Combination of compatible reduction orderings that are total on ground terms

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 Σ₁-ground terms and E₂-compatible reduction orderings total on Σ₂-ground terms can be used to construct an (E₁∪E₂)-compatible reduction ordering total on (Σ₁∪Σ₂)-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