YES

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

Proof:
 DP Processor:
  DPs:
   c#() -> f#()
  TRS:
   c() -> f()
   f() -> g()
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [f#] = 0,
    
    [c#] = 1,
    
    [g] = 0,
    
    [f] = 4,
    
    [c] = 5
   orientation:
    c#() = 1 >= 0 = f#()
    
    c() = 5 >= 4 = f()
    
    f() = 4 >= 0 = g()
   problem:
    DPs:
     
    TRS:
     c() -> f()
     f() -> g()
   Qed