MAYBE
MAYBE
TRS:
 {
           if(true(), X, Y) -> activate(X),
          if(false(), X, Y) -> activate(Y),
                  zero(0()) -> true(),
                 zero(s(X)) -> false(),
                    fact(X) -> if(zero(X), n__s(0()), n__prod(X, fact(p(X)))),
                    p(s(X)) -> X,
                add(0(), X) -> X,
               add(s(X), Y) -> s(add(X, Y)),
                       s(X) -> n__s(X),
               prod(X1, X2) -> n__prod(X1, X2),
               prod(0(), X) -> 0(),
              prod(s(X), Y) -> add(Y, prod(X, Y)),
                activate(X) -> X,
          activate(n__s(X)) -> s(X),
  activate(n__prod(X1, X2)) -> prod(X1, X2)
 }
 DUP: We consider a duplicating system.
  Trs:
   {
             if(true(), X, Y) -> activate(X),
            if(false(), X, Y) -> activate(Y),
                    zero(0()) -> true(),
                   zero(s(X)) -> false(),
                      fact(X) ->
    if(zero(X), n__s(0()), n__prod(X, fact(p(X)))),
                      p(s(X)) -> X,
                  add(0(), X) -> X,
                 add(s(X), Y) -> s(add(X, Y)),
                         s(X) -> n__s(X),
                 prod(X1, X2) -> n__prod(X1, X2),
                 prod(0(), X) -> 0(),
                prod(s(X), Y) -> add(Y, prod(X, Y)),
                  activate(X) -> X,
            activate(n__s(X)) -> s(X),
    activate(n__prod(X1, X2)) -> prod(X1, X2)
   }
  Fail