NO

Problem:
 a(b(x)) -> b(b(a(a(x))))

Proof:
 Unfolding Processor:
  loop length: 2
  terms:
   a(b(b(x4)))
   b(b(a(a(b(x4)))))
  context: b(b([]))
  substitution:
   x4 -> a(a(x4))
  Qed