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:
 RT 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
   interpretation:
    [b](x0) = x0 + 9,
    
    [a](x0) = x0 + 19
   orientation:
    a(b(a(x1))) = x1 + 47 >= x1 + 28 = b(a(x1))
    
    b(b(b(x1))) = x1 + 27 >= x1 + 37 = b(a(b(x1)))
    
    a(a(x1)) = x1 + 38 >= x1 + 27 = b(b(b(x1)))
   problem:
    strict:
     b(b(b(x1))) -> b(a(b(x1)))
    weak:
     a(b(a(x1))) -> b(a(x1))
     a(a(x1)) -> b(b(b(x1)))
   Matrix Interpretation Processor:
    dimension: 2
    interpretation:
               [1 0]     [4]
     [b](x0) = [0 0]x0 + [0],
     
               [1 2]     [2]
     [a](x0) = [0 1]x0 + [4]
    orientation:
                   [1 0]     [12]    [1 0]     [10]              
     b(b(b(x1))) = [0 0]x1 + [0 ] >= [0 0]x1 + [0 ] = b(a(b(x1)))
     
                   [1 2]     [8]    [1 2]     [6]           
     a(b(a(x1))) = [0 0]x1 + [4] >= [0 0]x1 + [0] = b(a(x1))
     
                [1 4]     [12]    [1 0]     [12]              
     a(a(x1)) = [0 1]x1 + [8 ] >= [0 0]x1 + [0 ] = b(b(b(x1)))
    problem:
     strict:
      
     weak:
      b(b(b(x1))) -> b(a(b(x1)))
      a(b(a(x1))) -> b(a(x1))
      a(a(x1)) -> b(b(b(x1)))
    Qed