A Universal Unification Algorithm Based on Unification-Driven Leftmost Outermost Narrowing

We formalize a universal uni cation algorithm for the class of equational theories which is induced by the class of canonical totally de ned not strictly subuni able term rewriting systems for short ctn trs For a ctn trs R and for two terms t and s the algorithm computes a ground complete set of ER uni ers of t and s where ER is the set of rewrite rules of R viewed as equations The algorithm is based on the uni cation driven leftmost outermost narrowing relation for short ulo narrowing relation which is introduced in this paper The ulo narrowing relation combines usual leftmost outermost narrowing steps and uni cation steps Since the uni cation steps are applied as early as possible some of the nonsuccessful derivations can be stopped earlier than in other approaches to ER uni cation Furthermore we formalize a deterministic version of our universal uni cation algorithm that is based on a depth rst left to right traversal through the narrowing trees The work of this author has been supported by the Deutsche Forschungsgemeinschaft DFG