YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0, x1) = x0 + x1 + 1,
   
   [g](x0, x1) = 4x0 + 4x1 + 1
  orientation:
   f(g(x,y),f(y,y)) = 4x + 6y + 3 >= 4x + 5y + 2 = f(g(y,x),y)
  problem:
   
  Qed