Automated theorem proving by test set induction
Journal of Symbolic Computation
Term rewriting and all that
Proving termination with multiset orderings
Communications of the ACM
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Incorporating decision procedures in implicit induction
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Proceedings of the 10th International Conference on Automated Deduction
Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm
Journal of Automated Reasoning
'Descente Infinie' Induction-Based Saturation Procedures
SYNASC '07 Proceedings of the Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Validation of the JavaCard platform with implicit induction techniques
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Automatic 'descente infinie' induction reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Dealing with non-orientable equations in rewriting induction
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Integrating implicit induction proofs into certified proof environments
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Automated certification of implicit induction proofs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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We propose a new (Noetherian) induction schema to reason on equalities and show how to integrate it into implicit induction-based inference systems. Non-orientable conjectures of the form lhs= rhsand their instances can be soundly used as induction hypotheses in rewrite operations. It covers the most important rewriting-based induction proof techniques: i)term rewriting inductionif lhs= rhsis orientable, ii) enhanced rewriting inductionif lhsand rhsare comparable, iii)ordered rewriting inductionif the instances of lhs= rhsare orientable, and iv) relaxed rewriting inductionif the instances of lhs= rhsare not comparable.In practice, it helps to automatize the (rewrite-based) reasoning on a larger class of non-orientable equalities, like the permutative and associativity equalities.