Equational inference, canonical proofs, and proof orderings

@article{Bachmair1994EquationalIC,
  title={Equational inference, canonical proofs, and proof orderings},
  author={Leo Bachmair and Nachum Dershowitz},
  journal={J. ACM},
  year={1994},
  volume={41},
  pages={236-276}
}
We describe the application of proof orderings—a technique for reasoning about inference systems-to various rewrite-based theorem-proving methods, including refinements of the standard Knuth-Bendix completion procedure based on critical pair criteria; Huet's procedure for rewriting modulo a congruence; ordered completion (a refutationally complete extension of standard completion); and a proof by consistency procedure for proving inductive theorems. 
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