Termination and completion modulo associativity, commutativity and identity

AbstractRewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of nontermination inherent to the use of identities. We build up on this idea in two ways: by giving a complete set of rules for completion modulo these axioms; by showing how to build appropriate orderings for proving termination of constrained rewriting modulo associativity, commutativity and identity