YES

Problem:
 strict:
  g(x,y) -> x
  g(x,y) -> y
  f(s(x),y,y) -> f(y,x,s(x))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
               
   [s](x0) = x0,
   
                [2 0]     [0]
   [rand](x0) = [0 2]x0 + [2],
   
                 [2 2]     [2 2]     [1]
   [g](x0, x1) = [2 2]x0 + [2 2]x1 + [2],
   
                     [2 3]     [1 2]     [1 1]  
   [f](x0, x1, x2) = [0 1]x0 + [0 1]x1 + [0 0]x2
  orientation:
            [2 2]    [2 2]    [1]         
   g(x,y) = [2 2]x + [2 2]y + [2] >= x = x
   
            [2 2]    [2 2]    [1]         
   g(x,y) = [2 2]x + [2 2]y + [2] >= y = y
   
                 [2 3]    [2 3]     [2 3]    [2 3]               
   f(s(x),y,y) = [0 1]x + [0 1]y >= [0 1]x + [0 1]y = f(y,x,s(x))
   
             [2 0]    [0]         
   rand(x) = [0 2]x + [2] >= x = x
   
             [2 0]    [0]    [2 0]    [0]             
   rand(x) = [0 2]x + [2] >= [0 2]x + [2] = rand(s(x))
  problem:
   strict:
    f(s(x),y,y) -> f(y,x,s(x))
   weak:
    rand(x) -> x
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                
    [s](x0) = x0,
    
                 [2 0]     [1]
    [rand](x0) = [0 3]x0 + [0],
    
                      [3 0]     [2 0]     [1 0]     [2]
    [f](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2 + [2]
   orientation:
                  [3 0]    [3 0]    [2]    [3 0]    [3 0]    [2]              
    f(s(x),y,y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(y,x,s(x))
    
              [2 0]    [1]         
    rand(x) = [0 3]x + [0] >= x = x
    
              [2 0]    [1]    [2 0]    [1]             
    rand(x) = [0 3]x + [0] >= [0 3]x + [0] = rand(s(x))
   problem:
    strict:
     f(s(x),y,y) -> f(y,x,s(x))
    weak:
     rand(x) -> rand(s(x))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [1 0]     [0]
     [s](x0) = [2 1]x0 + [1],
     
                  [2 0]     [3]
     [rand](x0) = [0 0]x0 + [0],
     
                       [1 1]     [1 1]     [2 0]     [0]
     [f](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2 + [2]
    orientation:
                   [3 1]    [3 1]    [1]    [3 1]    [1 1]    [0]              
     f(s(x),y,y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(y,x,s(x))
     
               [2 0]    [3]    [2 0]    [3]             
     rand(x) = [0 0]x + [0] >= [0 0]x + [0] = rand(s(x))
    problem:
     strict:
      
     weak:
      rand(x) -> rand(s(x))
    Qed