type match' =
  string (* home team *) * int (* goal difference *) * string (* away team *)

let matches =
  [
    ("foo", 1, "car");
    ("foo", 0, "bar");
    ("foo", 1, "far");
    ("car", 1, "bar");
    ("foo", ~-1, "bar");
    ("tar", 1, "fir");
    ("bar", 1, "qux");
    ("jor", ~-1, "far");
    ("xir", 1, "kar");
    ("car", ~-1, "qux");
    ("far", 1, "qux");
    ("car", 1, "foo");
  ]

let way a b =
  let rec aux (at : string) (visited : string list) (accum : match' list) =
    if at = b then [ List.rev accum ]
    else
      let matches =
        matches |> List.filter (function _, score, _ -> score <> 0)
      in
      let h =
        matches
        |> List.filter (function home, score, away ->
               score > 0 && home = at && not (List.exists (( = ) away) visited))
        |> List.map (function (_, _, away) as x ->
               aux away (at :: visited) (x :: accum))
        |> List.concat
      in
      let a =
        matches
        |> List.filter (function home, score, away ->
               score < 0 && away = at && not (List.exists (( = ) home) visited))
        |> List.map (function (home, _, _) as x ->
               aux home (at :: visited) (x :: accum))
        |> List.concat
      in
      a @ h
  in
  aux a [] []