YES
Input TRS:
      1: f(s(x1)) -> s(s(f(p(s(x1)))))
      2: f(0(x1)) -> 0(x1)
      3: p(s(x1)) -> x1
Number of strict rules: 3
Direct POLO(bPol) ... removes: 2
      s 	w: x1
      f 	w: x1 + 8366
      p 	w: x1
      0 	w: 2 * x1 + 1
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying p
      1: f(s(x1)) -> s(s(f(p^1_s(x1))))
      3: p^1_s(x1) -> x1
      4: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 2
Direct POLO(bPol) ... removes: 4
      s 	w: x1
      p^1_s	w: x1
      f 	w: x1 + 11798
      p 	w: x1 + 2
      0 	w: x1
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #f(s(x1)) -> #f(p^1_s(x1))
     #2: #f(s(x1)) -> #p^1_s(x1)
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      #p^1_s	w: 0
      p^1_s	w: x1 + 1
      f 	w: 0
      p 	w: 0
      0 	w: 0
      #f 	w: x1
    USABLE RULES: { 3 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0