YES
Input TRS:
AC symbols: plus times
      1: s(p(x)) -> x
      2: p(s(x)) -> x
      3: plus(0(),y) -> y
      4: plus(s(x),y) -> s(plus(x,y))
      5: plus(p(x),y) -> p(plus(x,y))
      6: plus(i(x),x) -> 0()
      7: plus(x,plus(i(x),y)) -> y
      8: i(0()) -> 0()
      9: i(s(x)) -> p(i(x))
      10: i(p(x)) -> s(i(x))
      11: i(i(x)) -> x
      12: i(plus(x,y)) -> plus(i(y),i(x))
      13: times(0(),y) -> 0()
      14: times(s(x),y) -> plus(times(x,y),y)
      15: times(p(x),y) -> plus(times(x,y),i(y))
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #i(s(x)) -> #p(i(x))
     #2: #i(s(x)) -> #i(x)
     #3: #i(plus(x,y)) -> #plus(i(y),i(x))
     #4: #i(plus(x,y)) -> #i(y)
     #5: #i(plus(x,y)) -> #i(x)
     #6: #times(s(x),y) -> #plus(times(x,y),y)
     #7: #times(s(x),y) -> #times(x,y)
     #8: #i(p(x)) -> #s(i(x))
     #9: #i(p(x)) -> #i(x)
     #10: #plus(p(x),y) -> #p(plus(x,y))
     #11: #plus(p(x),y) -> #plus(x,y)
     #12: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #13: #times(x,times(y,z)) ->= #times(x,y)
     #14: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #15: #plus(x,plus(y,z)) ->= #plus(x,y)
     #16: #times(p(x),y) -> #plus(times(x,y),i(y))
     #17: #times(p(x),y) -> #times(x,y)
     #18: #times(p(x),y) -> #i(y)
     #19: #plus(s(x),y) -> #s(plus(x,y))
     #20: #plus(s(x),y) -> #plus(x,y)
Number of SCCs: 3, DPs: 12
  SCC { #2 #4 #5 #9 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: 0
      #p 	w: 0
      p 	w: x1 + 1
      #times	w: 0
      0 	w: 0
      times	w: 0
      #s 	w: 0
      i 	w: 0
      plus	w: x1 + x2 + 1
      #i 	w: x1
    USABLE RULES: { }
    Removed DPs: #2 #4 #5 #9
Number of SCCs: 2, DPs: 8
  SCC { #7 #12 #13 #17 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      #p 	s: []	p: 0
      p 	s: [1]	p: 0
      #times	s: {1,2}	p: 3
      0 	s: []	p: 0
      times	s: {1,2}	p: 3
      #s 	s: []	p: 0
      i 	s: [1]	p: 2
      plus	s: {1,2}	p: 1
      #i 	s: 1
    USABLE RULES: { 1..17 }
    Removed DPs: #7 #13 #17
Number of SCCs: 2, DPs: 5
  SCC { #12 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #11 #14 #15 #20 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: x1 + x2
      #p 	w: 0
      p 	w: x1 + 2
      #times	w: 0
      0 	w: 1
      times	w: x1 + x2 + 40651
      #s 	w: 0
      i 	w: x1 + 1
      plus	w: x1 + x2 + 2
      #i 	w: 0
    USABLE RULES: { 1..7 16 }
    Removed DPs: #11 #15 #20
Number of SCCs: 1, DPs: 1
  SCC { #14 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #21: #plus(plus(i(x),x),_1) -> #plus(0(),_1)
     #22: #times(times(0(),y),_1) -> #times(0(),_1)
     #23: #times(times(s(x),y),_1) -> #times(plus(times(x,y),y),_1)
     #24: #plus(plus(x,plus(i(x),y)),_1) -> #plus(y,_1)
     #25: #plus(plus(p(x),y),_1) -> #plus(p(plus(x,y)),_1)
     #26: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #27: #times(x,times(y,z)) ->= #times(x,y)
     #28: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #29: #plus(x,plus(y,z)) ->= #plus(x,y)
     #30: #plus(plus(0(),y),_1) -> #plus(y,_1)
     #31: #times(times(p(x),y),_1) -> #times(plus(times(x,y),i(y)),_1)
     #32: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
Number of SCCs: 2, DPs: 12
  SCC { #22 #23 #26 #27 #31 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {}	p: 1
      #p 	s: []	p: 0
      p 	s: [1]	p: 0
      #times	s: {1,2}	p: 3
      0 	s: []	p: 0
      times	s: {1,2}	p: 3
      #s 	s: []	p: 0
      i 	s: 1
      plus	s: {1,2}	p: 1
      #i 	s: 1
    USABLE RULES: { 1..17 }
    Removed DPs: #22 #23 #27 #31
Number of SCCs: 2, DPs: 8
  SCC { #26 }
only weak rules.
Number of SCCs: 1, DPs: 7
  SCC { #21 #24 #25 #28..30 #32 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #plus	w: x1 + x2
      #p 	w: 0
      p 	w: x1 + 2
      #times	w: 0
      0 	w: 29525
      times	w: 1424
      #s 	w: 0
      i 	w: x1 + 1
      plus	w: x1 + x2 + 29525
      #i 	w: 0
    USABLE RULES: { 1..7 16 }
    Removed DPs: #21 #24 #29 #30
Number of SCCs: 1, DPs: 3
  SCC { #25 #28 #32 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #plus	s: {1,2}	p: 1
      #p 	s: []	p: 0
      p 	s: [1]	p: 0
      #times	s: {1,2}	p: 3
      0 	s: []	p: 0
      times	s: {1,2}	p: 3
      #s 	s: []	p: 0
      i 	s: 1
      plus	s: {1,2}	p: 1
      #i 	s: 1
    USABLE RULES: { 1..17 }
    Removed DPs: #25 #32
Number of SCCs: 1, DPs: 1
  SCC { #28 }
only weak rules.
Number of SCCs: 0, DPs: 0