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
  empty(nil()) -> true()
  empty(cons(n,x)) -> false()
  tail(nil()) -> nil()
  tail(cons(n,x)) -> x
  head(cons(n,x)) -> n
  weight(x) -> if(empty(x),empty(tail(x)),x)
  if(true(),b,x) -> weight_undefined_error()
  if(false(),b,x) -> if2(b,x)
  if2(true(),x) -> head(x)
  if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))

max/plus interpretations on N:

  sum_A(x1,x2) = max{35, -11, 1 + x2}
  sum#_A(x1,x2) = max{1, 46, 19 + x2}
  cons_A(x1,x2) = max{0, 26 + x1, 13 + x2}
  cons#_A(x1,x2) = max{0, 31, 29 + x2}
  s_A(x1) = max{1, 1}
  s#_A(x1) = max{20, -1 + x1}
  0_A = 0
  0#_A = 29
  nil_A = 13
  nil#_A = 10
  empty_A(x1) = max{35, 21 + x1}
  empty#_A(x1) = max{11, 13}
  true_A = 35
  true#_A = 9
  false_A = 47
  false#_A = 30
  tail_A(x1) = max{14, -13 + x1}
  tail#_A(x1) = max{0, 11}
  head_A(x1) = max{21, -26 + x1}
  head#_A(x1) = max{0, 0}
  weight_A(x1) = max{21, -14 + x1}
  weight#_A(x1) = max{38, 12 + x1}
  if_A(x1,x2,x3) = max{20, -14, 21, -14 + x3}
  if#_A(x1,x2,x3) = max{37, 1, 3 + x2, 7 + x3}
  weight_undefined_error_A = 21
  weight_undefined_error#_A = 8
  if2_A(x1,x2) = max{21, -26, -26 + x2}
  if2#_A(x1,x2) = max{2, x1, 6 + x2}

precedence:

  tail = if2 > sum = head = weight > nil = empty > true = false > cons = 0 = weight_undefined_error > s = if