YES(?,O(n^2))

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

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [1 6]     [1]
   [g](x0) = [0 0]x0 + [0],
   
         [8]
   [0] = [0],
   
             [1 4]     [4]
   [s](x0) = [0 0]x0 + [1],
   
             [1 0]     [5]
   [f](x0) = [0 0]x0 + [0]
  orientation:
             [1 0]    [10]    [1 0]    [5]       
   f(f(x)) = [0 0]x + [0 ] >= [0 0]x + [0] = f(x)
   
             [1 4]    [9]    [1 0]    [5]       
   f(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = f(x)
   
               [19]    [18]               
   g(s(0())) = [0 ] >= [0 ] = g(f(s(0())))
  problem:
   
  Qed