MAYBE
MAYBE
TRS:
 {
                 sel(X1, X2) -> n__sel(X1, X2),
       sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
        sel(0(), cons(X, Z)) -> X,
                 activate(X) -> X,
  activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)),
        activate(n__from(X)) -> from(activate(X)),
           activate(n__s(X)) -> s(activate(X)),
            activate(n__0()) -> 0(),
   activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
          activate(n__nil()) -> nil(),
    activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)),
                        s(X) -> n__s(X),
                cons(X1, X2) -> n__cons(X1, X2),
                         0() -> n__0(),
                       nil() -> n__nil(),
               first(X1, X2) -> n__first(X1, X2),
     first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))),
               first(0(), Z) -> nil(),
                     from(X) -> cons(X, n__from(n__s(X))),
                     from(X) -> n__from(X),
      sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z)),
       sel1(0(), cons(X, Z)) -> quote(X),
              quote(n__s(X)) -> s1(quote(activate(X))),
               quote(n__0()) -> 01(),
         quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z)),
    first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z))),
              first1(0(), Z) -> nil1(),
      quote1(n__first(X, Z)) -> first1(activate(X), activate(Z)),
       quote1(n__cons(X, Z)) ->
  cons1(quote(activate(X)), quote1(activate(Z))),
            quote1(n__nil()) -> nil1(),
               unquote(01()) -> 0(),
              unquote(s1(X)) -> s(unquote(X)),
            unquote1(nil1()) -> nil(),
       unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)),
                 fcons(X, Z) -> cons(X, Z)
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                   sel(X1, X2) -> n__sel(X1, X2),
         sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
          sel(0(), cons(X, Z)) -> X,
                   activate(X) -> X,
    activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)),
          activate(n__from(X)) -> from(activate(X)),
             activate(n__s(X)) -> s(activate(X)),
              activate(n__0()) -> 0(),
     activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
            activate(n__nil()) -> nil(),
      activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)),
                          s(X) -> n__s(X),
                  cons(X1, X2) -> n__cons(X1, X2),
                           0() -> n__0(),
                         nil() -> n__nil(),
                 first(X1, X2) -> n__first(X1, X2),
       first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))),
                 first(0(), Z) -> nil(),
                       from(X) -> cons(X, n__from(n__s(X))),
                       from(X) -> n__from(X),
        sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z)),
         sel1(0(), cons(X, Z)) -> quote(X),
                quote(n__s(X)) -> s1(quote(activate(X))),
                 quote(n__0()) -> 01(),
           quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z)),
      first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z))),
                first1(0(), Z) -> nil1(),
        quote1(n__first(X, Z)) -> first1(activate(X), activate(Z)),
         quote1(n__cons(X, Z)) ->
    cons1(quote(activate(X)), quote1(activate(Z))),
              quote1(n__nil()) -> nil1(),
                 unquote(01()) -> 0(),
                unquote(s1(X)) -> s(unquote(X)),
              unquote1(nil1()) -> nil(),
         unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)),
                   fcons(X, Z) -> cons(X, Z)
   }
  Fail