TRS: { a__zeros() -> cons(0(), zeros()), a__U11(tt(), V1) -> a__U12(a__isNatList(V1)), a__U12(tt()) -> tt(), a__U21(tt(), V1) -> a__U22(a__isNat(V1)), a__U22(tt()) -> tt(), a__U31(tt(), V) -> a__U32(a__isNatList(V)), a__U32(tt()) -> tt(), a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2), a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)), a__U43(tt()) -> tt(), a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2), a__U52(tt(), V2) -> a__U53(a__isNatList(V2)), a__U53(tt()) -> tt(), a__U61(tt(), V1, V2) -> a__U62(a__isNat(V1), V2), a__U62(tt(), V2) -> a__U63(a__isNatIList(V2)), a__U63(tt()) -> tt(), a__U71(tt(), L) -> s(a__length(mark(L))), a__U81(tt()) -> nil(), a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL)), a__and(tt(), X) -> mark(X), a__isNat(0()) -> tt(), a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1), a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1), a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V), a__isNatIList(zeros()) -> tt(), a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2), a__isNatIListKind(nil()) -> tt(), a__isNatIListKind(zeros()) -> tt(), a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)), a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)), a__isNatKind(0()) -> tt(), a__isNatKind(length(V1)) -> a__isNatIListKind(V1), a__isNatKind(s(V1)) -> a__isNatKind(V1), a__isNatList(nil()) -> tt(), a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2), a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2), a__length(nil()) -> 0(), a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L), a__take(0(), IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))), a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N), mark(zeros()) -> a__zeros(), mark(U11(X1, X2)) -> a__U11(mark(X1), X2), mark(U12(X)) -> a__U12(mark(X)), mark(isNatList(X)) -> a__isNatList(X), mark(U21(X1, X2)) -> a__U21(mark(X1), X2), mark(U22(X)) -> a__U22(mark(X)), mark(isNat(X)) -> a__isNat(X), mark(U31(X1, X2)) -> a__U31(mark(X1), X2), mark(U32(X)) -> a__U32(mark(X)), mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3), mark(U42(X1, X2)) -> a__U42(mark(X1), X2), mark(U43(X)) -> a__U43(mark(X)), mark(isNatIList(X)) -> a__isNatIList(X), mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3), mark(U52(X1, X2)) -> a__U52(mark(X1), X2), mark(U53(X)) -> a__U53(mark(X)), mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3), mark(U62(X1, X2)) -> a__U62(mark(X1), X2), mark(U63(X)) -> a__U63(mark(X)), mark(U71(X1, X2)) -> a__U71(mark(X1), X2), mark(length(X)) -> a__length(mark(X)), mark(U81(X)) -> a__U81(mark(X)), mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4), mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)), mark(and(X1, X2)) -> a__and(mark(X1), X2), mark(isNatIListKind(X)) -> a__isNatIListKind(X), mark(isNatKind(X)) -> a__isNatKind(X), mark(cons(X1, X2)) -> cons(mark(X1), X2), mark(0()) -> 0(), mark(tt()) -> tt(), mark(s(X)) -> s(mark(X)), mark(nil()) -> nil(), a__zeros() -> zeros(), a__U11(X1, X2) -> U11(X1, X2), a__U12(X) -> U12(X), a__isNatList(X) -> isNatList(X), a__U21(X1, X2) -> U21(X1, X2), a__U22(X) -> U22(X), a__isNat(X) -> isNat(X), a__U31(X1, X2) -> U31(X1, X2), a__U32(X) -> U32(X), a__U41(X1, X2, X3) -> U41(X1, X2, X3), a__U42(X1, X2) -> U42(X1, X2), a__U43(X) -> U43(X), a__isNatIList(X) -> isNatIList(X), a__U51(X1, X2, X3) -> U51(X1, X2, X3), a__U52(X1, X2) -> U52(X1, X2), a__U53(X) -> U53(X), a__U61(X1, X2, X3) -> U61(X1, X2, X3), a__U62(X1, X2) -> U62(X1, X2), a__U63(X) -> U63(X), a__U71(X1, X2) -> U71(X1, X2), a__length(X) -> length(X), a__U81(X) -> U81(X), a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4), a__take(X1, X2) -> take(X1, X2), a__and(X1, X2) -> and(X1, X2), a__isNatIListKind(X) -> isNatIListKind(X), a__isNatKind(X) -> isNatKind(X)} Fail