RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Automated Deduction Techniques for Studying Rough Algebras
Fundamenta Informaticae
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Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important role in automated deduction. This paper presents a general approach for combining such orderings: it shows how E1-compatible reduction orderings total on S1-ground terms and E2-compatible reduction orderings total on S2-ground terms can be used to construct an E-compatible reduction ordering total on S-ground terms (where F is the union of the theories E1 and E2, and S is the union of the signatures S1 and S2), provided that S1 and S2 are disjoint and some other (rather weak) restrictions are satisfied. This work was motivated by the observation that it is often easier to construct such orderings for "small" signatures and theories separately, rather than directly for their union.