YES

Problem:
 f(s(x)) -> s(s(f(p(s(x)))))
 f(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> p#(s(x))
   f#(s(x)) -> f#(p(s(x)))
  TRS:
   f(s(x)) -> s(s(f(p(s(x)))))
   f(0()) -> 0()
   p(s(x)) -> x
  EDG Processor:
   DPs:
    f#(s(x)) -> p#(s(x))
    f#(s(x)) -> f#(p(s(x)))
   TRS:
    f(s(x)) -> s(s(f(p(s(x)))))
    f(0()) -> 0()
    p(s(x)) -> x
   graph:
    f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> p#(s(x))
    f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(p(s(x)))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/4
    DPs:
     f#(s(x)) -> f#(p(s(x)))
    TRS:
     f(s(x)) -> s(s(f(p(s(x)))))
     f(0()) -> 0()
     p(s(x)) -> x
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {6}
      transitions:
       f{#,0}(8) -> 6*
       s0(5) -> 7*
       s0(2) -> 2*
       s0(4) -> 2*
       s0(1) -> 2*
       s0(3) -> 2*
       p0(7) -> 8*
       p0(2) -> 1*
       p0(4) -> 1*
       p0(1) -> 1*
       p0(3) -> 1*
       f0(2) -> 3*
       f0(4) -> 3*
       f0(1) -> 3*
       f0(3) -> 3*
       00() -> 4*
       f{#,1}(15) -> 16*
       p1(14) -> 15*
       s1(17) -> 18*
       s1(23) -> 24*
       s1(13) -> 14*
       1 -> 23,5
       2 -> 13,1,3,5
       3 -> 1,5
       4 -> 17,1,3,5
       5 -> 8*
       13 -> 15*
       16 -> 6*
       17 -> 15*
       18 -> 14*
       23 -> 15*
       24 -> 14*
     problem:
      DPs:
       
      TRS:
       f(s(x)) -> s(s(f(p(s(x)))))
       f(0()) -> 0()
       p(s(x)) -> x
     Qed