NO

Problem:
 f(a(),a()) -> c()
 f(b(),x) -> f(x,x)
 f(x,b()) -> f(x,x)
 a() -> b()

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