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
Modular termination proofs for rewriting using dependency pairs
Journal of Symbolic Computation
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Automatically Proving Termination Where Simplification Orderings Fail
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Certification of Termination Proofs Using CeTA
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Improved Matrix Interpretation
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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Although graphs are very common in computer science, they are still very difficult to handle for proof assistants as proving properties of graphs may require heavy computations. This is a problem when it comes to issues such as the certification of a proof of well-foundedness, since premises of generic theorems involving graph properties may be at least as difficult to prove as their conclusion. We define a framework and propose an original approach based on both shallow and deep embeddings for the mechanical certification of these kinds of proofs without the help of any graph library. This framework actually avoids concrete models of graphs and handles those implicitly. We illustrate this approach on a powerful refinement of the dependency pairs approach for proving termination. This refinement makes heavy use of graph analysis and our technique is powerful enough to deal efficiently ---and with full automation--- with graphs containing thousands of arcs, as they may occur in practice.