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) = -3x0 + 5x1 + 4x0x0 + 4x1x1 + 4,
   
   [f](x0, x1) = 5x0 + 5x1 + 4x0x0 + 4x1x1 + 5
  orientation:
   f(x,y) = 5x + 4x*x + 5y + 4y*y + 5 >= -3x + 4x*x + 5y + 4y*y + 4 = h(x,y)
   
   f(x,y) = 5x + 4x*x + 5y + 4y*y + 5 >= 5x + 4x*x + -3y + 4y*y + 4 = h(y,x)
   
   h(x,x) = 2x + 8x*x + 4 >= x = x
  problem:
   
  Qed