YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(x,s(y)) -> s(plus(x,y))
      3: plus(x,plus(s(y),z)) -> plus(s(plus(x,y)),z)
      4: times(x,0()) -> 0()
      5: times(x,times(0(),z)) -> times(0(),z)
      6: times(x,s(y)) -> plus(times(x,y),x)
      7: times(x,times(s(y),z)) -> times(plus(times(x,y),x),z)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #plus(x,s(y)) -> #plus(x,y)
     #2: #times(x,s(y)) -> #plus(times(x,y),x)
     #3: #times(x,s(y)) -> #times(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,times(s(y),z)) -> #times(plus(times(x,y),x),z)
     #7: #times(x,times(s(y),z)) -> #plus(times(x,y),x)
     #8: #times(x,times(s(y),z)) -> #times(x,y)
     #9: #plus(x,plus(s(y),z)) -> #plus(s(plus(x,y)),z)
     #10: #plus(x,plus(s(y),z)) -> #plus(x,y)
     #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #12: #plus(x,plus(y,z)) ->= #plus(x,y)
Number of SCCs: 2, DPs: 10
  SCC { #1 #9..12 }
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..3 8 }
    Removed DPs: #1 #10 #12
Number of SCCs: 2, DPs: 7
  SCC { #9 #11 }
POLO(Sum)... succeeded.
      s 	w: 40651
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 21277
      times	w: 0
      plus	w: x1 + x2 + 7720
    USABLE RULES: { 1..3 8 }
    Removed DPs: #9
Number of SCCs: 2, DPs: 6
  SCC { #11 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #3..6 #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..9 }
    Removed DPs: #3 #5 #6 #8
Number of SCCs: 1, DPs: 1
  SCC { #4 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #13: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #14: #times(times(x,s(y)),_1) -> #times(plus(times(x,y),x),_1)
     #15: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #16: #times(x,times(y,z)) ->= #times(x,y)
     #17: #times(times(x,times(s(y),z)),_1) -> #times(times(plus(times(x,y),x),z),_1)
     #18: #times(times(x,times(0(),z)),_1) -> #times(times(0(),z),_1)
     #19: #plus(plus(x,plus(s(y),z)),_1) -> #plus(plus(s(plus(x,y)),z),_1)
     #20: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #21: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #22: #plus(x,plus(y,z)) ->= #plus(x,y)
     #23: #times(times(x,0()),_1) -> #times(0(),_1)
Number of SCCs: 2, DPs: 11
  SCC { #14..18 #23 }
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..9 }
    Removed DPs: #14 #16..18 #23
Number of SCCs: 2, DPs: 6
  SCC { #15 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #13 #19..22 }
POLO(Sum)... succeeded.
      s 	w: 24867
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 46824
      times	w: 46823
      plus	w: x1 + x2 + 1
    USABLE RULES: { 1..3 8 }
    Removed DPs: #13 #19 #20 #22
Number of SCCs: 1, DPs: 1
  SCC { #21 }
only weak rules.
Number of SCCs: 0, DPs: 0