YES
Input TRS:
AC symbols: plus times
      1: p(s(x)) -> x
      2: plus(x,0()) -> x
      3: plus(x,s(y)) -> s(plus(x,y))
      4: times(x,0()) -> 0()
      5: times(x,s(y)) -> plus(x,times(x,y))
      6: minus(x,0()) -> x
      7: minus(s(x),s(y)) -> minus(p(s(x)),p(s(y)))
      8: div(0(),s(y)) -> 0()
      9: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Uncurrying p
AC symbols: plus times
      1: p^1_s(x) -> x
      2: plus(x,0()) -> x
      3: plus(x,s(y)) -> s(plus(x,y))
      4: times(x,0()) -> 0()
      5: times(x,s(y)) -> plus(x,times(x,y))
      6: minus(x,0()) -> x
      7: minus(s(x),s(y)) -> minus(p^1_s(x),p^1_s(y))
      8: div(0(),s(y)) -> 0()
      9: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
      10: p(s(_1)) ->= p^1_s(_1)
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #div(s(x),s(y)) -> #div(minus(x,y),s(y))
     #2: #div(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: #minus(s(x),s(y)) -> #minus(p^1_s(x),p^1_s(y))
     #8: #minus(s(x),s(y)) -> #p^1_s(x)
     #9: #minus(s(x),s(y)) -> #p^1_s(y)
     #10: #p(s(_1)) ->? #p^1_s(_1)
     #11: #times(x,s(y)) -> #plus(x,times(x,y))
     #12: #times(x,s(y)) -> #times(x,y)
     #13: #plus(x,s(y)) -> #plus(x,y)
Number of SCCs: 4, DPs: 8
  SCC { #7 }
POLO(Sum)... succeeded.
      #div	w: 0
      s 	w: x1 + 2
      #p^1_s	w: 0
      minus	w: 0
      #plus	w: 0
      div	w: 0
      p^1_s	w: x1 + 1
      #p 	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      #minus	w: x1 + x2
      plus	w: 0
    USABLE RULES: { 1 }
    Removed DPs: #7
Number of SCCs: 3, DPs: 7
  SCC { #1 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 2
      #p^1_s	w: 0
      minus	w: x1 + 1
      #plus	w: 0
      div	w: 0
      p^1_s	w: x1 + 2
      #p 	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 1
      times	w: 0
      #minus	w: x1 + x2
      plus	w: 0
    USABLE RULES: { 1 6 7 }
    Removed DPs: #1
Number of SCCs: 2, DPs: 6
  SCC { #5 #6 #12 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: [1,2]	p: 0
      s 	s: [1]	p: 0
      #p^1_s	s: []	p: 0
      minus	s: []	p: 0
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      p^1_s	s: []	p: 0
      #p 	s: []	p: 0
      p 	s: []	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: { 2..5 11 12 }
    Removed DPs: #6 #12
Number of SCCs: 2, DPs: 4
  SCC { #5 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #3 #4 #13 }
POLO(Sum)... succeeded.
      #div	w: x1
      s 	w: x1 + 1
      #p^1_s	w: 0
      minus	w: x1 + 1
      #plus	w: x1 + x2
      div	w: 0
      p^1_s	w: x1 + 1
      #p 	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 1143
      times	w: x1 + x2 + 1
      #minus	w: x1 + x2
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1..3 6 7 11 }
    Removed DPs: #4 #13
Number of SCCs: 1, DPs: 1
  SCC { #3 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #14: #plus(plus(x,0()),_1) -> #plus(x,_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(x,s(y)),_1) -> #times(plus(x,times(x,y)),_1)
     #20: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #21: #times(times(x,0()),_1) -> #times(0(),_1)
Number of SCCs: 2, DPs: 8
  SCC { #17..19 #21 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #div	s: [1,2]	p: 0
      s 	s: [1]	p: 0
      #p^1_s	s: []	p: 0
      minus	s: []	p: 0
      #plus	s: {}	p: 1
      div	s: [1,2]	p: 0
      p^1_s	s: []	p: 0
      #p 	s: []	p: 0
      p 	s: []	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: { 2..5 11 12 }
    Removed DPs: #18 #19 #21
Number of SCCs: 2, DPs: 5
  SCC { #17 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #14..16 #20 }
POLO(Sum)... succeeded.
      #div	w: 0
      s 	w: 42004
      #p^1_s	w: 0
      minus	w: x1 + x2 + 1
      #plus	w: x1 + x2
      div	w: 0
      p^1_s	w: x1
      #p 	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 31122
      #minus	w: x1 + x2
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1..3 6 11 }
    Removed DPs: #14 #16 #20
Number of SCCs: 1, DPs: 1
  SCC { #15 }
only weak rules.
Number of SCCs: 0, DPs: 0