A complete proof of correctness of the Knuth-Bendix completion algorithm

摘要

We give in this paper a complete description of the Knuth-Bendix completion algorithm. We prove its correctness in full, isolating carefully the essential abstract notions, so that the proof may be extended to other versions and extensions of the basic algorithm. We show that it defines a semidecision algorithm for the validity problem in the equational theories for which it applies, yielding a decision procedure whenever the algorithm terminates.