A Lower Bound of the Number of Rewrite Rules Obtained by Homological Methods

It is well-known that some equational theories such as groups or boolean algebras can be defined by fewer axioms than the original axioms. However, it not easy to determine if a given set of smallest not. Malbos and Mimram investigated general method find lower bound cardinality (or rewrite rules) equivalent theory term rewriting systems), using homological algebra. Their an analog Squier's homology on string systems. In this paper, we develop for systems more provide better under stronger notion equivalence their equivalence. The author also implemented program compute bounds, experimented with 64 complete TRSs.