Handbook of theoretical computer science (vol. B)
Journal of the ACM (JACM)
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Information and Computation
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Proving termination with multiset orderings
Communications of the ACM
Paramodulation and Knuth–Bendix Completion with Nontotal and Nonmonotonic Orderings
Journal of Automated Reasoning
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Well-Foundedness Is Sufficient for Completeness of Ordered Paramodulation
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Paramodulation with Non-Monotonic Orderings
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Paramodulation with Well-founded Orderings
Journal of Logic and Computation
Slothrop: Knuth-Bendix completion with a modern termination checker
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Termination tools in ordered completion
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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Ordered paramodulation and Knuth-Bendix completion are known to remain complete when using non-monotonic orderings. However, these results do not imply the compatibility of the calculus with essential redundancy elimination techniques such as demodulation, i.e., simplification by rewriting, which constitute the primary mode of computation in most successful automated theorem provers. In this paper we present a complete ordered paramodulation calculus for non-monotonic orderings which is compatible with powerful redundancy notions including demodulation, hence strictly improving the previous results and making the calculus more likely to be used in practice. As a side effect, we obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent term rewrite system for a given set of equations and a (possibly non-totalizable) reduction ordering.