MAYBE MAYBE TRS: { from(X) -> cons(X, n__from(n__s(X))), from(X) -> n__from(X), head(cons(X, XS)) -> X, activate(X) -> X, activate(n__from(X)) -> from(activate(X)), activate(n__s(X)) -> s(activate(X)), activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)), 2nd(cons(X, XS)) -> head(activate(XS)), take(X1, X2) -> n__take(X1, X2), take(0(), XS) -> nil(), take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))), s(X) -> n__s(X), sel(0(), cons(X, XS)) -> X, sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) } DUP: We consider a duplicating system. Trs: { from(X) -> cons(X, n__from(n__s(X))), from(X) -> n__from(X), head(cons(X, XS)) -> X, activate(X) -> X, activate(n__from(X)) -> from(activate(X)), activate(n__s(X)) -> s(activate(X)), activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)), 2nd(cons(X, XS)) -> head(activate(XS)), take(X1, X2) -> n__take(X1, X2), take(0(), XS) -> nil(), take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))), s(X) -> n__s(X), sel(0(), cons(X, XS)) -> X, sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) } Fail