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