#(mark(X1),X2,X3) -> U342#(X1,X2,X3) U342#(ok(X1),ok(X2),ok(X3)) -> U342#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U341#(mark(X1),X2,X3) -> U341#(X1,X2,X3) U341#(ok(X1),ok(X2),ok(X3)) -> U341#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U334#(mark(X1),X2) -> U334#(X1,X2) U334#(ok(X1),ok(X2)) -> U334#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U333#(mark(X1),X2) -> U333#(X1,X2) U333#(ok(X1),ok(X2)) -> U333#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U332#(mark(X1),X2) -> U332#(X1,X2) U332#(ok(X1),ok(X2)) -> U332#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U331#(mark(X1),X2,X3) -> U331#(X1,X2,X3) U331#(ok(X1),ok(X2),ok(X3)) -> U331#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U34#(mark(X1),X2) -> U34#(X1,X2) U34#(ok(X1),ok(X2)) -> U34#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U327#(mark(X1),X2) -> U327#(X1,X2) U327#(ok(X1),ok(X2)) -> U327#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U326#(mark(X1),X2,X3,X4) -> U326#(X1,X2,X3,X4) U326#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U326#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U325#(mark(X1),X2,X3,X4) -> U325#(X1,X2,X3,X4) U325#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U325#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U324#(mark(X1),X2,X3,X4) -> U324#(X1,X2,X3,X4) U324#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U324#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U323#(mark(X1),X2,X3,X4) -> U323#(X1,X2,X3,X4) U323#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U323#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U322#(mark(X1),X2,X3,X4) -> U322#(X1,X2,X3,X4) U322#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U322#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U321#(mark(X1),X2,X3,X4) -> U321#(X1,X2,X3,X4) U321#(ok(X1),ok(X2),ok(X3),ok(X4)) -> U321#(X1,X2,X3,X4) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U33#(ok(X1),ok(X2),ok(X3)) -> U33#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: pair#(mark(X1),X2) -> pair#(X1,X2) pair#(X1,mark(X2)) -> pair#(X1,X2) pair#(ok(X1),ok(X2)) -> pair#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U312#(mark(X1),X2) -> U312#(X1,X2) U312#(ok(X1),ok(X2)) -> U312#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U311#(mark(X1),X2) -> U311#(X1,X2) U311#(ok(X1),ok(X2)) -> U311#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U32#(ok(X1),ok(X2),ok(X3)) -> U32#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U31#(ok(X1),ok(X2),ok(X3)) -> U31#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U304#(mark(X1),X2) -> U304#(X1,X2) U304#(ok(X1),ok(X2)) -> U304#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U303#(mark(X1),X2) -> U303#(X1,X2) U303#(ok(X1),ok(X2)) -> U303#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U302#(mark(X1),X2) -> U302#(X1,X2) U302#(ok(X1),ok(X2)) -> U302#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U301#(mark(X1),X2,X3) -> U301#(X1,X2,X3) U301#(ok(X1),ok(X2),ok(X3)) -> U301#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: afterNth#(mark(X1),X2) -> afterNth#(X1,X2) afterNth#(X1,mark(X2)) -> afterNth#(X1,X2) afterNth#(ok(X1),ok(X2)) -> afterNth#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: head#(mark(X)) -> head#(X) head#(ok(X)) -> head#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U294#(mark(X1),X2,X3) -> U294#(X1,X2,X3) U294#(ok(X1),ok(X2),ok(X3)) -> U294#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U293#(mark(X1),X2,X3) -> U293#(X1,X2,X3) U293#(ok(X1),ok(X2),ok(X3)) -> U293#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U292#(mark(X1),X2,X3) -> U292#(X1,X2,X3) U292#(ok(X1),ok(X2),ok(X3)) -> U292#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U291#(mark(X1),X2,X3) -> U291#(X1,X2,X3) U291#(ok(X1),ok(X2),ok(X3)) -> U291#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: natsFrom#(mark(X)) -> natsFrom#(X) natsFrom#(ok(X)) -> natsFrom#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U282#(mark(X1),X2) -> U282#(X1,X2) U282#(ok(X1),ok(X2)) -> U282#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U281#(mark(X1),X2) -> U281#(X1,X2) U281#(ok(X1),ok(X2)) -> U281#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U272#(mark(X)) -> U272#(X) U272#(ok(X)) -> U272#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U271#(mark(X1),X2) -> U271#(X1,X2) U271#(ok(X1),ok(X2)) -> U271#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U262#(mark(X)) -> U262#(X) U262#(ok(X)) -> U262#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U261#(mark(X1),X2) -> U261#(X1,X2) U261#(ok(X1),ok(X2)) -> U261#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U256#(mark(X)) -> U256#(X) U256#(ok(X)) -> U256#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U255#(mark(X1),X2) -> U255#(X1,X2) U255#(ok(X1),ok(X2)) -> U255#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U254#(mark(X1),X2,X3) -> U254#(X1,X2,X3) U254#(ok(X1),ok(X2),ok(X3)) -> U254#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U253#(mark(X1),X2,X3) -> U253#(X1,X2,X3) U253#(ok(X1),ok(X2),ok(X3)) -> U253#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U252#(mark(X1),X2,X3) -> U252#(X1,X2,X3) U252#(ok(X1),ok(X2),ok(X3)) -> U252#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U251#(mark(X1),X2,X3) -> U251#(X1,X2,X3) U251#(ok(X1),ok(X2),ok(X3)) -> U251#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U246#(mark(X)) -> U246#(X) U246#(ok(X)) -> U246#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U245#(mark(X1),X2) -> U245#(X1,X2) U245#(ok(X1),ok(X2)) -> U245#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U244#(mark(X1),X2,X3) -> U244#(X1,X2,X3) U244#(ok(X1),ok(X2),ok(X3)) -> U244#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U243#(mark(X1),X2,X3) -> U243#(X1,X2,X3) U243#(ok(X1),ok(X2),ok(X3)) -> U243#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U242#(mark(X1),X2,X3) -> U242#(X1,X2,X3) U242#(ok(X1),ok(X2),ok(X3)) -> U242#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U241#(mark(X1),X2,X3) -> U241#(X1,X2,X3) U241#(ok(X1),ok(X2),ok(X3)) -> U241#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U232#(mark(X)) -> U232#(X) U232#(ok(X)) -> U232#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U231#(mark(X1),X2) -> U231#(X1,X2) U231#(ok(X1),ok(X2)) -> U231#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U24#(mark(X1),X2) -> U24#(X1,X2) U24#(ok(X1),ok(X2)) -> U24#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U221#(mark(X)) -> U221#(X) U221#(ok(X)) -> U221#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3) U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U211#(mark(X)) -> U211#(X) U211#(ok(X)) -> U211#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U206#(mark(X)) -> U206#(X) U206#(ok(X)) -> U206#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U205#(mark(X1),X2) -> U205#(X1,X2) U205#(ok(X1),ok(X2)) -> U205#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U204#(mark(X1),X2,X3) -> U204#(X1,X2,X3) U204#(ok(X1),ok(X2),ok(X3)) -> U204#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U203#(mark(X1),X2,X3) -> U203#(X1,X2,X3) U203#(ok(X1),ok(X2),ok(X3)) -> U203#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U202#(mark(X1),X2,X3) -> U202#(X1,X2,X3) U202#(ok(X1),ok(X2),ok(X3)) -> U202#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U201#(mark(X1),X2,X3) -> U201#(X1,X2,X3) U201#(ok(X1),ok(X2),ok(X3)) -> U201#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U193#(mark(X)) -> U193#(X) U193#(ok(X)) -> U193#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U192#(mark(X1),X2) -> U192#(X1,X2) U192#(ok(X1),ok(X2)) -> U192#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U191#(mark(X1),X2) -> U191#(X1,X2) U191#(ok(X1),ok(X2)) -> U191#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U183#(mark(X)) -> U183#(X) U183#(ok(X)) -> U183#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U182#(mark(X1),X2) -> U182#(X1,X2) U182#(ok(X1),ok(X2)) -> U182#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U181#(mark(X1),X2) -> U181#(X1,X2) U181#(ok(X1),ok(X2)) -> U181#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U172#(mark(X)) -> U172#(X) U172#(ok(X)) -> U172#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U171#(mark(X1),X2) -> U171#(X1,X2) U171#(ok(X1),ok(X2)) -> U171#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U161#(mark(X)) -> U161#(X) U161#(ok(X)) -> U161#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U151#(mark(X)) -> U151#(X) U151#(ok(X)) -> U151#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U141#(mark(X)) -> U141#(X) U141#(ok(X)) -> U141#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: splitAt#(mark(X1),X2) -> splitAt#(X1,X2) splitAt#(X1,mark(X2)) -> splitAt#(X1,X2) splitAt#(ok(X1),ok(X2)) -> splitAt#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: snd#(mark(X)) -> snd#(X) snd#(ok(X)) -> snd#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U131#(mark(X)) -> U131#(X) U131#(ok(X)) -> U131#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U122#(mark(X)) -> U122#(X) U122#(ok(X)) -> U122#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U121#(mark(X1),X2) -> U121#(X1,X2) U121#(ok(X1),ok(X2)) -> U121#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U112#(mark(X)) -> U112#(X) U112#(ok(X)) -> U112#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U111#(mark(X1),X2) -> U111#(X1,X2) U111#(ok(X1),ok(X2)) -> U111#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isLNat#(ok(X)) -> isLNat#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U106#(mark(X)) -> U106#(X) U106#(ok(X)) -> U106#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isNatural#(ok(X)) -> isNatural#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U105#(mark(X1),X2) -> U105#(X1,X2) U105#(ok(X1),ok(X2)) -> U105#(X1,X2) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(ok(X1),ok(X2),ok(X3)) -> U104#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isLNatKind#(ok(X)) -> isLNatKind#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(ok(X1),ok(X2),ok(X3)) -> U103#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: isNaturalKind#(ok(X)) -> isNaturalKind#(X) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(ok(X1),ok(X2),ok(X3)) -> U102#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(ok(X1),ok(X2),ok(X3)) -> U101#(X1,X2,X3) TRS: active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2)) active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2)) active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2)) active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2)) active(U105(tt(),V2)) -> mark(U106(isLNat(V2))) active(U106(tt())) -> mark(tt()) active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS)) active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2))) active(U112(tt())) -> mark(tt()) active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS)) active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2))) active(U122(tt())) -> mark(tt()) active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS)) active(U131(tt())) -> mark(tt()) active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS))) active(U141(tt())) -> mark(tt()) active(U151(tt())) -> mark(tt()) active(U161(tt())) -> mark(tt()) active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2))) active(U172(tt())) -> mark(tt()) active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1)) active(U182(tt(),V1)) -> mark(U183(isLNat(V1))) active(U183(tt())) -> mark(tt()) active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1)) active(U192(tt(),V1)) -> mark(U193(isNatural(V1))) active(U193(tt())) -> mark(tt()) active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2)) active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2)) active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2)) active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2)) active(U205(tt(),V2)) -> mark(U206(isLNat(V2))) active(U206(tt())) -> mark(tt()) active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y)) active(U211(tt())) -> mark(tt()) active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y)) active(U221(tt())) -> mark(tt()) active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X)) active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2))) active(U232(tt())) -> mark(tt()) active(U24(tt(),X)) -> mark(X) active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2)) active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2)) active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2)) active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2)) active(U245(tt(),V2)) -> mark(U246(isLNat(V2))) active(U246(tt())) -> mark(tt()) active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2)) active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2)) active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2)) active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2)) active(U255(tt(),V2)) -> mark(U256(isLNat(V2))) active(U256(tt())) -> mark(tt()) active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2))) active(U262(tt())) -> mark(tt()) active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2))) active(U272(tt())) -> mark(tt()) active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N)) active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N)))) active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS)) active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS)) active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS)) active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS))) active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y)) active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y)) active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y)) active(U304(tt(),Y)) -> mark(Y) active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS)) active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS)) active(U312(tt(),XS)) -> mark(pair(nil(),XS)) active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS)) active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS)) active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS)) active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS)) active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS)) active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS)) active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X)) active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS)) active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N)) active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS)) active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS)) active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS)) active(U334(tt(),XS)) -> mark(XS) active(U34(tt(),N)) -> mark(N) active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS)) active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS)) active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS)) active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS))) active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isLNat(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2)) active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2)) active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2)) active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2)) active(U55(tt(),V2)) -> mark(U56(isLNat(V2))) active(U56(tt())) -> mark(tt()) active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1)) active(U62(tt(),V1)) -> mark(U63(isPLNat(V1))) active(U63(tt())) -> mark(tt()) active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1)) active(U72(tt(),V1)) -> mark(U73(isNatural(V1))) active(U73(tt())) -> mark(tt()) active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1)) active(U82(tt(),V1)) -> mark(U83(isPLNat(V1))) active(U83(tt())) -> mark(tt()) active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1)) active(U92(tt(),V1)) -> mark(U93(isLNat(V1))) active(U93(tt())) -> mark(tt()) active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS)) active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y)) active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS)) active(isLNat(nil())) -> mark(tt()) active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2)) active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2)) active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1)) active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1)) active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1)) active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1)) active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2)) active(isLNatKind(nil())) -> mark(tt()) active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2)) active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2)) active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2)) active(isNatural(0())) -> mark(tt()) active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1)) active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1)) active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2)) active(isNaturalKind(0())) -> mark(tt()) active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2)) active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2)) active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2)) active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2)) active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2)) active(natsFrom(N)) -> mark(U281(isNatural(N),N)) active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS)) active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y)) active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS)) active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS)) active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS)) active(take(N,XS)) -> mark(U341(isNatural(N),N,XS)) active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3) active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3) active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3) active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3) active(U105(X1,X2)) -> U105(active(X1),X2) active(U106(X)) -> U106(active(X)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U111(X1,X2)) -> U111(active(X1),X2) active(U112(X)) -> U112(active(X)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U121(X1,X2)) -> U121(active(X1),X2) active(U122(X)) -> U122(active(X)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U131(X)) -> U131(active(X)) active(snd(X)) -> snd(active(X)) active(splitAt(X1,X2)) -> splitAt(active(X1),X2) active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) active(U141(X)) -> U141(active(X)) active(U151(X)) -> U151(active(X)) active(U161(X)) -> U161(active(X)) active(U171(X1,X2)) -> U171(active(X1),X2) active(U172(X)) -> U172(active(X)) active(U181(X1,X2)) -> U181(active(X1),X2) active(U182(X1,X2)) -> U182(active(X1),X2) active(U183(X)) -> U183(active(X)) active(U191(X1,X2)) -> U191(active(X1),X2) active(U192(X1,X2)) -> U192(active(X1),X2) active(U193(X)) -> U193(active(X)) active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3) active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3) active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3) active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3) active(U205(X1,X2)) -> U205(active(X1),X2) active(U206(X)) -> U206(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(U211(X)) -> U211(active(X)) active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3) active(U221(X)) -> U221(active(X)) active(U24(X1,X2)) -> U24(active(X1),X2) active(U231(X1,X2)) -> U231(active(X1),X2) active(U232(X)) -> U232(active(X)) active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3) active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3) active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3) active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3) active(U245(X1,X2)) -> U245(active(X1),X2) active(U246(X)) -> U246(active(X)) active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3) active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3) active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3) active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3) active(U255(X1,X2)) -> U255(active(X1),X2) active(U256(X)) -> U256(active(X)) active(U261(X1,X2)) -> U261(active(X1),X2) active(U262(X)) -> U262(active(X)) active(U271(X1,X2)) -> U271(active(X1),X2) active(U272(X)) -> U272(active(X)) active(U281(X1,X2)) -> U281(active(X1),X2) active(U282(X1,X2)) -> U282(active(X1),X2) active(cons(X1,X2)) -> cons(active(X1),X2) active(natsFrom(X)) -> natsFrom(active(X)) active(s(X)) -> s(active(X)) active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3) active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3) active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3) active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3) active(head(X)) -> head(active(X)) active(afterNth(X1,X2)) -> afterNth(active(X1),X2) active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3) active(U302(X1,X2)) -> U302(active(X1),X2) active(U303(X1,X2)) -> U303(active(X1),X2) active(U304(X1,X2)) -> U304(active(X1),X2) active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3) active(U311(X1,X2)) -> U311(active(X1),X2) active(U312(X1,X2)) -> U312(active(X1),X2) active(pair(X1,X2)) -> pair(active(X1),X2) active(pair(X1,X2)) -> pair(X1,active(X2)) active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3) active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4) active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4) active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4) active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4) active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4) active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4) active(U327(X1,X2)) -> U327(active(X1),X2) active(U34(X1,X2)) -> U34(active(X1),X2) active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3) active(U332(X1,X2)) -> U332(active(X1),X2) active(U333(X1,X2)) -> U333(active(X1),X2) active(U334(X1,X2)) -> U334(active(X1),X2) active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3) active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3) active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3) active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3) active(fst(X)) -> fst(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3) active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3) active(U45(X1,X2)) -> U45(active(X1),X2) active(U46(X)) -> U46(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3) active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3) active(U55(X1,X2)) -> U55(active(X1),X2) active(U56(X)) -> U56(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X1,X2)) -> U62(active(X1),X2) active(U63(X)) -> U63(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X1,X2)) -> U72(active(X1),X2) active(U73(X)) -> U73(active(X)) active(U81(X1,X2)) -> U81(active(X1),X2) active(U82(X1,X2)) -> U82(active(X1),X2) active(U83(X)) -> U83(active(X)) active(U91(X1,X2)) -> U91(active(X1),X2) active(U92(X1,X2)) -> U92(active(X1),X2) active(U93(X)) -> U93(active(X)) active(tail(X)) -> tail(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3)) U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3)) U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3)) U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3)) U105(mark(X1),X2) -> mark(U105(X1,X2)) U106(mark(X)) -> mark(U106(X)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U111(mark(X1),X2) -> mark(U111(X1,X2)) U112(mark(X)) -> mark(U112(X)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U121(mark(X1),X2) -> mark(U121(X1,X2)) U122(mark(X)) -> mark(U122(X)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U131(mark(X)) -> mark(U131(X)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) U141(mark(X)) -> mark(U141(X)) U151(mark(X)) -> mark(U151(X)) U161(mark(X)) -> mark(U161(X)) U171(mark(X1),X2) -> mark(U171(X1,X2)) U172(mark(X)) -> mark(U172(X)) U181(mark(X1),X2) -> mark(U181(X1,X2)) U182(mark(X1),X2) -> mark(U182(X1,X2)) U183(mark(X)) -> mark(U183(X)) U191(mark(X1),X2) -> mark(U191(X1,X2)) U192(mark(X1),X2) -> mark(U192(X1,X2)) U193(mark(X)) -> mark(U193(X)) U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3)) U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3)) U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3)) U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3)) U205(mark(X1),X2) -> mark(U205(X1,X2)) U206(mark(X)) -> mark(U206(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) U211(mark(X)) -> mark(U211(X)) U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3)) U221(mark(X)) -> mark(U221(X)) U24(mark(X1),X2) -> mark(U24(X1,X2)) U231(mark(X1),X2) -> mark(U231(X1,X2)) U232(mark(X)) -> mark(U232(X)) U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3)) U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3)) U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3)) U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3)) U245(mark(X1),X2) -> mark(U245(X1,X2)) U246(mark(X)) -> mark(U246(X)) U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3)) U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3)) U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3)) U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3)) U255(mark(X1),X2) -> mark(U255(X1,X2)) U256(mark(X)) -> mark(U256(X)) U261(mark(X1),X2) -> mark(U261(X1,X2)) U262(mark(X)) -> mark(U262(X)) U271(mark(X1),X2) -> mark(U271(X1,X2)) U272(mark(X)) -> mark(U272(X)) U281(mark(X1),X2) -> mark(U281(X1,X2)) U282(mark(X1),X2) -> mark(U282(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) s(mark(X)) -> mark(s(X)) U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3)) U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3)) U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3)) U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3)) head(mark(X)) -> mark(head(X)) afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3)) U302(mark(X1),X2) -> mark(U302(X1,X2)) U303(mark(X1),X2) -> mark(U303(X1,X2)) U304(mark(X1),X2) -> mark(U304(X1,X2)) U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3)) U311(mark(X1),X2) -> mark(U311(X1,X2)) U312(mark(X1),X2) -> mark(U312(X1,X2)) pair(mark(X1),X2) -> mark(pair(X1,X2)) pair(X1,mark(X2)) -> mark(pair(X1,X2)) U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3)) U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4)) U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4)) U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4)) U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4)) U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4)) U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4)) U327(mark(X1),X2) -> mark(U327(X1,X2)) U34(mark(X1),X2) -> mark(U34(X1,X2)) U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3)) U332(mark(X1),X2) -> mark(U332(X1,X2)) U333(mark(X1),X2) -> mark(U333(X1,X2)) U334(mark(X1),X2) -> mark(U334(X1,X2)) U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3)) U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3)) U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3)) U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3)) fst(mark(X)) -> mark(fst(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3)) U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3)) U45(mark(X1),X2) -> mark(U45(X1,X2)) U46(mark(X)) -> mark(U46(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3)) U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3)) U55(mark(X1),X2) -> mark(U55(X1,X2)) U56(mark(X)) -> mark(U56(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X1),X2) -> mark(U62(X1,X2)) U63(mark(X)) -> mark(U63(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X1),X2) -> mark(U72(X1,X2)) U73(mark(X)) -> mark(U73(X)) U81(mark(X1),X2) -> mark(U81(X1,X2)) U82(mark(X1),X2) -> mark(U82(X1,X2)) U83(mark(X)) -> mark(U83(X)) U91(mark(X1),X2) -> mark(U91(X1,X2)) U92(mark(X1),X2) -> mark(U92(X1,X2)) U93(mark(X)) -> mark(U93(X)) tail(mark(X)) -> mark(tail(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3)) proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3)) proper(isLNatKind(X)) -> isLNatKind(proper(X)) proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3)) proper(U105(X1,X2)) -> U105(proper(X1),proper(X2)) proper(isNatural(X)) -> isNatural(proper(X)) proper(U106(X)) -> U106(proper(X)) proper(isLNat(X)) -> isLNat(proper(X)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(U111(X1,X2)) -> U111(proper(X1),proper(X2)) proper(U112(X)) -> U112(proper(X)) proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U121(X1,X2)) -> U121(proper(X1),proper(X2)) proper(U122(X)) -> U122(proper(X)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U131(X)) -> U131(proper(X)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) proper(U141(X)) -> U141(proper(X)) proper(U151(X)) -> U151(proper(X)) proper(U161(X)) -> U161(proper(X)) proper(U171(X1,X2)) -> U171(proper(X1),proper(X2)) proper(U172(X)) -> U172(proper(X)) proper(U181(X1,X2)) -> U181(proper(X1),proper(X2)) proper(U182(X1,X2)) -> U182(proper(X1),proper(X2)) proper(U183(X)) -> U183(proper(X)) proper(U191(X1,X2)) -> U191(proper(X1),proper(X2)) proper(U192(X1,X2)) -> U192(proper(X1),proper(X2)) proper(U193(X)) -> U193(proper(X)) proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3)) proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3)) proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3)) proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3)) proper(U205(X1,X2)) -> U205(proper(X1),proper(X2)) proper(U206(X)) -> U206(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(U211(X)) -> U211(proper(X)) proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3)) proper(U221(X)) -> U221(proper(X)) proper(U24(X1,X2)) -> U24(proper(X1),proper(X2)) proper(U231(X1,X2)) -> U231(proper(X1),proper(X2)) proper(U232(X)) -> U232(proper(X)) proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3)) proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3)) proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3)) proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3)) proper(U245(X1,X2)) -> U245(proper(X1),proper(X2)) proper(U246(X)) -> U246(proper(X)) proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3)) proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3)) proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3)) proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3)) proper(U255(X1,X2)) -> U255(proper(X1),proper(X2)) proper(U256(X)) -> U256(proper(X)) proper(U261(X1,X2)) -> U261(proper(X1),proper(X2)) proper(U262(X)) -> U262(proper(X)) proper(U271(X1,X2)) -> U271(proper(X1),proper(X2)) proper(U272(X)) -> U272(proper(X)) proper(U281(X1,X2)) -> U281(proper(X1),proper(X2)) proper(U282(X1,X2)) -> U282(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(s(X)) -> s(proper(X)) proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3)) proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3)) proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3)) proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3)) proper(head(X)) -> head(proper(X)) proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3)) proper(U302(X1,X2)) -> U302(proper(X1),proper(X2)) proper(U303(X1,X2)) -> U303(proper(X1),proper(X2)) proper(U304(X1,X2)) -> U304(proper(X1),proper(X2)) proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3)) proper(U311(X1,X2)) -> U311(proper(X1),proper(X2)) proper(U312(X1,X2)) -> U312(proper(X1),proper(X2)) proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3)) proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4)) proper(U327(X1,X2)) -> U327(proper(X1),proper(X2)) proper(U34(X1,X2)) -> U34(proper(X1),proper(X2)) proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3)) proper(U332(X1,X2)) -> U332(proper(X1),proper(X2)) proper(U333(X1,X2)) -> U333(proper(X1),proper(X2)) proper(U334(X1,X2)) -> U334(proper(X1),proper(X2)) proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3)) proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3)) proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3)) proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3)) proper(fst(X)) -> fst(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3)) proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3)) proper(U45(X1,X2)) -> U45(proper(X1),proper(X2)) proper(U46(X)) -> U46(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3)) proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3)) proper(U55(X1,X2)) -> U55(proper(X1),proper(X2)) proper(U56(X)) -> U56(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) proper(U63(X)) -> U63(proper(X)) proper(isPLNat(X)) -> isPLNat(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) proper(U73(X)) -> U73(proper(X)) proper(U81(X1,X2)) -> U81(proper(X1),proper(X2)) proper(U82(X1,X2)) -> U82(proper(X1),proper(X2)) proper(U83(X)) -> U83(proper(X)) proper(U91(X1,X2)) -> U91(proper(X1),proper(X2)) proper(U92(X1,X2)) -> U92(proper(X1),proper(X2)) proper(U93(X)) -> U93(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3)) U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3)) isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3)) isLNatKind(ok(X)) -> ok(isLNatKind(X)) U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3)) U105(ok(X1),ok(X2)) -> ok(U105(X1,X2)) isNatural(ok(X)) -> ok(isNatural(X)) U106(ok(X)) -> ok(U106(X)) isLNat(ok(X)) -> ok(isLNat(X)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) U111(ok(X1),ok(X2)) -> ok(U111(X1,X2)) U112(ok(X)) -> ok(U112(X)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U121(ok(X1),ok(X2)) -> ok(U121(X1,X2)) U122(ok(X)) -> ok(U122(X)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U131(ok(X)) -> ok(U131(X)) snd(ok(X)) -> ok(snd(X)) splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) U141(ok(X)) -> ok(U141(X)) U151(ok(X)) -> ok(U151(X)) U161(ok(X)) -> ok(U161(X)) U171(ok(X1),ok(X2)) -> ok(U171(X1,X2)) U172(ok(X)) -> ok(U172(X)) U181(ok(X1),ok(X2)) -> ok(U181(X1,X2)) U182(ok(X1),ok(X2)) -> ok(U182(X1,X2)) U183(ok(X)) -> ok(U183(X)) U191(ok(X1),ok(X2)) -> ok(U191(X1,X2)) U192(ok(X1),ok(X2)) -> ok(U192(X1,X2)) U193(ok(X)) -> ok(U193(X)) U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3)) U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3)) U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3)) U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3)) U205(ok(X1),ok(X2)) -> ok(U205(X1,X2)) U206(ok(X)) -> ok(U206(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) U211(ok(X)) -> ok(U211(X)) U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3)) U221(ok(X)) -> ok(U221(X)) U24(ok(X1),ok(X2)) -> ok(U24(X1,X2)) U231(ok(X1),ok(X2)) -> ok(U231(X1,X2)) U232(ok(X)) -> ok(U232(X)) U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3)) U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3)) U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3)) U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3)) U245(ok(X1),ok(X2)) -> ok(U245(X1,X2)) U246(ok(X)) -> ok(U246(X)) U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3)) U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3)) U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3)) U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3)) U255(ok(X1),ok(X2)) -> ok(U255(X1,X2)) U256(ok(X)) -> ok(U256(X)) U261(ok(X1),ok(X2)) -> ok(U261(X1,X2)) U262(ok(X)) -> ok(U262(X)) U271(ok(X1),ok(X2)) -> ok(U271(X1,X2)) U272(ok(X)) -> ok(U272(X)) U281(ok(X1),ok(X2)) -> ok(U281(X1,X2)) U282(ok(X1),ok(X2)) -> ok(U282(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) s(ok(X)) -> ok(s(X)) U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3)) U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3)) U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3)) U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3)) head(ok(X)) -> ok(head(X)) afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3)) U302(ok(X1),ok(X2)) -> ok(U302(X1,X2)) U303(ok(X1),ok(X2)) -> ok(U303(X1,X2)) U304(ok(X1),ok(X2)) -> ok(U304(X1,X2)) U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3)) U311(ok(X1),ok(X2)) -> ok(U311(X1,X2)) U312(ok(X1),ok(X2)) -> ok(U312(X1,X2)) pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3)) U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4)) U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4)) U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4)) U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4)) U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4)) U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4)) U327(ok(X1),ok(X2)) -> ok(U327(X1,X2)) U34(ok(X1),ok(X2)) -> ok(U34(X1,X2)) U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3)) U332(ok(X1),ok(X2)) -> ok(U332(X1,X2)) U333(ok(X1),ok(X2)) -> ok(U333(X1,X2)) U334(ok(X1),ok(X2)) -> ok(U334(X1,X2)) U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3)) U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3)) U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3)) U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3)) fst(ok(X)) -> ok(fst(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3)) U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3)) U45(ok(X1),ok(X2)) -> ok(U45(X1,X2)) U46(ok(X)) -> ok(U46(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3)) U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3)) U55(ok(X1),ok(X2)) -> ok(U55(X1,X2)) U56(ok(X)) -> ok(U56(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) U63(ok(X)) -> ok(U63(X)) isPLNat(ok(X)) -> ok(isPLNat(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) U73(ok(X)) -> ok(U73(X)) U81(ok(X1),ok(X2)) -> ok(U81(X1,X2)) U82(ok(X1),ok(X2)) -> ok(U82(X1,X2)) U83(ok(X)) -> ok(U83(X)) U91(ok(X1),ok(X2)) -> ok(U91(X1,X2)) U92(ok(X1),ok(X2)) -> ok(U92(X1,X2)) U93(ok(X)) -> ok(U93(X)) tail(ok(X)) -> ok(tail(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open