YES
Input TRS:
AC symbols: plus
      1: sum(x,y) -> S(int(x,y))
      2: S(nil()) -> 0()
      3: S(cons(x,xs)) -> plus(x,S(xs))
      4: plus(x,0()) -> x
      5: plus(x,s(y)) -> s(plus(x,y))
      6: int(0(),0()) -> cons(0(),nil())
      7: int(0(),s(y)) -> cons(0(),int(s(0()),s(y)))
      8: int(s(x),0()) -> nil()
      9: int(s(x),s(y)) -> intlist(int(x,y))
      10: intlist(nil()) -> nil()
      11: intlist(cons(x,y)) -> cons(s(x),intlist(y))
Number of strict rules: 11
Direct POLO(bPol) ... removes: 8 1 6 2
      s 	w: x1
      S 	w: 2 * x1
      sum	w: 2 * x1 + 2 * x2 + 5
      0 	w: 0
      nil	w: 1
      intlist	w: x1
      int	w: x1 + x2 + 2
      plus	w: x1 + x2
      cons	w: x1 + x2
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying int
AC symbols: plus
      3: S(cons(x,xs)) -> plus(x,S(xs))
      4: plus(x,0()) -> x
      5: plus(x,s(y)) -> s(plus(x,y))
      7: int^1_0(s(y)) -> cons(0(),int^1_s(0(),s(y)))
      9: int^1_s(x,s(y)) -> intlist(int(x,y))
      10: intlist(nil()) -> nil()
      11: intlist(cons(x,y)) -> cons(s(x),intlist(y))
      12: int(0(),_1) ->= int^1_0(_1)
      13: int(s(_1),_2) ->= int^1_s(_1,_2)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #int(s(_1),_2) ->? #int^1_s(_1,_2)
     #2: #int^1_s(x,s(y)) -> #intlist(int(x,y))
     #3: #int^1_s(x,s(y)) -> #int(x,y)
     #4: #intlist(cons(x,y)) -> #intlist(y)
     #5: #int(0(),_1) ->? #int^1_0(_1)
     #6: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #7: #plus(x,plus(y,z)) ->= #plus(x,y)
     #8: #int^1_0(s(y)) -> #int^1_s(0(),s(y))
     #9: #plus(x,s(y)) -> #plus(x,y)
     #10: #S(cons(x,xs)) -> #plus(x,S(xs))
     #11: #S(cons(x,xs)) -> #S(xs)
Number of SCCs: 4, DPs: 9
  SCC { #11 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: 0
      s 	w: 0
      S 	w: 0
      #plus	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: 0
      int	w: 0
      #S 	w: x1
      plus	w: 0
      cons	w: x2 + 1
      int^1_s	w: 0
      #int^1_s	w: 0
      #int	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 3, DPs: 8
  SCC { #4 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: x1
      s 	w: 0
      S 	w: 0
      #plus	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: 0
      int	w: 0
      #S 	w: 0
      plus	w: 0
      cons	w: x2 + 1
      int^1_s	w: 0
      #int^1_s	w: 0
      #int	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 7
  SCC { #6 #7 #9 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: 0
      s 	w: x1 + 1
      S 	w: 0
      #plus	w: x1 + x2
      sum	w: 0
      0 	w: 21277
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: 0
      int	w: 0
      #S 	w: 0
      plus	w: x1 + x2 + 7720
      cons	w: 1
      int^1_s	w: 0
      #int^1_s	w: 0
      #int	w: 0
    USABLE RULES: { 4 5 14 }
    Removed DPs: #7 #9
Number of SCCs: 2, DPs: 5
  SCC { #6 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #1 #3 #5 #8 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: 0
      s 	w: x1 + 3
      S 	w: 0
      #plus	w: x1 + x2
      sum	w: 0
      0 	w: 1
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: x1 + 2
      int	w: 0
      #S 	w: 0
      plus	w: x1 + x2 + 20163
      cons	w: 1
      int^1_s	w: 0
      #int^1_s	w: x1 + x2
      #int	w: x1 + x2 + 2
    USABLE RULES: { 4 5 14 }
    Removed DPs: #1 #3 #5 #8
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #12: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #13: #plus(x,plus(y,z)) ->= #plus(x,y)
     #14: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #15: #plus(plus(x,0()),_1) -> #plus(x,_1)
Number of SCCs: 1, DPs: 4
  SCC { #12..15 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: 0
      s 	w: x1 + 1
      S 	w: 0
      #plus	w: x1 + x2
      sum	w: 0
      0 	w: 62898
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: 2
      int	w: 0
      #S 	w: 0
      plus	w: x1 + x2 + 10451
      cons	w: 1
      int^1_s	w: 0
      #int^1_s	w: 0
      #int	w: 2
    USABLE RULES: { 4 5 14 }
    Removed DPs: #13 #15
Number of SCCs: 1, DPs: 2
  SCC { #12 #14 }
POLO(Sum)... succeeded.
      int^1_0	w: 0
      #intlist	w: 0
      s 	w: 1
      S 	w: 0
      #plus	w: x1 + x2
      sum	w: 0
      0 	w: 20819
      nil	w: 0
      intlist	w: 0
      #int^1_0	w: 2
      int	w: 0
      #S 	w: 0
      plus	w: x1 + x2 + 1
      cons	w: 1
      int^1_s	w: 0
      #int^1_s	w: 0
      #int	w: 2
    USABLE RULES: { 4 5 14 }
    Removed DPs: #14
Number of SCCs: 1, DPs: 1
  SCC { #12 }
only weak rules.
Number of SCCs: 0, DPs: 0