YES(?,O(n^2))

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

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