YES

Problem:
 b(b(0(),y),x) -> y
 c(c(c(y))) -> c(c(a(a(c(b(0(),y)),0()),0())))
 a(y,0()) -> b(y,0())

Proof:
 DP Processor:
  DPs:
   c#(c(c(y))) -> b#(0(),y)
   c#(c(c(y))) -> c#(b(0(),y))
   c#(c(c(y))) -> a#(c(b(0(),y)),0())
   c#(c(c(y))) -> a#(a(c(b(0(),y)),0()),0())
   c#(c(c(y))) -> c#(a(a(c(b(0(),y)),0()),0()))
   c#(c(c(y))) -> c#(c(a(a(c(b(0(),y)),0()),0())))
   a#(y,0()) -> b#(y,0())
  TRS:
   b(b(0(),y),x) -> y
   c(c(c(y))) -> c(c(a(a(c(b(0(),y)),0()),0())))
   a(y,0()) -> b(y,0())
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    b(b(0(),y),x) -> y
    c(c(c(y))) -> c(c(a(a(c(b(0(),y)),0()),0())))
    a(y,0()) -> b(y,0())
   interpretation:
    [a#](x0, x1) = x0 + 5/2,
    
    [c#](x0) = 2x0 + 2,
    
    [b#](x0, x1) = x0 + 2,
    
    [a](x0, x1) = 1/2x0,
    
    [c](x0) = 2x0 + 2,
    
    [b](x0, x1) = 1/2x0 + 2x1,
    
    [0] = 0
   orientation:
    c#(c(c(y))) = 8y + 14 >= 2 = b#(0(),y)
    
    c#(c(c(y))) = 8y + 14 >= 4y + 2 = c#(b(0(),y))
    
    c#(c(c(y))) = 8y + 14 >= 4y + 9/2 = a#(c(b(0(),y)),0())
    
    c#(c(c(y))) = 8y + 14 >= 2y + 7/2 = a#(a(c(b(0(),y)),0()),0())
    
    c#(c(c(y))) = 8y + 14 >= 2y + 3 = c#(a(a(c(b(0(),y)),0()),0()))
    
    c#(c(c(y))) = 8y + 14 >= 4y + 8 = c#(c(a(a(c(b(0(),y)),0()),0())))
    
    a#(y,0()) = y + 5/2 >= y + 2 = b#(y,0())
    
    b(b(0(),y),x) = 2x + y >= y = y
    
    c(c(c(y))) = 8y + 14 >= 4y + 8 = c(c(a(a(c(b(0(),y)),0()),0())))
    
    a(y,0()) = 1/2y >= 1/2y = b(y,0())
   problem:
    DPs:
     
    TRS:
     b(b(0(),y),x) -> y
     c(c(c(y))) -> c(c(a(a(c(b(0(),y)),0()),0())))
     a(y,0()) -> b(y,0())
   Qed