YES

Proof:
This system is quasi-decreasing.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  pos(s(0)) -> true
  pos(0) -> false
  pos(s(x)) -> true
  pos(s(x)) -> pos(x)
  pos(p(x)) -> false
  pos(p(x)) -> pos(x)
  pos(x) -> x
  p(x) -> x
  s(x) -> x

 DP Processor:
  DPs:
   pos#(s(x)) -> pos#(x)
   pos#(p(x)) -> pos#(x)
  TRS:
   pos(s(0())) -> true()
   pos(0()) -> false()
   pos(s(x)) -> true()
   pos(s(x)) -> pos(x)
   pos(p(x)) -> false()
   pos(p(x)) -> pos(x)
   pos(x) -> x
   p(x) -> x
   s(x) -> x
  Subterm Criterion Processor:
   simple projection:
    pi(pos#) = 0
   problem:
    DPs:
     
    TRS:
     pos(s(0())) -> true()
     pos(0()) -> false()
     pos(s(x)) -> true()
     pos(s(x)) -> pos(x)
     pos(p(x)) -> false()
     pos(p(x)) -> pos(x)
     pos(x) -> x
     p(x) -> x
     s(x) -> x
   Qed