MAYBE MAYBE TRS: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(tt()) -> active(tt()), mark(nil()) -> active(nil()), mark(U21(X)) -> active(U21(mark(X))), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(U31(X1, X2, X3, X4)) -> active(U31(mark(X1), X2, X3, X4)), mark(and(X1, X2)) -> active(and(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(isNatList(X)) -> active(isNatList(X)), mark(isNatIList(X)) -> active(isNatIList(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(length(cons(N, L))) -> mark(U11(and(isNatList(L), isNat(N)), L)), active(length(nil())) -> mark(0()), active(U11(tt(), L)) -> mark(s(length(L))), active(U21(tt())) -> mark(nil()), active(take(0(), IL)) -> mark(U21(isNatIList(IL))), active(take(s(M), cons(N, IL))) -> mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N)), active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(and(tt(), X)) -> mark(X), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(isNat(V1)), active(isNat(length(V1))) -> mark(isNatList(V1)), active(isNatList(cons(V1, V2))) -> mark(and(isNat(V1), isNatList(V2))), active(isNatList(nil())) -> mark(tt()), active(isNatList(take(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))), active(isNatIList(V)) -> mark(isNatList(V)), active(isNatIList(cons(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))), active(isNatIList(zeros())) -> mark(tt()), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), 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), U21(mark(X)) -> U21(X), U21(active(X)) -> U21(X), 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), U31(X1, X2, X3, mark(X4)) -> U31(X1, X2, X3, X4), U31(X1, X2, X3, active(X4)) -> U31(X1, X2, X3, X4), U31(X1, X2, mark(X3), X4) -> U31(X1, X2, X3, X4), U31(X1, X2, active(X3), X4) -> U31(X1, X2, X3, X4), U31(X1, mark(X2), X3, X4) -> U31(X1, X2, X3, X4), U31(X1, active(X2), X3, X4) -> U31(X1, X2, X3, X4), U31(mark(X1), X2, X3, X4) -> U31(X1, X2, X3, X4), U31(active(X1), X2, X3, X4) -> U31(X1, X2, X3, X4), and(X1, mark(X2)) -> and(X1, X2), and(X1, active(X2)) -> and(X1, X2), and(mark(X1), X2) -> and(X1, X2), and(active(X1), X2) -> and(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(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(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(tt()) -> active(tt()), mark(nil()) -> active(nil()), mark(U21(X)) -> active(U21(mark(X))), mark(take(X1, X2)) -> active(take(mark(X1), mark(X2))), mark(U31(X1, X2, X3, X4)) -> active(U31(mark(X1), X2, X3, X4)), mark(and(X1, X2)) -> active(and(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(isNatList(X)) -> active(isNatList(X)), mark(isNatIList(X)) -> active(isNatIList(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(length(cons(N, L))) -> mark(U11(and(isNatList(L), isNat(N)), L)), active(length(nil())) -> mark(0()), active(U11(tt(), L)) -> mark(s(length(L))), active(U21(tt())) -> mark(nil()), active(take(0(), IL)) -> mark(U21(isNatIList(IL))), active(take(s(M), cons(N, IL))) -> mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N)), active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))), active(and(tt(), X)) -> mark(X), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(isNat(V1)), active(isNat(length(V1))) -> mark(isNatList(V1)), active(isNatList(cons(V1, V2))) -> mark(and(isNat(V1), isNatList(V2))), active(isNatList(nil())) -> mark(tt()), active(isNatList(take(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))), active(isNatIList(V)) -> mark(isNatList(V)), active(isNatIList(cons(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))), active(isNatIList(zeros())) -> mark(tt()), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X), 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), U21(mark(X)) -> U21(X), U21(active(X)) -> U21(X), 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), U31(X1, X2, X3, mark(X4)) -> U31(X1, X2, X3, X4), U31(X1, X2, X3, active(X4)) -> U31(X1, X2, X3, X4), U31(X1, X2, mark(X3), X4) -> U31(X1, X2, X3, X4), U31(X1, X2, active(X3), X4) -> U31(X1, X2, X3, X4), U31(X1, mark(X2), X3, X4) -> U31(X1, X2, X3, X4), U31(X1, active(X2), X3, X4) -> U31(X1, X2, X3, X4), U31(mark(X1), X2, X3, X4) -> U31(X1, X2, X3, X4), U31(active(X1), X2, X3, X4) -> U31(X1, X2, X3, X4), and(X1, mark(X2)) -> and(X1, X2), and(X1, active(X2)) -> and(X1, X2), and(mark(X1), X2) -> and(X1, X2), and(active(X1), X2) -> and(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(X) } Fail