The observation that unification under associativity and commutativity reduces to the solution of certain linear diophantine equations is the basis for a complete and minimal unification algorithm. It is also shown that completeness and minimality is closely related to the notion of a basis for the linear solution space of these equations . Terms under associativity (A) and commutativity (C) closely resemble the datastructure multi sets (sets which may contain multiple occurrences of the same element) , which is used in the matching of patterns (pattern directed invocation) in many Al-languages. The problem was first investigated in [ 40], this paper presents an alternative solution, which is an improvement over [ 40]. Unification under a...