A procedure for automatically proving the termination of a set of rewrite rules
Proc. of the first international conference on Rewriting techniques and applications
Theoretical Computer Science
Theory of linear and integer programming
Theory of linear and integer programming
How to choose the weights in the Knuth Bendix ordering
on Rewriting techniques and applications
Automating the Knuth Bendix ordering
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Simple LPO constraint solving methods
Information Processing Letters
Term rewriting and all that
Verifying Orientability of Rewrite Rules Using the Knuth-Bendix Order
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
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Proceedings of the 12th International Workshop on Computer Science Logic
Term Rewriting Systems and Algebra
Proceedings of the 7th International Conference on Automated Deduction
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A Decision Procedure for the Existential Theory of Term Algebras with the Knuth-Bendix Ordering
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The Decidability of the First-Order Theory of the Knuth-Bendix Order in the Case of Unary Signatures
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Verifying Orientability of Rewrite Rules Using the Knuth-Bendix Order
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Finite satisfiability of UML class diagrams with constrained class hierarchy
ACM Transactions on Software Engineering and Methodology (TOSEM) - In memoriam, fault detection and localization, formal methods, modeling and design
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We consider two decision problems related to the Knuth-Bendix order (KBO). The first problem is orientability: given a system of rewrite rules R, does there exist some KBO which orients every ground instance of every rewrite rule in R. The second problem is whether a given KBO orients a rewrite rule. This problem can also be reformulated as the problem of solving a single ordering constraint for the KBO. We prove that both problems can be solved in polynomial time. The algorithm builds upon an algorithm for solving systems of homogeneous linear inequalities over integers. Also we show that if a system is orientable using a real-valued KBO, then it is also orientable using an integer-valued KBO.