YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(b(b(x1))) -> a(x1)
   a(a(a(x1))) -> b(b(x1))
   a(a(x1)) -> a(b(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = x0 + 5,
    
    [b](x0) = x0 + 19
   orientation:
    b(b(b(x1))) = x1 + 57 >= x1 + 5 = a(x1)
    
    a(a(a(x1))) = x1 + 15 >= x1 + 38 = b(b(x1))
    
    a(a(x1)) = x1 + 10 >= x1 + 29 = a(b(a(x1)))
   problem:
    strict:
     a(a(a(x1))) -> b(b(x1))
     a(a(x1)) -> a(b(a(x1)))
    weak:
     b(b(b(x1))) -> a(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [a](x0) = x0 + 5,
     
     [b](x0) = x0 + 2
    orientation:
     a(a(a(x1))) = x1 + 15 >= x1 + 4 = b(b(x1))
     
     a(a(x1)) = x1 + 10 >= x1 + 12 = a(b(a(x1)))
     
     b(b(b(x1))) = x1 + 6 >= x1 + 5 = a(x1)
    problem:
     strict:
      a(a(x1)) -> a(b(a(x1)))
     weak:
      a(a(a(x1))) -> b(b(x1))
      b(b(b(x1))) -> a(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
                [0 1]  
      [a](x0) = [2 3]x0,
      
                [2  0 ]  
      [b](x0) = [1  -&]x0
     orientation:
                 [3 4]      [2 3]                
      a(a(x1)) = [5 6]x1 >= [4 5]x1 = a(b(a(x1)))
      
                    [6 7]      [4 2]             
      a(a(a(x1))) = [8 9]x1 >= [3 1]x1 = b(b(x1))
      
                    [6 4]      [0 1]          
      b(b(b(x1))) = [5 3]x1 >= [2 3]x1 = a(x1)
     problem:
      strict:
       
      weak:
       a(a(x1)) -> a(b(a(x1)))
       a(a(a(x1))) -> b(b(x1))
       b(b(b(x1))) -> a(x1)
     Qed