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
Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Proving Termination by Bounded Increase
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Turning Inductive into Equational Specifications
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Certification of Termination Proofs Using CeTA
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Partial and Nested Recursive Function Definitions in Higher-order Logic
Journal of Automated Reasoning
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
Automated termination proofs for haskell by term rewriting
ACM Transactions on Programming Languages and Systems (TOPLAS)
Termination of Isabelle functions via termination of rewriting
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Code generation via higher-order rewrite systems
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
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Bounded increase is a termination technique where it is tried to find an argument x of a recursive function that is increased repeatedly until it reaches a bound b, which might be ensured by a condition xb. Since the predicates like In this paper, we present a full formalization of bounded increase in the theorem prover Isabelle/HOL. It fills one large gap in the pen-and-paper proof, and it includes generalized inference rules for the induction calculus as well as variants of the Babylonian algorithm to compute square roots. These algorithms were required to write executable functions which can certify untrusted termination proofs from termination tools that make use of bounded increase. And indeed, the resulting certifier was already useful: it detected an implementation error that remained undetected since 2007.