YES(?,O(n^2))

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

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [1 0]     [4]
   [g](x0) = [0 0]x0 + [0],
   
             [1 2]     [7]
   [f](x0) = [0 0]x0 + [8]
  orientation:
             [1 2]    [30]    [1 2]    [29]                   
   f(f(X)) = [0 0]X + [8 ] >= [0 0]X + [8 ] = f(g(f(g(f(X)))))
   
                [1 2]    [18]    [1 0]    [11]          
   f(g(f(X))) = [0 0]X + [8 ] >= [0 0]X + [8 ] = f(g(X))
  problem:
   
  Qed