Registered orderings use information in a registry to orient formulas into rewrite rules. There are two kinds of information in a registry: height information and status information.
When the current registry does not contain enough information to orient a formula, LP will generate minimal sets of extensions to the registry, called suggestions, that permit the formula to be oriented. If the automatic-registry setting is on, LP picks one of these extensions to orient a formula without user interaction; it does not try all extensions. If the setting is off, LP will interact with the user, who must pick the desired extension.