MAYBE MAYBE TRS: { U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)), U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)), isNaturalKind(ok(X)) -> ok(isNaturalKind(X)), active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3), active(U102(tt(), V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)), active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))), active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))), active(isNaturalKind(0())) -> mark(tt()), active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)), active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3), active(U101(tt(), V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)), active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3), active(U103(tt(), V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)), active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))), active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)), active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))), active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)), active(isLNatKind(nil())) -> mark(tt()), active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))), active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))), active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)), active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3), active(U104(tt(), V1, V2)) -> mark(U105(isNatural(V1), V2)), active(U105(X1, X2)) -> U105(active(X1), X2), active(U105(tt(), V2)) -> mark(U106(isLNat(V2))), active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)), active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)), active(isNatural(0())) -> mark(tt()), active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)), active(U106(X)) -> U106(active(X)), active(U106(tt())) -> mark(tt()), active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)), active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)), active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)), active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)), active(isLNat(nil())) -> mark(tt()), active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)), active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)), active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)), active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3), active(U12(tt(), N, XS)) -> mark(U13(isLNat(XS), N, XS)), active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3), active(U11(tt(), N, XS)) -> mark(U12(isNaturalKind(N), N, XS)), active(U112(X)) -> U112(active(X)), active(U112(tt())) -> mark(tt()), active(U111(X1, X2)) -> U111(active(X1), X2), active(U111(tt(), V2)) -> mark(U112(isLNatKind(V2))), active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3), active(U13(tt(), N, XS)) -> mark(U14(isLNatKind(XS), N, XS)), active(U122(X)) -> U122(active(X)), active(U122(tt())) -> mark(tt()), active(U121(X1, X2)) -> U121(active(X1), X2), active(U121(tt(), V2)) -> mark(U122(isLNatKind(V2))), active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3), active(U14(tt(), N, XS)) -> mark(snd(splitAt(N, XS))), active(U131(X)) -> U131(active(X)), active(U131(tt())) -> mark(tt()), active(snd(X)) -> snd(active(X)), active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)), active(splitAt(X1, X2)) -> splitAt(X1, active(X2)), active(splitAt(X1, X2)) -> splitAt(active(X1), X2), active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)), active(splitAt(0(), XS)) -> mark(U311(isLNat(XS), XS)), active(U141(X)) -> U141(active(X)), active(U141(tt())) -> mark(tt()), active(U151(X)) -> U151(active(X)), active(U151(tt())) -> mark(tt()), active(U161(X)) -> U161(active(X)), active(U161(tt())) -> mark(tt()), active(U172(X)) -> U172(active(X)), active(U172(tt())) -> mark(tt()), active(U171(X1, X2)) -> U171(active(X1), X2), active(U171(tt(), V2)) -> mark(U172(isLNatKind(V2))), active(U182(X1, X2)) -> U182(active(X1), X2), active(U182(tt(), V1)) -> mark(U183(isLNat(V1))), active(U181(X1, X2)) -> U181(active(X1), X2), active(U181(tt(), V1)) -> mark(U182(isLNatKind(V1), V1)), active(U183(X)) -> U183(active(X)), active(U183(tt())) -> mark(tt()), active(U192(X1, X2)) -> U192(active(X1), X2), active(U192(tt(), V1)) -> mark(U193(isNatural(V1))), active(U191(X1, X2)) -> U191(active(X1), X2), active(U191(tt(), V1)) -> mark(U192(isNaturalKind(V1), V1)), active(U193(X)) -> U193(active(X)), active(U193(tt())) -> mark(tt()), active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3), active(U202(tt(), V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)), active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3), active(U201(tt(), V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)), active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3), active(U203(tt(), V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)), active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3), active(U204(tt(), V1, V2)) -> mark(U205(isNatural(V1), V2)), active(U205(X1, X2)) -> U205(active(X1), X2), active(U205(tt(), V2)) -> mark(U206(isLNat(V2))), active(U206(X)) -> U206(active(X)), active(U206(tt())) -> mark(tt()), active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3), active(U22(tt(), X, Y)) -> mark(U23(isLNat(Y), X, Y)), active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3), active(U21(tt(), X, Y)) -> mark(U22(isLNatKind(X), X, Y)), active(U211(X)) -> U211(active(X)), active(U211(tt())) -> mark(tt()), active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3), active(U23(tt(), X, Y)) -> mark(U24(isLNatKind(Y), X)), active(U221(X)) -> U221(active(X)), active(U221(tt())) -> mark(tt()), active(U24(X1, X2)) -> U24(active(X1), X2), active(U24(tt(), X)) -> mark(X), active(U232(X)) -> U232(active(X)), active(U232(tt())) -> mark(tt()), active(U231(X1, X2)) -> U231(active(X1), X2), active(U231(tt(), V2)) -> mark(U232(isLNatKind(V2))), active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3), active(U242(tt(), V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)), active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3), active(U241(tt(), V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)), active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3), active(U243(tt(), V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)), active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3), active(U244(tt(), V1, V2)) -> mark(U245(isLNat(V1), V2)), active(U245(X1, X2)) -> U245(active(X1), X2), active(U245(tt(), V2)) -> mark(U246(isLNat(V2))), active(U246(X)) -> U246(active(X)), active(U246(tt())) -> mark(tt()), active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3), active(U252(tt(), V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)), active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3), active(U251(tt(), V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)), active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3), active(U253(tt(), V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)), active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3), active(U254(tt(), V1, V2)) -> mark(U255(isNatural(V1), V2)), active(U255(X1, X2)) -> U255(active(X1), X2), active(U255(tt(), V2)) -> mark(U256(isLNat(V2))), active(U256(X)) -> U256(active(X)), active(U256(tt())) -> mark(tt()), active(U262(X)) -> U262(active(X)), active(U262(tt())) -> mark(tt()), active(U261(X1, X2)) -> U261(active(X1), X2), active(U261(tt(), V2)) -> mark(U262(isLNatKind(V2))), active(U272(X)) -> U272(active(X)), active(U272(tt())) -> mark(tt()), active(U271(X1, X2)) -> U271(active(X1), X2), active(U271(tt(), V2)) -> mark(U272(isLNatKind(V2))), active(U282(X1, X2)) -> U282(active(X1), X2), active(U282(tt(), N)) -> mark(cons(N, natsFrom(s(N)))), active(U281(X1, X2)) -> U281(active(X1), X2), active(U281(tt(), N)) -> mark(U282(isNaturalKind(N), N)), active(cons(X1, X2)) -> cons(active(X1), X2), active(natsFrom(N)) -> mark(U281(isNatural(N), N)), active(natsFrom(X)) -> natsFrom(active(X)), active(s(X)) -> s(active(X)), active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3), active(U292(tt(), N, XS)) -> mark(U293(isLNat(XS), N, XS)), active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3), active(U291(tt(), N, XS)) -> mark(U292(isNaturalKind(N), N, XS)), active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3), active(U293(tt(), N, XS)) -> mark(U294(isLNatKind(XS), N, XS)), active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3), active(U294(tt(), N, XS)) -> mark(head(afterNth(N, XS))), active(head(X)) -> head(active(X)), active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)), active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)), active(afterNth(X1, X2)) -> afterNth(X1, active(X2)), active(afterNth(X1, X2)) -> afterNth(active(X1), X2), active(U302(X1, X2)) -> U302(active(X1), X2), active(U302(tt(), Y)) -> mark(U303(isLNat(Y), Y)), active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3), active(U301(tt(), X, Y)) -> mark(U302(isLNatKind(X), Y)), active(U303(X1, X2)) -> U303(active(X1), X2), active(U303(tt(), Y)) -> mark(U304(isLNatKind(Y), Y)), active(U304(X1, X2)) -> U304(active(X1), X2), active(U304(tt(), Y)) -> mark(Y), active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3), active(U32(tt(), N, XS)) -> mark(U33(isLNat(XS), N, XS)), active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3), active(U31(tt(), N, XS)) -> mark(U32(isNaturalKind(N), N, XS)), active(U312(X1, X2)) -> U312(active(X1), X2), active(U312(tt(), XS)) -> mark(pair(nil(), XS)), active(U311(X1, X2)) -> U311(active(X1), X2), active(U311(tt(), XS)) -> mark(U312(isLNatKind(XS), XS)), active(pair(X1, X2)) -> pair(X1, active(X2)), active(pair(X1, X2)) -> pair(active(X1), X2), active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3), active(U33(tt(), N, XS)) -> mark(U34(isLNatKind(XS), N)), active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4), active(U322(tt(), N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)), active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4), active(U321(tt(), N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)), active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4), active(U323(tt(), N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)), active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4), active(U324(tt(), N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)), active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4), active(U325(tt(), N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)), active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4), active(U326(tt(), N, X, XS)) -> mark(U327(splitAt(N, XS), X)), active(U327(X1, X2)) -> U327(active(X1), X2), active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)), active(U34(X1, X2)) -> U34(active(X1), X2), active(U34(tt(), N)) -> mark(N), active(U332(X1, X2)) -> U332(active(X1), X2), active(U332(tt(), XS)) -> mark(U333(isLNat(XS), XS)), active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3), active(U331(tt(), N, XS)) -> mark(U332(isNaturalKind(N), XS)), active(U333(X1, X2)) -> U333(active(X1), X2), active(U333(tt(), XS)) -> mark(U334(isLNatKind(XS), XS)), active(U334(X1, X2)) -> U334(active(X1), X2), active(U334(tt(), XS)) -> mark(XS), active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3), active(U342(tt(), N, XS)) -> mark(U343(isLNat(XS), N, XS)), active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3), active(U341(tt(), N, XS)) -> mark(U342(isNaturalKind(N), N, XS)), active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3), active(U343(tt(), N, XS)) -> mark(U344(isLNatKind(XS), N, XS)), active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3), active(U344(tt(), N, XS)) -> mark(fst(splitAt(N, XS))), active(fst(X)) -> fst(active(X)), active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)), active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3), active(U42(tt(), V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)), active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3), active(U41(tt(), V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)), active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3), active(U43(tt(), V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)), active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3), active(U44(tt(), V1, V2)) -> mark(U45(isNatural(V1), V2)), active(U45(X1, X2)) -> U45(active(X1), X2), active(U45(tt(), V2)) -> mark(U46(isLNat(V2))), active(U46(X)) -> U46(active(X)), active(U46(tt())) -> mark(tt()), active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3), active(U52(tt(), V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)), active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3), active(U51(tt(), V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)), active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3), active(U53(tt(), V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)), active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3), active(U54(tt(), V1, V2)) -> mark(U55(isNatural(V1), V2)), active(U55(X1, X2)) -> U55(active(X1), X2), active(U55(tt(), V2)) -> mark(U56(isLNat(V2))), active(U56(X)) -> U56(active(X)), active(U56(tt())) -> mark(tt()), active(U62(X1, X2)) -> U62(active(X1), X2), active(U62(tt(), V1)) -> mark(U63(isPLNat(V1))), active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)), active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)), active(U61(X1, X2)) -> U61(active(X1), X2), active(U61(tt(), V1)) -> mark(U62(isPLNatKind(V1), V1)), active(U63(X)) -> U63(active(X)), active(U63(tt())) -> mark(tt()), active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)), active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)), active(U72(X1, X2)) -> U72(active(X1), X2), active(U72(tt(), V1)) -> mark(U73(isNatural(V1))), active(U71(X1, X2)) -> U71(active(X1), X2), active(U71(tt(), V1)) -> mark(U72(isNaturalKind(V1), V1)), active(U73(X)) -> U73(active(X)), active(U73(tt())) -> mark(tt()), active(U82(X1, X2)) -> U82(active(X1), X2), active(U82(tt(), V1)) -> mark(U83(isPLNat(V1))), active(U81(X1, X2)) -> U81(active(X1), X2), active(U81(tt(), V1)) -> mark(U82(isPLNatKind(V1), V1)), active(U83(X)) -> U83(active(X)), active(U83(tt())) -> mark(tt()), active(U92(X1, X2)) -> U92(active(X1), X2), active(U92(tt(), V1)) -> mark(U93(isLNat(V1))), active(U91(X1, X2)) -> U91(active(X1), X2), active(U91(tt(), V1)) -> mark(U92(isLNatKind(V1), V1)), active(U93(X)) -> U93(active(X)), active(U93(tt())) -> mark(tt()), active(tail(X)) -> tail(active(X)), active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)), active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)), U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)), U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)), U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)), isLNatKind(ok(X)) -> ok(isLNatKind(X)), U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)), U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)), U105(mark(X1), X2) -> mark(U105(X1, X2)), U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)), isNatural(ok(X)) -> ok(isNatural(X)), U106(mark(X)) -> mark(U106(X)), U106(ok(X)) -> ok(U106(X)), isLNat(ok(X)) -> ok(isLNat(X)), U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)), U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)), U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)), U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)), U112(mark(X)) -> mark(U112(X)), U112(ok(X)) -> ok(U112(X)), U111(mark(X1), X2) -> mark(U111(X1, X2)), U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)), U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)), U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)), U122(mark(X)) -> mark(U122(X)), U122(ok(X)) -> ok(U122(X)), U121(mark(X1), X2) -> mark(U121(X1, X2)), U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)), U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)), U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)), U131(mark(X)) -> mark(U131(X)), U131(ok(X)) -> ok(U131(X)), snd(mark(X)) -> mark(snd(X)), snd(ok(X)) -> ok(snd(X)), splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)), splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)), splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)), U141(mark(X)) -> mark(U141(X)), U141(ok(X)) -> ok(U141(X)), U151(mark(X)) -> mark(U151(X)), U151(ok(X)) -> ok(U151(X)), U161(mark(X)) -> mark(U161(X)), U161(ok(X)) -> ok(U161(X)), U172(mark(X)) -> mark(U172(X)), U172(ok(X)) -> ok(U172(X)), U171(mark(X1), X2) -> mark(U171(X1, X2)), U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)), U182(mark(X1), X2) -> mark(U182(X1, X2)), U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)), U181(mark(X1), X2) -> mark(U181(X1, X2)), U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)), U183(mark(X)) -> mark(U183(X)), U183(ok(X)) -> ok(U183(X)), U192(mark(X1), X2) -> mark(U192(X1, X2)), U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)), U191(mark(X1), X2) -> mark(U191(X1, X2)), U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)), U193(mark(X)) -> mark(U193(X)), U193(ok(X)) -> ok(U193(X)), U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)), U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)), U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)), U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)), U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)), U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)), U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)), U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)), U205(mark(X1), X2) -> mark(U205(X1, X2)), U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)), U206(mark(X)) -> mark(U206(X)), U206(ok(X)) -> ok(U206(X)), U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)), U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)), U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)), U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)), U211(mark(X)) -> mark(U211(X)), U211(ok(X)) -> ok(U211(X)), U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)), U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)), U221(mark(X)) -> mark(U221(X)), U221(ok(X)) -> ok(U221(X)), U24(mark(X1), X2) -> mark(U24(X1, X2)), U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)), U232(mark(X)) -> mark(U232(X)), U232(ok(X)) -> ok(U232(X)), U231(mark(X1), X2) -> mark(U231(X1, X2)), U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)), U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)), U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)), U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)), U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)), U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)), U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)), U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)), U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)), U245(mark(X1), X2) -> mark(U245(X1, X2)), U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)), U246(mark(X)) -> mark(U246(X)), U246(ok(X)) -> ok(U246(X)), U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)), U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)), U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)), U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)), U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)), U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)), U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)), U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)), U255(mark(X1), X2) -> mark(U255(X1, X2)), U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)), U256(mark(X)) -> mark(U256(X)), U256(ok(X)) -> ok(U256(X)), U262(mark(X)) -> mark(U262(X)), U262(ok(X)) -> ok(U262(X)), U261(mark(X1), X2) -> mark(U261(X1, X2)), U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)), U272(mark(X)) -> mark(U272(X)), U272(ok(X)) -> ok(U272(X)), U271(mark(X1), X2) -> mark(U271(X1, X2)), U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)), U282(mark(X1), X2) -> mark(U282(X1, X2)), U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)), U281(mark(X1), X2) -> mark(U281(X1, X2)), U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), natsFrom(mark(X)) -> mark(natsFrom(X)), natsFrom(ok(X)) -> ok(natsFrom(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)), U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)), U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)), U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)), U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)), U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)), U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)), U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)), afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)), afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)), U302(mark(X1), X2) -> mark(U302(X1, X2)), U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)), U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)), U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)), U303(mark(X1), X2) -> mark(U303(X1, X2)), U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)), U304(mark(X1), X2) -> mark(U304(X1, X2)), U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)), U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)), U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)), U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)), U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)), U312(mark(X1), X2) -> mark(U312(X1, X2)), U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)), U311(mark(X1), X2) -> mark(U311(X1, X2)), U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)), pair(X1, mark(X2)) -> mark(pair(X1, X2)), pair(mark(X1), X2) -> mark(pair(X1, X2)), pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)), U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)), U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)), U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)), U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)), U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)), U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)), U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)), U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)), U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)), U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)), U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)), U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)), U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)), U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)), U327(mark(X1), X2) -> mark(U327(X1, X2)), U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)), U34(mark(X1), X2) -> mark(U34(X1, X2)), U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)), U332(mark(X1), X2) -> mark(U332(X1, X2)), U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)), U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)), U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)), U333(mark(X1), X2) -> mark(U333(X1, X2)), U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)), U334(mark(X1), X2) -> mark(U334(X1, X2)), U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)), U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)), U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)), U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)), U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)), U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)), U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)), U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)), U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)), fst(mark(X)) -> mark(fst(X)), fst(ok(X)) -> ok(fst(X)), U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)), U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)), U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)), U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)), U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)), U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)), U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)), U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)), U45(mark(X1), X2) -> mark(U45(X1, X2)), U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)), U46(mark(X)) -> mark(U46(X)), U46(ok(X)) -> ok(U46(X)), U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)), U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)), U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)), U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)), U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)), U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)), U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)), U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)), U55(mark(X1), X2) -> mark(U55(X1, X2)), U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)), U56(mark(X)) -> mark(U56(X)), U56(ok(X)) -> ok(U56(X)), U62(mark(X1), X2) -> mark(U62(X1, X2)), U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)), isPLNatKind(ok(X)) -> ok(isPLNatKind(X)), U61(mark(X1), X2) -> mark(U61(X1, X2)), U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)), U63(mark(X)) -> mark(U63(X)), U63(ok(X)) -> ok(U63(X)), isPLNat(ok(X)) -> ok(isPLNat(X)), U72(mark(X1), X2) -> mark(U72(X1, X2)), U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)), U71(mark(X1), X2) -> mark(U71(X1, X2)), U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)), U73(mark(X)) -> mark(U73(X)), U73(ok(X)) -> ok(U73(X)), U82(mark(X1), X2) -> mark(U82(X1, X2)), U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)), U81(mark(X1), X2) -> mark(U81(X1, X2)), U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)), U83(mark(X)) -> mark(U83(X)), U83(ok(X)) -> ok(U83(X)), U92(mark(X1), X2) -> mark(U92(X1, X2)), U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)), U91(mark(X1), X2) -> mark(U91(X1, X2)), U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)), U93(mark(X)) -> mark(U93(X)), U93(ok(X)) -> ok(U93(X)), tail(mark(X)) -> mark(tail(X)), tail(ok(X)) -> ok(tail(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)), proper(isNaturalKind(X)) -> isNaturalKind(proper(X)), proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)), proper(tt()) -> ok(tt()), 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(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)), proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)), proper(U112(X)) -> U112(proper(X)), proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)), proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)), proper(U122(X)) -> U122(proper(X)), proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)), 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(U172(X)) -> U172(proper(X)), proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)), proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)), proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)), proper(U183(X)) -> U183(proper(X)), proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)), proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)), proper(U193(X)) -> U193(proper(X)), proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)), proper(U201(X1, X2, X3)) -> U201(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(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)), proper(U21(X1, X2, X3)) -> U21(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(U232(X)) -> U232(proper(X)), proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)), proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)), proper(U241(X1, X2, X3)) -> U241(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(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)), proper(U251(X1, X2, X3)) -> U251(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(U262(X)) -> U262(proper(X)), proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)), proper(U272(X)) -> U272(proper(X)), proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)), proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)), proper(U281(X1, X2)) -> U281(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(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)), proper(U291(X1, X2, X3)) -> U291(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(U302(X1, X2)) -> U302(proper(X1), proper(X2)), proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)), proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)), proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)), proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)), proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)), proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)), proper(U311(X1, X2)) -> U311(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(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)), proper(U321(X1, X2, X3, X4)) -> U321(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(U332(X1, X2)) -> U332(proper(X1), proper(X2)), proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)), proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)), proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)), proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)), proper(U341(X1, X2, X3)) -> U341(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(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)), proper(U41(X1, X2, X3)) -> U41(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(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)), proper(U51(X1, X2, X3)) -> U51(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(U62(X1, X2)) -> U62(proper(X1), proper(X2)), proper(isPLNatKind(X)) -> isPLNatKind(proper(X)), proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)), proper(U63(X)) -> U63(proper(X)), proper(isPLNat(X)) -> isPLNat(proper(X)), proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)), proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)), proper(U73(X)) -> U73(proper(X)), proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)), proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)), proper(U83(X)) -> U83(proper(X)), proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)), proper(U91(X1, X2)) -> U91(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)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } DUP: We consider a duplicating system. Trs: { U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)), U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)), isNaturalKind(ok(X)) -> ok(isNaturalKind(X)), active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3), active(U102(tt(), V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)), active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))), active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))), active(isNaturalKind(0())) -> mark(tt()), active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)), active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3), active(U101(tt(), V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)), active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3), active(U103(tt(), V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)), active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))), active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)), active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))), active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)), active(isLNatKind(nil())) -> mark(tt()), active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))), active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))), active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)), active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3), active(U104(tt(), V1, V2)) -> mark(U105(isNatural(V1), V2)), active(U105(X1, X2)) -> U105(active(X1), X2), active(U105(tt(), V2)) -> mark(U106(isLNat(V2))), active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)), active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)), active(isNatural(0())) -> mark(tt()), active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)), active(U106(X)) -> U106(active(X)), active(U106(tt())) -> mark(tt()), active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)), active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)), active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)), active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)), active(isLNat(nil())) -> mark(tt()), active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)), active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)), active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)), active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3), active(U12(tt(), N, XS)) -> mark(U13(isLNat(XS), N, XS)), active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3), active(U11(tt(), N, XS)) -> mark(U12(isNaturalKind(N), N, XS)), active(U112(X)) -> U112(active(X)), active(U112(tt())) -> mark(tt()), active(U111(X1, X2)) -> U111(active(X1), X2), active(U111(tt(), V2)) -> mark(U112(isLNatKind(V2))), active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3), active(U13(tt(), N, XS)) -> mark(U14(isLNatKind(XS), N, XS)), active(U122(X)) -> U122(active(X)), active(U122(tt())) -> mark(tt()), active(U121(X1, X2)) -> U121(active(X1), X2), active(U121(tt(), V2)) -> mark(U122(isLNatKind(V2))), active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3), active(U14(tt(), N, XS)) -> mark(snd(splitAt(N, XS))), active(U131(X)) -> U131(active(X)), active(U131(tt())) -> mark(tt()), active(snd(X)) -> snd(active(X)), active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)), active(splitAt(X1, X2)) -> splitAt(X1, active(X2)), active(splitAt(X1, X2)) -> splitAt(active(X1), X2), active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)), active(splitAt(0(), XS)) -> mark(U311(isLNat(XS), XS)), active(U141(X)) -> U141(active(X)), active(U141(tt())) -> mark(tt()), active(U151(X)) -> U151(active(X)), active(U151(tt())) -> mark(tt()), active(U161(X)) -> U161(active(X)), active(U161(tt())) -> mark(tt()), active(U172(X)) -> U172(active(X)), active(U172(tt())) -> mark(tt()), active(U171(X1, X2)) -> U171(active(X1), X2), active(U171(tt(), V2)) -> mark(U172(isLNatKind(V2))), active(U182(X1, X2)) -> U182(active(X1), X2), active(U182(tt(), V1)) -> mark(U183(isLNat(V1))), active(U181(X1, X2)) -> U181(active(X1), X2), active(U181(tt(), V1)) -> mark(U182(isLNatKind(V1), V1)), active(U183(X)) -> U183(active(X)), active(U183(tt())) -> mark(tt()), active(U192(X1, X2)) -> U192(active(X1), X2), active(U192(tt(), V1)) -> mark(U193(isNatural(V1))), active(U191(X1, X2)) -> U191(active(X1), X2), active(U191(tt(), V1)) -> mark(U192(isNaturalKind(V1), V1)), active(U193(X)) -> U193(active(X)), active(U193(tt())) -> mark(tt()), active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3), active(U202(tt(), V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)), active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3), active(U201(tt(), V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)), active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3), active(U203(tt(), V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)), active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3), active(U204(tt(), V1, V2)) -> mark(U205(isNatural(V1), V2)), active(U205(X1, X2)) -> U205(active(X1), X2), active(U205(tt(), V2)) -> mark(U206(isLNat(V2))), active(U206(X)) -> U206(active(X)), active(U206(tt())) -> mark(tt()), active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3), active(U22(tt(), X, Y)) -> mark(U23(isLNat(Y), X, Y)), active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3), active(U21(tt(), X, Y)) -> mark(U22(isLNatKind(X), X, Y)), active(U211(X)) -> U211(active(X)), active(U211(tt())) -> mark(tt()), active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3), active(U23(tt(), X, Y)) -> mark(U24(isLNatKind(Y), X)), active(U221(X)) -> U221(active(X)), active(U221(tt())) -> mark(tt()), active(U24(X1, X2)) -> U24(active(X1), X2), active(U24(tt(), X)) -> mark(X), active(U232(X)) -> U232(active(X)), active(U232(tt())) -> mark(tt()), active(U231(X1, X2)) -> U231(active(X1), X2), active(U231(tt(), V2)) -> mark(U232(isLNatKind(V2))), active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3), active(U242(tt(), V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)), active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3), active(U241(tt(), V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)), active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3), active(U243(tt(), V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)), active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3), active(U244(tt(), V1, V2)) -> mark(U245(isLNat(V1), V2)), active(U245(X1, X2)) -> U245(active(X1), X2), active(U245(tt(), V2)) -> mark(U246(isLNat(V2))), active(U246(X)) -> U246(active(X)), active(U246(tt())) -> mark(tt()), active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3), active(U252(tt(), V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)), active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3), active(U251(tt(), V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)), active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3), active(U253(tt(), V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)), active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3), active(U254(tt(), V1, V2)) -> mark(U255(isNatural(V1), V2)), active(U255(X1, X2)) -> U255(active(X1), X2), active(U255(tt(), V2)) -> mark(U256(isLNat(V2))), active(U256(X)) -> U256(active(X)), active(U256(tt())) -> mark(tt()), active(U262(X)) -> U262(active(X)), active(U262(tt())) -> mark(tt()), active(U261(X1, X2)) -> U261(active(X1), X2), active(U261(tt(), V2)) -> mark(U262(isLNatKind(V2))), active(U272(X)) -> U272(active(X)), active(U272(tt())) -> mark(tt()), active(U271(X1, X2)) -> U271(active(X1), X2), active(U271(tt(), V2)) -> mark(U272(isLNatKind(V2))), active(U282(X1, X2)) -> U282(active(X1), X2), active(U282(tt(), N)) -> mark(cons(N, natsFrom(s(N)))), active(U281(X1, X2)) -> U281(active(X1), X2), active(U281(tt(), N)) -> mark(U282(isNaturalKind(N), N)), active(cons(X1, X2)) -> cons(active(X1), X2), active(natsFrom(N)) -> mark(U281(isNatural(N), N)), active(natsFrom(X)) -> natsFrom(active(X)), active(s(X)) -> s(active(X)), active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3), active(U292(tt(), N, XS)) -> mark(U293(isLNat(XS), N, XS)), active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3), active(U291(tt(), N, XS)) -> mark(U292(isNaturalKind(N), N, XS)), active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3), active(U293(tt(), N, XS)) -> mark(U294(isLNatKind(XS), N, XS)), active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3), active(U294(tt(), N, XS)) -> mark(head(afterNth(N, XS))), active(head(X)) -> head(active(X)), active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)), active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)), active(afterNth(X1, X2)) -> afterNth(X1, active(X2)), active(afterNth(X1, X2)) -> afterNth(active(X1), X2), active(U302(X1, X2)) -> U302(active(X1), X2), active(U302(tt(), Y)) -> mark(U303(isLNat(Y), Y)), active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3), active(U301(tt(), X, Y)) -> mark(U302(isLNatKind(X), Y)), active(U303(X1, X2)) -> U303(active(X1), X2), active(U303(tt(), Y)) -> mark(U304(isLNatKind(Y), Y)), active(U304(X1, X2)) -> U304(active(X1), X2), active(U304(tt(), Y)) -> mark(Y), active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3), active(U32(tt(), N, XS)) -> mark(U33(isLNat(XS), N, XS)), active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3), active(U31(tt(), N, XS)) -> mark(U32(isNaturalKind(N), N, XS)), active(U312(X1, X2)) -> U312(active(X1), X2), active(U312(tt(), XS)) -> mark(pair(nil(), XS)), active(U311(X1, X2)) -> U311(active(X1), X2), active(U311(tt(), XS)) -> mark(U312(isLNatKind(XS), XS)), active(pair(X1, X2)) -> pair(X1, active(X2)), active(pair(X1, X2)) -> pair(active(X1), X2), active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3), active(U33(tt(), N, XS)) -> mark(U34(isLNatKind(XS), N)), active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4), active(U322(tt(), N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)), active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4), active(U321(tt(), N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)), active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4), active(U323(tt(), N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)), active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4), active(U324(tt(), N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)), active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4), active(U325(tt(), N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)), active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4), active(U326(tt(), N, X, XS)) -> mark(U327(splitAt(N, XS), X)), active(U327(X1, X2)) -> U327(active(X1), X2), active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)), active(U34(X1, X2)) -> U34(active(X1), X2), active(U34(tt(), N)) -> mark(N), active(U332(X1, X2)) -> U332(active(X1), X2), active(U332(tt(), XS)) -> mark(U333(isLNat(XS), XS)), active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3), active(U331(tt(), N, XS)) -> mark(U332(isNaturalKind(N), XS)), active(U333(X1, X2)) -> U333(active(X1), X2), active(U333(tt(), XS)) -> mark(U334(isLNatKind(XS), XS)), active(U334(X1, X2)) -> U334(active(X1), X2), active(U334(tt(), XS)) -> mark(XS), active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3), active(U342(tt(), N, XS)) -> mark(U343(isLNat(XS), N, XS)), active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3), active(U341(tt(), N, XS)) -> mark(U342(isNaturalKind(N), N, XS)), active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3), active(U343(tt(), N, XS)) -> mark(U344(isLNatKind(XS), N, XS)), active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3), active(U344(tt(), N, XS)) -> mark(fst(splitAt(N, XS))), active(fst(X)) -> fst(active(X)), active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)), active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3), active(U42(tt(), V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)), active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3), active(U41(tt(), V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)), active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3), active(U43(tt(), V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)), active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3), active(U44(tt(), V1, V2)) -> mark(U45(isNatural(V1), V2)), active(U45(X1, X2)) -> U45(active(X1), X2), active(U45(tt(), V2)) -> mark(U46(isLNat(V2))), active(U46(X)) -> U46(active(X)), active(U46(tt())) -> mark(tt()), active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3), active(U52(tt(), V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)), active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3), active(U51(tt(), V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)), active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3), active(U53(tt(), V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)), active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3), active(U54(tt(), V1, V2)) -> mark(U55(isNatural(V1), V2)), active(U55(X1, X2)) -> U55(active(X1), X2), active(U55(tt(), V2)) -> mark(U56(isLNat(V2))), active(U56(X)) -> U56(active(X)), active(U56(tt())) -> mark(tt()), active(U62(X1, X2)) -> U62(active(X1), X2), active(U62(tt(), V1)) -> mark(U63(isPLNat(V1))), active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)), active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)), active(U61(X1, X2)) -> U61(active(X1), X2), active(U61(tt(), V1)) -> mark(U62(isPLNatKind(V1), V1)), active(U63(X)) -> U63(active(X)), active(U63(tt())) -> mark(tt()), active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)), active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)), active(U72(X1, X2)) -> U72(active(X1), X2), active(U72(tt(), V1)) -> mark(U73(isNatural(V1))), active(U71(X1, X2)) -> U71(active(X1), X2), active(U71(tt(), V1)) -> mark(U72(isNaturalKind(V1), V1)), active(U73(X)) -> U73(active(X)), active(U73(tt())) -> mark(tt()), active(U82(X1, X2)) -> U82(active(X1), X2), active(U82(tt(), V1)) -> mark(U83(isPLNat(V1))), active(U81(X1, X2)) -> U81(active(X1), X2), active(U81(tt(), V1)) -> mark(U82(isPLNatKind(V1), V1)), active(U83(X)) -> U83(active(X)), active(U83(tt())) -> mark(tt()), active(U92(X1, X2)) -> U92(active(X1), X2), active(U92(tt(), V1)) -> mark(U93(isLNat(V1))), active(U91(X1, X2)) -> U91(active(X1), X2), active(U91(tt(), V1)) -> mark(U92(isLNatKind(V1), V1)), active(U93(X)) -> U93(active(X)), active(U93(tt())) -> mark(tt()), active(tail(X)) -> tail(active(X)), active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)), active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)), U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)), U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)), U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)), isLNatKind(ok(X)) -> ok(isLNatKind(X)), U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)), U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)), U105(mark(X1), X2) -> mark(U105(X1, X2)), U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)), isNatural(ok(X)) -> ok(isNatural(X)), U106(mark(X)) -> mark(U106(X)), U106(ok(X)) -> ok(U106(X)), isLNat(ok(X)) -> ok(isLNat(X)), U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)), U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)), U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)), U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)), U112(mark(X)) -> mark(U112(X)), U112(ok(X)) -> ok(U112(X)), U111(mark(X1), X2) -> mark(U111(X1, X2)), U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)), U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)), U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)), U122(mark(X)) -> mark(U122(X)), U122(ok(X)) -> ok(U122(X)), U121(mark(X1), X2) -> mark(U121(X1, X2)), U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)), U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)), U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)), U131(mark(X)) -> mark(U131(X)), U131(ok(X)) -> ok(U131(X)), snd(mark(X)) -> mark(snd(X)), snd(ok(X)) -> ok(snd(X)), splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)), splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)), splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)), U141(mark(X)) -> mark(U141(X)), U141(ok(X)) -> ok(U141(X)), U151(mark(X)) -> mark(U151(X)), U151(ok(X)) -> ok(U151(X)), U161(mark(X)) -> mark(U161(X)), U161(ok(X)) -> ok(U161(X)), U172(mark(X)) -> mark(U172(X)), U172(ok(X)) -> ok(U172(X)), U171(mark(X1), X2) -> mark(U171(X1, X2)), U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)), U182(mark(X1), X2) -> mark(U182(X1, X2)), U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)), U181(mark(X1), X2) -> mark(U181(X1, X2)), U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)), U183(mark(X)) -> mark(U183(X)), U183(ok(X)) -> ok(U183(X)), U192(mark(X1), X2) -> mark(U192(X1, X2)), U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)), U191(mark(X1), X2) -> mark(U191(X1, X2)), U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)), U193(mark(X)) -> mark(U193(X)), U193(ok(X)) -> ok(U193(X)), U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)), U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)), U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)), U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)), U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)), U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)), U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)), U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)), U205(mark(X1), X2) -> mark(U205(X1, X2)), U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)), U206(mark(X)) -> mark(U206(X)), U206(ok(X)) -> ok(U206(X)), U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)), U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)), U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)), U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)), U211(mark(X)) -> mark(U211(X)), U211(ok(X)) -> ok(U211(X)), U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)), U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)), U221(mark(X)) -> mark(U221(X)), U221(ok(X)) -> ok(U221(X)), U24(mark(X1), X2) -> mark(U24(X1, X2)), U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)), U232(mark(X)) -> mark(U232(X)), U232(ok(X)) -> ok(U232(X)), U231(mark(X1), X2) -> mark(U231(X1, X2)), U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)), U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)), U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)), U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)), U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)), U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)), U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)), U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)), U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)), U245(mark(X1), X2) -> mark(U245(X1, X2)), U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)), U246(mark(X)) -> mark(U246(X)), U246(ok(X)) -> ok(U246(X)), U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)), U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)), U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)), U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)), U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)), U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)), U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)), U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)), U255(mark(X1), X2) -> mark(U255(X1, X2)), U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)), U256(mark(X)) -> mark(U256(X)), U256(ok(X)) -> ok(U256(X)), U262(mark(X)) -> mark(U262(X)), U262(ok(X)) -> ok(U262(X)), U261(mark(X1), X2) -> mark(U261(X1, X2)), U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)), U272(mark(X)) -> mark(U272(X)), U272(ok(X)) -> ok(U272(X)), U271(mark(X1), X2) -> mark(U271(X1, X2)), U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)), U282(mark(X1), X2) -> mark(U282(X1, X2)), U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)), U281(mark(X1), X2) -> mark(U281(X1, X2)), U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), natsFrom(mark(X)) -> mark(natsFrom(X)), natsFrom(ok(X)) -> ok(natsFrom(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)), U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)), U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)), U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)), U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)), U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)), U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)), U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)), afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)), afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)), U302(mark(X1), X2) -> mark(U302(X1, X2)), U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)), U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)), U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)), U303(mark(X1), X2) -> mark(U303(X1, X2)), U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)), U304(mark(X1), X2) -> mark(U304(X1, X2)), U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)), U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)), U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)), U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)), U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)), U312(mark(X1), X2) -> mark(U312(X1, X2)), U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)), U311(mark(X1), X2) -> mark(U311(X1, X2)), U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)), pair(X1, mark(X2)) -> mark(pair(X1, X2)), pair(mark(X1), X2) -> mark(pair(X1, X2)), pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)), U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)), U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)), U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)), U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)), U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)), U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)), U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)), U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)), U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)), U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)), U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)), U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)), U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)), U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)), U327(mark(X1), X2) -> mark(U327(X1, X2)), U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)), U34(mark(X1), X2) -> mark(U34(X1, X2)), U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)), U332(mark(X1), X2) -> mark(U332(X1, X2)), U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)), U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)), U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)), U333(mark(X1), X2) -> mark(U333(X1, X2)), U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)), U334(mark(X1), X2) -> mark(U334(X1, X2)), U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)), U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)), U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)), U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)), U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)), U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)), U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)), U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)), U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)), fst(mark(X)) -> mark(fst(X)), fst(ok(X)) -> ok(fst(X)), U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)), U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)), U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)), U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)), U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)), U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)), U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)), U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)), U45(mark(X1), X2) -> mark(U45(X1, X2)), U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)), U46(mark(X)) -> mark(U46(X)), U46(ok(X)) -> ok(U46(X)), U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)), U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)), U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)), U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)), U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)), U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)), U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)), U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)), U55(mark(X1), X2) -> mark(U55(X1, X2)), U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)), U56(mark(X)) -> mark(U56(X)), U56(ok(X)) -> ok(U56(X)), U62(mark(X1), X2) -> mark(U62(X1, X2)), U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)), isPLNatKind(ok(X)) -> ok(isPLNatKind(X)), U61(mark(X1), X2) -> mark(U61(X1, X2)), U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)), U63(mark(X)) -> mark(U63(X)), U63(ok(X)) -> ok(U63(X)), isPLNat(ok(X)) -> ok(isPLNat(X)), U72(mark(X1), X2) -> mark(U72(X1, X2)), U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)), U71(mark(X1), X2) -> mark(U71(X1, X2)), U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)), U73(mark(X)) -> mark(U73(X)), U73(ok(X)) -> ok(U73(X)), U82(mark(X1), X2) -> mark(U82(X1, X2)), U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)), U81(mark(X1), X2) -> mark(U81(X1, X2)), U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)), U83(mark(X)) -> mark(U83(X)), U83(ok(X)) -> ok(U83(X)), U92(mark(X1), X2) -> mark(U92(X1, X2)), U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)), U91(mark(X1), X2) -> mark(U91(X1, X2)), U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)), U93(mark(X)) -> mark(U93(X)), U93(ok(X)) -> ok(U93(X)), tail(mark(X)) -> mark(tail(X)), tail(ok(X)) -> ok(tail(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)), proper(isNaturalKind(X)) -> isNaturalKind(proper(X)), proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)), proper(tt()) -> ok(tt()), 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(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)), proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)), proper(U112(X)) -> U112(proper(X)), proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)), proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)), proper(U122(X)) -> U122(proper(X)), proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)), 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(U172(X)) -> U172(proper(X)), proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)), proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)), proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)), proper(U183(X)) -> U183(proper(X)), proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)), proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)), proper(U193(X)) -> U193(proper(X)), proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)), proper(U201(X1, X2, X3)) -> U201(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(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)), proper(U21(X1, X2, X3)) -> U21(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(U232(X)) -> U232(proper(X)), proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)), proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)), proper(U241(X1, X2, X3)) -> U241(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(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)), proper(U251(X1, X2, X3)) -> U251(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(U262(X)) -> U262(proper(X)), proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)), proper(U272(X)) -> U272(proper(X)), proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)), proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)), proper(U281(X1, X2)) -> U281(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(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)), proper(U291(X1, X2, X3)) -> U291(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(U302(X1, X2)) -> U302(proper(X1), proper(X2)), proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)), proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)), proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)), proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)), proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)), proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)), proper(U311(X1, X2)) -> U311(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(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)), proper(U321(X1, X2, X3, X4)) -> U321(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(U332(X1, X2)) -> U332(proper(X1), proper(X2)), proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)), proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)), proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)), proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)), proper(U341(X1, X2, X3)) -> U341(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(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)), proper(U41(X1, X2, X3)) -> U41(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(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)), proper(U51(X1, X2, X3)) -> U51(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(U62(X1, X2)) -> U62(proper(X1), proper(X2)), proper(isPLNatKind(X)) -> isPLNatKind(proper(X)), proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)), proper(U63(X)) -> U63(proper(X)), proper(isPLNat(X)) -> isPLNat(proper(X)), proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)), proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)), proper(U73(X)) -> U73(proper(X)), proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)), proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)), proper(U83(X)) -> U83(proper(X)), proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)), proper(U91(X1, X2)) -> U91(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)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } Fail