YES
Input TRS:
      1: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
      2: sum(cons(0(),x),y) -> sum(x,y)
      3: sum(nil(),y) -> y
      4: weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
      5: weight(cons(n,nil())) -> n
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying sum
      1: sum^1_cons(s(n),x,cons(m,y)) -> sum^1_cons(n,x,cons(s(m),y))
      2: sum^1_cons(0(),x,y) -> sum(x,y)
      3: sum^1_nil(y) -> y
      4: weight(cons(n,cons(m,x))) -> weight(sum^1_cons(n,cons(m,x),cons(0(),x)))
      5: weight(cons(n,nil())) -> n
      6: sum(cons(_1,_2),_3) ->= sum^1_cons(_1,_2,_3)
      7: sum(nil(),_1) ->= sum^1_nil(_1)
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 3 5 7 6 2
      s 	w: x1 + 1
      sum^1_cons	w: x1 + x2 + x3 + 23611
      sum	w: x1 + x2
      0 	w: 2
      sum^1_nil	w: x1 + 1
      nil	w: 2
      weight	w: 2 * x1
      cons	w: x1 + 2 * x2 + 44851
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #sum^1_cons(s(n),x,cons(m,y)) -> #sum^1_cons(n,x,cons(s(m),y))
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      sum^1_cons	w: 0
      sum	w: 0
      0 	w: 0
      sum^1_nil	w: 0
      nil	w: 0
      #sum^1_cons	w: x1 + x3
      weight	w: 0
      cons	w: 23676
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0