A strong restriction of the inductive completion procedure
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Proof by induction using test sets
Proc. of the 8th international conference on Automated deduction
Artificial Intelligence
Automatic proofs by induction in theories without constructors
Information and Computation
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A Confluence Criterion Based on the Generalised Neman Lemma
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
A decidability result about sufficient-completeness of axiomatically specified abstract data types
Proceedings of the 6th GI-Conference on Theoretical Computer Science
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
RRL: A Rewrite Rule Laboratory
Proceedings of the 8th International Conference on Automated Deduction
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
RRL: A Rewrite Rule Laboratory
Proceedings of the 9th International Conference on Automated Deduction
Deductive and inductive synthesis of equational programs
Journal of Symbolic Computation - Special issue on automatic programming
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
An automated tool for analyzing completeness of equational specifications
ISSTA '94 Proceedings of the 1994 ACM SIGSOFT international symposium on Software testing and analysis
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Observational proofs by rewriting
Theoretical Computer Science
Test Sets for the Universal and Existential Closure of Regular Tree Languages
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Superposition for Fixed Domains
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
A survey of automated deduction
Artificial intelligence today
Superposition for fixed domains
ACM Transactions on Computational Logic (TOCL)
Deciding the inductive validity of ∀∃* queries
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Inductive decidability using implicit induction
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
Coverset induction with partiality and subsorts: a powerlist case study
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Rewriting induction + linear arithmetic = decision procedure
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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The inductionless induction (also called proof by consistency) approach for proving equations by induction from an equational theory, requires a consistency check for equational theories. A new method using test sets for checking consistency of an equational theory is proposed. Using this method, a variation of the Knuth-Bendix completion procedure can be used for automatically proving equations by induction. The method does not suffer from limitations imposed by the methods proposed by Musser as well as by Huet and Hullot, and is as powerful as Jouannaud and Kounalis' method based on ground-reducibility. A theoretical comparison of the test set method with Jouannaud and Kounalis' method is given showing that the test set method is generally much better. Both the methods have been implemented in RRL, Rewrite Rule Laboratory, a theorem proving environment based on rewriting techniques and completion. In practice also, the test set method is faster than Jouannaud and Kounalis' method. The test set construction can also be used to check for the sufficient-completeness property of equational axiomatizations including algebraic specifications of abstract data types as well as for identifying constructors in an algebraic specification.