NO

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> a(a(c(b(a(x1)))))
  c(a(x1)) -> a(b(x1))
  Unfolding Processor:
   loop length: 16
   terms:
    b(a(a(a(a(a(a(x352677)))))))
    a(a(c(b(a(a(a(a(a(x352677)))))))))
    a(a(c(a(a(c(b(a(a(a(a(x352677)))))))))))
    a(a(a(b(a(c(b(a(a(a(a(x352677)))))))))))
    a(a(a(b(a(c(a(a(c(b(a(a(a(x352677)))))))))))))
    a(a(a(b(a(a(b(a(c(b(a(a(a(x352677)))))))))))))
    a(a(a(b(a(a(b(a(c(a(a(c(b(a(a(x352677)))))))))))))))
    a(a(a(b(a(a(b(a(a(b(a(c(b(a(a(x352677)))))))))))))))
    a(a(a(b(a(a(a(a(c(b(a(b(a(c(b(a(a(x352677)))))))))))))))))
    a(a(a(b(a(a(a(a(c(b(a(b(a(c(a(a(c(b(a(x352677)))))))))))))))))))
    a(a(a(b(a(a(a(a(c(b(a(b(a(a(b(a(c(b(a(x352677)))))))))))))))))))
    a(a(a(b(a(a(a(a(c(b(a(a(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))))))
    a(a(a(b(a(a(a(a(c(a(a(c(b(a(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))))))))
    a(a(a(b(a(a(a(a(a(b(a(c(b(a(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))))))))
    a(a(a(b(a(a(a(a(a(b(a(c(a(a(c(b(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))))))))))
    a(a(a(b(a(a(a(a(a(b(a(a(b(a(c(b(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))))))))))
   context: a(a(a([])))
   substitution:
    x352677 -> a(c(b(a(b(a(c(b(a(c(b(a(b(a(c(b(a(x352677)))))))))))))))))
   Qed