YES

Problem:
 f(0()) -> cons(0(),n__f(n__s(n__0())))
 f(s(0())) -> f(p(s(0())))
 p(s(0())) -> 0()
 f(X) -> n__f(X)
 s(X) -> n__s(X)
 0() -> n__0()
 activate(n__f(X)) -> f(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__0()) -> 0()
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(s(0())) -> p#(s(0()))
   f#(s(0())) -> f#(p(s(0())))
   activate#(n__f(X)) -> activate#(X)
   activate#(n__f(X)) -> f#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__0()) -> 0#()
  TRS:
   f(0()) -> cons(0(),n__f(n__s(n__0())))
   f(s(0())) -> f(p(s(0())))
   p(s(0())) -> 0()
   f(X) -> n__f(X)
   s(X) -> n__s(X)
   0() -> n__0()
   activate(n__f(X)) -> f(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__0()) -> 0()
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(s(0())) -> p#(s(0()))
    f#(s(0())) -> f#(p(s(0())))
    activate#(n__f(X)) -> activate#(X)
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__0()) -> 0#()
   TRS:
    f(0()) -> cons(0(),n__f(n__s(n__0())))
    f(s(0())) -> f(p(s(0())))
    p(s(0())) -> 0()
    f(X) -> n__f(X)
    s(X) -> n__s(X)
    0() -> n__0()
    activate(n__f(X)) -> f(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(n__0()) -> 0()
    activate(X) -> X
   graph:
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__0()) -> 0#()
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> activate#(X)
    activate#(n__f(X)) -> f#(activate(X)) ->
    f#(s(0())) -> f#(p(s(0())))
    activate#(n__f(X)) -> f#(activate(X)) ->
    f#(s(0())) -> p#(s(0()))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__0()) -> 0#()
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__f(X)) -> activate#(X)
    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()))
   CDG Processor:
    DPs:
     f#(s(0())) -> p#(s(0()))
     f#(s(0())) -> f#(p(s(0())))
     activate#(n__f(X)) -> activate#(X)
     activate#(n__f(X)) -> f#(activate(X))
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__0()) -> 0#()
    TRS:
     f(0()) -> cons(0(),n__f(n__s(n__0())))
     f(s(0())) -> f(p(s(0())))
     p(s(0())) -> 0()
     f(X) -> n__f(X)
     s(X) -> n__s(X)
     0() -> n__0()
     activate(n__f(X)) -> f(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(n__0()) -> 0()
     activate(X) -> X
    graph:
     activate#(n__f(X)) -> f#(activate(X)) ->
     f#(s(0())) -> p#(s(0()))
     activate#(n__f(X)) -> f#(activate(X)) -> f#(s(0())) -> f#(p(s(0())))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 2/49