WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 5677 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 15 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (7) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence U204(ok(X1), ok(X2), ok(X3)) ->^+ ok(U204(X1, X2, X3)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [X1 / ok(X1), X2 / ok(X2), X3 / ok(X3)]. The result substitution is [ ]. ---------------------------------------- (8) Complex Obligation (BEST) ---------------------------------------- (9) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (10) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (11) BOUNDS(n^1, INF) ---------------------------------------- (12) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following 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)) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(mark(x_1)) -> mark(encArg(x_1)) encArg(nil) -> nil encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_U101(x_1, x_2, x_3)) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U102(x_1, x_2, x_3)) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U103(x_1, x_2, x_3)) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U104(x_1, x_2, x_3)) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U105(x_1, x_2)) -> U105(encArg(x_1), encArg(x_2)) encArg(cons_U106(x_1)) -> U106(encArg(x_1)) encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U111(x_1, x_2)) -> U111(encArg(x_1), encArg(x_2)) encArg(cons_U112(x_1)) -> U112(encArg(x_1)) encArg(cons_U13(x_1, x_2, x_3)) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U121(x_1, x_2)) -> U121(encArg(x_1), encArg(x_2)) encArg(cons_U122(x_1)) -> U122(encArg(x_1)) encArg(cons_U14(x_1, x_2, x_3)) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U131(x_1)) -> U131(encArg(x_1)) encArg(cons_snd(x_1)) -> snd(encArg(x_1)) encArg(cons_splitAt(x_1, x_2)) -> splitAt(encArg(x_1), encArg(x_2)) encArg(cons_U141(x_1)) -> U141(encArg(x_1)) encArg(cons_U151(x_1)) -> U151(encArg(x_1)) encArg(cons_U161(x_1)) -> U161(encArg(x_1)) encArg(cons_U171(x_1, x_2)) -> U171(encArg(x_1), encArg(x_2)) encArg(cons_U172(x_1)) -> U172(encArg(x_1)) encArg(cons_U181(x_1, x_2)) -> U181(encArg(x_1), encArg(x_2)) encArg(cons_U182(x_1, x_2)) -> U182(encArg(x_1), encArg(x_2)) encArg(cons_U183(x_1)) -> U183(encArg(x_1)) encArg(cons_U191(x_1, x_2)) -> U191(encArg(x_1), encArg(x_2)) encArg(cons_U192(x_1, x_2)) -> U192(encArg(x_1), encArg(x_2)) encArg(cons_U193(x_1)) -> U193(encArg(x_1)) encArg(cons_U201(x_1, x_2, x_3)) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U202(x_1, x_2, x_3)) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U203(x_1, x_2, x_3)) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U204(x_1, x_2, x_3)) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U205(x_1, x_2)) -> U205(encArg(x_1), encArg(x_2)) encArg(cons_U206(x_1)) -> U206(encArg(x_1)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U22(x_1, x_2, x_3)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U211(x_1)) -> U211(encArg(x_1)) encArg(cons_U23(x_1, x_2, x_3)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U221(x_1)) -> U221(encArg(x_1)) encArg(cons_U24(x_1, x_2)) -> U24(encArg(x_1), encArg(x_2)) encArg(cons_U231(x_1, x_2)) -> U231(encArg(x_1), encArg(x_2)) encArg(cons_U232(x_1)) -> U232(encArg(x_1)) encArg(cons_U241(x_1, x_2, x_3)) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U242(x_1, x_2, x_3)) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U243(x_1, x_2, x_3)) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U244(x_1, x_2, x_3)) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U245(x_1, x_2)) -> U245(encArg(x_1), encArg(x_2)) encArg(cons_U246(x_1)) -> U246(encArg(x_1)) encArg(cons_U251(x_1, x_2, x_3)) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U252(x_1, x_2, x_3)) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U253(x_1, x_2, x_3)) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U254(x_1, x_2, x_3)) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U255(x_1, x_2)) -> U255(encArg(x_1), encArg(x_2)) encArg(cons_U256(x_1)) -> U256(encArg(x_1)) encArg(cons_U261(x_1, x_2)) -> U261(encArg(x_1), encArg(x_2)) encArg(cons_U262(x_1)) -> U262(encArg(x_1)) encArg(cons_U271(x_1, x_2)) -> U271(encArg(x_1), encArg(x_2)) encArg(cons_U272(x_1)) -> U272(encArg(x_1)) encArg(cons_U281(x_1, x_2)) -> U281(encArg(x_1), encArg(x_2)) encArg(cons_U282(x_1, x_2)) -> U282(encArg(x_1), encArg(x_2)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_natsFrom(x_1)) -> natsFrom(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_U291(x_1, x_2, x_3)) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U292(x_1, x_2, x_3)) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U293(x_1, x_2, x_3)) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U294(x_1, x_2, x_3)) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_afterNth(x_1, x_2)) -> afterNth(encArg(x_1), encArg(x_2)) encArg(cons_U301(x_1, x_2, x_3)) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U302(x_1, x_2)) -> U302(encArg(x_1), encArg(x_2)) encArg(cons_U303(x_1, x_2)) -> U303(encArg(x_1), encArg(x_2)) encArg(cons_U304(x_1, x_2)) -> U304(encArg(x_1), encArg(x_2)) encArg(cons_U31(x_1, x_2, x_3)) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U32(x_1, x_2, x_3)) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U311(x_1, x_2)) -> U311(encArg(x_1), encArg(x_2)) encArg(cons_U312(x_1, x_2)) -> U312(encArg(x_1), encArg(x_2)) encArg(cons_pair(x_1, x_2)) -> pair(encArg(x_1), encArg(x_2)) encArg(cons_U33(x_1, x_2, x_3)) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U321(x_1, x_2, x_3, x_4)) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U322(x_1, x_2, x_3, x_4)) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U323(x_1, x_2, x_3, x_4)) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U324(x_1, x_2, x_3, x_4)) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U325(x_1, x_2, x_3, x_4)) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U326(x_1, x_2, x_3, x_4)) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U327(x_1, x_2)) -> U327(encArg(x_1), encArg(x_2)) encArg(cons_U34(x_1, x_2)) -> U34(encArg(x_1), encArg(x_2)) encArg(cons_U331(x_1, x_2, x_3)) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U332(x_1, x_2)) -> U332(encArg(x_1), encArg(x_2)) encArg(cons_U333(x_1, x_2)) -> U333(encArg(x_1), encArg(x_2)) encArg(cons_U334(x_1, x_2)) -> U334(encArg(x_1), encArg(x_2)) encArg(cons_U341(x_1, x_2, x_3)) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U342(x_1, x_2, x_3)) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U343(x_1, x_2, x_3)) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U344(x_1, x_2, x_3)) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_fst(x_1)) -> fst(encArg(x_1)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U43(x_1, x_2, x_3)) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U44(x_1, x_2, x_3)) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U45(x_1, x_2)) -> U45(encArg(x_1), encArg(x_2)) encArg(cons_U46(x_1)) -> U46(encArg(x_1)) encArg(cons_U51(x_1, x_2, x_3)) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U52(x_1, x_2, x_3)) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U53(x_1, x_2, x_3)) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U54(x_1, x_2, x_3)) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U55(x_1, x_2)) -> U55(encArg(x_1), encArg(x_2)) encArg(cons_U56(x_1)) -> U56(encArg(x_1)) encArg(cons_U61(x_1, x_2)) -> U61(encArg(x_1), encArg(x_2)) encArg(cons_U62(x_1, x_2)) -> U62(encArg(x_1), encArg(x_2)) encArg(cons_U63(x_1)) -> U63(encArg(x_1)) encArg(cons_U71(x_1, x_2)) -> U71(encArg(x_1), encArg(x_2)) encArg(cons_U72(x_1, x_2)) -> U72(encArg(x_1), encArg(x_2)) encArg(cons_U73(x_1)) -> U73(encArg(x_1)) encArg(cons_U81(x_1, x_2)) -> U81(encArg(x_1), encArg(x_2)) encArg(cons_U82(x_1, x_2)) -> U82(encArg(x_1), encArg(x_2)) encArg(cons_U83(x_1)) -> U83(encArg(x_1)) encArg(cons_U91(x_1, x_2)) -> U91(encArg(x_1), encArg(x_2)) encArg(cons_U92(x_1, x_2)) -> U92(encArg(x_1), encArg(x_2)) encArg(cons_U93(x_1)) -> U93(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_isNaturalKind(x_1)) -> isNaturalKind(encArg(x_1)) encArg(cons_isLNatKind(x_1)) -> isLNatKind(encArg(x_1)) encArg(cons_isNatural(x_1)) -> isNatural(encArg(x_1)) encArg(cons_isLNat(x_1)) -> isLNat(encArg(x_1)) encArg(cons_isPLNatKind(x_1)) -> isPLNatKind(encArg(x_1)) encArg(cons_isPLNat(x_1)) -> isPLNat(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U101(x_1, x_2, x_3) -> U101(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U102(x_1, x_2, x_3) -> U102(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isNaturalKind(x_1) -> isNaturalKind(encArg(x_1)) encode_U103(x_1, x_2, x_3) -> U103(encArg(x_1), encArg(x_2), encArg(x_3)) encode_isLNatKind(x_1) -> isLNatKind(encArg(x_1)) encode_U104(x_1, x_2, x_3) -> U104(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U105(x_1, x_2) -> U105(encArg(x_1), encArg(x_2)) encode_isNatural(x_1) -> isNatural(encArg(x_1)) encode_U106(x_1) -> U106(encArg(x_1)) encode_isLNat(x_1) -> isLNat(encArg(x_1)) encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U111(x_1, x_2) -> U111(encArg(x_1), encArg(x_2)) encode_U112(x_1) -> U112(encArg(x_1)) encode_U13(x_1, x_2, x_3) -> U13(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U121(x_1, x_2) -> U121(encArg(x_1), encArg(x_2)) encode_U122(x_1) -> U122(encArg(x_1)) encode_U14(x_1, x_2, x_3) -> U14(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U131(x_1) -> U131(encArg(x_1)) encode_snd(x_1) -> snd(encArg(x_1)) encode_splitAt(x_1, x_2) -> splitAt(encArg(x_1), encArg(x_2)) encode_U141(x_1) -> U141(encArg(x_1)) encode_U151(x_1) -> U151(encArg(x_1)) encode_U161(x_1) -> U161(encArg(x_1)) encode_U171(x_1, x_2) -> U171(encArg(x_1), encArg(x_2)) encode_U172(x_1) -> U172(encArg(x_1)) encode_U181(x_1, x_2) -> U181(encArg(x_1), encArg(x_2)) encode_U182(x_1, x_2) -> U182(encArg(x_1), encArg(x_2)) encode_U183(x_1) -> U183(encArg(x_1)) encode_U191(x_1, x_2) -> U191(encArg(x_1), encArg(x_2)) encode_U192(x_1, x_2) -> U192(encArg(x_1), encArg(x_2)) encode_U193(x_1) -> U193(encArg(x_1)) encode_U201(x_1, x_2, x_3) -> U201(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U202(x_1, x_2, x_3) -> U202(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U203(x_1, x_2, x_3) -> U203(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U204(x_1, x_2, x_3) -> U204(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U205(x_1, x_2) -> U205(encArg(x_1), encArg(x_2)) encode_U206(x_1) -> U206(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U22(x_1, x_2, x_3) -> U22(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U211(x_1) -> U211(encArg(x_1)) encode_U23(x_1, x_2, x_3) -> U23(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U221(x_1) -> U221(encArg(x_1)) encode_U24(x_1, x_2) -> U24(encArg(x_1), encArg(x_2)) encode_U231(x_1, x_2) -> U231(encArg(x_1), encArg(x_2)) encode_U232(x_1) -> U232(encArg(x_1)) encode_U241(x_1, x_2, x_3) -> U241(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U242(x_1, x_2, x_3) -> U242(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U243(x_1, x_2, x_3) -> U243(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U244(x_1, x_2, x_3) -> U244(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U245(x_1, x_2) -> U245(encArg(x_1), encArg(x_2)) encode_U246(x_1) -> U246(encArg(x_1)) encode_U251(x_1, x_2, x_3) -> U251(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U252(x_1, x_2, x_3) -> U252(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U253(x_1, x_2, x_3) -> U253(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U254(x_1, x_2, x_3) -> U254(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U255(x_1, x_2) -> U255(encArg(x_1), encArg(x_2)) encode_U256(x_1) -> U256(encArg(x_1)) encode_U261(x_1, x_2) -> U261(encArg(x_1), encArg(x_2)) encode_U262(x_1) -> U262(encArg(x_1)) encode_U271(x_1, x_2) -> U271(encArg(x_1), encArg(x_2)) encode_U272(x_1) -> U272(encArg(x_1)) encode_U281(x_1, x_2) -> U281(encArg(x_1), encArg(x_2)) encode_U282(x_1, x_2) -> U282(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_natsFrom(x_1) -> natsFrom(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_U291(x_1, x_2, x_3) -> U291(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U292(x_1, x_2, x_3) -> U292(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U293(x_1, x_2, x_3) -> U293(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U294(x_1, x_2, x_3) -> U294(encArg(x_1), encArg(x_2), encArg(x_3)) encode_head(x_1) -> head(encArg(x_1)) encode_afterNth(x_1, x_2) -> afterNth(encArg(x_1), encArg(x_2)) encode_U301(x_1, x_2, x_3) -> U301(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U302(x_1, x_2) -> U302(encArg(x_1), encArg(x_2)) encode_U303(x_1, x_2) -> U303(encArg(x_1), encArg(x_2)) encode_U304(x_1, x_2) -> U304(encArg(x_1), encArg(x_2)) encode_U31(x_1, x_2, x_3) -> U31(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U32(x_1, x_2, x_3) -> U32(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U311(x_1, x_2) -> U311(encArg(x_1), encArg(x_2)) encode_U312(x_1, x_2) -> U312(encArg(x_1), encArg(x_2)) encode_pair(x_1, x_2) -> pair(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_U33(x_1, x_2, x_3) -> U33(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U321(x_1, x_2, x_3, x_4) -> U321(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U322(x_1, x_2, x_3, x_4) -> U322(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U323(x_1, x_2, x_3, x_4) -> U323(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U324(x_1, x_2, x_3, x_4) -> U324(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U325(x_1, x_2, x_3, x_4) -> U325(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U326(x_1, x_2, x_3, x_4) -> U326(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U327(x_1, x_2) -> U327(encArg(x_1), encArg(x_2)) encode_U34(x_1, x_2) -> U34(encArg(x_1), encArg(x_2)) encode_U331(x_1, x_2, x_3) -> U331(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U332(x_1, x_2) -> U332(encArg(x_1), encArg(x_2)) encode_U333(x_1, x_2) -> U333(encArg(x_1), encArg(x_2)) encode_U334(x_1, x_2) -> U334(encArg(x_1), encArg(x_2)) encode_U341(x_1, x_2, x_3) -> U341(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U342(x_1, x_2, x_3) -> U342(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U343(x_1, x_2, x_3) -> U343(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U344(x_1, x_2, x_3) -> U344(encArg(x_1), encArg(x_2), encArg(x_3)) encode_fst(x_1) -> fst(encArg(x_1)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U43(x_1, x_2, x_3) -> U43(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U44(x_1, x_2, x_3) -> U44(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U45(x_1, x_2) -> U45(encArg(x_1), encArg(x_2)) encode_U46(x_1) -> U46(encArg(x_1)) encode_U51(x_1, x_2, x_3) -> U51(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U52(x_1, x_2, x_3) -> U52(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U53(x_1, x_2, x_3) -> U53(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U54(x_1, x_2, x_3) -> U54(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U55(x_1, x_2) -> U55(encArg(x_1), encArg(x_2)) encode_U56(x_1) -> U56(encArg(x_1)) encode_U61(x_1, x_2) -> U61(encArg(x_1), encArg(x_2)) encode_U62(x_1, x_2) -> U62(encArg(x_1), encArg(x_2)) encode_isPLNatKind(x_1) -> isPLNatKind(encArg(x_1)) encode_U63(x_1) -> U63(encArg(x_1)) encode_isPLNat(x_1) -> isPLNat(encArg(x_1)) encode_U71(x_1, x_2) -> U71(encArg(x_1), encArg(x_2)) encode_U72(x_1, x_2) -> U72(encArg(x_1), encArg(x_2)) encode_U73(x_1) -> U73(encArg(x_1)) encode_U81(x_1, x_2) -> U81(encArg(x_1), encArg(x_2)) encode_U82(x_1, x_2) -> U82(encArg(x_1), encArg(x_2)) encode_U83(x_1) -> U83(encArg(x_1)) encode_U91(x_1, x_2) -> U91(encArg(x_1), encArg(x_2)) encode_U92(x_1, x_2) -> U92(encArg(x_1), encArg(x_2)) encode_U93(x_1) -> U93(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) Rewrite Strategy: INNERMOST