MAYBE MAYBE TRS: { from(X) -> cons(X, n__from(s(X))), from(X) -> n__from(X), sel(s(N), cons(X, XS)) -> sel(N, activate(XS)), sel(0(), cons(X, XS)) -> X, activate(X) -> X, activate(n__from(X)) -> from(X), activate(n__zWquot(X1, X2)) -> zWquot(X1, X2), minus(X, 0()) -> 0(), minus(s(X), s(Y)) -> minus(X, Y), quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))), quot(0(), s(Y)) -> 0(), zWquot(XS, nil()) -> nil(), zWquot(X1, X2) -> n__zWquot(X1, X2), zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))), zWquot(nil(), XS) -> nil() } DUP: We consider a duplicating system. Trs: { from(X) -> cons(X, n__from(s(X))), from(X) -> n__from(X), sel(s(N), cons(X, XS)) -> sel(N, activate(XS)), sel(0(), cons(X, XS)) -> X, activate(X) -> X, activate(n__from(X)) -> from(X), activate(n__zWquot(X1, X2)) -> zWquot(X1, X2), minus(X, 0()) -> 0(), minus(s(X), s(Y)) -> minus(X, Y), quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))), quot(0(), s(Y)) -> 0(), zWquot(XS, nil()) -> nil(), zWquot(X1, X2) -> n__zWquot(X1, X2), zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))), zWquot(nil(), XS) -> nil() } Fail