Expensive linear programming inequality analysis may be reduced by projecting each candidate word onto the axis hyperplanes, yielding m new (m-1)-symbol words which are necessarily also billiard, and can be validated from a precomputed list for dimension m-1. If any of these fails, the candidate fails; and if only one candidate remains after n-th symbols are attached to a valid (n-1)-length word, there is still no need for inequality analysis --- the ball cannot avoid bouncing next against some wall pair!

EXAMPLE

For n = 5 there are a(5) = 856 words, permutations on {1,2,3,4} of the 42 words