MAYBE
Input TRS:
      1: p(0(x1)) -> 0(s(s(p(x1))))
      2: p(s(x1)) -> x1
      3: p(p(s(x1))) -> p(x1)
      4: f(s(x1)) -> g(s(x1))
      5: g(x1) -> i(s(half(x1)))
      6: i(x1) -> f(p(x1))
      7: half(0(x1)) -> 0(s(s(half(x1))))
      8: half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
      9: 0(x1) -> x1
      10: rd(0(x1)) -> 0(0(0(0(0(0(rd(x1)))))))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #i(x1) -> #f(p(x1))
     #2: #i(x1) -> #p(x1)
     #3: #half(0(x1)) -> #0(s(s(half(x1))))
     #4: #half(0(x1)) -> #half(x1)
     #5: #rd(0(x1)) -> #0(0(0(0(0(0(rd(x1)))))))
     #6: #rd(0(x1)) -> #0(0(0(0(0(rd(x1))))))
     #7: #rd(0(x1)) -> #0(0(0(0(rd(x1)))))
     #8: #rd(0(x1)) -> #0(0(0(rd(x1))))
     #9: #rd(0(x1)) -> #0(0(rd(x1)))
     #10: #rd(0(x1)) -> #0(rd(x1))
     #11: #rd(0(x1)) -> #rd(x1)
     #12: #g(x1) -> #i(s(half(x1)))
     #13: #g(x1) -> #half(x1)
     #14: #p(p(s(x1))) -> #p(x1)
     #15: #p(0(x1)) -> #0(s(s(p(x1))))
     #16: #p(0(x1)) -> #p(x1)
     #17: #half(s(s(x1))) -> #half(p(p(s(s(x1)))))
     #18: #half(s(s(x1))) -> #p(p(s(s(x1))))
     #19: #half(s(s(x1))) -> #p(s(s(x1)))
     #20: #f(s(x1)) -> #g(s(x1))
Number of SCCs: 4, DPs: 8
  SCC { #11 }
POLO(Sum)... succeeded.
      #0 	w: 0
      s 	w: 0
      rd	w: 0
      #half	w: 0
      #p 	w: 0
      #rd	w: x1
      f 	w: 0
      half	w: 0
      p 	w: 0
      0 	w: x1 + 1
      #f 	w: 0
      #g 	w: 0
      i 	w: 0
      g 	w: 0
      #i 	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 3, DPs: 7
  SCC { #14 #16 }
POLO(Sum)... succeeded.
      #0 	w: 0
      s 	w: x1 + 1
      rd	w: 0
      #half	w: 0
      #p 	w: x1
      #rd	w: 0
      f 	w: 0
      half	w: 0
      p 	w: x1
      0 	w: x1 + 1
      #f 	w: 0
      #g 	w: 0
      i 	w: 0
      g 	w: 0
      #i 	w: 0
    USABLE RULES: { }
    Removed DPs: #14 #16
Number of SCCs: 2, DPs: 5
  SCC { #4 #17 }
POLO(Sum)... succeeded.
      #0 	w: 0
      s 	w: x1
      rd	w: 0
      #half	w: x1
      #p 	w: 0
      #rd	w: 0
      f 	w: 0
      half	w: 0
      p 	w: x1
      0 	w: x1 + 1
      #f 	w: 0
      #g 	w: 0
      i 	w: 0
      g 	w: 0
      #i 	w: 0
    USABLE RULES: { 1..3 9 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4
  SCC { #17 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.