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Rooks vs Rook

What exactly is the strategy in this endgame?

Not even in the most extense lists of endgames can I find this case.

Just push the king to the side and checkmate.
Yeah, it should be easy to build a staircase mate and force an exchange of rooks, but the checks by the defending rook are annoying.

I considered using a rook and the king to push the defending king, and the other rook to defend your king against checks.

I just wonder if there's a simple method to follow.
Your king shelters behind one of your rooks. Your rooks push the king to the side and checkmate.
For example 49 R4e6+ Kb5 50 Rb7+ Ka5 51 Rb8 Rc5+ 52 Kf6

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