YES

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

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [f] = 4,
   
   [c] = 5,
   
   [g] = 0
  orientation:
   c() = 5 >= 4 = f()
   
   f() = 4 >= 0 = g()
  problem:
   
  Qed