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