NO

Problem:
 a(b(x)) -> b(c(x))
 a(c(x)) -> c(a(x))
 b(b(x)) -> a(c(x))
 c(b(x)) -> b(c(x))
 c(b(x)) -> c(c(x))
 c(c(x)) -> c(b(x))
 0(1(2(x))) -> 2(0(1(x)))
 2(2(2(2(2(2(2(1(1(1(1(2(x)))))))))))) -> 2(1(2(2(0(1(2(1(1(0(1(0(x))))))))))))

Proof:
 sorted: (order-sorted)
 0:0(1(2(x))) -> 2(0(1(x)))
   2(2(2(2(2(2(2(1(1(1(1(2(x)))))))))))) -> 2(1(2(2(0(1(2(1(1(0(1(0(x))))))))))))
 1:a(b(x)) -> b(c(x))
   a(c(x)) -> c(a(x))
   b(b(x)) -> a(c(x))
   c(b(x)) -> b(c(x))
   c(b(x)) -> c(c(x))
   c(c(x)) -> c(b(x))
 -----
 sorts
   []
 sort attachment (non-strict)
   a : 1 -> 1
   b : 1 -> 1
   c : 1 -> 1
   0 : 0 -> 0
   1 : 0 -> 0
   2 : 0 -> 0
 -----
 0:0(1(2(x))) -> 2(0(1(x)))
   2(2(2(2(2(2(2(1(1(1(1(2(x)))))))))))) -> 2(1(2(2(0(1(2(1(1(0(1(0(x))))))))))))
   Nonconfluence Processor:
    terms: 2(0(1(1(2(2(2(0(1(1(1(0(1(0(x270)))))))))))))) *<- 0(1(2(2
                                                                    (
                                                                    2
                                                                    (
                                                                    2(2(2(2(1(1(1(1(2(x270)))))))))))))) ->* 
    2(2(2(2(2(2(2(0(1(1(1(1(1(2(x270))))))))))))))
    Qed
 
 
 1:a(b(x)) -> b(c(x))
   a(c(x)) -> c(a(x))
   b(b(x)) -> a(c(x))
   c(b(x)) -> b(c(x))
   c(b(x)) -> c(c(x))
   c(c(x)) -> c(b(x))
   Open