NO

Problem:
 f(x,x) -> g(x)
 f(x,g(x)) -> b()
 h(c(),y) -> f(h(y,c()),h(y,y))

Proof:
 Unfolding Processor:
  loop length: 1
  terms:
   h(c(),c())
  context: f(h(c(),c()),[])
  substitution:
   
  Qed