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