MAYBE MAYBE TRS: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3)), mark(isNatKind(X)) -> active(isNatKind(X)), mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3)), mark(tt()) -> active(tt()), mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3)), mark(isNatIListKind(X)) -> active(isNatIListKind(X)), mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3)), mark(U105(X1, X2)) -> active(U105(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(U106(X)) -> active(U106(mark(X))), mark(isNatIList(X)) -> active(isNatIList(X)), mark(U12(X1, X2)) -> active(U12(mark(X1), X2)), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(U112(X1, X2, X3)) -> active(U112(mark(X1), X2, X3)), mark(U111(X1, X2, X3)) -> active(U111(mark(X1), X2, X3)), mark(U113(X1, X2, X3)) -> active(U113(mark(X1), X2, X3)), mark(U114(X1, X2)) -> active(U114(mark(X1), X2)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U13(X)) -> active(U13(mark(X))), mark(isNatList(X)) -> active(isNatList(X)), mark(U122(X)) -> active(U122(mark(X))), mark(U121(X1, X2)) -> active(U121(mark(X1), X2)), mark(nil()) -> active(nil()), mark(U132(X1, X2, X3, X4)) -> active(U132(mark(X1), X2, X3, X4)), mark(U131(X1, X2, X3, X4)) -> active(U131(mark(X1), X2, X3, X4)), mark(U133(X1, X2, X3, X4)) -> active(U133(mark(X1), X2, X3, X4)), mark(U134(X1, X2, X3, X4)) -> active(U134(mark(X1), X2, X3, X4)), mark(U135(X1, X2, X3, X4)) -> active(U135(mark(X1), X2, X3, X4)), mark(U136(X1, X2, X3, X4)) -> active(U136(mark(X1), X2, X3, X4)), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(U22(X1, X2)) -> active(U22(mark(X1), X2)), mark(U21(X1, X2)) -> active(U21(mark(X1), X2)), mark(U23(X)) -> active(U23(mark(X))), mark(U32(X1, X2)) -> active(U32(mark(X1), X2)), mark(U31(X1, X2)) -> active(U31(mark(X1), X2)), mark(U33(X)) -> active(U33(mark(X))), mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)), mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)), mark(U43(X1, X2, X3)) -> active(U43(mark(X1), X2, X3)), mark(U44(X1, X2, X3)) -> active(U44(mark(X1), X2, X3)), mark(U45(X1, X2)) -> active(U45(mark(X1), X2)), mark(U46(X)) -> active(U46(mark(X))), mark(U52(X)) -> active(U52(mark(X))), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X)) -> active(U62(mark(X))), mark(U61(X1, X2)) -> active(U61(mark(X1), X2)), mark(U71(X)) -> active(U71(mark(X))), mark(U81(X)) -> active(U81(mark(X))), mark(U92(X1, X2, X3)) -> active(U92(mark(X1), X2, X3)), mark(U91(X1, X2, X3)) -> active(U91(mark(X1), X2, X3)), mark(U93(X1, X2, X3)) -> active(U93(mark(X1), X2, X3)), mark(U94(X1, X2, X3)) -> active(U94(mark(X1), X2, X3)), mark(U95(X1, X2)) -> active(U95(mark(X1), X2)), mark(U96(X)) -> active(U96(mark(X))), cons(X1, mark(X2)) -> cons(X1, X2), cons(X1, active(X2)) -> cons(X1, X2), cons(mark(X1), X2) -> cons(X1, X2), cons(active(X1), X2) -> cons(X1, X2), active(zeros()) -> mark(cons(0(), zeros())), active(U102(tt(), V1, V2)) -> mark(U103(isNatIListKind(V2), V1, V2)), active(isNatKind(0())) -> mark(tt()), active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1))), active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1))), active(U101(tt(), V1, V2)) -> mark(U102(isNatKind(V1), V1, V2)), active(U103(tt(), V1, V2)) -> mark(U104(isNatIListKind(V2), V1, V2)), active(isNatIListKind(cons(V1, V2))) -> mark(U51(isNatKind(V1), V2)), active(isNatIListKind(zeros())) -> mark(tt()), active(isNatIListKind(nil())) -> mark(tt()), active(isNatIListKind(take(V1, V2))) -> mark(U61(isNatKind(V1), V2)), active(U104(tt(), V1, V2)) -> mark(U105(isNat(V1), V2)), active(U105(tt(), V2)) -> mark(U106(isNatIList(V2))), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)), active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)), active(U106(tt())) -> mark(tt()), active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)), active(isNatIList(cons(V1, V2))) -> mark(U41(isNatKind(V1), V1, V2)), active(isNatIList(zeros())) -> mark(tt()), active(U12(tt(), V1)) -> mark(U13(isNatList(V1))), active(U11(tt(), V1)) -> mark(U12(isNatIListKind(V1), V1)), active(U112(tt(), L, N)) -> mark(U113(isNat(N), L, N)), active(U111(tt(), L, N)) -> mark(U112(isNatIListKind(L), L, N)), active(U113(tt(), L, N)) -> mark(U114(isNatKind(N), L)), active(U114(tt(), L)) -> mark(s(length(L))), active(length(cons(N, L))) -> mark(U111(isNatList(L), L, N)), active(length(nil())) -> mark(0()), active(U13(tt())) -> mark(tt()), active(isNatList(cons(V1, V2))) -> mark(U91(isNatKind(V1), V1, V2)), active(isNatList(nil())) -> mark(tt()), active(isNatList(take(V1, V2))) -> mark(U101(isNatKind(V1), V1, V2)), active(U122(tt())) -> mark(nil()), active(U121(tt(), IL)) -> mark(U122(isNatIListKind(IL))), active(U132(tt(), IL, M, N)) -> mark(U133(isNat(M), IL, M, N)), active(U131(tt(), IL, M, N)) -> mark(U132(isNatIListKind(IL), IL, M, N)), active(U133(tt(), IL, M, N)) -> mark(U134(isNatKind(M), IL, M, N)), active(U134(tt(), IL, M, N)) -> mark(U135(isNat(N), IL, M, N)), active(U135(tt(), IL, M, N)) -> mark(U136(isNatKind(N), IL, M, N)), active(U136(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(take(0(), IL)) -> mark(U121(isNatIList(IL), IL)), active(take(s(M), cons(N, IL))) -> mark(U131(isNatIList(IL), IL, M, N)), active(U22(tt(), V1)) -> mark(U23(isNat(V1))), active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)), active(U23(tt())) -> mark(tt()), active(U32(tt(), V)) -> mark(U33(isNatList(V))), active(U31(tt(), V)) -> mark(U32(isNatIListKind(V), V)), active(U33(tt())) -> mark(tt()), active(U42(tt(), V1, V2)) -> mark(U43(isNatIListKind(V2), V1, V2)), active(U41(tt(), V1, V2)) -> mark(U42(isNatKind(V1), V1, V2)), active(U43(tt(), V1, V2)) -> mark(U44(isNatIListKind(V2), V1, V2)), active(U44(tt(), V1, V2)) -> mark(U45(isNat(V1), V2)), active(U45(tt(), V2)) -> mark(U46(isNatIList(V2))), active(U46(tt())) -> mark(tt()), active(U52(tt())) -> mark(tt()), active(U51(tt(), V2)) -> mark(U52(isNatIListKind(V2))), active(U62(tt())) -> mark(tt()), active(U61(tt(), V2)) -> mark(U62(isNatIListKind(V2))), active(U71(tt())) -> mark(tt()), active(U81(tt())) -> mark(tt()), active(U92(tt(), V1, V2)) -> mark(U93(isNatIListKind(V2), V1, V2)), active(U91(tt(), V1, V2)) -> mark(U92(isNatKind(V1), V1, V2)), active(U93(tt(), V1, V2)) -> mark(U94(isNatIListKind(V2), V1, V2)), active(U94(tt(), V1, V2)) -> mark(U95(isNat(V1), V2)), active(U95(tt(), V2)) -> mark(U96(isNatList(V2))), active(U96(tt())) -> mark(tt()), U102(X1, X2, mark(X3)) -> U102(X1, X2, X3), U102(X1, X2, active(X3)) -> U102(X1, X2, X3), U102(X1, mark(X2), X3) -> U102(X1, X2, X3), U102(X1, active(X2), X3) -> U102(X1, X2, X3), U102(mark(X1), X2, X3) -> U102(X1, X2, X3), U102(active(X1), X2, X3) -> U102(X1, X2, X3), isNatKind(mark(X)) -> isNatKind(X), isNatKind(active(X)) -> isNatKind(X), U101(X1, X2, mark(X3)) -> U101(X1, X2, X3), U101(X1, X2, active(X3)) -> U101(X1, X2, X3), U101(X1, mark(X2), X3) -> U101(X1, X2, X3), U101(X1, active(X2), X3) -> U101(X1, X2, X3), U101(mark(X1), X2, X3) -> U101(X1, X2, X3), U101(active(X1), X2, X3) -> U101(X1, X2, X3), U103(X1, X2, mark(X3)) -> U103(X1, X2, X3), U103(X1, X2, active(X3)) -> U103(X1, X2, X3), U103(X1, mark(X2), X3) -> U103(X1, X2, X3), U103(X1, active(X2), X3) -> U103(X1, X2, X3), U103(mark(X1), X2, X3) -> U103(X1, X2, X3), U103(active(X1), X2, X3) -> U103(X1, X2, X3), isNatIListKind(mark(X)) -> isNatIListKind(X), isNatIListKind(active(X)) -> isNatIListKind(X), U104(X1, X2, mark(X3)) -> U104(X1, X2, X3), U104(X1, X2, active(X3)) -> U104(X1, X2, X3), U104(X1, mark(X2), X3) -> U104(X1, X2, X3), U104(X1, active(X2), X3) -> U104(X1, X2, X3), U104(mark(X1), X2, X3) -> U104(X1, X2, X3), U104(active(X1), X2, X3) -> U104(X1, X2, X3), U105(X1, mark(X2)) -> U105(X1, X2), U105(X1, active(X2)) -> U105(X1, X2), U105(mark(X1), X2) -> U105(X1, X2), U105(active(X1), X2) -> U105(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U106(mark(X)) -> U106(X), U106(active(X)) -> U106(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(X), U12(X1, mark(X2)) -> U12(X1, X2), U12(X1, active(X2)) -> U12(X1, X2), U12(mark(X1), X2) -> U12(X1, X2), U12(active(X1), X2) -> U12(X1, X2), U11(X1, mark(X2)) -> U11(X1, X2), U11(X1, active(X2)) -> U11(X1, X2), U11(mark(X1), X2) -> U11(X1, X2), U11(active(X1), X2) -> U11(X1, X2), U112(X1, X2, mark(X3)) -> U112(X1, X2, X3), U112(X1, X2, active(X3)) -> U112(X1, X2, X3), U112(X1, mark(X2), X3) -> U112(X1, X2, X3), U112(X1, active(X2), X3) -> U112(X1, X2, X3), U112(mark(X1), X2, X3) -> U112(X1, X2, X3), U112(active(X1), X2, X3) -> U112(X1, X2, X3), U111(X1, X2, mark(X3)) -> U111(X1, X2, X3), U111(X1, X2, active(X3)) -> U111(X1, X2, X3), U111(X1, mark(X2), X3) -> U111(X1, X2, X3), U111(X1, active(X2), X3) -> U111(X1, X2, X3), U111(mark(X1), X2, X3) -> U111(X1, X2, X3), U111(active(X1), X2, X3) -> U111(X1, X2, X3), U113(X1, X2, mark(X3)) -> U113(X1, X2, X3), U113(X1, X2, active(X3)) -> U113(X1, X2, X3), U113(X1, mark(X2), X3) -> U113(X1, X2, X3), U113(X1, active(X2), X3) -> U113(X1, X2, X3), U113(mark(X1), X2, X3) -> U113(X1, X2, X3), U113(active(X1), X2, X3) -> U113(X1, X2, X3), U114(X1, mark(X2)) -> U114(X1, X2), U114(X1, active(X2)) -> U114(X1, X2), U114(mark(X1), X2) -> U114(X1, X2), U114(active(X1), X2) -> U114(X1, X2), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), U13(mark(X)) -> U13(X), U13(active(X)) -> U13(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), U122(mark(X)) -> U122(X), U122(active(X)) -> U122(X), U121(X1, mark(X2)) -> U121(X1, X2), U121(X1, active(X2)) -> U121(X1, X2), U121(mark(X1), X2) -> U121(X1, X2), U121(active(X1), X2) -> U121(X1, X2), U132(X1, X2, X3, mark(X4)) -> U132(X1, X2, X3, X4), U132(X1, X2, X3, active(X4)) -> U132(X1, X2, X3, X4), U132(X1, X2, mark(X3), X4) -> U132(X1, X2, X3, X4), U132(X1, X2, active(X3), X4) -> U132(X1, X2, X3, X4), U132(X1, mark(X2), X3, X4) -> U132(X1, X2, X3, X4), U132(X1, active(X2), X3, X4) -> U132(X1, X2, X3, X4), U132(mark(X1), X2, X3, X4) -> U132(X1, X2, X3, X4), U132(active(X1), X2, X3, X4) -> U132(X1, X2, X3, X4), U131(X1, X2, X3, mark(X4)) -> U131(X1, X2, X3, X4), U131(X1, X2, X3, active(X4)) -> U131(X1, X2, X3, X4), U131(X1, X2, mark(X3), X4) -> U131(X1, X2, X3, X4), U131(X1, X2, active(X3), X4) -> U131(X1, X2, X3, X4), U131(X1, mark(X2), X3, X4) -> U131(X1, X2, X3, X4), U131(X1, active(X2), X3, X4) -> U131(X1, X2, X3, X4), U131(mark(X1), X2, X3, X4) -> U131(X1, X2, X3, X4), U131(active(X1), X2, X3, X4) -> U131(X1, X2, X3, X4), U133(X1, X2, X3, mark(X4)) -> U133(X1, X2, X3, X4), U133(X1, X2, X3, active(X4)) -> U133(X1, X2, X3, X4), U133(X1, X2, mark(X3), X4) -> U133(X1, X2, X3, X4), U133(X1, X2, active(X3), X4) -> U133(X1, X2, X3, X4), U133(X1, mark(X2), X3, X4) -> U133(X1, X2, X3, X4), U133(X1, active(X2), X3, X4) -> U133(X1, X2, X3, X4), U133(mark(X1), X2, X3, X4) -> U133(X1, X2, X3, X4), U133(active(X1), X2, X3, X4) -> U133(X1, X2, X3, X4), U134(X1, X2, X3, mark(X4)) -> U134(X1, X2, X3, X4), U134(X1, X2, X3, active(X4)) -> U134(X1, X2, X3, X4), U134(X1, X2, mark(X3), X4) -> U134(X1, X2, X3, X4), U134(X1, X2, active(X3), X4) -> U134(X1, X2, X3, X4), U134(X1, mark(X2), X3, X4) -> U134(X1, X2, X3, X4), U134(X1, active(X2), X3, X4) -> U134(X1, X2, X3, X4), U134(mark(X1), X2, X3, X4) -> U134(X1, X2, X3, X4), U134(active(X1), X2, X3, X4) -> U134(X1, X2, X3, X4), U135(X1, X2, X3, mark(X4)) -> U135(X1, X2, X3, X4), U135(X1, X2, X3, active(X4)) -> U135(X1, X2, X3, X4), U135(X1, X2, mark(X3), X4) -> U135(X1, X2, X3, X4), U135(X1, X2, active(X3), X4) -> U135(X1, X2, X3, X4), U135(X1, mark(X2), X3, X4) -> U135(X1, X2, X3, X4), U135(X1, active(X2), X3, X4) -> U135(X1, X2, X3, X4), U135(mark(X1), X2, X3, X4) -> U135(X1, X2, X3, X4), U135(active(X1), X2, X3, X4) -> U135(X1, X2, X3, X4), U136(X1, X2, X3, mark(X4)) -> U136(X1, X2, X3, X4), U136(X1, X2, X3, active(X4)) -> U136(X1, X2, X3, X4), U136(X1, X2, mark(X3), X4) -> U136(X1, X2, X3, X4), U136(X1, X2, active(X3), X4) -> U136(X1, X2, X3, X4), U136(X1, mark(X2), X3, X4) -> U136(X1, X2, X3, X4), U136(X1, active(X2), X3, X4) -> U136(X1, X2, X3, X4), U136(mark(X1), X2, X3, X4) -> U136(X1, X2, X3, X4), U136(active(X1), X2, X3, X4) -> U136(X1, X2, X3, X4), take(X1, mark(X2)) -> take(X1, X2), take(X1, active(X2)) -> take(X1, X2), take(mark(X1), X2) -> take(X1, X2), take(active(X1), X2) -> take(X1, X2), U22(X1, mark(X2)) -> U22(X1, X2), U22(X1, active(X2)) -> U22(X1, X2), U22(mark(X1), X2) -> U22(X1, X2), U22(active(X1), X2) -> U22(X1, X2), U21(X1, mark(X2)) -> U21(X1, X2), U21(X1, active(X2)) -> U21(X1, X2), U21(mark(X1), X2) -> U21(X1, X2), U21(active(X1), X2) -> U21(X1, X2), U23(mark(X)) -> U23(X), U23(active(X)) -> U23(X), U32(X1, mark(X2)) -> U32(X1, X2), U32(X1, active(X2)) -> U32(X1, X2), U32(mark(X1), X2) -> U32(X1, X2), U32(active(X1), X2) -> U32(X1, X2), U31(X1, mark(X2)) -> U31(X1, X2), U31(X1, active(X2)) -> U31(X1, X2), U31(mark(X1), X2) -> U31(X1, X2), U31(active(X1), X2) -> U31(X1, X2), U33(mark(X)) -> U33(X), U33(active(X)) -> U33(X), U42(X1, X2, mark(X3)) -> U42(X1, X2, X3), U42(X1, X2, active(X3)) -> U42(X1, X2, X3), U42(X1, mark(X2), X3) -> U42(X1, X2, X3), U42(X1, active(X2), X3) -> U42(X1, X2, X3), U42(mark(X1), X2, X3) -> U42(X1, X2, X3), U42(active(X1), X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark(X3)) -> U41(X1, X2, X3), U41(X1, X2, active(X3)) -> U41(X1, X2, X3), U41(X1, mark(X2), X3) -> U41(X1, X2, X3), U41(X1, active(X2), X3) -> U41(X1, X2, X3), U41(mark(X1), X2, X3) -> U41(X1, X2, X3), U41(active(X1), X2, X3) -> U41(X1, X2, X3), U43(X1, X2, mark(X3)) -> U43(X1, X2, X3), U43(X1, X2, active(X3)) -> U43(X1, X2, X3), U43(X1, mark(X2), X3) -> U43(X1, X2, X3), U43(X1, active(X2), X3) -> U43(X1, X2, X3), U43(mark(X1), X2, X3) -> U43(X1, X2, X3), U43(active(X1), X2, X3) -> U43(X1, X2, X3), U44(X1, X2, mark(X3)) -> U44(X1, X2, X3), U44(X1, X2, active(X3)) -> U44(X1, X2, X3), U44(X1, mark(X2), X3) -> U44(X1, X2, X3), U44(X1, active(X2), X3) -> U44(X1, X2, X3), U44(mark(X1), X2, X3) -> U44(X1, X2, X3), U44(active(X1), X2, X3) -> U44(X1, X2, X3), U45(X1, mark(X2)) -> U45(X1, X2), U45(X1, active(X2)) -> U45(X1, X2), U45(mark(X1), X2) -> U45(X1, X2), U45(active(X1), X2) -> U45(X1, X2), U46(mark(X)) -> U46(X), U46(active(X)) -> U46(X), U52(mark(X)) -> U52(X), U52(active(X)) -> U52(X), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(mark(X)) -> U62(X), U62(active(X)) -> U62(X), U61(X1, mark(X2)) -> U61(X1, X2), U61(X1, active(X2)) -> U61(X1, X2), U61(mark(X1), X2) -> U61(X1, X2), U61(active(X1), X2) -> U61(X1, X2), U71(mark(X)) -> U71(X), U71(active(X)) -> U71(X), U81(mark(X)) -> U81(X), U81(active(X)) -> U81(X), U92(X1, X2, mark(X3)) -> U92(X1, X2, X3), U92(X1, X2, active(X3)) -> U92(X1, X2, X3), U92(X1, mark(X2), X3) -> U92(X1, X2, X3), U92(X1, active(X2), X3) -> U92(X1, X2, X3), U92(mark(X1), X2, X3) -> U92(X1, X2, X3), U92(active(X1), X2, X3) -> U92(X1, X2, X3), U91(X1, X2, mark(X3)) -> U91(X1, X2, X3), U91(X1, X2, active(X3)) -> U91(X1, X2, X3), U91(X1, mark(X2), X3) -> U91(X1, X2, X3), U91(X1, active(X2), X3) -> U91(X1, X2, X3), U91(mark(X1), X2, X3) -> U91(X1, X2, X3), U91(active(X1), X2, X3) -> U91(X1, X2, X3), U93(X1, X2, mark(X3)) -> U93(X1, X2, X3), U93(X1, X2, active(X3)) -> U93(X1, X2, X3), U93(X1, mark(X2), X3) -> U93(X1, X2, X3), U93(X1, active(X2), X3) -> U93(X1, X2, X3), U93(mark(X1), X2, X3) -> U93(X1, X2, X3), U93(active(X1), X2, X3) -> U93(X1, X2, X3), U94(X1, X2, mark(X3)) -> U94(X1, X2, X3), U94(X1, X2, active(X3)) -> U94(X1, X2, X3), U94(X1, mark(X2), X3) -> U94(X1, X2, X3), U94(X1, active(X2), X3) -> U94(X1, X2, X3), U94(mark(X1), X2, X3) -> U94(X1, X2, X3), U94(active(X1), X2, X3) -> U94(X1, X2, X3), U95(X1, mark(X2)) -> U95(X1, X2), U95(X1, active(X2)) -> U95(X1, X2), U95(mark(X1), X2) -> U95(X1, X2), U95(active(X1), X2) -> U95(X1, X2), U96(mark(X)) -> U96(X), U96(active(X)) -> U96(X) } DUP: We consider a duplicating system. Trs: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(U102(X1, X2, X3)) -> active(U102(mark(X1), X2, X3)), mark(isNatKind(X)) -> active(isNatKind(X)), mark(U101(X1, X2, X3)) -> active(U101(mark(X1), X2, X3)), mark(tt()) -> active(tt()), mark(U103(X1, X2, X3)) -> active(U103(mark(X1), X2, X3)), mark(isNatIListKind(X)) -> active(isNatIListKind(X)), mark(U104(X1, X2, X3)) -> active(U104(mark(X1), X2, X3)), mark(U105(X1, X2)) -> active(U105(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(U106(X)) -> active(U106(mark(X))), mark(isNatIList(X)) -> active(isNatIList(X)), mark(U12(X1, X2)) -> active(U12(mark(X1), X2)), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(U112(X1, X2, X3)) -> active(U112(mark(X1), X2, X3)), mark(U111(X1, X2, X3)) -> active(U111(mark(X1), X2, X3)), mark(U113(X1, X2, X3)) -> active(U113(mark(X1), X2, X3)), mark(U114(X1, X2)) -> active(U114(mark(X1), X2)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U13(X)) -> active(U13(mark(X))), mark(isNatList(X)) -> active(isNatList(X)), mark(U122(X)) -> active(U122(mark(X))), mark(U121(X1, X2)) -> active(U121(mark(X1), X2)), mark(nil()) -> active(nil()), mark(U132(X1, X2, X3, X4)) -> active(U132(mark(X1), X2, X3, X4)), mark(U131(X1, X2, X3, X4)) -> active(U131(mark(X1), X2, X3, X4)), mark(U133(X1, X2, X3, X4)) -> active(U133(mark(X1), X2, X3, X4)), mark(U134(X1, X2, X3, X4)) -> active(U134(mark(X1), X2, X3, X4)), mark(U135(X1, X2, X3, X4)) -> active(U135(mark(X1), X2, X3, X4)), mark(U136(X1, X2, X3, X4)) -> active(U136(mark(X1), X2, X3, X4)), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(U22(X1, X2)) -> active(U22(mark(X1), X2)), mark(U21(X1, X2)) -> active(U21(mark(X1), X2)), mark(U23(X)) -> active(U23(mark(X))), mark(U32(X1, X2)) -> active(U32(mark(X1), X2)), mark(U31(X1, X2)) -> active(U31(mark(X1), X2)), mark(U33(X)) -> active(U33(mark(X))), mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)), mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)), mark(U43(X1, X2, X3)) -> active(U43(mark(X1), X2, X3)), mark(U44(X1, X2, X3)) -> active(U44(mark(X1), X2, X3)), mark(U45(X1, X2)) -> active(U45(mark(X1), X2)), mark(U46(X)) -> active(U46(mark(X))), mark(U52(X)) -> active(U52(mark(X))), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X)) -> active(U62(mark(X))), mark(U61(X1, X2)) -> active(U61(mark(X1), X2)), mark(U71(X)) -> active(U71(mark(X))), mark(U81(X)) -> active(U81(mark(X))), mark(U92(X1, X2, X3)) -> active(U92(mark(X1), X2, X3)), mark(U91(X1, X2, X3)) -> active(U91(mark(X1), X2, X3)), mark(U93(X1, X2, X3)) -> active(U93(mark(X1), X2, X3)), mark(U94(X1, X2, X3)) -> active(U94(mark(X1), X2, X3)), mark(U95(X1, X2)) -> active(U95(mark(X1), X2)), mark(U96(X)) -> active(U96(mark(X))), cons(X1, mark(X2)) -> cons(X1, X2), cons(X1, active(X2)) -> cons(X1, X2), cons(mark(X1), X2) -> cons(X1, X2), cons(active(X1), X2) -> cons(X1, X2), active(zeros()) -> mark(cons(0(), zeros())), active(U102(tt(), V1, V2)) -> mark(U103(isNatIListKind(V2), V1, V2)), active(isNatKind(0())) -> mark(tt()), active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1))), active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1))), active(U101(tt(), V1, V2)) -> mark(U102(isNatKind(V1), V1, V2)), active(U103(tt(), V1, V2)) -> mark(U104(isNatIListKind(V2), V1, V2)), active(isNatIListKind(cons(V1, V2))) -> mark(U51(isNatKind(V1), V2)), active(isNatIListKind(zeros())) -> mark(tt()), active(isNatIListKind(nil())) -> mark(tt()), active(isNatIListKind(take(V1, V2))) -> mark(U61(isNatKind(V1), V2)), active(U104(tt(), V1, V2)) -> mark(U105(isNat(V1), V2)), active(U105(tt(), V2)) -> mark(U106(isNatIList(V2))), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)), active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)), active(U106(tt())) -> mark(tt()), active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)), active(isNatIList(cons(V1, V2))) -> mark(U41(isNatKind(V1), V1, V2)), active(isNatIList(zeros())) -> mark(tt()), active(U12(tt(), V1)) -> mark(U13(isNatList(V1))), active(U11(tt(), V1)) -> mark(U12(isNatIListKind(V1), V1)), active(U112(tt(), L, N)) -> mark(U113(isNat(N), L, N)), active(U111(tt(), L, N)) -> mark(U112(isNatIListKind(L), L, N)), active(U113(tt(), L, N)) -> mark(U114(isNatKind(N), L)), active(U114(tt(), L)) -> mark(s(length(L))), active(length(cons(N, L))) -> mark(U111(isNatList(L), L, N)), active(length(nil())) -> mark(0()), active(U13(tt())) -> mark(tt()), active(isNatList(cons(V1, V2))) -> mark(U91(isNatKind(V1), V1, V2)), active(isNatList(nil())) -> mark(tt()), active(isNatList(take(V1, V2))) -> mark(U101(isNatKind(V1), V1, V2)), active(U122(tt())) -> mark(nil()), active(U121(tt(), IL)) -> mark(U122(isNatIListKind(IL))), active(U132(tt(), IL, M, N)) -> mark(U133(isNat(M), IL, M, N)), active(U131(tt(), IL, M, N)) -> mark(U132(isNatIListKind(IL), IL, M, N)), active(U133(tt(), IL, M, N)) -> mark(U134(isNatKind(M), IL, M, N)), active(U134(tt(), IL, M, N)) -> mark(U135(isNat(N), IL, M, N)), active(U135(tt(), IL, M, N)) -> mark(U136(isNatKind(N), IL, M, N)), active(U136(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(take(0(), IL)) -> mark(U121(isNatIList(IL), IL)), active(take(s(M), cons(N, IL))) -> mark(U131(isNatIList(IL), IL, M, N)), active(U22(tt(), V1)) -> mark(U23(isNat(V1))), active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)), active(U23(tt())) -> mark(tt()), active(U32(tt(), V)) -> mark(U33(isNatList(V))), active(U31(tt(), V)) -> mark(U32(isNatIListKind(V), V)), active(U33(tt())) -> mark(tt()), active(U42(tt(), V1, V2)) -> mark(U43(isNatIListKind(V2), V1, V2)), active(U41(tt(), V1, V2)) -> mark(U42(isNatKind(V1), V1, V2)), active(U43(tt(), V1, V2)) -> mark(U44(isNatIListKind(V2), V1, V2)), active(U44(tt(), V1, V2)) -> mark(U45(isNat(V1), V2)), active(U45(tt(), V2)) -> mark(U46(isNatIList(V2))), active(U46(tt())) -> mark(tt()), active(U52(tt())) -> mark(tt()), active(U51(tt(), V2)) -> mark(U52(isNatIListKind(V2))), active(U62(tt())) -> mark(tt()), active(U61(tt(), V2)) -> mark(U62(isNatIListKind(V2))), active(U71(tt())) -> mark(tt()), active(U81(tt())) -> mark(tt()), active(U92(tt(), V1, V2)) -> mark(U93(isNatIListKind(V2), V1, V2)), active(U91(tt(), V1, V2)) -> mark(U92(isNatKind(V1), V1, V2)), active(U93(tt(), V1, V2)) -> mark(U94(isNatIListKind(V2), V1, V2)), active(U94(tt(), V1, V2)) -> mark(U95(isNat(V1), V2)), active(U95(tt(), V2)) -> mark(U96(isNatList(V2))), active(U96(tt())) -> mark(tt()), U102(X1, X2, mark(X3)) -> U102(X1, X2, X3), U102(X1, X2, active(X3)) -> U102(X1, X2, X3), U102(X1, mark(X2), X3) -> U102(X1, X2, X3), U102(X1, active(X2), X3) -> U102(X1, X2, X3), U102(mark(X1), X2, X3) -> U102(X1, X2, X3), U102(active(X1), X2, X3) -> U102(X1, X2, X3), isNatKind(mark(X)) -> isNatKind(X), isNatKind(active(X)) -> isNatKind(X), U101(X1, X2, mark(X3)) -> U101(X1, X2, X3), U101(X1, X2, active(X3)) -> U101(X1, X2, X3), U101(X1, mark(X2), X3) -> U101(X1, X2, X3), U101(X1, active(X2), X3) -> U101(X1, X2, X3), U101(mark(X1), X2, X3) -> U101(X1, X2, X3), U101(active(X1), X2, X3) -> U101(X1, X2, X3), U103(X1, X2, mark(X3)) -> U103(X1, X2, X3), U103(X1, X2, active(X3)) -> U103(X1, X2, X3), U103(X1, mark(X2), X3) -> U103(X1, X2, X3), U103(X1, active(X2), X3) -> U103(X1, X2, X3), U103(mark(X1), X2, X3) -> U103(X1, X2, X3), U103(active(X1), X2, X3) -> U103(X1, X2, X3), isNatIListKind(mark(X)) -> isNatIListKind(X), isNatIListKind(active(X)) -> isNatIListKind(X), U104(X1, X2, mark(X3)) -> U104(X1, X2, X3), U104(X1, X2, active(X3)) -> U104(X1, X2, X3), U104(X1, mark(X2), X3) -> U104(X1, X2, X3), U104(X1, active(X2), X3) -> U104(X1, X2, X3), U104(mark(X1), X2, X3) -> U104(X1, X2, X3), U104(active(X1), X2, X3) -> U104(X1, X2, X3), U105(X1, mark(X2)) -> U105(X1, X2), U105(X1, active(X2)) -> U105(X1, X2), U105(mark(X1), X2) -> U105(X1, X2), U105(active(X1), X2) -> U105(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U106(mark(X)) -> U106(X), U106(active(X)) -> U106(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(X), U12(X1, mark(X2)) -> U12(X1, X2), U12(X1, active(X2)) -> U12(X1, X2), U12(mark(X1), X2) -> U12(X1, X2), U12(active(X1), X2) -> U12(X1, X2), U11(X1, mark(X2)) -> U11(X1, X2), U11(X1, active(X2)) -> U11(X1, X2), U11(mark(X1), X2) -> U11(X1, X2), U11(active(X1), X2) -> U11(X1, X2), U112(X1, X2, mark(X3)) -> U112(X1, X2, X3), U112(X1, X2, active(X3)) -> U112(X1, X2, X3), U112(X1, mark(X2), X3) -> U112(X1, X2, X3), U112(X1, active(X2), X3) -> U112(X1, X2, X3), U112(mark(X1), X2, X3) -> U112(X1, X2, X3), U112(active(X1), X2, X3) -> U112(X1, X2, X3), U111(X1, X2, mark(X3)) -> U111(X1, X2, X3), U111(X1, X2, active(X3)) -> U111(X1, X2, X3), U111(X1, mark(X2), X3) -> U111(X1, X2, X3), U111(X1, active(X2), X3) -> U111(X1, X2, X3), U111(mark(X1), X2, X3) -> U111(X1, X2, X3), U111(active(X1), X2, X3) -> U111(X1, X2, X3), U113(X1, X2, mark(X3)) -> U113(X1, X2, X3), U113(X1, X2, active(X3)) -> U113(X1, X2, X3), U113(X1, mark(X2), X3) -> U113(X1, X2, X3), U113(X1, active(X2), X3) -> U113(X1, X2, X3), U113(mark(X1), X2, X3) -> U113(X1, X2, X3), U113(active(X1), X2, X3) -> U113(X1, X2, X3), U114(X1, mark(X2)) -> U114(X1, X2), U114(X1, active(X2)) -> U114(X1, X2), U114(mark(X1), X2) -> U114(X1, X2), U114(active(X1), X2) -> U114(X1, X2), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), U13(mark(X)) -> U13(X), U13(active(X)) -> U13(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), U122(mark(X)) -> U122(X), U122(active(X)) -> U122(X), U121(X1, mark(X2)) -> U121(X1, X2), U121(X1, active(X2)) -> U121(X1, X2), U121(mark(X1), X2) -> U121(X1, X2), U121(active(X1), X2) -> U121(X1, X2), U132(X1, X2, X3, mark(X4)) -> U132(X1, X2, X3, X4), U132(X1, X2, X3, active(X4)) -> U132(X1, X2, X3, X4), U132(X1, X2, mark(X3), X4) -> U132(X1, X2, X3, X4), U132(X1, X2, active(X3), X4) -> U132(X1, X2, X3, X4), U132(X1, mark(X2), X3, X4) -> U132(X1, X2, X3, X4), U132(X1, active(X2), X3, X4) -> U132(X1, X2, X3, X4), U132(mark(X1), X2, X3, X4) -> U132(X1, X2, X3, X4), U132(active(X1), X2, X3, X4) -> U132(X1, X2, X3, X4), U131(X1, X2, X3, mark(X4)) -> U131(X1, X2, X3, X4), U131(X1, X2, X3, active(X4)) -> U131(X1, X2, X3, X4), U131(X1, X2, mark(X3), X4) -> U131(X1, X2, X3, X4), U131(X1, X2, active(X3), X4) -> U131(X1, X2, X3, X4), U131(X1, mark(X2), X3, X4) -> U131(X1, X2, X3, X4), U131(X1, active(X2), X3, X4) -> U131(X1, X2, X3, X4), U131(mark(X1), X2, X3, X4) -> U131(X1, X2, X3, X4), U131(active(X1), X2, X3, X4) -> U131(X1, X2, X3, X4), U133(X1, X2, X3, mark(X4)) -> U133(X1, X2, X3, X4), U133(X1, X2, X3, active(X4)) -> U133(X1, X2, X3, X4), U133(X1, X2, mark(X3), X4) -> U133(X1, X2, X3, X4), U133(X1, X2, active(X3), X4) -> U133(X1, X2, X3, X4), U133(X1, mark(X2), X3, X4) -> U133(X1, X2, X3, X4), U133(X1, active(X2), X3, X4) -> U133(X1, X2, X3, X4), U133(mark(X1), X2, X3, X4) -> U133(X1, X2, X3, X4), U133(active(X1), X2, X3, X4) -> U133(X1, X2, X3, X4), U134(X1, X2, X3, mark(X4)) -> U134(X1, X2, X3, X4), U134(X1, X2, X3, active(X4)) -> U134(X1, X2, X3, X4), U134(X1, X2, mark(X3), X4) -> U134(X1, X2, X3, X4), U134(X1, X2, active(X3), X4) -> U134(X1, X2, X3, X4), U134(X1, mark(X2), X3, X4) -> U134(X1, X2, X3, X4), U134(X1, active(X2), X3, X4) -> U134(X1, X2, X3, X4), U134(mark(X1), X2, X3, X4) -> U134(X1, X2, X3, X4), U134(active(X1), X2, X3, X4) -> U134(X1, X2, X3, X4), U135(X1, X2, X3, mark(X4)) -> U135(X1, X2, X3, X4), U135(X1, X2, X3, active(X4)) -> U135(X1, X2, X3, X4), U135(X1, X2, mark(X3), X4) -> U135(X1, X2, X3, X4), U135(X1, X2, active(X3), X4) -> U135(X1, X2, X3, X4), U135(X1, mark(X2), X3, X4) -> U135(X1, X2, X3, X4), U135(X1, active(X2), X3, X4) -> U135(X1, X2, X3, X4), U135(mark(X1), X2, X3, X4) -> U135(X1, X2, X3, X4), U135(active(X1), X2, X3, X4) -> U135(X1, X2, X3, X4), U136(X1, X2, X3, mark(X4)) -> U136(X1, X2, X3, X4), U136(X1, X2, X3, active(X4)) -> U136(X1, X2, X3, X4), U136(X1, X2, mark(X3), X4) -> U136(X1, X2, X3, X4), U136(X1, X2, active(X3), X4) -> U136(X1, X2, X3, X4), U136(X1, mark(X2), X3, X4) -> U136(X1, X2, X3, X4), U136(X1, active(X2), X3, X4) -> U136(X1, X2, X3, X4), U136(mark(X1), X2, X3, X4) -> U136(X1, X2, X3, X4), U136(active(X1), X2, X3, X4) -> U136(X1, X2, X3, X4), take(X1, mark(X2)) -> take(X1, X2), take(X1, active(X2)) -> take(X1, X2), take(mark(X1), X2) -> take(X1, X2), take(active(X1), X2) -> take(X1, X2), U22(X1, mark(X2)) -> U22(X1, X2), U22(X1, active(X2)) -> U22(X1, X2), U22(mark(X1), X2) -> U22(X1, X2), U22(active(X1), X2) -> U22(X1, X2), U21(X1, mark(X2)) -> U21(X1, X2), U21(X1, active(X2)) -> U21(X1, X2), U21(mark(X1), X2) -> U21(X1, X2), U21(active(X1), X2) -> U21(X1, X2), U23(mark(X)) -> U23(X), U23(active(X)) -> U23(X), U32(X1, mark(X2)) -> U32(X1, X2), U32(X1, active(X2)) -> U32(X1, X2), U32(mark(X1), X2) -> U32(X1, X2), U32(active(X1), X2) -> U32(X1, X2), U31(X1, mark(X2)) -> U31(X1, X2), U31(X1, active(X2)) -> U31(X1, X2), U31(mark(X1), X2) -> U31(X1, X2), U31(active(X1), X2) -> U31(X1, X2), U33(mark(X)) -> U33(X), U33(active(X)) -> U33(X), U42(X1, X2, mark(X3)) -> U42(X1, X2, X3), U42(X1, X2, active(X3)) -> U42(X1, X2, X3), U42(X1, mark(X2), X3) -> U42(X1, X2, X3), U42(X1, active(X2), X3) -> U42(X1, X2, X3), U42(mark(X1), X2, X3) -> U42(X1, X2, X3), U42(active(X1), X2, X3) -> U42(X1, X2, X3), U41(X1, X2, mark(X3)) -> U41(X1, X2, X3), U41(X1, X2, active(X3)) -> U41(X1, X2, X3), U41(X1, mark(X2), X3) -> U41(X1, X2, X3), U41(X1, active(X2), X3) -> U41(X1, X2, X3), U41(mark(X1), X2, X3) -> U41(X1, X2, X3), U41(active(X1), X2, X3) -> U41(X1, X2, X3), U43(X1, X2, mark(X3)) -> U43(X1, X2, X3), U43(X1, X2, active(X3)) -> U43(X1, X2, X3), U43(X1, mark(X2), X3) -> U43(X1, X2, X3), U43(X1, active(X2), X3) -> U43(X1, X2, X3), U43(mark(X1), X2, X3) -> U43(X1, X2, X3), U43(active(X1), X2, X3) -> U43(X1, X2, X3), U44(X1, X2, mark(X3)) -> U44(X1, X2, X3), U44(X1, X2, active(X3)) -> U44(X1, X2, X3), U44(X1, mark(X2), X3) -> U44(X1, X2, X3), U44(X1, active(X2), X3) -> U44(X1, X2, X3), U44(mark(X1), X2, X3) -> U44(X1, X2, X3), U44(active(X1), X2, X3) -> U44(X1, X2, X3), U45(X1, mark(X2)) -> U45(X1, X2), U45(X1, active(X2)) -> U45(X1, X2), U45(mark(X1), X2) -> U45(X1, X2), U45(active(X1), X2) -> U45(X1, X2), U46(mark(X)) -> U46(X), U46(active(X)) -> U46(X), U52(mark(X)) -> U52(X), U52(active(X)) -> U52(X), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(mark(X)) -> U62(X), U62(active(X)) -> U62(X), U61(X1, mark(X2)) -> U61(X1, X2), U61(X1, active(X2)) -> U61(X1, X2), U61(mark(X1), X2) -> U61(X1, X2), U61(active(X1), X2) -> U61(X1, X2), U71(mark(X)) -> U71(X), U71(active(X)) -> U71(X), U81(mark(X)) -> U81(X), U81(active(X)) -> U81(X), U92(X1, X2, mark(X3)) -> U92(X1, X2, X3), U92(X1, X2, active(X3)) -> U92(X1, X2, X3), U92(X1, mark(X2), X3) -> U92(X1, X2, X3), U92(X1, active(X2), X3) -> U92(X1, X2, X3), U92(mark(X1), X2, X3) -> U92(X1, X2, X3), U92(active(X1), X2, X3) -> U92(X1, X2, X3), U91(X1, X2, mark(X3)) -> U91(X1, X2, X3), U91(X1, X2, active(X3)) -> U91(X1, X2, X3), U91(X1, mark(X2), X3) -> U91(X1, X2, X3), U91(X1, active(X2), X3) -> U91(X1, X2, X3), U91(mark(X1), X2, X3) -> U91(X1, X2, X3), U91(active(X1), X2, X3) -> U91(X1, X2, X3), U93(X1, X2, mark(X3)) -> U93(X1, X2, X3), U93(X1, X2, active(X3)) -> U93(X1, X2, X3), U93(X1, mark(X2), X3) -> U93(X1, X2, X3), U93(X1, active(X2), X3) -> U93(X1, X2, X3), U93(mark(X1), X2, X3) -> U93(X1, X2, X3), U93(active(X1), X2, X3) -> U93(X1, X2, X3), U94(X1, X2, mark(X3)) -> U94(X1, X2, X3), U94(X1, X2, active(X3)) -> U94(X1, X2, X3), U94(X1, mark(X2), X3) -> U94(X1, X2, X3), U94(X1, active(X2), X3) -> U94(X1, X2, X3), U94(mark(X1), X2, X3) -> U94(X1, X2, X3), U94(active(X1), X2, X3) -> U94(X1, X2, X3), U95(X1, mark(X2)) -> U95(X1, X2), U95(X1, active(X2)) -> U95(X1, X2), U95(mark(X1), X2) -> U95(X1, X2), U95(active(X1), X2) -> U95(X1, X2), U96(mark(X)) -> U96(X), U96(active(X)) -> U96(X) } Fail