YES

Problem:
 f(x) -> g(a())
 g(x) -> x
 h(x,x) -> 0()
 a() -> 1()

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [1] = 0,
   
   [0] = 0,
   
   [h](x0, x1) = -1x0 + 2x1 + 2x0x0 + x0x1 + 2,
   
   [g](x0) = 2x0 + 1,
   
   [a] = 1,
   
   [f](x0) = 2x0 + 4x0x0 + 4
  orientation:
   f(x) = 2x + 4x*x + 4 >= 3 = g(a())
   
   g(x) = 2x + 1 >= x = x
   
   h(x,x) = x + 3x*x + 2 >= 0 = 0()
   
   a() = 1 >= 0 = 1()
  problem:
   
  Qed