A simple non-termination test for the Knuth-Bendix method
Proc. of the 8th international conference on Automated deduction
Projections for strictness analysis
Proc. of a conference on Functional programming languages and computer architecture
Journal of Symbolic Computation
Theoretical Computer Science
Comparing curried and uncurried rewriting
Journal of Symbolic Computation
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Introduction to Functional Programming
Introduction to Functional Programming
Modular termination proofs for rewriting using dependency pairs
Journal of Symbolic Computation
A Monotonic Higher-Order Semantic Path Ordering
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
An LPO-based Termination Ordering for Higher-Order Terms without lambda-abstraction
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
The Theory and Practice of Transforming Call-by-need into Call-by-value
Proceedings of the Fourth 'Colloque International sur la Programmation' on International Symposium on Programming
Automated Termination Proofs with Measure Functions
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
A Fast Algorithm for Uniform Semi-Unification
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems
IEICE - Transactions on Information and Systems
Termination of String Rewriting Proved Automatically
Journal of Automated Reasoning
Termination of simply typed term rewriting by translation and labelling
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Dependency pairs for simply typed term rewriting
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Polymorphic higher-order recursive path orderings
Journal of the ACM (JACM)
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Termination analysis and call graph construction for higher-order functional programs
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
Termination of Lazy Rewriting Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Proving operational termination of membership equational programs
Higher-Order and Symbolic Computation
Loop detection in term rewriting using the eliminating unfoldings
Theoretical Computer Science
Dependency Pairs for Rewriting with Built-In Numbers and Semantic Data Structures
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Match-Bounds with Dependency Pairs for Proving Termination of Rewrite Systems
Language and Automata Theory and Applications
Improving Context-Sensitive Dependency Pairs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Complexity, Graphs, and the Dependency Pair Method
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
From Outermost Termination to Innermost Termination
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
A non-termination criterion for binary constraint logic programs
Theory and Practice of Logic Programming
Journal of Automated Reasoning
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Dependency Pairs and Polynomial Path Orders
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Certification of Termination Proofs Using CeTA
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Information and Computation
Annals of Mathematics and Artificial Intelligence
Experiments with Non-Termination Analysis for Java Bytecode
Electronic Notes in Theoretical Computer Science (ENTCS)
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Detecting non-termination of term rewriting systems using an unfolding operator
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Non-termination checking for imperative programs
TAP'08 Proceedings of the 2nd international conference on Tests and proofs
Typing termination in a higher-order concurrent imperative language
Information and Computation
Argument filterings and usable rules for simply typed dependency pairs
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Context-sensitive dependency pairs
Information and Computation
Automated termination proofs for haskell by term rewriting
ACM Transactions on Programming Languages and Systems (TOPLAS)
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Harnessing first order termination provers using higher order dependency pairs
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Generalized and formalized uncurrying
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
SAT solving for argument filterings
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Termination analysis of higher-order functional programs
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Matrix interpretations for proving termination of term rewriting
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Partial recursive functions in higher-order logic
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Automated termination analysis for Haskell: from term rewriting to programming languages
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Confluence of non-left-linear TRSs via relative termination
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
Proving non-looping non-termination automatically
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Automated detection of non-termination and nullpointerexceptions for Java Bytecode
FoVeOOS'11 Proceedings of the 2011 international conference on Formal Verification of Object-Oriented Software
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The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems (TRSs). We present two important extensions of this technique: First, we show how to prove termination of higher-order functions using dependency pairs. To this end, the dependency pair technique is extended to handle (untyped) applicative TRSs. Second, we introduce a method to prove non-termination with dependency pairs, while up to now dependency pairs were only used to verify termination. Our results lead to a framework for combining termination and non-termination techniques for first- and higher-order functions in a very flexible way. We implemented and evaluated our results in the automated termination prover AProVE.