Building both at once
Start both relations empty and evaluate all three rules each round, over num = {0, 1, 2, 3}:
| round | even | odd |
|---|---|---|
| 0 | {} | {} |
| 1 | {0} | {} |
| 2 | {0} | {1} |
| 3 | {0, 2} | {1} |
| 4 | {0, 2} | {1, 3} |
| 5 | (no change) | (no change) |
Each round feeds the next, the relations growing in turn, until a round adds nothing new.