YES(?,O(n^2))

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(x)) -> b(b(x))
   b(b(a(x))) -> a(b(b(x)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 6,
    
    [a](x0) = x0 + 22
   orientation:
    a(a(x)) = x + 44 >= x + 12 = b(b(x))
    
    b(b(a(x))) = x + 34 >= x + 34 = 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
    interpretation:
               [1 2]     [0]
     [b](x0) = [0 1]x0 + [2],
     
               [1 3]     [1]
     [a](x0) = [0 1]x0 + [6]
    orientation:
                  [1 7]    [29]    [1 7]    [17]             
     b(b(a(x))) = [0 1]x + [10] >= [0 1]x + [10] = a(b(b(x)))
     
               [1 6]    [20]    [1 4]    [4]          
     a(a(x)) = [0 1]x + [12] >= [0 1]x + [4] = b(b(x))
    problem:
     strict:
      
     weak:
      b(b(a(x))) -> a(b(b(x)))
      a(a(x)) -> b(b(x))
    Qed