YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0, x1, x2) = 2x0 + 2x1 + x2,
   
   [s](x0) = 5x0,
   
   [g](x0, x1) = x0 + x1 + 1
  orientation:
   g(x,y) = x + y + 1 >= x = x
   
   g(x,y) = x + y + 1 >= y = y
   
   f(s(x),y,y) = 10x + 3y >= 7x + 2y = f(y,x,s(x))
  problem:
   f(s(x),y,y) -> f(y,x,s(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1, x2) = 3x0 + x1 + 2x2,
    
    [s](x0) = x0 + 1
   orientation:
    f(s(x),y,y) = 3x + 3y + 3 >= 3x + 3y + 2 = f(y,x,s(x))
   problem:
    
   Qed