YES(?,O(n^3))

Problem:
 f(1()) -> f(g(1()))
 f(f(x)) -> f(x)
 g(0()) -> g(f(0()))
 g(g(x)) -> g(x)

Proof:
 Matrix Interpretation Processor:
  dimension: 3
  interpretation:
         [0]
   [0] = [2]
         [3],
   
             [1 0 4]     [0]
   [g](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [2],
   
             [1 1 0]     [0]
   [f](x0) = [0 0 0]x0 + [4]
             [0 0 0]     [2],
   
         [0]
   [1] = [1]
         [0]
  orientation:
            [1]    [0]            
   f(1()) = [4] >= [4] = f(g(1()))
            [2]    [2]            
   
             [1 1 0]    [4]    [1 1 0]    [0]       
   f(f(x)) = [0 0 0]x + [4] >= [0 0 0]x + [4] = f(x)
             [0 0 0]    [2]    [0 0 0]    [2]       
   
            [12]    [10]            
   g(0()) = [0 ] >= [0 ] = g(f(0()))
            [2 ]    [2 ]            
   
             [1 0 4]    [8]    [1 0 4]    [0]       
   g(g(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = g(x)
             [0 0 0]    [2]    [0 0 0]    [2]       
  problem:
   
  Qed