YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(0(),y) -> y
      3: plus(s(x),y) -> s(plus(x,y))
      4: times(0(),y) -> 0()
      5: times(s(0()),y) -> y
      6: times(s(x),y) -> plus(y,times(x,y))
      7: div(0(),y) -> 0()
      8: div(x,y) -> quot(x,y,y)
      9: quot(0(),s(y),z) -> 0()
      10: quot(s(x),s(y),z) -> quot(x,y,z)
      11: quot(x,0(),s(z)) -> s(div(x,s(z)))
      12: div(div(x,y),z) -> div(x,times(y,z))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #times(s(x),y) -> #plus(y,times(x,y))
     #2: #times(s(x),y) -> #times(x,y)
     #3: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #4: #plus(x,plus(y,z)) ->= #plus(x,y)
     #5: #quot(x,0(),s(z)) -> #div(x,s(z))
     #6: #div(div(x,y),z) -> #div(x,times(y,z))
     #7: #div(div(x,y),z) -> #times(y,z)
     #8: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #9: #times(x,times(y,z)) ->= #times(x,y)
     #10: #quot(s(x),s(y),z) -> #quot(x,y,z)
     #11: #plus(s(x),y) -> #plus(x,y)
     #12: #div(x,y) -> #quot(x,y,y)
Number of SCCs: 3, DPs: 10
  SCC { #2 #8 #9 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: 1
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      quot	s: [3,1]	p: 0
      times	s: {1,2}	p: 2
      plus	s: {1,2}	p: 1
      #quot	s: [3,2,1]	p: 0
    USABLE RULES: { 1..6 13 14 }
    Removed DPs: #2 #9
Number of SCCs: 3, DPs: 8
  SCC { #8 }
only weak rules.
Number of SCCs: 2, DPs: 7
  SCC { #3 #4 #11 }
POLO(Sum)... succeeded.
      #div	w: 0
      s 	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 0
      #times	w: 0
      0 	w: 1
      quot	w: 0
      times	w: x1 + x2 + 1
      plus	w: x1 + x2 + 2
      #quot	w: 0
    USABLE RULES: { 1..3 13 }
    Removed DPs: #4 #11
Number of SCCs: 2, DPs: 5
  SCC { #3 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #5 #6 #10 #12 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 2998
      #plus	w: 0
      div	w: x1 + x2 + 1
      #times	w: 0
      0 	w: 1
      quot	w: 0
      times	w: x1 + x2 + 40966
      plus	w: x1 + x2 + 2999
      #quot	w: x1
    USABLE RULES: { }
    Removed DPs: #6 #10
Number of SCCs: 1, DPs: 2
  SCC { #5 #12 }
POLO(Sum)... POLO(max)... succeeded.
      #div	w: max(x2 + 33037)
      s 	w: 1
      #plus	w: 0
      div	w: 0
      #times	w: 0
      0 	w: 2
      quot	w: 0
      times	w: 0
      plus	w: max(x1, x2)
      #quot	w: max(x2 + 33036, x3 + 8856)
    USABLE RULES: { 1..3 13 }
    Removed DPs: #12
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #13: #plus(plus(0(),y),_1) -> #plus(y,_1)
     #14: #times(times(s(x),y),_1) -> #times(plus(y,times(x,y)),_1)
     #15: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #16: #plus(x,plus(y,z)) ->= #plus(x,y)
     #17: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #18: #times(x,times(y,z)) ->= #times(x,y)
     #19: #times(times(s(0()),y),_1) -> #times(y,_1)
     #20: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
     #21: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #22: #times(times(0(),y),_1) -> #times(0(),_1)
Number of SCCs: 2, DPs: 10
  SCC { #14 #17..19 #22 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: 1
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      #times	s: {1,2}	p: 2
      0 	s: []	p: 3
      quot	s: [3,1]	p: 0
      times	s: {1,2}	p: 2
      plus	s: {1,2}	p: 1
      #quot	s: [3,2,1]	p: 0
    USABLE RULES: { 1..6 13 14 }
    Removed DPs: #14 #18 #19 #22
Number of SCCs: 2, DPs: 6
  SCC { #17 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #13 #15 #16 #20 #21 }
POLO(Sum)... succeeded.
      #div	w: 1
      s 	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 1
      #times	w: 0
      0 	w: 1
      quot	w: 0
      times	w: 21656
      plus	w: x1 + x2 + 25907
      #quot	w: 0
    USABLE RULES: { 1..3 13 }
    Removed DPs: #13 #16 #21
Number of SCCs: 1, DPs: 2
  SCC { #15 #20 }
POLO(Sum)... succeeded.
      #div	w: 1
      s 	w: 28882
      #plus	w: x1 + x2
      div	w: 1
      #times	w: 0
      0 	w: 1324
      quot	w: 0
      times	w: 1324
      plus	w: x1 + x2 + 25907
      #quot	w: 0
    USABLE RULES: { 1..3 13 }
    Removed DPs: #20
Number of SCCs: 1, DPs: 1
  SCC { #15 }
only weak rules.
Number of SCCs: 0, DPs: 0