Proving termination of normalization functions for conditional expressions
Journal of Automated Reasoning
Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Journal of Symbolic Computation
Efficient tests for top-down termination of logical rules
Journal of the ACM (JACM)
Journal of Automated Reasoning
Termination proofs for logic programs
Termination proofs for logic programs
Proofs of termination and the “91” function
Artificial intelligence and mathematical theory of computation
Textbook examples of recursion
Artificial intelligence and mathematical theory of computation
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming
On proving the termination of algorithms by machine
Artificial Intelligence
Automatizing termination proofs of recursively defined functions
Theoretical Computer Science
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Termination Analysis for Functional Programs using Term Orderings
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Automatic Termination Proofs With Transformation Orderings
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Automated Termination Proofs with Measure Functions
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Argument-Bounded Algorithms as a Basis for Automated Termination Proofs
Proceedings of the 9th International Conference on Automated Deduction
Generating Polynomial Orderings for Termination Proofs
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Termination of Constructor Systems
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Induction Proofs with Partial Functions
Journal of Automated Reasoning
Extensions to the Estimation Calculus
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Another Look at Nested Recursion
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Nested General Recursion and Partiality in Type Theory
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Adapting functional programs to higher order logic
Higher-Order and Symbolic Computation
Partial and Nested Recursive Function Definitions in Higher-order Logic
Journal of Automated Reasoning
General recursion in type theory
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Proof obligation generation and discharging for recursive definitions in VDM
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
Dependency triples for improving termination analysis of logic programs with cut
LOPSTR'10 Proceedings of the 20th international conference on Logic-based program synthesis and transformation
Partial recursive functions in higher-order logic
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion.We show that termination proofs for nested and mutually recursive algorithms can be performed without having to prove the correctness of the algorithms simultaneously. Using this result, nested and mutually recursive algorithms do no longer constitute a special problem and the existing methods for automated termination analysis can be extended to nested and mutual recursion in a straightforward way. We give some examples of algorithms whose termination can now be proved automatically (including well-known challenge problems such as McCarthy’s f_91 function).