Look people, it would be to your benefit to actually WATCH the episodes where the explanations and reasons are divulged for Graham's course of action. Making asinine assumptions are not to your benefit when discussing the matter. It kills your credibility a fair bit.
1) Freezing Hayate before she merged with the Tome would be pointless because without the unison between Tome and Master, the Tome will be free to hop on to the next master. Cue massive headache because they need to search for the next spawnpoint AGAIN.
2) This is the reason why they needed the program to go "berserk", because that is when the total unison occurs. Trapped by its bond with Hayate, freezing Hayate with Durandal would have sealed the Tome as well.
3) Graham paid for Hayate's expenses because he felt guilty for what he was about to do to her.
4) The Arc-en-Ciel was not what Graham wanted to do, because it would have solved NOTHING.
5) Hayate seizing control of the administrative program and separating the Defence Program from the main program was what made the Arc-en-Ciel viable. This was not something that Graham could have anticipated.
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Those are some of the main points. You can find out more by watching the relevant episodes.
Cheers.
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