YES

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

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