YES
Input TRS:
      1: fac(s(x)) -> *(fac(p(s(x))),s(x))
      2: p(s(0())) -> 0()
      3: p(s(s(x))) -> s(p(s(x)))
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying p
      1: fac(s(x)) -> *(fac(p^1_s(x)),s(x))
      2: p^1_s(0()) -> 0()
      3: p^1_s(s(x)) -> s(p^1_s(x))
      4: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4 1
      s 	w: 2 * x1 + 3
      p^1_s	w: x1
      p 	w: x1 + 1323
      0 	w: 1
      fac	w: 2 * x1 + 2
      * 	w: x1 + x2 + 2
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #p^1_s(s(x)) -> #p^1_s(x)
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #p^1_s	w: x1
      p^1_s	w: 0
      p 	w: 0
      0 	w: 0
      fac	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0