Problem Transformed CSR 04 LISTUTILITIES complete noand C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete noand C

stdout:

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:
Open

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete noand C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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 Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete noand C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  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 Output:
  Computation stopped due to timeout after 60.0 seconds