Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Tyrolean termination tool: Techniques and features
Information and Computation
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Certifying a Termination Criterion Based on Graphs, without Graphs
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques 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
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Signature extensions preserve termination: an alternative proof via dependency pairs
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Verification of certifying computations
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Termination of Isabelle functions via termination of rewriting
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Animating the formalised semantics of a Java-like language
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Proving Termination by Dependency Pairs and Inductive Theorem Proving
Journal of Automated Reasoning
Generalized and formalized uncurrying
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Code generation via higher-order rewrite systems
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
A decision procedure for regular expression equivalence in type theory
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Proof Pearl: Regular Expression Equivalence and Relation Algebra
Journal of Automated Reasoning
KBCV: knuth-bendix completion visualizer
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Proof Pearl--A Mechanized Proof of GHC's Mergesort
Journal of Automated Reasoning
A Framework for the Verification of Certifying Computations
Journal of Automated Reasoning
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There are many automatic tools to prove termination of term rewrite systems, nowadays. Most of these tools use a combination of many complex termination criteria. Hence generated proofs may be of tremendous size, which makes it very tedious (if not impossible) for humans to check those proofs for correctness. In this paper we use the theorem prover Isabelle/HOL to automatically certify termination proofs. To this end, we first formalized the required theory of term rewriting including three major termination criteria: dependency pairs, dependency graphs, and reduction pairs. Second, for each of these techniques we developed an executable check which guarantees the correct application of that technique as it occurs in the generated proofs. Moreover, if a proof is not accepted, a readable error message is displayed. Finally, we used Isabelle's code generation facilities to generate a highly efficient and certified Haskell program, CeTA, which can be used to certify termination proofs without even having Isabelle installed.