MAYBE MAYBE TRS: { a__first(X1, X2) -> first(X1, X2), a__first(0(), X) -> nil(), a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)), mark(nil()) -> nil(), mark(0()) -> 0(), mark(cons(X1, X2)) -> cons(mark(X1), X2), mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)), mark(s(X)) -> s(mark(X)), mark(from(X)) -> a__from(mark(X)), a__from(X) -> cons(mark(X), from(s(X))), a__from(X) -> from(X) } DUP: We consider a duplicating system. Trs: { a__first(X1, X2) -> first(X1, X2), a__first(0(), X) -> nil(), a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)), mark(nil()) -> nil(), mark(0()) -> 0(), mark(cons(X1, X2)) -> cons(mark(X1), X2), mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)), mark(s(X)) -> s(mark(X)), mark(from(X)) -> a__from(mark(X)), a__from(X) -> cons(mark(X), from(s(X))), a__from(X) -> from(X) } Fail