NO

Problem:
 h(f(f(x))) -> h(f(g(f(x))))
 f(g(f(x))) -> f(f(x))

Proof:
 Unfolding Processor:
  loop length: 2
  terms:
   h(f(f(x8)))
   h(f(g(f(x8))))
  context: []
  substitution:
   x8 -> x8
  Qed