YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 3
  interpretation:
             [0  -& 0 ]  
   [g](x0) = [-& -& 0 ]x0
             [-& -& -&]  ,
   
             [1  3  -&]  
   [f](x0) = [0  2  3 ]x0
             [0  2  -&]  
  orientation:
                [3  5  -&]     [2  4  -&]                    
   f(g(f(x))) = [2  4  -&]x >= [1  3  -&]x = f(g(g(g(f(x)))))
                [2  4  -&]     [1  3  -&]                    
   
          [0  -& 0 ]     [0  -& 0 ]           
   g(x) = [-& -& 0 ]x >= [-& -& -&]x = g(g(x))
          [-& -& -&]     [-& -& -&]           
  problem:
   strict:
    
   weak:
    g(x) -> g(g(x))
  Qed