MAYBE
MAYBE
TRS:
 {
                 activate(X) -> X,
    activate(n__add(X1, X2)) -> add(activate(X1), X2),
  activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)),
        activate(n__from(X)) -> from(X),
           activate(n__s(X)) -> s(X),
              and(true(), X) -> activate(X),
             and(false(), Y) -> false(),
            if(true(), X, Y) -> activate(X),
           if(false(), X, Y) -> activate(Y),
                 add(X1, X2) -> n__add(X1, X2),
                 add(0(), X) -> activate(X),
                add(s(X), Y) -> s(n__add(activate(X), activate(Y))),
                        s(X) -> n__s(X),
               first(X1, X2) -> n__first(X1, X2),
               first(0(), X) -> nil(),
     first(s(X), cons(Y, Z)) ->
  cons(activate(Y), n__first(activate(X), activate(Z))),
                     from(X) -> cons(activate(X), n__from(n__s(activate(X)))),
                     from(X) -> n__from(X)
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                   activate(X) -> X,
      activate(n__add(X1, X2)) -> add(activate(X1), X2),
    activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)),
          activate(n__from(X)) -> from(X),
             activate(n__s(X)) -> s(X),
                and(true(), X) -> activate(X),
               and(false(), Y) -> false(),
              if(true(), X, Y) -> activate(X),
             if(false(), X, Y) -> activate(Y),
                   add(X1, X2) -> n__add(X1, X2),
                   add(0(), X) -> activate(X),
                  add(s(X), Y) -> s(n__add(activate(X), activate(Y))),
                          s(X) -> n__s(X),
                 first(X1, X2) -> n__first(X1, X2),
                 first(0(), X) -> nil(),
       first(s(X), cons(Y, Z)) ->
    cons(activate(Y), n__first(activate(X), activate(Z))),
                       from(X) ->
    cons(activate(X), n__from(n__s(activate(X)))),
                       from(X) -> n__from(X)
   }
  Fail