YES

Problem:
 f(0()) -> cons(0(),n__f(n__s(n__0())))
 f(s(0())) -> f(p(s(0())))
 p(s(X)) -> X
 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(X)) -> X
   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(X)) -> X
    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()))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 14/49
    DPs:
     activate#(n__f(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X)
    TRS:
     f(0()) -> cons(0(),n__f(n__s(n__0())))
     f(s(0())) -> f(p(s(0())))
     p(s(X)) -> X
     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
    Subterm Criterion Processor:
     simple projection:
      pi(activate#) = 0
     problem:
      DPs:
       
      TRS:
       f(0()) -> cons(0(),n__f(n__s(n__0())))
       f(s(0())) -> f(p(s(0())))
       p(s(X)) -> X
       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
     Qed
    
    DPs:
     f#(s(0())) -> f#(p(s(0())))
    TRS:
     f(0()) -> cons(0(),n__f(n__s(n__0())))
     f(s(0())) -> f(p(s(0())))
     p(s(X)) -> X
     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
    CDG Processor:
     DPs:
      f#(s(0())) -> f#(p(s(0())))
     TRS:
      f(0()) -> cons(0(),n__f(n__s(n__0())))
      f(s(0())) -> f(p(s(0())))
      p(s(X)) -> X
      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:
      
     Qed