Combination of matching algorithms
This paper addresses the problem of systematically building a matching algorithm for the union of two disjoint equational theories. The question is under which conditions matching algorithms in the single theories are sufficient to obtain a matching algorithm in the combination? In general, the blind use of combination techniques introduces unification. Two different restrictions are considered in order to reduce this unification to matching. First, we show that combining matching algorithms (with linear constant restriction) is always sufficient for solving a pure fragment of combined matching problems. Second, we present a combined matching algorithm which is complete for the largest class of theories where unification is not needed, including collapse-free regular theories and linear theories.
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