YES(?,O(n^2))

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

Proof:
 RT Transformation Processor:
  strict:
   b(a(x1)) -> a(b(x1))
   a(a(a(x1))) -> b(a(a(b(x1))))
   b(b(b(b(x1)))) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 2,
    
    [a](x0) = x0
   orientation:
    b(a(x1)) = x1 + 2 >= x1 + 2 = a(b(x1))
    
    a(a(a(x1))) = x1 >= x1 + 4 = b(a(a(b(x1))))
    
    b(b(b(b(x1)))) = x1 + 8 >= x1 = a(x1)
   problem:
    strict:
     b(a(x1)) -> a(b(x1))
     a(a(a(x1))) -> b(a(a(b(x1))))
    weak:
     b(b(b(b(x1)))) -> a(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = x0 + 1,
     
     [a](x0) = x0 + 3
    orientation:
     b(a(x1)) = x1 + 4 >= x1 + 4 = a(b(x1))
     
     a(a(a(x1))) = x1 + 9 >= x1 + 8 = b(a(a(b(x1))))
     
     b(b(b(b(x1)))) = x1 + 4 >= x1 + 3 = a(x1)
    problem:
     strict:
      b(a(x1)) -> a(b(x1))
     weak:
      a(a(a(x1))) -> b(a(a(b(x1))))
      b(b(b(b(x1)))) -> a(x1)
    Matrix Interpretation Processor:
     dimension: 2
     interpretation:
                [1 1]     [2]
      [b](x0) = [0 1]x0 + [1],
      
                [1 2]     [1]
      [a](x0) = [0 1]x0 + [4]
     orientation:
                 [1 3]     [7]    [1 3]     [5]           
      b(a(x1)) = [0 1]x1 + [5] >= [0 1]x1 + [5] = a(b(x1))
      
                    [1 6]     [27]    [1 6]     [27]                 
      a(a(a(x1))) = [0 1]x1 + [12] >= [0 1]x1 + [10] = b(a(a(b(x1))))
      
                       [1 4]     [14]    [1 2]     [1]        
      b(b(b(b(x1)))) = [0 1]x1 + [4 ] >= [0 1]x1 + [4] = a(x1)
     problem:
      strict:
       
      weak:
       b(a(x1)) -> a(b(x1))
       a(a(a(x1))) -> b(a(a(b(x1))))
       b(b(b(b(x1)))) -> a(x1)
     Qed