NO

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

Proof:
 Unfolding Processor:
  loop length: 4
  terms:
   c(b(a(b(a(b(a(b(a(b(a(b(a(x82)))))))))))))
   a(b(a(b(a(b(c(b(c(b(a(b(a(b(a(b(a(x82)))))))))))))))))
   a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(c(b(a(b(a(x82)))))))))))))))))))))
   a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(a(b(a(b(a(b(c(b(c(x82)))))))))))))))))))))))))
  context: a(b(a(b(a(b([]))))))
  substitution:
   x82 -> b(c(b(c(b(a(b(c(b(c(x82))))))))))
  Qed