YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(b(x1)) -> a(a(a(x1)))
   b(a(b(x1))) -> a(x1)
   b(a(a(x1))) -> b(a(b(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [a](x0) = x0 + 20,
    
    [b](x0) = x0 + 15
   orientation:
    b(b(x1)) = x1 + 30 >= x1 + 60 = a(a(a(x1)))
    
    b(a(b(x1))) = x1 + 50 >= x1 + 20 = a(x1)
    
    b(a(a(x1))) = x1 + 55 >= x1 + 50 = b(a(b(x1)))
   problem:
    strict:
     b(b(x1)) -> a(a(a(x1)))
    weak:
     b(a(b(x1))) -> a(x1)
     b(a(a(x1))) -> b(a(b(x1)))
   Arctic Interpretation Processor:
    dimension: 3
    interpretation:
               [0  -& -&]  
     [a](x0) = [0  -& 0 ]x0
               [0  0  -&]  ,
     
               [0  -& 0 ]  
     [b](x0) = [0  -& 0 ]x0
               [1  0  2 ]  
    orientation:
                [1 0 2]      [0  -& -&]                
     b(b(x1)) = [1 0 2]x1 >= [0  -& 0 ]x1 = a(a(a(x1)))
                [3 2 4]      [0  0  -&]                
     
                   [0  -& 0 ]      [0  -& -&]          
     b(a(b(x1))) = [0  -& 0 ]x1 >= [0  -& 0 ]x1 = a(x1)
                   [2  0  2 ]      [0  0  -&]          
     
                   [0  -& 0 ]      [0  -& 0 ]                
     b(a(a(x1))) = [0  -& 0 ]x1 >= [0  -& 0 ]x1 = b(a(b(x1)))
                   [2  0  2 ]      [2  0  2 ]                
    problem:
     strict:
      
     weak:
      b(b(x1)) -> a(a(a(x1)))
      b(a(b(x1))) -> a(x1)
      b(a(a(x1))) -> b(a(b(x1)))
    Qed