Any step in a derivation that is allowed by the basic rules (that is, for now, all rules except LFR and Adj) is safe and will take the derivation some way towards completion. We call the system of derivations limited to those rules the basic system. There will often be different orders in which the basic rules can be applied, and such differences may lead to longer or shorter derivations. The use of non-basic rules can sometimes shorten derivations still further, but they may not bring a derivation any closer to is final state.

Although insight or foresight can help to shorten a derivation, all that is needed to complete a derivation is an understanding of what rules may be applied at any given stage. This is illustrated in the commentary on an extended example.

Derivations can be approached systematically through a 5-step procedure that is applied repeatedly until all gaps close or the derviation reaches a dead end.