What sequences of union/find queries will achieve the worst case complexity of a DSU? I'm specifically interested in a DSU with path compression but without union by rank/size, which has worst case complexity $$$\mathcal{O}(m \log n + n)$$$, but constructions for other variations are welcome as well.

A nice proof for the $$$\mathcal{O}(m \log n + n)$$$ bound would also be appreciated.