NO

Problem:
 f(g(x),s(0())) -> f(g(x),g(x))
 g(s(x)) -> s(g(x))
 g(0()) -> 0()

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   f(g(s(0())),g(s(0())))
   f(g(s(0())),s(g(0())))
   f(g(s(0())),s(0()))
  context: []
  substitution:
   
  Qed