YES

Problem:
 f(0()) -> cons(0(),n__f(s(0())))
 f(s(0())) -> f(p(s(0())))
 p(s(0())) -> 0()
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(s(0())) -> p#(s(0()))
   f#(s(0())) -> f#(p(s(0())))
   activate#(n__f(X)) -> f#(X)
  TRS:
   f(0()) -> cons(0(),n__f(s(0())))
   f(s(0())) -> f(p(s(0())))
   p(s(0())) -> 0()
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(s(0())) -> p#(s(0()))
    f#(s(0())) -> f#(p(s(0())))
    activate#(n__f(X)) -> f#(X)
   TRS:
    f(0()) -> cons(0(),n__f(s(0())))
    f(s(0())) -> f(p(s(0())))
    p(s(0())) -> 0()
    f(X) -> n__f(X)
    activate(n__f(X)) -> f(X)
    activate(X) -> X
   graph:
    activate#(n__f(X)) -> f#(X) -> f#(s(0())) -> f#(p(s(0())))
    activate#(n__f(X)) -> f#(X) -> f#(s(0())) -> p#(s(0()))
    f#(s(0())) -> f#(p(s(0()))) -> f#(s(0())) -> f#(p(s(0())))
    f#(s(0())) -> f#(p(s(0()))) -> f#(s(0())) -> p#(s(0()))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/9
    DPs:
     f#(s(0())) -> f#(p(s(0())))
    TRS:
     f(0()) -> cons(0(),n__f(s(0())))
     f(s(0())) -> f(p(s(0())))
     p(s(0())) -> 0()
     f(X) -> n__f(X)
     activate(n__f(X)) -> f(X)
     activate(X) -> X
    CDG Processor:
     DPs:
      f#(s(0())) -> f#(p(s(0())))
     TRS:
      f(0()) -> cons(0(),n__f(s(0())))
      f(s(0())) -> f(p(s(0())))
      p(s(0())) -> 0()
      f(X) -> n__f(X)
      activate(n__f(X)) -> f(X)
      activate(X) -> X
     graph:
      
     Qed