MAYBE
MAYBE
TRS:
 {
   if(true(), X, Y) -> X,
  if(false(), X, Y) -> Y,
         zero(s(X)) -> false(),
          zero(0()) -> true(),
      prod(s(X), Y) -> add(Y, prod(X, Y)),
       prod(0(), X) -> 0(),
            fact(X) -> if(zero(X), s(0()), prod(X, fact(p(X)))),
            p(s(X)) -> X,
       add(s(X), Y) -> s(add(X, Y)),
        add(0(), X) -> X
 }
 DUP: We consider a duplicating system.
  Trs:
   {
     if(true(), X, Y) -> X,
    if(false(), X, Y) -> Y,
           zero(s(X)) -> false(),
            zero(0()) -> true(),
        prod(s(X), Y) -> add(Y, prod(X, Y)),
         prod(0(), X) -> 0(),
              fact(X) -> if(zero(X), s(0()), prod(X, fact(p(X)))),
              p(s(X)) -> X,
         add(s(X), Y) -> s(add(X, Y)),
          add(0(), X) -> X
   }
  Fail