MAYBE
Input TRS:
      1: cond1(true(),x,y) -> cond2(gr(x,y),x,y)
      2: cond2(true(),x,y) -> cond3(gr(x,0()),x,y)
      3: cond2(false(),x,y) -> cond4(gr(y,0()),x,y)
      4: cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y)
      5: cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
      6: cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y))
      7: cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
      8: gr(0(),x) -> false()
      9: gr(s(x),0()) -> true()
      10: gr(s(x),s(y)) -> gr(x,y)
      11: and(true(),true()) -> true()
      12: and(false(),x) -> false()
      13: and(x,false()) -> false()
      14: p(0()) -> 0()
      15: p(s(x)) -> x
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #cond2(true(),x,y) -> #cond3(gr(x,0()),x,y)
     #2: #cond2(true(),x,y) -> #gr(x,0())
     #3: #cond4(true(),x,y) -> #cond4(gr(y,0()),x,p(y))
     #4: #cond4(true(),x,y) -> #gr(y,0())
     #5: #cond4(true(),x,y) -> #p(y)
     #6: #cond4(false(),x,y) -> #cond1(and(gr(x,0()),gr(y,0())),x,y)
     #7: #cond4(false(),x,y) -> #and(gr(x,0()),gr(y,0()))
     #8: #cond4(false(),x,y) -> #gr(x,0())
     #9: #cond4(false(),x,y) -> #gr(y,0())
     #10: #gr(s(x),s(y)) -> #gr(x,y)
     #11: #cond3(false(),x,y) -> #cond1(and(gr(x,0()),gr(y,0())),x,y)
     #12: #cond3(false(),x,y) -> #and(gr(x,0()),gr(y,0()))
     #13: #cond3(false(),x,y) -> #gr(x,0())
     #14: #cond3(false(),x,y) -> #gr(y,0())
     #15: #cond2(false(),x,y) -> #cond4(gr(y,0()),x,y)
     #16: #cond2(false(),x,y) -> #gr(y,0())
     #17: #cond1(true(),x,y) -> #cond2(gr(x,y),x,y)
     #18: #cond1(true(),x,y) -> #gr(x,y)
     #19: #cond3(true(),x,y) -> #cond3(gr(x,0()),p(x),y)
     #20: #cond3(true(),x,y) -> #gr(x,0())
     #21: #cond3(true(),x,y) -> #p(x)
Number of SCCs: 2, DPs: 8
  SCC { #10 }
POLO(Sum)... succeeded.
      cond2	w: 0
      #cond3	w: 0
      s 	w: x1 + 1
      #cond1	w: 0
      and	w: 0
      #cond4	w: 0
      false	w: 0
      #p 	w: 0
      cond4	w: 0
      true	w: 0
      cond1	w: 0
      p 	w: 0
      0 	w: 0
      #gr	w: x2
      cond3	w: 0
      #cond2	w: 0
      gr	w: 0
      #and	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 7
  SCC { #1 #3 #6 #11 #15 #17 #19 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      cond2	w: max(x1 - 1, 0)
      #cond3	w: max(x3 + 2, 0)
      s 	w: max(x1 + 2, 0)
      #cond1	w: max(x3 + 2, 0)
      and	w: 0
      #cond4	w: max(x1 - 2, x3 + 2, 0)
      false	w: 1
      #p 	w: max(x1 - 1, 0)
      cond4	w: max(x1 - 1, 0)
      true	w: 5
      cond1	w: 0
      p 	w: max(x1 - 1, 0)
      0 	w: 0
      #gr	w: 0
      cond3	w: max(x1 - 1, 0)
      #cond2	w: max(x3 + 2, 0)
      gr	w: max(x1 + 3, 0)
      #and	w: 0
    USABLE RULES: { 8 9 14 15 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 6
  SCC { #1 #6 #11 #15 #17 #19 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      cond2	w: max(x1 - 1, 0)
      #cond3	w: max(x1 - 240, x2 + 27692, 0)
      s 	w: max(x1 + 2, 0)
      #cond1	w: max(x2 + 27692, 0)
      and	w: 0
      #cond4	w: max(x2 + 27692, 0)
      false	w: 27931
      #p 	w: max(x1 - 1, 0)
      cond4	w: max(x1 - 1, 0)
      true	w: 27933
      cond1	w: 0
      p 	w: max(x1 - 1, 0)
      0 	w: 0
      #gr	w: 0
      cond3	w: max(x1 - 1, 0)
      #cond2	w: max(x2 + 27692, 0)
      gr	w: max(x1 + 27931, 0)
      #and	w: 0
    USABLE RULES: { 8 9 14 15 }
    Removed DPs: #19
Number of SCCs: 1, DPs: 5
  SCC { #1 #6 #11 #15 #17 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.