YES
TRS:
 {         f(X, X) -> f(a(), n__b()),
               b() -> a(),
               b() -> n__b(),
       activate(X) -> X,
  activate(n__b()) -> b()}
 RUF:
  Strict:
   {f(X, X) -> f(a(), n__b()),
        b() -> a(),
        b() -> n__b()}
  Weak:
   {}
  RUF:
   Strict:
    {f(X, X) -> f(a(), n__b())}
   Weak:
    {}
   DP:
    Strict:
     {f#(X, X) -> f#(a(), n__b())}
    Weak:
    {f(X, X) -> f(a(), n__b())}
    EDG:
     {}
     SCCS:
      
      Qed