YES

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

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