YES(?,O(n^2))

Problem:
 f(f(x)) -> g(f(x))
 g(g(x)) -> f(x)

Proof:
 Complexity Transformation Processor:
  strict:
   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [g](x0) = x0 + 1,
     
     [f](x0) = x0
    orientation:
     f(f(x)) = x >= x + 1 = g(f(x))
     
     g(g(x)) = x + 2 >= x = f(x)
    problem:
     strict:
      f(f(x)) -> g(f(x))
     weak:
      g(g(x)) -> f(x)
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 1]
      interpretation:
                 [1 1]     [0]
       [g](x0) = [0 1]x0 + [1],
       
                 [1 1]     [1]
       [f](x0) = [0 1]x0 + [1]
      orientation:
                 [1 2]    [3]    [1 2]    [2]          
       f(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = g(f(x))
       
                 [1 2]    [1]    [1 1]    [1]       
       g(g(x)) = [0 1]x + [2] >= [0 1]x + [1] = f(x)
      problem:
       strict:
        
       weak:
        f(f(x)) -> g(f(x))
        g(g(x)) -> f(x)
      Qed