YES

Problem:
 c() -> f()
 f() -> g()

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [g] = 0,
   
   [f] = 2,
   
   [c] = 3
  orientation:
   c() = 3 >= 2 = f()
   
   f() = 2 >= 0 = g()
  problem:
   
  Qed