YES
Input TRS:
      1: v(s(x1)) -> s(p(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1))))))))))))))))))))
      2: v(0(x1)) -> p(p(s(s(0(p(p(s(s(s(s(s(x1))))))))))))
      3: w(s(x1)) -> s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(s(s(x1))))))))))))))))))))
      4: w(0(x1)) -> p(s(p(p(p(p(p(p(p(p(s(s(0(s(s(s(s(s(s(x1)))))))))))))))))))
      5: p(p(s(x1))) -> p(x1)
      6: p(s(x1)) -> x1
      7: p(0(x1)) -> 0(s(s(s(s(s(s(s(p(s(x1))))))))))
Number of strict rules: 7
Direct POLO(bPol) ... removes: 4 2
      s 	w: x1
      v 	w: x1 + 12280
      w 	w: x1 + 12280
      p 	w: x1
      0 	w: x1 + 29405
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying p
      1: v(s(x1)) -> s(p(p^1_s(s(s(s(s(s(s(s(w(p(p^1_s(s(p^1_s(p^1_s(x1))))))))))))))))
      3: w(s(x1)) -> s(s(s(s(s(s(p(p^1_s(s(v(p(p^1_s(s(s(p(p^1_s(s(x1)))))))))))))))))
      5: p(p^1_s(x1)) -> p(x1)
      6: p^1_s(x1) -> x1
      7: p^1_0(x1) -> 0(s(s(s(s(s(s(s(p^1_s(x1)))))))))
      8: p(0(_1)) ->= p^1_0(_1)
      9: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #p(s(_1)) ->? #p^1_s(_1)
     #2: #p^1_0(x1) -> #p^1_s(x1)
     #3: #p(p^1_s(x1)) -> #p(x1)
     #4: #w(s(x1)) -> #p(p^1_s(s(v(p(p^1_s(s(s(p(p^1_s(s(x1)))))))))))
     #5: #w(s(x1)) -> #p^1_s(s(v(p(p^1_s(s(s(p(p^1_s(s(x1))))))))))
     #6: #w(s(x1)) -> #v(p(p^1_s(s(s(p(p^1_s(s(x1))))))))
     #7: #w(s(x1)) -> #p(p^1_s(s(s(p(p^1_s(s(x1)))))))
     #8: #w(s(x1)) -> #p^1_s(s(s(p(p^1_s(s(x1))))))
     #9: #w(s(x1)) -> #p(p^1_s(s(x1)))
     #10: #w(s(x1)) -> #p^1_s(s(x1))
     #11: #v(s(x1)) -> #p(p^1_s(s(s(s(s(s(s(s(w(p(p^1_s(s(p^1_s(p^1_s(x1)))))))))))))))
     #12: #v(s(x1)) -> #p^1_s(s(s(s(s(s(s(s(w(p(p^1_s(s(p^1_s(p^1_s(x1))))))))))))))
     #13: #v(s(x1)) -> #w(p(p^1_s(s(p^1_s(p^1_s(x1))))))
     #14: #v(s(x1)) -> #p(p^1_s(s(p^1_s(p^1_s(x1)))))
     #15: #v(s(x1)) -> #p^1_s(s(p^1_s(p^1_s(x1))))
     #16: #v(s(x1)) -> #p^1_s(p^1_s(x1))
     #17: #v(s(x1)) -> #p^1_s(x1)
     #18: #p(0(_1)) ->? #p^1_0(_1)
Number of SCCs: 2, DPs: 3
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: 0
      v 	w: 0
      #p^1_0	w: 0
      #w 	w: 0
      #p^1_s	w: 0
      p^1_0	w: 0
      w 	w: 0
      p^1_s	w: x1 + 1
      #p 	w: x1
      p 	w: 0
      0 	w: 0
      #v 	w: 0
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #6 #13 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 26841, 0)
      v 	w: max(x1 - 1, 0)
      #p^1_0	w: 0
      #w 	w: max(x1 - 8947, 0)
      #p^1_s	w: 0
      p^1_0	w: 0
      w 	w: max(x1 - 1, 0)
      p^1_s	w: max(x1, 0)
      #p 	w: max(x1 - 1, 0)
      p 	w: max(x1 - 17895, 0)
      0 	w: 0
      #v 	w: max(x1 - 26840, 0)
    USABLE RULES: { 5..9 }
    Removed DPs: #6 #13
Number of SCCs: 0, DPs: 0