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No she wasn't bested because she wasn't trying. Yuuya just showed her that he learns quickly and finally figured out what Yui was trying to teach him.
Furthermore the duel ended because Yui got what she wanted, it didn't end because he "Beat" her or that she couldn't fight anymore which is clearly not the case at all. Even Yuuya knows he didn't beat Yui at all and this was all part of her plan.
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