Journal of Symbolic Computation
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Testing Positiveness of Polynomials
Journal of Automated Reasoning
Applicable Algebra in Engineering, Communication and Computing
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Tyrolean termination tool: Techniques and features
Information and Computation
Practical use of polynomials over the reals in proofs of termination
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Innermost Termination of Rewrite Systems by Labeling
Electronic Notes in Theoretical Computer Science (ENTCS)
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
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Matrix interpretations for proving termination of term rewriting
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Improving Context-Sensitive Dependency Pairs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
From matrix interpretations over the rationals to matrix interpretations over the naturals
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
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Polynomial interpretations are a standard technique used in almost all tools for proving termination of term rewrite systems (TRSs) automatically. Traditionally, one applies interpretations with polynomials over the naturals. But recently, it was shown that interpretations with polynomials over the rationals can be significantly more powerful. However, searching for such interpretations is considerably more difficult than for natural polynomials. Moreover, while there exist highly efficient SAT-based techniques for finding natural polynomials, no such techniques had been developed for rational polynomials yet. In this paper, we tackle the two main problems when applying rational polynomial interpretations in practice: (1) We develop new criteria to decide when to use rational instead of natural polynomial interpretations. (2) Afterwards, we present SAT-based methods for finding rational polynomial interpretations and evaluate them empirically.