YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(x,s(y)) -> s(plus(x,y))
      3: times(x,0()) -> 0()
      4: times(x,s(y)) -> plus(x,times(x,y))
      5: minus(x,0()) -> x
      6: minus(s(x),s(y)) -> minus(x,y)
      7: div(0(),s(y)) -> 0()
      8: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #plus(x,s(y)) -> #plus(x,y)
     #2: #minus(s(x),s(y)) -> #minus(x,y)
     #3: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #4: #plus(x,plus(y,z)) ->= #plus(x,y)
     #5: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #6: #times(x,times(y,z)) ->= #times(x,y)
     #7: #div(s(x),s(y)) -> #div(minus(x,y),s(y))
     #8: #div(s(x),s(y)) -> #minus(x,y)
     #9: #times(x,s(y)) -> #plus(x,times(x,y))
     #10: #times(x,s(y)) -> #times(x,y)
Number of SCCs: 4, DPs: 8
  SCC { #2 }
POLO(Sum)... succeeded.
      #div	w: 0
      s 	w: x1 + 1
      minus	w: 0
      #plus	w: 0
      div	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      #minus	w: x1 + x2
      plus	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 3, DPs: 7
  SCC { #7 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 2
      minus	w: x1 + 1
      #plus	w: 0
      div	w: 0
      #times	w: 0
      0 	w: 1
      times	w: 0
      #minus	w: 0
      plus	w: 0
    USABLE RULES: { 5 6 }
    Removed DPs: #7
Number of SCCs: 2, DPs: 6
  SCC { #5 #6 #10 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: 2
      s 	s: [1]	p: 0
      minus	s: 1
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      #minus	s: [1,2]	p: 0
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..4 9 10 }
    Removed DPs: #6 #10
Number of SCCs: 2, DPs: 4
  SCC { #5 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #1 #3 #4 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 1
      minus	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 0
      #times	w: 0
      0 	w: 38139
      times	w: x1 + x2 + 41063
      #minus	w: 0
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1 2 5 6 9 }
    Removed DPs: #1 #4
Number of SCCs: 1, DPs: 1
  SCC { #3 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #11: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #12: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #13: #plus(x,plus(y,z)) ->= #plus(x,y)
     #14: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #15: #times(x,times(y,z)) ->= #times(x,y)
     #16: #times(times(x,0()),_1) -> #times(0(),_1)
     #17: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #18: #times(times(x,s(y)),_1) -> #times(plus(x,times(x,y)),_1)
Number of SCCs: 2, DPs: 8
  SCC { #14..16 #18 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: 2
      s 	s: [1]	p: 0
      minus	s: 1
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      #times	s: {1,2}	p: 2
      0 	s: []	p: 3
      times	s: {1,2}	p: 2
      #minus	s: [1,2]	p: 0
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..4 9 10 }
    Removed DPs: #15 #16 #18
Number of SCCs: 2, DPs: 5
  SCC { #14 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #11..13 #17 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 1
      minus	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 0
      #times	w: 0
      0 	w: 46823
      times	w: x1 + x2 + 24867
      #minus	w: 0
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1 2 5 6 9 }
    Removed DPs: #13 #17
Number of SCCs: 1, DPs: 2
  SCC { #11 #12 }
POLO(Sum)... succeeded.
      #div	w: 0
      s 	w: 1
      minus	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 0
      #times	w: 0
      0 	w: 50349
      times	w: x1 + x2 + 47562
      #minus	w: 0
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1 2 9 }
    Removed DPs: #11
Number of SCCs: 1, DPs: 1
  SCC { #12 }
only weak rules.
Number of SCCs: 0, DPs: 0