NO

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

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