Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Reducing right-hand sides for termination
Processes, Terms and Cycles
Tyrolean termination tool: Techniques and features
Information and Computation
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Predictive Labeling with Dependency Pairs Using SAT
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Proving Termination Using Recursive Path Orders and SAT Solving
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Normalization of Infinite Terms
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Search Techniques for Rational Polynomial Orders
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Proving Termination with (Boolean) Satisfaction
Logic-Based Program Synthesis and Transformation
Termination Analysis of Logic Programs Based on Dependency Graphs
Logic-Based Program Synthesis and Transformation
Proving Infinitary Normalization
Types for Proofs and Programs
From Outermost to Context-Sensitive Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Automated termination proofs for logic programs by term rewriting
ACM Transactions on Computational Logic (TOCL)
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Termination by quasi-periodic interpretations
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Certification of proving termination of term rewriting by matrix interpretations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Weighted automata for proving termination of string rewriting
Journal of Automata, Languages and Combinatorics
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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We present a new method for automatically proving termination of term rewriting. It is based on the well-known idea of interpretation of terms where every rewrite step causes a decrease, but instead of the usual natural numbers we use vectors of natural numbers, ordered by a particular non-total well-founded ordering. Function symbols are interpreted by linear mappings represented by matrices. This method allows to prove termination and relative termination. A modification of the latter in which strict steps are only allowed at the top, turns out to be helpful in combination with the dependency pair transformation. By bounding the dimension and the matrix coefficients, the search problem becomes finite. Our implementation transforms it to a Boolean satisfiability problem (SAT), to be solved by a state-of-the-art SAT solver. Our implementation performs well on the Termination Problem Data Base: better than 5 out of 6 tools that participated in the 2005 termination competition in the category of term rewriting.