MAYBE
MAYBE
TRS:
 {
                0() -> n__0(),
             p(0()) -> 0(),
            p(s(X)) -> X,
               s(X) -> n__s(X),
        leq(0(), Y) -> true(),
     leq(s(X), 0()) -> false(),
    leq(s(X), s(Y)) -> leq(X, Y),
        activate(X) -> X,
   activate(n__0()) -> 0(),
  activate(n__s(X)) -> s(X),
   if(true(), X, Y) -> activate(X),
  if(false(), X, Y) -> activate(Y),
         diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), Y)))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                  0() -> n__0(),
               p(0()) -> 0(),
              p(s(X)) -> X,
                 s(X) -> n__s(X),
          leq(0(), Y) -> true(),
       leq(s(X), 0()) -> false(),
      leq(s(X), s(Y)) -> leq(X, Y),
          activate(X) -> X,
     activate(n__0()) -> 0(),
    activate(n__s(X)) -> s(X),
     if(true(), X, Y) -> activate(X),
    if(false(), X, Y) -> activate(Y),
           diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), Y)))
   }
  Fail