YES
Input TRS:
AC symbols: plus times
      1: times(x,0()) -> 0()
      2: times(x,s(y)) -> plus(times(x,y),x)
      3: plus(x,0()) -> x
      4: plus(0(),x) -> x
      5: plus(x,s(y)) -> s(plus(x,y))
      6: plus(s(x),y) -> s(plus(x,y))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #times(x,s(y)) -> #plus(times(x,y),x)
     #2: #times(x,s(y)) -> #times(x,y)
     #3: #plus(s(x),y) -> #plus(x,y)
     #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #5: #plus(x,plus(y,z)) ->= #plus(x,y)
     #6: #plus(x,s(y)) -> #plus(x,y)
     #7: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #8: #times(x,times(y,z)) ->= #times(x,y)
Number of SCCs: 2, DPs: 7
  SCC { #2 #7 #8 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..8 }
    Removed DPs: #2 #8
Number of SCCs: 2, DPs: 5
  SCC { #7 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #3..6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 10157
      times	w: x1 + x2 + 30094
      plus	w: x1 + x2 + 2
    USABLE RULES: { 3..7 }
    Removed DPs: #3 #5 #6
Number of SCCs: 1, DPs: 1
  SCC { #4 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #9: #times(times(x,s(y)),_1) -> #times(plus(times(x,y),x),_1)
     #10: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
     #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #12: #plus(x,plus(y,z)) ->= #plus(x,y)
     #13: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #14: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #15: #times(times(x,0()),_1) -> #times(0(),_1)
     #16: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #17: #times(x,times(y,z)) ->= #times(x,y)
     #18: #plus(plus(0(),x),_1) -> #plus(x,_1)
Number of SCCs: 2, DPs: 10
  SCC { #9 #15..17 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..8 }
    Removed DPs: #9 #15 #17
Number of SCCs: 2, DPs: 7
  SCC { #16 }
only weak rules.
Number of SCCs: 1, DPs: 6
  SCC { #10..14 #18 }
POLO(Sum)... succeeded.
      s 	w: 282
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 1143
      times	w: 30094
      plus	w: x1 + x2 + 1
    USABLE RULES: { 3..7 }
    Removed DPs: #10 #12..14 #18
Number of SCCs: 1, DPs: 1
  SCC { #11 }
only weak rules.
Number of SCCs: 0, DPs: 0