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So are you supposed to find the shortest checkmate for white? I'm a bit new to forums.
No, to=discuss the options for white and analyse the game
So considering black's best option is to take one of the rooks in most situation, I would close the box, and move 1. Rg2, that way the rook on e3 can take care of the bishop.... however the Bishop can just threaten the rook and move 1. ... Bd4, or 1. ... Bf1. This might just prolong the game though. I don't see any strategy for black to be able to win, but that maybe just me.
Doesn't 1.Rxh3+ win trivially?
Which side of the board is which? Is the Black pawn about to promote on g1 or is it on its original b7 square?
I put coordinates and yes it is about to promote!
If the pawns are going up (on a6 and b7), there is very little to analyze or discuss in this position. White's advantage is overwhelming. (edit *I see you've added coordinates while I was typing*)
If the pawns are going down (on h3 and g2)...I think pfren's Rxh3+ wins... other moves (Re2 for instance) might just draw. (There's obviously no win for black as white can always sack rooks on pawns leaving black without mating material.)
1.Rg7 and 1.Rh7 also win very easily, and I'm sure white has more winning first moves.
Sorry, but the position is not interesting at all.