Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Handbook of theoretical computer science (vol. B)
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Arctic Termination ...Below Zero
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Certifying a Termination Criterion Based on Graphs, without Graphs
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
A3PAT, an approach for certified automated termination proofs
Proceedings of the 2010 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
On the domain and dimension hierarchy of matrix interpretations
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
| Hi-index | 0.00 |
We present a new technique to prove termination of Term Rewriting Systems, with full automation. A crucial task in this context is to find suitable well-founded orderings. A popular approach consists in interpreting terms into a domain equipped with an adequate well-founded ordering. In addition to the usual interpretations: natural numbers or polynomials over integer/rational numbers, the recently introduced matrix based interpretations have proved to be very efficient regarding termination of string rewriting and of term rewriting. In this spirit we propose to interpret terms as polynomials over integer matrices. Designed for term rewriting, our generalisation subsumes previous approaches allowing for more orderings without increasing the search space. Thus it performs better than the original version. Another advantage is that, interpreting terms to actual polynomials of matrices, it opens the way to matrix non linear interpretations. This result is implemented in the CiME3 rewriting toolkit.