In the previous chapter we described a completely general, albeit impractical, procedure to find a group's automatic structure. In this chapter we trade generality for expediency, and limit ourselves to searching for a Shortlexautomatic (see page 56). This is a much less daunting task than to search among all automatic structures, for at least two reasons: First, Shortlex is a prefix closed language with uniqueness. This allows us to greatly simplify the axioms given in Section 5.1. We will essentially reprove the results of Section 5.1 in this context; the repetition is justified by the greater simplicity of the proof of the specialized result. A second reason is that we can use the Knuth-Bendix procedure [BL82] to find reduction rules that encode, in a much more efficient way, the same information given by the Cayley graph of the group.