The rules feed back

Here is the mutual even/odd from before:

Diagram of one evaluation round for the mutual even/odd rules. A left box labelled 'before' holds even and odd; arrows lead from both into a central diamond labelled 'evaluation round'; arrows lead on to a right box labelled 'after' that also holds even and odd. A dashed arrow labelled 'feed back' loops from the 'after' box back to the 'before' box, showing that each round's output seeds the next.

Each round updates even/odd for the next.

When a round adds nothing new, the rules map the relations to themselves: we have found a fixed point.

Naive evaluation stops exactly at a fixed point. But which one?