YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(a(x1))) -> b(x1)
   b(b(x1)) -> b(a(b(x1)))
   b(b(x1)) -> a(a(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 20,
    
    [a](x0) = x0 + 9
   orientation:
    a(a(a(x1))) = x1 + 27 >= x1 + 20 = b(x1)
    
    b(b(x1)) = x1 + 40 >= x1 + 49 = b(a(b(x1)))
    
    b(b(x1)) = x1 + 40 >= x1 + 18 = a(a(x1))
   problem:
    strict:
     b(b(x1)) -> b(a(b(x1)))
    weak:
     a(a(a(x1))) -> b(x1)
     b(b(x1)) -> a(a(x1))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [0 2]  
     [b](x0) = [4 7]x0,
     
               [3  1 ]  
     [a](x0) = [3  -&]x0
    orientation:
                [6  9 ]      [5  8 ]                
     b(b(x1)) = [11 14]x1 >= [10 12]x1 = b(a(b(x1)))
     
                   [9 7]      [0 2]          
     a(a(a(x1))) = [9 7]x1 >= [4 7]x1 = b(x1)
     
                [6  9 ]      [6 4]             
     b(b(x1)) = [11 14]x1 >= [6 4]x1 = a(a(x1))
    problem:
     strict:
      
     weak:
      b(b(x1)) -> b(a(b(x1)))
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> a(a(x1))
    Qed