NO

Problem:
 a(a(b(b(x1)))) -> b(b(b(b(b(a(a(a(a(a(x1))))))))))

Proof:
 String Reversal Processor:
  b(b(a(a(x1)))) -> a(a(a(a(a(b(b(b(b(b(x1))))))))))
  Unfolding Processor:
   loop length: 2
   terms:
    b(b(a(a(a(a(x18))))))
    a(a(a(a(a(b(b(b(b(b(a(a(x18))))))))))))
   context: a(a(a(a(a(b([]))))))
   substitution:
    x18 -> a(b(b(b(b(b(x18))))))
   Qed