YES

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

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [h](x0, x1) = x0 + 2x1 + x1x1 + 2,
   
   [f](x0, x1) = 2x0 + 2x1 + x0x0 + x1x1 + 4
  orientation:
   f(x,y) = 2x + x*x + 2y + y*y + 4 >= x + 2y + y*y + 2 = h(x,y)
   
   f(x,y) = 2x + x*x + 2y + y*y + 4 >= 2x + x*x + y + 2 = h(y,x)
   
   h(x,x) = 3x + x*x + 2 >= x = x
  problem:
   
  Qed