NO

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

Proof:
 Unfolding Processor:
  loop length: 4
  terms:
   c(a(a(b(a(a(a(x67)))))))
   a(a(b(a(c(c(a(a(b(a(a(x67)))))))))))
   a(a(b(a(c(a(a(b(a(c(c(a(a(b(a(x67)))))))))))))))
   a(a(b(a(c(a(a(b(a(c(a(a(b(a(c(c(a(a(b(x67)))))))))))))))))))
  context: a(a(b(a([]))))
  substitution:
   x67 -> b(a(c(c(a(a(b(c(c(a(a(b(x67))))))))))))
  Qed