YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(x,i(x)) -> 0()
      3: i(0()) -> 0()
      4: i(i(x)) -> x
      5: i(plus(x,y)) -> plus(i(x),i(y))
      6: times(x,plus(y,z)) -> plus(times(x,y),times(x,z))
      7: times(x,0()) -> 0()
      8: times(x,i(y)) -> i(times(x,y))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #times(x,plus(y,z)) -> #plus(times(x,y),times(x,z))
     #2: #times(x,plus(y,z)) -> #times(x,y)
     #3: #times(x,plus(y,z)) -> #times(x,z)
     #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #5: #plus(x,plus(y,z)) ->= #plus(x,y)
     #6: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #7: #times(x,times(y,z)) ->= #times(x,y)
     #8: #i(plus(x,y)) -> #plus(i(x),i(y))
     #9: #i(plus(x,y)) -> #i(x)
     #10: #i(plus(x,y)) -> #i(y)
     #11: #times(x,i(y)) -> #i(times(x,y))
     #12: #times(x,i(y)) -> #times(x,y)
Number of SCCs: 3, DPs: 9
  SCC { #9 #10 }
POLO(Sum)... succeeded.
      #plus	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      i 	w: 0
      plus	w: x1 + x2 + 1
      #i 	w: x1
    USABLE RULES: { }
    Removed DPs: #9 #10
Number of SCCs: 2, DPs: 7
  SCC { #4 #5 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #2 #3 #6 #7 #12 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 3
      0 	s: []	p: 0
      times	s: {1,2}	p: 3
      i 	s: [1]	p: 2
      plus	s: {1,2}	p: 1
      #i 	s: []	p: 0
    USABLE RULES: { 1..10 }
    Removed DPs: #2 #3 #7 #12
Number of SCCs: 1, DPs: 1
  SCC { #6 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #13: #plus(plus(x,i(x)),_1) -> #plus(0(),_1)
     #14: #times(times(x,plus(y,z)),_1) -> #times(plus(times(x,y),times(x,z)),_1)
     #15: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #16: #plus(x,plus(y,z)) ->= #plus(x,y)
     #17: #times(times(x,0()),_1) -> #times(0(),_1)
     #18: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #19: #times(x,times(y,z)) ->= #times(x,y)
     #20: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #21: #times(times(x,i(y)),_1) -> #times(i(times(x,y)),_1)
Number of SCCs: 2, DPs: 9
  SCC { #14 #17..19 #21 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      i 	s: 1
      plus	s: {1,2}	p: 1
      #i 	s: []	p: 0
    USABLE RULES: { 1..10 }
    Removed DPs: #14 #17 #19 #21
Number of SCCs: 2, DPs: 5
  SCC { #18 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #13 #15 #16 #20 }
POLO(Sum)... succeeded.
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 1
      times	w: x1 + x2 + 11798
      i 	w: x1 + 2085
      plus	w: x1 + x2 + 6282
      #i 	w: 0
    USABLE RULES: { 1 2 9 }
    Removed DPs: #13 #16 #20
Number of SCCs: 1, DPs: 1
  SCC { #15 }
only weak rules.
Number of SCCs: 0, DPs: 0