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

max/plus interpretations on N:

  sum_A(x1,x2) = max{27, -1, 3 + x2}
  sum#_A(x1,x2) = max{20, 21, 23}
  cons_A(x1,x2) = max{4, 8 + x1, 14 + x2}
  cons#_A(x1,x2) = max{2, 3, 23}
  s_A(x1) = max{7, -12}
  s#_A(x1) = max{22, 22}
  0_A = 16
  0#_A = 20
  nil_A = 0
  nil#_A = 0
  weight_A(x1) = max{0, 1 + x1}
  weight#_A(x1) = max{0, -3 + x1}

precedence:

  nil = weight > sum > cons > s = 0