Lucier's split conjecture for online binary search trees

Let ${\mathcal{A}}$ be an online binary search tree algorithm. Starting with any initial tree $T$ with $n$ elements, consider any sequence of $n$ splits. A split at an element $x$ deletes $x$ and produces two trees, whose elements are respectively smaller and larger than $x$, each subject to further splitting. Split conjecture. The cost of splitting $T$ by any such sequence is $O(n)$. This is one of the classical deque-, traversal-, and split conjectures for splay trees; its status is not resolved in the supplied source.