YES

Problem:
 f(f(X)) -> c()
 c() -> d()
 h(X) -> c()

Proof:
 DP Processor:
  DPs:
   f#(f(X)) -> c#()
   h#(X) -> c#()
  TRS:
   f(f(X)) -> c()
   c() -> d()
   h(X) -> c()
  Usable Rule Processor:
   DPs:
    f#(f(X)) -> c#()
    h#(X) -> c#()
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [h#](x0) = x0 + 9,
     
     [c#] = 0,
     
     [f#](x0) = 4x0 + 12,
     
     [f](x0) = x0
    orientation:
     f#(f(X)) = 4X + 12 >= 0 = c#()
     
     h#(X) = X + 9 >= 0 = c#()
    problem:
     DPs:
      
     TRS:
      
    Qed