YES(?,O(n^3))

Problem:
 c(b(a(X))) -> a(a(b(b(c(c(X))))))
 a(X) -> e()
 b(X) -> e()
 c(X) -> e()

Proof:
 Complexity Transformation Processor:
  strict:
   c(b(a(X))) -> a(a(b(b(c(c(X))))))
   a(X) -> e()
   b(X) -> e()
   c(X) -> e()
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [e] = 0,
     
     [c](x0) = x0,
     
     [b](x0) = x0 + 1,
     
     [a](x0) = x0
    orientation:
     c(b(a(X))) = X + 1 >= X + 2 = a(a(b(b(c(c(X))))))
     
     a(X) = X >= 0 = e()
     
     b(X) = X + 1 >= 0 = e()
     
     c(X) = X >= 0 = e()
    problem:
     strict:
      c(b(a(X))) -> a(a(b(b(c(c(X))))))
      a(X) -> e()
      c(X) -> e()
     weak:
      b(X) -> e()
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [e] = 0,
       
       [c](x0) = x0,
       
       [b](x0) = x0,
       
       [a](x0) = x0 + 1
      orientation:
       c(b(a(X))) = X + 1 >= X + 2 = a(a(b(b(c(c(X))))))
       
       a(X) = X + 1 >= 0 = e()
       
       c(X) = X >= 0 = e()
       
       b(X) = X >= 0 = e()
      problem:
       strict:
        c(b(a(X))) -> a(a(b(b(c(c(X))))))
        c(X) -> e()
       weak:
        a(X) -> e()
        b(X) -> e()
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [e] = 0,
         
         [c](x0) = x0 + 1,
         
         [b](x0) = x0,
         
         [a](x0) = x0
        orientation:
         c(b(a(X))) = X + 1 >= X + 2 = a(a(b(b(c(c(X))))))
         
         c(X) = X + 1 >= 0 = e()
         
         a(X) = X >= 0 = e()
         
         b(X) = X >= 0 = e()
        problem:
         strict:
          c(b(a(X))) -> a(a(b(b(c(c(X))))))
         weak:
          c(X) -> e()
          a(X) -> e()
          b(X) -> e()
        Matrix Interpretation Processor:
         dimension: 3
         max_matrix:
          [1 1 1]
          [0 0 1]
          [0 0 0]
          interpretation:
                 [0]
           [e] = [0]
                 [0],
           
                     [1 0 1]     [1]
           [c](x0) = [0 0 1]x0 + [0]
                     [0 0 0]     [0],
           
                     [1 1 0]     [0]
           [b](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [1],
           
                     [1 0 0]     [0]
           [a](x0) = [0 0 1]x0 + [1]
                     [0 0 0]     [0]
          orientation:
                        [1 0 1]    [3]    [1 0 1]    [2]                      
           c(b(a(X))) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a(a(b(b(c(c(X))))))
                        [0 0 0]    [0]    [0 0 0]    [0]                      
           
                  [1 0 1]    [1]    [0]      
           c(X) = [0 0 1]X + [0] >= [0] = e()
                  [0 0 0]    [0]    [0]      
           
                  [1 0 0]    [0]    [0]      
           a(X) = [0 0 1]X + [1] >= [0] = e()
                  [0 0 0]    [0]    [0]      
           
                  [1 1 0]    [0]    [0]      
           b(X) = [0 0 0]X + [0] >= [0] = e()
                  [0 0 0]    [1]    [0]      
          problem:
           strict:
            
           weak:
            c(b(a(X))) -> a(a(b(b(c(c(X))))))
            c(X) -> e()
            a(X) -> e()
            b(X) -> e()
          Qed