YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(s(x),y) -> s(plus(x,y))
      3: times(x,0()) -> 0()
      4: times(s(x),y) -> plus(times(x,y),y)
      5: times(x,plus(y,z)) -> plus(times(x,y),times(x,z))
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #plus(s(x),y) -> #plus(x,y)
     #2: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #3: #plus(x,plus(y,z)) ->= #plus(x,y)
     #4: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #5: #times(x,times(y,z)) ->= #times(x,y)
     #6: #times(x,plus(y,z)) -> #plus(times(x,y),times(x,z))
     #7: #times(x,plus(y,z)) -> #times(x,y)
     #8: #times(x,plus(y,z)) -> #times(x,z)
     #9: #times(s(x),y) -> #plus(times(x,y),y)
     #10: #times(s(x),y) -> #times(x,y)
Number of SCCs: 2, DPs: 8
  SCC { #1..3 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 21277
      times	w: 0
      plus	w: x1 + x2 + 7720
    USABLE RULES: { 1 2 6 }
    Removed DPs: #1 #3
Number of SCCs: 2, DPs: 6
  SCC { #2 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #4 #5 #7 #8 #10 }
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..7 }
    Removed DPs: #5 #7 #8 #10
Number of SCCs: 1, DPs: 1
  SCC { #4 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #11: #plus(plus(s(x),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,plus(y,z)),_1) -> #times(plus(times(x,y),times(x,z)),_1)
     #17: #times(times(x,0()),_1) -> #times(0(),_1)
     #18: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #19: #times(times(s(x),y),_1) -> #times(plus(times(x,y),y),_1)
Number of SCCs: 2, DPs: 9
  SCC { #11..13 #18 }
POLO(Sum)... succeeded.
      s 	w: 36459
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 21277
      times	w: 282
      plus	w: x1 + x2 + 7720
    USABLE RULES: { 1 2 6 }
    Removed DPs: #11 #13 #18
Number of SCCs: 2, DPs: 6
  SCC { #12 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #14..17 #19 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 3
      times	s: {1,2}	p: 2
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..7 }
    Removed DPs: #15..17 #19
Number of SCCs: 1, DPs: 1
  SCC { #14 }
only weak rules.
Number of SCCs: 0, DPs: 0