  Tits has defined Kac-Moody groups for all root systems, over all commutative
rings with unit. A central concept is the idea of a prenilpotent pair of (real)
roots. In particular, writing down his group presentation explicitly would
require knowing all the Weyl-group orbits of such pairs. We show that for the
hyperbolic root system E10 there are so many orbits that any attempt at direct
enumeration is impractical. Namely, the number of orbits of prenilpotent pairs
having inner product k grows at least as fast as (constant)(7th power of k).
Our purpose is to motivate alternate approaches to Tits' groups.
