YES(?,O(n^2))

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

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