ML for the working programmer
On proving the termination of algorithms by machine
Artificial Intelligence
Termination of Nested and Mutually Recursive Algorithms
Journal of Automated Reasoning
Termination Analysis for Functional Programs using Term Orderings
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Automated Termination Proofs with Measure Functions
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Termination of Algorithms over Non-freely Generated Data Types
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Termination Analysis by Inductive Evaluation
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
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Walther's estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules. However, there are certain features of the goal formulae which are more common to the problem of induction rule well-foundedness than the problem of termination, and which the calculus cannot handle. We present a sound extension of the calculus that is capable of dealing with these features. The extension develops Walther's concept of an argument bounded function in two ways: firstly, so that the function may be bounded below by its cirgument, and secondly, so that a bound may exist between two arguments of a predicate. Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captiued by the original calculus.