NO

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

Proof:
 String Reversal Processor:
  a(a(a(a(x1)))) -> a(a(a(b(x1))))
  b(b(x1)) -> b(a(a(x1)))
  Unfolding Processor:
   loop length: 9
   terms:
    a(a(a(a(b(a(a(a(b(a(a(a(b(x9122)))))))))))))
    a(a(a(b(b(a(a(a(b(a(a(a(b(x9122)))))))))))))
    a(a(a(b(a(a(a(a(a(b(a(a(a(b(x9122))))))))))))))
    a(a(a(b(a(a(a(a(b(b(a(a(a(b(x9122))))))))))))))
    a(a(a(b(a(a(a(a(b(a(a(a(a(a(b(x9122)))))))))))))))
    a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x9122)))))))))))))))
    a(a(a(b(a(a(a(a(b(a(a(a(b(b(b(x9122)))))))))))))))
    a(a(a(b(a(a(a(a(b(a(a(a(b(b(a(a(x9122))))))))))))))))
    a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(x9122)))))))))))))))))
   context: a(a(a(b([]))))
   substitution:
    x9122 -> x9122
   Qed