YES

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

Proof:
 DP Processor:
  DPs:
   c#() -> f#()
  TRS:
   c() -> f()
   f() -> g()
  Usable Rule Processor:
   DPs:
    c#() -> f#()
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#] = 1,
     
     [c#] = 2
    orientation:
     c#() = 2 >= 1 = f#()
    problem:
     DPs:
      
     TRS:
      
    Qed