YES

Problem:
 f(x,y) -> x
 g(a()) -> h(a(),b(),a())
 i(x) -> f(x,x)
 h(x,x,y) -> g(x)

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [i](x0) = 7x0 + 7x0x0 + 5,
   
   [h](x0, x1, x2) = 4x0 + 5x1 + 2x2 + x1x1 + 1,
   
   [b] = 0,
   
   [g](x0) = 4x0 + x0x0,
   
   [a] = 4,
   
   [f](x0, x1) = 3x0 + 4x1 + 6x0x0 + x1x1 + 4
  orientation:
   f(x,y) = 3x + 6x*x + 4y + y*y + 4 >= x = x
   
   g(a()) = 32 >= 25 = h(a(),b(),a())
   
   i(x) = 7x + 7x*x + 5 >= 7x + 7x*x + 4 = f(x,x)
   
   h(x,x,y) = 9x + x*x + 2y + 1 >= 4x + x*x = g(x)
  problem:
   
  Qed