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