YES(?,O(n^3))

Problem:
 a(b(x1)) -> b(a(x1))
 b(a(x1)) -> a(a(c(b(x1))))

Proof:
 Complexity Transformation Processor:
  strict:
   a(b(x1)) -> b(a(x1))
   b(a(x1)) -> a(a(c(b(x1))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 2
   max_matrix:
    [1 1]
    [0 1]
    interpretation:
               [1 0]  
     [c](x0) = [0 0]x0,
     
               [1 1]  
     [a](x0) = [0 1]x0,
     
                    [1]
     [b](x0) = x0 + [1]
    orientation:
                [1 1]     [2]    [1 1]     [1]           
     a(b(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = b(a(x1))
     
                [1 1]     [1]    [1 0]     [1]                 
     b(a(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [0] = a(a(c(b(x1))))
    problem:
     strict:
      b(a(x1)) -> a(a(c(b(x1))))
     weak:
      a(b(x1)) -> b(a(x1))
    Matrix Interpretation Processor:
     dimension: 3
     max_matrix:
      [1 1 1]
      [0 1 0]
      [0 0 1]
      interpretation:
                 [1 0 0]  
       [c](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
                 [1 0 1]     [0]
       [a](x0) = [0 1 0]x0 + [1]
                 [0 0 1]     [0],
       
                 [1 1 0]     [0]
       [b](x0) = [0 1 0]x0 + [1]
                 [0 0 1]     [1]
      orientation:
                  [1 1 1]     [1]    [1 1 0]     [0]                 
       b(a(x1)) = [0 1 0]x1 + [2] >= [0 0 0]x1 + [2] = a(a(c(b(x1))))
                  [0 0 1]     [1]    [0 0 0]     [0]                 
       
                  [1 1 1]     [1]    [1 1 1]     [1]           
       a(b(x1)) = [0 1 0]x1 + [2] >= [0 1 0]x1 + [2] = b(a(x1))
                  [0 0 1]     [1]    [0 0 1]     [1]           
      problem:
       strict:
        
       weak:
        b(a(x1)) -> a(a(c(b(x1))))
        a(b(x1)) -> b(a(x1))
      Qed