TRS: { a__and(tt(), T) -> mark(T), a__isNatIList(IL) -> a__isNatList(IL), a__isNat(0()) -> tt(), a__isNat(s(N)) -> a__isNat(N), a__isNat(length(L)) -> a__isNatList(L), a__isNatIList(zeros()) -> tt(), a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)), a__isNatList(nil()) -> tt(), a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)), a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)), a__zeros() -> cons(0(), zeros()), a__take(0(), IL) -> a__uTake1(a__isNatIList(IL)), a__uTake1(tt()) -> nil(), a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL), a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL)), a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L), a__uLength(tt(), L) -> s(a__length(mark(L))), mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)), mark(isNatIList(X)) -> a__isNatIList(X), mark(isNatList(X)) -> a__isNatList(X), mark(isNat(X)) -> a__isNat(X), mark(length(X)) -> a__length(mark(X)), mark(zeros()) -> a__zeros(), mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)), mark(uTake1(X)) -> a__uTake1(mark(X)), mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4), mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2), mark(tt()) -> tt(), mark(0()) -> 0(), mark(s(X)) -> s(mark(X)), mark(cons(X1, X2)) -> cons(mark(X1), X2), mark(nil()) -> nil(), a__and(X1, X2) -> and(X1, X2), a__isNatIList(X) -> isNatIList(X), a__isNatList(X) -> isNatList(X), a__isNat(X) -> isNat(X), a__length(X) -> length(X), a__zeros() -> zeros(), a__take(X1, X2) -> take(X1, X2), a__uTake1(X) -> uTake1(X), a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4), a__uLength(X1, X2) -> uLength(X1, X2)} Fail