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()
  TDG Processor:
   DPs:
    f#(f(X)) -> c#()
    h#(X) -> c#()
   TRS:
    f(f(X)) -> c()
    c() -> d()
    h(X) -> c()
   graph:
    
   Qed