YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(b(b(x1))) -> a(b(x1))
   a(a(x1)) -> a(b(a(x1)))
   a(a(a(x1))) -> a(b(b(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = x0,
    
    [b](x0) = x0 + 19
   orientation:
    b(b(b(x1))) = x1 + 57 >= x1 + 19 = a(b(x1))
    
    a(a(x1)) = x1 >= x1 + 19 = a(b(a(x1)))
    
    a(a(a(x1))) = x1 >= x1 + 38 = a(b(b(x1)))
   problem:
    strict:
     a(a(x1)) -> a(b(a(x1)))
     a(a(a(x1))) -> a(b(b(x1)))
    weak:
     b(b(b(x1))) -> a(b(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [a](x0) = x0 + 12,
     
     [b](x0) = x0 + 8
    orientation:
     a(a(x1)) = x1 + 24 >= x1 + 32 = a(b(a(x1)))
     
     a(a(a(x1))) = x1 + 36 >= x1 + 28 = a(b(b(x1)))
     
     b(b(b(x1))) = x1 + 24 >= x1 + 20 = a(b(x1))
    problem:
     strict:
      a(a(x1)) -> a(b(a(x1)))
     weak:
      a(a(a(x1))) -> a(b(b(x1)))
      b(b(b(x1))) -> a(b(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
                [0 2]  
      [a](x0) = [2 5]x0,
      
                [3  -&]  
      [b](x0) = [1  -&]x0
     orientation:
                 [4  7 ]      [3 5]                
      a(a(x1)) = [7  10]x1 >= [6 8]x1 = a(b(a(x1)))
      
                    [9  12]      [6  -&]                
      a(a(a(x1))) = [12 15]x1 >= [9  -&]x1 = a(b(b(x1)))
      
                    [9  -&]      [3  -&]             
      b(b(b(x1))) = [7  -&]x1 >= [6  -&]x1 = a(b(x1))
     problem:
      strict:
       
      weak:
       a(a(x1)) -> a(b(a(x1)))
       a(a(a(x1))) -> a(b(b(x1)))
       b(b(b(x1))) -> a(b(x1))
     Qed