So what exactly are we supposed to figure out? A winning line for green after Bg13+?
Puzzle?

@Darksquareman
It seems green cannot checkmate blue in time before yellow promotes and therefore the game is still balanced at move 43 where blue decided to stop playing. With optimal play the position will reach something like the image below.. Please correct me if you find a better line. Once one of the 2 green queens is traded there will no longer be any mating threats and the game will be balanced again.
It is difficult, probably impossible to determine whether or not green is winning. But I think you are right, it would be to difficult for green to play the right moves to challenge yb, and objectively they can hold. But what I was saying was that yellow unnecessarily took blues rook, when instead he could have played Bc11, controlling the queening square. That would certainly have been a balanced game.
https://www.chess.com/variants/4-player-chess/game/27188557/137/4 Figure this out lol. Lets see how many people will make fun of me.