Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Simple termination of rewrite systems
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Computer experiments with the REVE term rewriting system generator
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Extensions and Comparison of Simplification Orderings
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Orienting rewrite rules with the Knuth--Bendix order
Information and Computation - RTA 2001
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Constraints for Argument Filterings
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Journal of Automated Reasoning
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Max/plus tree automata for termination of term rewriting
Acta Cybernetica
An extension of the Knuth-Bendix ordering with LPO-like properties
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
A SAT-based approach to size change termination with global ranking functions
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
On transfinite Knuth-Bendix orders
CADE'11 Proceedings of the 23rd international conference on Automated deduction
SAT solving for argument filterings
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Ordinals and knuth-bendix orders
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
The recursive path and polynomial ordering for first-order and higher-order terms
Journal of Logic and Computation
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We introduce a simplification order called the weighted path order (WPO). WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by an arbitrary interpretation which is weakly monotone and weakly simple. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we obtain an instance of WPO that unifies KBO, LPO and POLO. We also present SMT encodings of our orders, as well as incorporating them in the dependency pair framework.