YES
Input TRS:
      1: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1)))))))))
      2: i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
      3: j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
      4: j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(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(s(x1)))))))))
Number of strict rules: 7
Direct POLO(bPol) ... removes: 1 3
      s 	w: x1
      p 	w: x1
      0 	w: 2 * x1 + 841
      j 	w: x1 + 247015
      i 	w: x1 + 247015
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying p
      2: i(s(x1)) -> p^1_s(p^1_s(s(j(p^1_s(p^1_s(p(p(p(p^1_s(s(s(s(x1)))))))))))))
      4: j(s(x1)) -> s(s(s(s(p(p^1_s(s(i(p^1_s(p^1_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(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: #i(s(x1)) -> #p^1_s(p^1_s(s(j(p^1_s(p^1_s(p(p(p(p^1_s(s(s(s(x1)))))))))))))
     #2: #i(s(x1)) -> #p^1_s(s(j(p^1_s(p^1_s(p(p(p(p^1_s(s(s(s(x1))))))))))))
     #3: #i(s(x1)) -> #j(p^1_s(p^1_s(p(p(p(p^1_s(s(s(s(x1))))))))))
     #4: #i(s(x1)) -> #p^1_s(p^1_s(p(p(p(p^1_s(s(s(s(x1)))))))))
     #5: #i(s(x1)) -> #p^1_s(p(p(p(p^1_s(s(s(s(x1))))))))
     #6: #i(s(x1)) -> #p(p(p(p^1_s(s(s(s(x1)))))))
     #7: #i(s(x1)) -> #p(p(p^1_s(s(s(s(x1))))))
     #8: #i(s(x1)) -> #p(p^1_s(s(s(s(x1)))))
     #9: #i(s(x1)) -> #p^1_s(s(s(s(x1))))
     #10: #p(s(_1)) ->? #p^1_s(_1)
     #11: #p(p^1_s(x1)) -> #p(x1)
     #12: #p(0(_1)) ->? #p^1_0(_1)
     #13: #j(s(x1)) -> #p(p^1_s(s(i(p^1_s(p^1_s(x1))))))
     #14: #j(s(x1)) -> #p^1_s(s(i(p^1_s(p^1_s(x1)))))
     #15: #j(s(x1)) -> #i(p^1_s(p^1_s(x1)))
     #16: #j(s(x1)) -> #p^1_s(p^1_s(x1))
     #17: #j(s(x1)) -> #p^1_s(x1)
Number of SCCs: 2, DPs: 3
  SCC { #11 }
POLO(Sum)... succeeded.
      s 	w: 0
      #p^1_0	w: 0
      #p^1_s	w: 0
      p^1_0	w: 0
      p^1_s	w: x1 + 1
      #p 	w: x1
      p 	w: 0
      0 	w: 0
      #j 	w: 0
      j 	w: 0
      i 	w: 0
      #i 	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 2
  SCC { #3 #15 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 147916, 0)
      #p^1_0	w: 0
      #p^1_s	w: max(x1 - 1, 0)
      p^1_0	w: 0
      p^1_s	w: max(x1 + 15922, 0)
      #p 	w: max(x1 - 1, 0)
      p 	w: max(x1 - 131994, 0)
      0 	w: 0
      #j 	w: max(x1 + 1, 0)
      j 	w: 0
      i 	w: max(x1 - 1, 0)
      #i 	w: max(x1 - 31845, 0)
    USABLE RULES: { 5..9 }
    Removed DPs: #3 #15
Number of SCCs: 0, DPs: 0