# Complexity of sorting algorthms

I've read an article (German) about different sorting algorithms where the author states this:

[Smoothsort] is a sorting algorithm that uses swaps to sort and does not need any extra external allocated memory. Because of this it can't be stable, because if it was, it needed $O(n^2)$ comparisons in the worst case. (This statement is a hypothesis of mine. I'm very sure it holds, although I have yet to show it)

I wasn't able to find an algorithm on my own that satisfies the criteria (in-place, stable, faster than $O(n^2)$ in the worst case). Is that hypothesis true? If yes, how can one show that it holds?

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