YES

Problem:
 g(b()) -> f(b())
 f(a()) -> g(a())
 b() -> a()

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [a] = 1,
   
   [f](x0) = 4x0,
   
   [g](x0) = -5x0 + 6x0x0 + 2,
   
   [b] = 2
  orientation:
   g(b()) = 16 >= 8 = f(b())
   
   f(a()) = 4 >= 3 = g(a())
   
   b() = 2 >= 1 = a()
  problem:
   
  Qed