YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 3
  interpretation:
             [0  0  1 ]  
   [g](x0) = [0  0  1 ]x0
             [-& -& -&]  ,
   
             [0 1 0]  
   [f](x0) = [2 1 1]x0
             [0 0 0]  
  orientation:
             [3 2 2]     [2  1  1 ]           
   f(f(x)) = [3 3 2]x >= [2  1  1 ]x = g(f(x))
             [2 1 1]     [-& -& -&]           
  problem:
   
  Qed