Combination of compatible reduction orderings that are total on ground terms

Abstract

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 E/sub 1/-compatible reduction orderings total on /spl Sigma//sub 1/-ground terms and E/sub 2/-compatible reduction orderings total on /spl Sigma//sub 2/-ground terms can be used to construct an (E/sub 1//spl cup/E/sub 2/)-compatible reduction ordering total on (/spl Sigma//sub 1//spl cup//spl Sigma//sub 2/)-ground terms, provided that the signatures 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.