MAYBE MAYBE TRS: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(U12(X1, X2)) -> active(U12(mark(X1), X2)), mark(tt()) -> active(tt()), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U22(X1, X2, X3, X4)) -> active(U22(mark(X1), X2, X3, X4)), mark(U21(X1, X2, X3, X4)) -> active(U21(mark(X1), X2, X3, X4)), mark(U23(X1, X2, X3, X4)) -> active(U23(mark(X1), X2, X3, X4)), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(nil()) -> active(nil()), 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(U12(tt(), L)) -> mark(s(length(L))), active(U11(tt(), L)) -> mark(U12(tt(), L)), active(length(cons(N, L))) -> mark(U11(tt(), L)), active(length(nil())) -> mark(0()), active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N)), active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N)), active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(take(0(), IL)) -> mark(nil()), active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N)), 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), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), U22(X1, X2, X3, mark(X4)) -> U22(X1, X2, X3, X4), U22(X1, X2, X3, active(X4)) -> U22(X1, X2, X3, X4), U22(X1, X2, mark(X3), X4) -> U22(X1, X2, X3, X4), U22(X1, X2, active(X3), X4) -> U22(X1, X2, X3, X4), U22(X1, mark(X2), X3, X4) -> U22(X1, X2, X3, X4), U22(X1, active(X2), X3, X4) -> U22(X1, X2, X3, X4), U22(mark(X1), X2, X3, X4) -> U22(X1, X2, X3, X4), U22(active(X1), X2, X3, X4) -> U22(X1, X2, X3, X4), U21(X1, X2, X3, mark(X4)) -> U21(X1, X2, X3, X4), U21(X1, X2, X3, active(X4)) -> U21(X1, X2, X3, X4), U21(X1, X2, mark(X3), X4) -> U21(X1, X2, X3, X4), U21(X1, X2, active(X3), X4) -> U21(X1, X2, X3, X4), U21(X1, mark(X2), X3, X4) -> U21(X1, X2, X3, X4), U21(X1, active(X2), X3, X4) -> U21(X1, X2, X3, X4), U21(mark(X1), X2, X3, X4) -> U21(X1, X2, X3, X4), U21(active(X1), X2, X3, X4) -> U21(X1, X2, X3, X4), U23(X1, X2, X3, mark(X4)) -> U23(X1, X2, X3, X4), U23(X1, X2, X3, active(X4)) -> U23(X1, X2, X3, X4), U23(X1, X2, mark(X3), X4) -> U23(X1, X2, X3, X4), U23(X1, X2, active(X3), X4) -> U23(X1, X2, X3, X4), U23(X1, mark(X2), X3, X4) -> U23(X1, X2, X3, X4), U23(X1, active(X2), X3, X4) -> U23(X1, X2, X3, X4), U23(mark(X1), X2, X3, X4) -> U23(X1, X2, X3, X4), U23(active(X1), X2, X3, X4) -> U23(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) } DUP: We consider a non-duplicating system. Trs: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(U12(X1, X2)) -> active(U12(mark(X1), X2)), mark(tt()) -> active(tt()), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U22(X1, X2, X3, X4)) -> active(U22(mark(X1), X2, X3, X4)), mark(U21(X1, X2, X3, X4)) -> active(U21(mark(X1), X2, X3, X4)), mark(U23(X1, X2, X3, X4)) -> active(U23(mark(X1), X2, X3, X4)), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(nil()) -> active(nil()), 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(U12(tt(), L)) -> mark(s(length(L))), active(U11(tt(), L)) -> mark(U12(tt(), L)), active(length(cons(N, L))) -> mark(U11(tt(), L)), active(length(nil())) -> mark(0()), active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N)), active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N)), active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(take(0(), IL)) -> mark(nil()), active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N)), 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), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), U22(X1, X2, X3, mark(X4)) -> U22(X1, X2, X3, X4), U22(X1, X2, X3, active(X4)) -> U22(X1, X2, X3, X4), U22(X1, X2, mark(X3), X4) -> U22(X1, X2, X3, X4), U22(X1, X2, active(X3), X4) -> U22(X1, X2, X3, X4), U22(X1, mark(X2), X3, X4) -> U22(X1, X2, X3, X4), U22(X1, active(X2), X3, X4) -> U22(X1, X2, X3, X4), U22(mark(X1), X2, X3, X4) -> U22(X1, X2, X3, X4), U22(active(X1), X2, X3, X4) -> U22(X1, X2, X3, X4), U21(X1, X2, X3, mark(X4)) -> U21(X1, X2, X3, X4), U21(X1, X2, X3, active(X4)) -> U21(X1, X2, X3, X4), U21(X1, X2, mark(X3), X4) -> U21(X1, X2, X3, X4), U21(X1, X2, active(X3), X4) -> U21(X1, X2, X3, X4), U21(X1, mark(X2), X3, X4) -> U21(X1, X2, X3, X4), U21(X1, active(X2), X3, X4) -> U21(X1, X2, X3, X4), U21(mark(X1), X2, X3, X4) -> U21(X1, X2, X3, X4), U21(active(X1), X2, X3, X4) -> U21(X1, X2, X3, X4), U23(X1, X2, X3, mark(X4)) -> U23(X1, X2, X3, X4), U23(X1, X2, X3, active(X4)) -> U23(X1, X2, X3, X4), U23(X1, X2, mark(X3), X4) -> U23(X1, X2, X3, X4), U23(X1, X2, active(X3), X4) -> U23(X1, X2, X3, X4), U23(X1, mark(X2), X3, X4) -> U23(X1, X2, X3, X4), U23(X1, active(X2), X3, X4) -> U23(X1, X2, X3, X4), U23(mark(X1), X2, X3, X4) -> U23(X1, X2, X3, X4), U23(active(X1), X2, X3, X4) -> U23(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) } Fail