YES(?,O(n^2))

Problem:
 w(r(x)) -> r(w(x))
 b(r(x)) -> r(b(x))
 b(w(x)) -> w(b(x))

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