Combination of Compatible Reduction

Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important r^ ole in automated deduction. We present a general approach for combining such orderings. To be more precise, we show how E 1-compatible reduction orderings total on 1-ground terms and E 2-compatible reduction orderings total on 2-ground terms can be used to construct an (E 1 E 2)-compatible reduction ordering total on ((1 2)-ground terms, provided that the signatures are disjoint and some other (rather weak) restrictions are satissed. 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.