YES

TRS:

  sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
  sum(cons(0(),x),y) -> sum(x,y)
  sum(nil(),y) -> y
  weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
  weight(cons(n,nil())) -> n

linear polynomial interpretations on N:

  sum_A(x1,x2) = x2
  sum#_A(x1,x2) = 3
  cons_A(x1,x2) = x1 + x2 + 2
  cons#_A(x1,x2) = 2
  s_A(x1) = 0
  s#_A(x1) = 1
  0_A = 1
  0#_A = 1
  nil_A = 1
  nil#_A = 0
  weight_A(x1) = x1
  weight#_A(x1) = x1

precedence:

  weight > cons = nil > sum = s = 0