Tarjan's deque 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 inserting or deleting the current minimum or maximum elements $m$ times. Deque conjecture. The cost of these operations is $O(m+n)$. This is one of the classical conjectures about the efficiency of splay trees and online binary search trees; its status is not resolved in the supplied source.