Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
On termination of the direct sum of term-rewriting systems
Information Processing Letters
Journal of Symbolic Computation
A sufficient condition for the termination of the direct sum of term rewriting systems
Proceedings of the Fourth Annual Symposium on Logic in computer science
Automating the Knuth Bendix ordering
Acta Informatica
Handbook of theoretical computer science (vol. B)
Modularity of simple termination of term rewriting systems with shared constructors
Theoretical Computer Science
Completeness of combinations of constructor systems
Journal of Symbolic Computation
Handbook of logic in computer science (vol. 2)
Generating polynomial orderings
Information Processing Letters
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
On the modularity of termination of term rewriting systems
Theoretical Computer Science
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Modular properties of composable term rewriting systems
Journal of Symbolic Computation
Termination for direct sums of left-linear complete term rewriting systems
Journal of the ACM (JACM)
Simple termination of rewrite systems
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Type introduction for equational rewriting
Acta Informatica
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Simple Termination of Hierarchical Combinations of Term Rewriting Systems
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Modular Termination of Term Rewriting Systems Revisited
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
Modularity of Termination Using Dependency pairs
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
TALP: A Tool for the Termination Analysis of Logic Programs
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
System Description: The Dependency Pair Method
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
On Proving Termination by Innermost Termination
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Syntactical Analysis of Total Termination
ALP '94 Proceedings of the 4th International Conference on Algebraic and Logic Programming
Approximating Dependency Graphs Using Tree Automata Techniques
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Automated Incremental Termination Proofs for Hierarchically Defined Term Rewriting Systems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Generating Polynomial Orderings for Termination Proofs
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Abstract Relations Between Restricted Termination And Confluence Properties Of Rewrite Systems
Fundamenta Informaticae
Simplification Orderings: History Of Results
Fundamenta Informaticae
Hierarchical termination revisited
Information Processing Letters
Transformation techniques for context-sensitive rewrite systems
Journal of Functional Programming
Proving termination of membership equational programs
Proceedings of the 2004 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Relaxing monotonicity for innermost termination
Information Processing Letters
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Verifying Termination and Reduction Properties about Higher-Order Logic Programs
Journal of Automated Reasoning
Knuth-Bendix completion of theories of commuting group endomorphisms
Information Processing Letters
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Elimination Transformations for Associative---Commutative Rewriting Systems
Journal of Automated Reasoning
Proving termination of context-sensitive rewriting by transformation
Information and Computation
Tyrolean termination tool: Techniques and features
Information and Computation
Practical use of polynomials over the reals in proofs of termination
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Comparing CSP and SAT Solvers for Polynomial Constraints in Termination Provers
Electronic Notes in Theoretical Computer Science (ENTCS)
Proving operational termination of membership equational programs
Higher-Order and Symbolic Computation
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
Constraints for Argument Filterings
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Termination of Innermost Context-Sensitive Rewriting Using Dependency Pairs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Usable Rules for Context-Sensitive Rewrite Systems
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Arctic Termination ...Below Zero
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Complexity Analysis Based on the Dependency Pair Method
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Certifying a Termination Criterion Based on Graphs, without Graphs
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Complexity, Graphs, and the Dependency Pair Method
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Termination Analysis of Logic Programs Based on Dependency Graphs
Logic-Based Program Synthesis and Transformation
Proving Termination of Integer Term Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
A3PAT, an approach for certified automated termination proofs
Proceedings of the 2010 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Relaxing monotonicity for innermost termination
Information Processing Letters
Knuth--Bendix completion of theories of commuting group endomorphisms
Information Processing Letters
Size-change termination for term rewriting
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Termination by quasi-periodic interpretations
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Context-sensitive dependency pairs
Information and Computation
Context-sensitive dependency pairs
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
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
Dependency pairs for simply typed term rewriting
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Rewriting Computation and Proof
Hi-index | 0.00 |
Recently, Arts and Giesl developed the dependency pair approach which allows automated termination and innermost termination proofs for many term rewriting systems (TRSs) for which such proofs were not possible before. The motivation for this approach was that virtually all previous techniques for automated termination proofs of TRSs were based on simplification orderings. In practice, however, many rewrite systems are not simply terminating, i.e. their termination cannot be verified by any simplification ordering.In this paper we introduce a refinement of the dependency pair framework which further extends the class of TRSs for which termination or innermost termination can be shown automatically. By means of this refinement, one can now prove termination in a modular way. Thus, this refinement is inevitable in order to verify the termination of large rewrite systems occurring in practice. To be more precise, one may use several different orderings in one termination proof.Subsequently, we present several new modularity results based on dependency pairs. First, we show that the well-known modularity of simple termination for disjoint unions can be extended to DP quasi-simple termination, i.e. to the class of rewrite systems where termination can be shown automatically by the dependency pair technique in combination with quasi-simplification orderings. Under certain additional conditions, this new result also holds for constructor-sharing and composable systems. Second, the above-mentioned refinement of the dependency pair method yields new modularity criteria for innermost termination which extend previous results in this area considerably. In particular, existing results for modularity of innermost termination can easily be shown to be direct consequences of our new criteria.