YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   a(b(a(x1))) -> b(x1)
   b(a(b(x1))) -> b(b(b(x1)))
   b(b(x1)) -> a(a(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 20,
    
    [a](x0) = x0 + 1
   orientation:
    a(b(a(x1))) = x1 + 22 >= x1 + 20 = b(x1)
    
    b(a(b(x1))) = x1 + 41 >= x1 + 60 = b(b(b(x1)))
    
    b(b(x1)) = x1 + 40 >= x1 + 3 = a(a(a(x1)))
   problem:
    strict:
     b(a(b(x1))) -> b(b(b(x1)))
    weak:
     a(b(a(x1))) -> b(x1)
     b(b(x1)) -> a(a(a(x1)))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [1 4]  
     [b](x0) = [1 4]x0,
     
               [0  -&]  
     [a](x0) = [5  0 ]x0
    orientation:
                   [10 13]      [9  12]                
     b(a(b(x1))) = [10 13]x1 >= [9  12]x1 = b(b(b(x1)))
     
                   [9  4 ]      [1 4]          
     a(b(a(x1))) = [14 9 ]x1 >= [1 4]x1 = b(x1)
     
                [5 8]      [0  -&]                
     b(b(x1)) = [5 8]x1 >= [5  0 ]x1 = a(a(a(x1)))
    problem:
     strict:
      
     weak:
      b(a(b(x1))) -> b(b(b(x1)))
      a(b(a(x1))) -> b(x1)
      b(b(x1)) -> a(a(a(x1)))
    Qed