YES

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

Proof:
 String Reversal Processor:
  strict:
   f(f(x)) -> x
  weak:
   f(x) -> f(g(f(g(x))))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 0]  
    [g](x0) = [0 0]x0,
    
              [1 1]     [0]
    [f](x0) = [2 0]x0 + [2]
   orientation:
              [3 1]    [2]         
    f(f(x)) = [2 2]x + [2] >= x = x
    
           [1 1]    [0]    [1 0]    [0]                
    f(x) = [2 0]x + [2] >= [2 0]x + [2] = f(g(f(g(x))))
   problem:
    strict:
     
    weak:
     f(x) -> f(g(f(g(x))))
   Qed