YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(b(b(x1))) -> a(x1)
   a(a(x1)) -> a(b(a(x1)))
   a(a(a(x1))) -> b(a(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = x0 + 19,
    
    [b](x0) = x0 + 17
   orientation:
    b(b(b(x1))) = x1 + 51 >= x1 + 19 = a(x1)
    
    a(a(x1)) = x1 + 38 >= x1 + 55 = a(b(a(x1)))
    
    a(a(a(x1))) = x1 + 57 >= x1 + 55 = b(a(a(x1)))
   problem:
    strict:
     a(a(x1)) -> a(b(a(x1)))
    weak:
     b(b(b(x1))) -> a(x1)
     a(a(a(x1))) -> b(a(a(x1)))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [0 1]  
     [a](x0) = [4 5]x0,
     
               [2  0 ]  
     [b](x0) = [3  -&]x0
    orientation:
                [5  6 ]      [4 5]                
     a(a(x1)) = [9  10]x1 >= [8 9]x1 = a(b(a(x1)))
     
                   [6 4]      [0 1]          
     b(b(b(x1))) = [7 5]x1 >= [4 5]x1 = a(x1)
     
                   [10 11]      [9  10]                
     a(a(a(x1))) = [14 15]x1 >= [8  9 ]x1 = b(a(a(x1)))
    problem:
     strict:
      
     weak:
      a(a(x1)) -> a(b(a(x1)))
      b(b(b(x1))) -> a(x1)
      a(a(a(x1))) -> b(a(a(x1)))
    Qed