YES

Problem:
 f(0()) -> f(0())
 0() -> 1()

Proof:
 DP Processor:
  DPs:
   f#(0()) -> f#(0())
  TRS:
   f(0()) -> f(0())
   0() -> 1()
  EDG Processor:
   DPs:
    f#(0()) -> f#(0())
   TRS:
    f(0()) -> f(0())
    0() -> 1()
   graph:
    
   Qed