YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   a(b(b(x1))) -> a(x1)
   a(a(x1)) -> b(b(b(x1)))
   b(b(a(x1))) -> a(b(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = x0 + 7,
    
    [b](x0) = x0 + 10
   orientation:
    a(b(b(x1))) = x1 + 27 >= x1 + 7 = a(x1)
    
    a(a(x1)) = x1 + 14 >= x1 + 30 = b(b(b(x1)))
    
    b(b(a(x1))) = x1 + 27 >= x1 + 24 = a(b(a(x1)))
   problem:
    strict:
     a(a(x1)) -> b(b(b(x1)))
    weak:
     a(b(b(x1))) -> a(x1)
     b(b(a(x1))) -> a(b(a(x1)))
   Arctic Interpretation Processor:
    dimension: 3
    interpretation:
               [0  -& 0 ]  
     [a](x0) = [-& -& 0 ]x0
               [1  0  1 ]  ,
     
               [0  -& -&]  
     [b](x0) = [-& -& 0 ]x0
               [0  0  -&]  
    orientation:
                [1 0 1]      [0  -& -&]                
     a(a(x1)) = [1 0 1]x1 >= [0  -& 0 ]x1 = b(b(b(x1)))
                [2 1 2]      [0  0  -&]                
     
                   [0  -& 0 ]      [0  -& 0 ]          
     a(b(b(x1))) = [0  -& 0 ]x1 >= [-& -& 0 ]x1 = a(x1)
                   [1  0  1 ]      [1  0  1 ]          
     
                   [0  -& 0 ]      [0  -& 0 ]                
     b(b(a(x1))) = [0  -& 0 ]x1 >= [0  -& 0 ]x1 = a(b(a(x1)))
                   [1  0  1 ]      [1  0  1 ]                
    problem:
     strict:
      
     weak:
      a(a(x1)) -> b(b(b(x1)))
      a(b(b(x1))) -> a(x1)
      b(b(a(x1))) -> a(b(a(x1)))
    Qed