We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a Davenport-Schinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct this technique towards Tarjan's deque conjecture and prove that n deque operations take only O(nα~*(n)) time, where α~* (n) is the minimum number of applications of the inverse-Ackermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.
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