YES
Input TRS:
      1: f(0()) -> cons(0(),n__f(n__s(n__0())))
      2: f(s(0())) -> f(p(s(0())))
      3: p(s(X)) -> X
      4: f(X) -> n__f(X)
      5: s(X) -> n__s(X)
      6: 0() -> n__0()
      7: activate(n__f(X)) -> f(activate(X))
      8: activate(n__s(X)) -> s(activate(X))
      9: activate(n__0()) -> 0()
      10: activate(X) -> X
Number of strict rules: 10
Direct POLO(bPol) ... removes: 4 10 9 6
      s 	w: x1
      activate	w: 2 * x1 + 21657
      f 	w: x1 + 2
      n__s	w: x1
      p 	w: x1
      0 	w: 21656
      n__f	w: x1 + 1
      n__0	w: 0
      cons	w: x1 + 2 * x2
Number of strict rules: 6
Direct POLO(bPol) ... removes: 1 3 5
      s 	w: x1 + 2
      activate	w: 2 * x1 + 28224
      f 	w: x1 + 20684
      n__s	w: x1 + 1
      p 	w: x1
      0 	w: 10339
      n__f	w: x1 + 10342
      n__0	w: 1
      cons	w: 2 * x1 + x2
Number of strict rules: 3
Direct POLO(bPol) ... removes: 8 7
      s 	w: x1 + 1
      activate	w: 2 * x1 + 7579
      f 	w: x1 + 20683
      n__s	w: x1 + 1
      p 	w: x1
      0 	w: 1
      n__f	w: x1 + 10342
      n__0	w: 1
      cons	w: 2 * x1 + x2
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying f
      2: f^1_s(0()) -> f^1_p(s(0()))
      11: f(p(_1)) ->= f^1_p(_1)
      12: f(s(_1)) ->= f^1_s(_1)
Number of strict rules: 1
Direct POLO(bPol) ... removes: 12 11 2
      s 	w: 2 * x1 + 1
      activate	w: x1
      f 	w: 2 * x1 + 7723
      n__s	w: x1
      p 	w: 2 * x1 + 1
      0 	w: 1
      n__f	w: x1
      f^1_p	w: 2 * x1 + 7719
      n__0	w: 0
      cons	w: x1 + x2
      f^1_s	w: 2 * x1 + 7724
Number of strict rules: 0