YES(?,O(n^2))

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

Proof:
 Complexity Transformation Processor:
  strict:
   a(x1) -> b(b(x1))
   b(b(b(x1))) -> a(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0,
     
     [a](x0) = x0 + 1
    orientation:
     a(x1) = x1 + 1 >= x1 = b(b(x1))
     
     b(b(b(x1))) = x1 >= x1 + 1 = a(x1)
    problem:
     strict:
      b(b(b(x1))) -> a(x1)
     weak:
      a(x1) -> b(b(x1))
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 0]
      interpretation:
                 [1 1]     [0]
       [b](x0) = [0 0]x0 + [1],
       
                 [1 1]     [1]
       [a](x0) = [0 0]x0 + [1]
      orientation:
                     [1 1]     [2]    [1 1]     [1]        
       b(b(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(x1)
       
               [1 1]     [1]    [1 1]     [1]           
       a(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(b(x1))
      problem:
       strict:
        
       weak:
        b(b(b(x1))) -> a(x1)
        a(x1) -> b(b(x1))
      Qed