YES(?,O(n^2))

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

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