Matthias Fuchs

• In this report we present a case study of employing goal-oriented heuristics whenproving equational theorems with the (unfailing) Knut-Bendix completion proce-dure. The theorems are taken from the domain of lattice ordered groups. It will bedemonstrated that goal-oriented (heuristic) criteria for selecting the next critical paircan in many cases significantly reduce the search effort and hence increase per-formance of the proving system considerably. The heuristic, goalADoriented criteriaare on the one hand based on so-called "measures" measuring occurrences andnesting of function symbols, and on the other hand based on matching subterms.We also deal with the property of goal-oriented heuristics to be particularly helpfulin certain stages of a proof. This fact can be addressed by using them in a frame-work for distributed (equational) theorem proving, namely the "teamwork-method".