NO

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> a(a(a(b(c(b(x1))))))
  c(a(x1)) -> b(x1)
  Unfolding Processor:
   loop length: 12
   terms:
    b(a(a(a(a(a(a(x78575)))))))
    a(a(a(b(c(b(a(a(a(a(x78575))))))))))
    a(a(a(b(c(a(a(a(b(c(b(a(a(x78575)))))))))))))
    a(a(a(b(b(a(a(b(c(b(a(a(x78575))))))))))))
    a(a(a(b(a(a(a(b(c(b(b(c(b(a(a(x78575)))))))))))))))
    a(a(a(b(a(a(a(b(c(b(b(c(a(a(a(b(c(b(x78575))))))))))))))))))
    a(a(a(b(a(a(a(b(c(b(b(b(a(a(b(c(b(x78575)))))))))))))))))
    a(a(a(b(a(a(a(b(c(b(b(a(a(a(b(c(b(b(c(b(x78575))))))))))))))))))))
    a(a(a(b(a(a(a(b(c(b(a(a(a(b(c(b(a(b(c(b(b(c(b(x78575)))))))))))))))))))))))
    a(a(a(b(a(a(a(b(c(a(a(a(b(c(b(a(b(c(b(a(b(c(b(b(c(b(x78575))))))))))))))))))))))))))
    a(a(a(b(a(a(a(b(b(a(a(b(c(b(a(b(c(b(a(b(c(b(b(c(b(x78575)))))))))))))))))))))))))
    a(a(a(b(a(a(a(b(a(a(a(b(c(b(b(c(b(a(b(c(b(a(b(c(b(b(c(b(x78575))))))))))))))))))))))))))))
   context: a(a(a([])))
   substitution:
    x78575 -> b(c(b(a(b(c(b(b(c(b(a(b(c(b(a(b(c(b(b(c(b(x78575)))))))))))))))))))))
   Qed