Automatic proofs by induction in theories without constructors
Information and Computation
Automating inductionless induction using test sets
Journal of Symbolic Computation
How to prove equivalence of term rewriting systems without induction
Theoretical Computer Science
Deductive and inductive synthesis of equational programs
Journal of Symbolic Computation - Special issue on automatic programming
Automated theorem proving by test set induction
Journal of Symbolic Computation
Term rewriting and all that
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 10th International Conference on Automated Deduction
Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Annals of Mathematics and Artificial Intelligence
Rewriting induction + linear arithmetic = decision procedure
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order. Thus, when the given conjecture is not orientable by the reduction order in use, any proof attempts for that conjecture fails; also conjectures such as a commutativity equation are out of the scope of the rewriting induction because they can not be oriented by any reduction order. In this paper, we give an enhanced rewriting induction which can deal with non-orientable conjectures. We also present an extension which intends an incremental use of our enhanced rewriting induction.