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Going over PHP's 30 second time limit normally indicates a bug in the GAME
Code program, usually an infinite loop. Try debugging your code.

Storing the position on the form would have little effect on speed, since
automation and checking the legality of moves doesn't really take that
long. The only thing I've tried that is really time consuming is checking
for checkmate and stalemate, which both involve trying out alternate moves.
So I normally put code for this in the Post-Game sections, so that it gets
done only at the end of a series of moves.

As for resetting the time limit, I don't think that's doable. It is a
built-in feature of PHP, which Game Courier is written in, not of Game
Courier itself.