YES

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

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