YES(?,O(n^2))

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

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