Final answer:
Alice believes the algorithm ZETA has a lower bound of Omega(n logn) while Oya claims an upper bound of O(n²). There is no sufficient information to support the algorithm being O(n). Instead, ZETA's time complexity is at least n logn and at most n².
Step-by-step explanation:
The question is centered on determining the time complexity of an algorithm called ZETA based on empirical studies presented by two individuals, Alice and Oya. Alice claims that the algorithm is Omega(n logn), which means the algorithm's running time grows at least as fast as n logn for large enough n. Oya states the algorithm is O(n²), indicating that the running time does not grow faster than the function n².
Based on these claims, the correct statement is not provided in the original question. It would be incorrect to conclude that the algorithm is definitely O(n) given the previous statements made by Alice and Oya. Without additional information, it is only safe to say that ZETA's complexity is bounded below by n logn (per Alice's claim) and above by n² (per Oya's claim).