Optimistic Analysis of Algorithm ZETA's Runtime Complexity

What are the possible runtime complexities of Algorithm ZETA based on Alice and Oya's empirical studies?

The algorithm ZETA has a lower bound of n log n and an upper bound of n^2 based on the given statements. It cannot be concluded whether it is O(n) or O(n^3), but it can potentially be Ω(n^2) and Θ(n^2).

Alice's statement suggests that the lower bound for ZETA's runtime is Omega(n log n), and Oya's statement suggests that the upper bound is O(n^2). Since Omega(n^2) is a possible lower bound and O(n^2) is a possible upper bound, we can conclude that ZETA's runtime can be Omega(n^2) and can also be Theta(n^2), as it's bounded both from above and below by functions that are proportional to n^2.