Zhuge and Sima Yi were definitely big time rivals. They were arguably the two greatest minds of the era, the fought several times and were always trying to outsmart the other. Zhuge was fighting for Shu's survival against Sima Yi, while Sima was fighting to eliminate the man he saw as his biggest threat. You could probably say the most climactic battle of the period was Wuzhang Plains which pitted the two against each other. I don't know, it's possible the novel may have embellished the rivalry for entertainment purposes, but that's what we're going off of anyway, the Dynasty Warriors games which are based on the novel. After Liu Bei and Cao Cao died, Zhuge and Sima became the key figures for their dynasties, with Liu Shan being a worthless piece of s*** and the Cao line mostly serving as figureheads.
The Zhuge/Zhou Yu rivalry is certainly a good example, but it didn't last too long as Zhuge dominated Zhou Yu. Maybe Zhuge and Sima didn't converse much, if at all, but they did command massive armies against each other on several occasions. These two fought epic wars against each other that weren't going to end until one of them was dead.
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Booyah, Grandma. Booyah.