You're not describing an eventually consistent system, you're describing a system that diverges. By definition, eventually consistent means that, after some time, all readers across the entire system are guaranteed to find the same values, even if before that time they may see different values.

Any eventually consistent system has to have a strategy for ensuring that all nodes eventually agree on a final value. R1 and R2 need to communicate their respective states, and agree to a single one of them - maybe using timestamps if R2's value is newer, R1 will replace its own value when they communicate), maybe using a quorum (say there is also an R3 which agrees with R1, then R2 will change its value to match the other two), maybe using an explicit priority list (say, R1's value is assumed better than R2's).

Yes. See https://news.ycombinator.com/item?id=45221779