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Computers are no help - I need human eyes on this one.

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ChessSoldier

The following game took place at a local ladder match.  I felt that I was much better during most of the game but the computer shows that it was mostly even for the whole match.  Then, near the end, I offer to trade into a winning endgame that the computer thinks is only a slight advantage.  Help me prove it wrong:

So am I right?  Is it better to trade rooks in that endgame or should I listen to the computer and go Rb4-a4?  In the crowded middlegame, am I as winning as I feel, or did White still have some way to uncoil?  Was I right to preserve the two bishops or should I have pinned/traded his knight in order to win over d4?