Examples for lower bounds proof except sorting

Question

After i read this question here.

All non-trivial examples of lower bounds always mention sorting, but i do not find other non-trivial examples, which do not rely (partly) on the sorting proof.

What are other non-trivial examples?

Answer 1

Here are some examples:

1. Finding an element in a sorted list takes time $\Omega(\log n)$ in the RAM model.
2. Implementing a disjoint sets data structure requires an amortized $\Omega(\alpha(n))$ operations in the cell probe model.
3. Determining whether the input string is a palindrome requires $\Omega(n^2)$ operations on a single tape Turing machine.

There are many others.