Kirito carries Alice and climbs up to the Cloudtop Garden, whereupon Kirito casts a spell to track the Blue Rose Sword. Find the Sword, Find Eugeo is his logic. The spell leads them to the bathhouse, still covered and ice, and to the petrified Bercouli, whom Alice affectionately refers to as Uncle.
They cannot free Bercouli from his stone prison; their options are either to get Prime Senator Chedulkin to break the spell, or kill him for his refusal to do so. Bercouli gives Alice his blessing, telling her she has nothing more to learn from him.
Alice and Kirito ascend to the Senate level, where Kirito learns that the weird bald headed dude who appeared after he attacked the noble rapists was a Senator. They observe and detect breaches of the Taboo Index, then dispatch Integrity Knights as needed.
The existence and function of the Senate is something previously unknown to both Kirito and ourselves, and even Alice is a bit fuzzy about it. But it makes sense for Administrator to leave the day-to-day operations to proxies in the form of the Senate rather than be hands-on about everything and never get any beauty rest.
They locate Prime Senator Chedulkin’s tacky chambers (which somewhat resemble those of the giant baby in Spirited Away), but when Alice confronts him, he merely reminisces on the day four years ago when young Alice first appeared, tearfully begging not to have her memories of those she loved erased.
Chedulkin’s deeply goofy appearance is matched by his boundless cruelty and sadism, but when Alice runs him through with her sword, he merely explodes into a puff of smoke. Getting rid of the little chud won’t be so easy.
More distressingly, he largely succeeded in his mission to stall Alice and Kirito with stories that only served to further boil Alice’s blood. And clearly, Administrator used that extra time wisely, quickly transforming Eugeo into her thirty-second and newest Integrity Knight.
When Eugeo appears before Kirito and Alice, he has no memory of his relationship to either, nor does he care. The Pontifex has given him something he’s apparently been missing his whole life, and something neither of his friends could provide to his satisfaction. So Kirito and Alice are naught but rebels and enemies of his Pontifex to be eliminated without delay.
While Kirito warns Eugeo that he’s the master and Eugeo the student in their imminent duel, I imagine Admin didn’t send Eugeo to fight Kirito without a few tricks up his swanky new sleeves Kirito might not be able to predict. And then there’s the whole matter of Kirito not wanting to go all out lest he accidentally kill Eugeo, while Eugeo is completely wrapped around Admin’s finger. In any case, it should be some duel.