YES

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

Proof:
 DP Processor:
  DPs:
   f#(g(X)) -> f#(X)
  TRS:
   f(g(X)) -> f(X)
  CDG Processor:
   DPs:
    f#(g(X)) -> f#(X)
   TRS:
    f(g(X)) -> f(X)
   graph:
    
   Qed