  This paper takes another look at the cost of traversing a binary tree using
repeated splay-to-root. This was shown to cost $O(n)$ (in rotations) by Tarjan
and later, in different ways, by Elmasry and others.
  It would be interesting to know the minimal possible coefficient implied by
the $O(n)$ cost; call this coefficient $\beta$. In this paper we define a
related coefficient $\alpha$ describing the cost of splay-to-root traversal on
maximal (i.e., complete) binary trees, and show that $\beta \geq 2 + \alpha$.
We give the first 3009 digits of $\alpha$, including the decimal point, and
show that every digit is correct.
  We make two conjectures: first, that $\beta = 2 + \alpha$, and second, that
$\alpha$ is irrational.
