Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Testing Positiveness of Polynomials
Journal of Automated Reasoning
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
IEA/AIE'2004 Proceedings of the 17th international conference on Innovations in applied artificial intelligence
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Tyrolean termination tool: Techniques and features
Information and Computation
On tree automata that certify termination of left-linear term rewriting systems
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
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Proving termination of rewrite systems using bounds
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
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Reducing right-hand sides for termination
Processes, Terms and Cycles
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
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The article at hand introduces a refinement of interpretation-based termination criteria for term rewrite systems in the dependency pair setting. Traditional methods share the property that--in order to be successful--all rewrite rules must (weakly) decrease with respect to some measure. One novelty of our approach is that we allow some rules to increase the interpreted value. These rules are found by simultaneously searching for adequate polynomial interpretations while considering the information of the dependency graph. We prove that our method extends the termination proving power of linear interpretations. Furthermore, this generalization perfectly fits the dependency pair framework which is implemented in virtually every termination prover dealing with term rewrite systems. We present two dependency pair processors for increasing interpretations. The novelty of the second one is that it can be used to eliminate single edges from the dependency graph.