Check if RB-Tree has more B nodes

type 'a rb_tree =
    | Black of 'a rb_tree * 'a * 'a rb_tree
    | Red of 'a rb_tree * 'a * 'a rb_tree
    | Nil

let more_black tree =
    let rec aux sums = function
        | Black (l, _, r) -> sigma sums (1, 0) (aux sums l) (aux sums r)
        | Red (l, _, r) -> sigma sums (0, 1) (aux sums l) (aux sums r)
        | Nil -> sums
    and sigma (a, b) (c, d) (e, f) (g, h) = (a + c + e + g, b + d + f + h) in
    let blacks, reds = aux (0, 0) tree in
    blacks > reds

let rbt = Red (Black (Black (Nil, 4, Red (Nil, 11, Nil)), 1, Nil), 8, Red (Nil, 4, Black (Nil, 7, Black (Nil, 4, Nil))))

let () = more_black rbt |> string_of_bool |> print_endline