YES
Input TRS:
      1: f(0(x1)) -> s(0(x1))
      2: d(0(x1)) -> 0(x1)
      3: d(s(x1)) -> s(s(d(p(s(x1)))))
      4: f(s(x1)) -> d(f(p(s(x1))))
      5: p(s(x1)) -> x1
Number of strict rules: 5
Direct POLO(bPol) ... removes: 1
      d 	w: x1
      s 	w: x1
      f 	w: x1 + 2243
      p 	w: x1
      0 	w: x1 + 9726
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying p
      2: d(0(x1)) -> 0(x1)
      3: d(s(x1)) -> s(s(d(p^1_s(x1))))
      4: f(s(x1)) -> d(f(p^1_s(x1)))
      5: p^1_s(x1) -> x1
      6: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 6
      d 	w: x1
      s 	w: x1
      p^1_s	w: x1
      f 	w: x1 + 26286
      p 	w: x1 + 2998
      0 	w: x1 + 14681
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #d(s(x1)) -> #d(p^1_s(x1))
     #2: #d(s(x1)) -> #p^1_s(x1)
     #3: #f(s(x1)) -> #d(f(p^1_s(x1)))
     #4: #f(s(x1)) -> #f(p^1_s(x1))
     #5: #f(s(x1)) -> #p^1_s(x1)
Number of SCCs: 2, DPs: 2
  SCC { #4 }
POLO(Sum)... succeeded.
      d 	w: 0
      s 	w: x1 + 2
      #p^1_s	w: 0
      p^1_s	w: x1 + 1
      f 	w: 0
      p 	w: 0
      0 	w: 0
      #d 	w: 0
      #f 	w: x1
    USABLE RULES: { 5 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... succeeded.
      d 	w: 0
      s 	w: x1 + 2
      #p^1_s	w: 0
      p^1_s	w: x1 + 1
      f 	w: 0
      p 	w: 0
      0 	w: 0
      #d 	w: x1
      #f 	w: x1
    USABLE RULES: { 5 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0