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