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It is known that the first-order theory of rewriting is decidable for groundterm rewrite systems, but the general technique uses tree automata and oftentakes exponential time. For many properties, including confluence (CR),uniqueness of normal forms with respect to reductions (UNR) and with respect toconversions (UNC), polynomial time decision procedures are known for groundterm rewrite systems. However, this is not the case for the normal formproperty (NFP). In this work, we present a cubic time algorithm for NFP, analmost cubic time algorithm for UNR, and an almost linear time algorithm forUNC, improving previous bounds. We also present a cubic time algorithm for CR.

Deciding Confluence and Normal Form Properties of Ground Term Rewrite Systems Efficiently