  Consider a graph with vertex set S. A word in the alphabet S has the
intervening neighbours property if any two occurrences of the same letter are
separated by all its graph neighbours. For a Coxeter graph, words represent
group elements. Speyer recently proved that words with the intervening
neighbours property are irreducible if the group is infinite and irreducible.
We present a new and shorter proof using the root automaton for recognition of
irreducible words.
