YES
Input TRS:
      1: a__minus(0(),Y) -> 0()
      2: a__minus(s(X),s(Y)) -> a__minus(X,Y)
      3: a__geq(X,0()) -> true()
      4: a__geq(0(),s(Y)) -> false()
      5: a__geq(s(X),s(Y)) -> a__geq(X,Y)
      6: a__div(0(),s(Y)) -> 0()
      7: a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
      8: a__if(true(),X,Y) -> mark(X)
      9: a__if(false(),X,Y) -> mark(Y)
      10: mark(minus(X1,X2)) -> a__minus(X1,X2)
      11: mark(geq(X1,X2)) -> a__geq(X1,X2)
      12: mark(div(X1,X2)) -> a__div(mark(X1),X2)
      13: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
      14: mark(0()) -> 0()
      15: mark(s(X)) -> s(mark(X))
      16: mark(true()) -> true()
      17: mark(false()) -> false()
      18: a__minus(X1,X2) -> minus(X1,X2)
      19: a__geq(X1,X2) -> geq(X1,X2)
      20: a__div(X1,X2) -> div(X1,X2)
      21: a__if(X1,X2,X3) -> if(X1,X2,X3)
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__minus(s(X),s(Y)) -> #a__minus(X,Y)
     #2: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),X2,X3)
     #3: #mark(if(X1,X2,X3)) -> #mark(X1)
     #4: #a__if(false(),X,Y) -> #mark(Y)
     #5: #mark(geq(X1,X2)) -> #a__geq(X1,X2)
     #6: #mark(div(X1,X2)) -> #a__div(mark(X1),X2)
     #7: #mark(div(X1,X2)) -> #mark(X1)
     #8: #a__div(s(X),s(Y)) -> #a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
     #9: #a__div(s(X),s(Y)) -> #a__geq(X,Y)
     #10: #mark(minus(X1,X2)) -> #a__minus(X1,X2)
     #11: #a__geq(s(X),s(Y)) -> #a__geq(X,Y)
     #12: #a__if(true(),X,Y) -> #mark(X)
     #13: #mark(s(X)) -> #mark(X)
Number of SCCs: 3, DPs: 10
  SCC { #11 }
POLO(Sum)... succeeded.
      a__minus	w: 0
      s 	w: x1 + 1
      minus	w: 0
      false	w: 0
      div	w: 0
      a__div	w: 0
      geq	w: 0
      true	w: 0
      #mark	w: 0
      0 	w: 0
      if	w: 0
      #a__minus	w: 0
      a__geq	w: 0
      mark	w: 0
      #a__geq	w: x1
      #a__if	w: 0
      #a__div	w: 0
      a__if	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 2, DPs: 9
  SCC { #1 }
POLO(Sum)... succeeded.
      a__minus	w: 0
      s 	w: x1 + 1
      minus	w: 0
      false	w: 0
      div	w: 0
      a__div	w: 0
      geq	w: 0
      true	w: 0
      #mark	w: 0
      0 	w: 0
      if	w: 0
      #a__minus	w: x1 + x2
      a__geq	w: 0
      mark	w: 0
      #a__geq	w: 0
      #a__if	w: 0
      #a__div	w: 0
      a__if	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 8
  SCC { #2..4 #6..8 #12 #13 }
POLO(Sum)... succeeded.
      a__minus	w: 2
      s 	w: x1
      minus	w: 0
      false	w: 1
      div	w: x1 + 31894
      a__div	w: 2
      geq	w: x2 + 3
      true	w: 3
      #mark	w: x1
      0 	w: 0
      if	w: x1 + x2 + x3 + 4
      #a__minus	w: 0
      a__geq	w: 2
      mark	w: 1
      #a__geq	w: 0
      #a__if	w: x2 + x3
      #a__div	w: 31894
      a__if	w: 3
    USABLE RULES: { }
    Removed DPs: #2 #3 #7
Number of SCCs: 1, DPs: 5
  SCC { #4 #6 #8 #12 #13 }
POLO(Sum)... succeeded.
      a__minus	w: 0
      s 	w: x1 + 1
      minus	w: 0
      false	w: 1
      div	w: x1 + x2 + 38870
      a__div	w: x1 + x2 + 38870
      geq	w: 1
      true	w: 1
      #mark	w: x1
      0 	w: 0
      if	w: x2 + x3
      #a__minus	w: 0
      a__geq	w: 1
      mark	w: x1
      #a__geq	w: 0
      #a__if	w: x2 + x3
      #a__div	w: x1 + x2 + 38870
      a__if	w: x2 + x3
    USABLE RULES: { 1..21 }
    Removed DPs: #13
Number of SCCs: 1, DPs: 4
  SCC { #4 #6 #8 #12 }
POLO(Sum)... succeeded.
      a__minus	w: 1
      s 	w: 1
      minus	w: 1
      false	w: 1
      div	w: x1 + 4
      a__div	w: x1 + 4
      geq	w: 1
      true	w: 1
      #mark	w: x1
      0 	w: 0
      if	w: x2 + x3
      #a__minus	w: 0
      a__geq	w: 1
      mark	w: x1 + 1
      #a__geq	w: 0
      #a__if	w: x2 + x3 + 1
      #a__div	w: x1 + 2
      a__if	w: x2 + x3 + 1
    USABLE RULES: { 1..21 }
    Removed DPs: #4 #6 #8 #12
Number of SCCs: 0, DPs: 0