Equational logic as a programming language
Equational logic as a programming language
On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
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
Termination for the direct sum of left-linear term rewriting systems
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
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
Modular term rewriting systems and the termination
Information Processing Letters
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)
Modular properties of conditional term rewriting systems
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
On the modularity of termination of term rewriting systems
Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Simple Termination of Hierarchical Combinations of Term Rewriting Systems
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Completeness of Hierarchical Combinations of term Rewriting Systems
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Generalized Sufficient Conditions for Modular Termination of Rewriting
Proceedings of the Third International Conference on Algebraic and Logic Programming
On Modularity of Termination and Confluence Properties of Conditional Rewrite Systems
ALP '94 Proceedings of the 4th International Conference on Algebraic and Logic Programming
Sufficient Conditions for Modular Termination of Conditional Term Rewriting Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Completeness of Combinations of Conditional Constructor Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Simplifying termination proofs for rewrite systems by preprocessing
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
Modular termination of context-sensitive rewriting
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Hierarchical termination revisited
Information Processing Letters
Modular termination proofs for rewriting using dependency pairs
Journal of Symbolic Computation
Transforming Conditional Rewrite Systems with Extra Variables into Unconditional Systems
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Transforming Context-Sensitive Rewrite Systems
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Decidability for Left-Linaer Growing Term Rewriting Systems
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Recursive Derivational Length Bounds for Confluent Term Rewrite Systems
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Closure Induction in a Z-Like Language
ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
Applying Rewriting Techniques to the Verification of Erlang Processes
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Induction for positive almost sure termination
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Termination of Innermost Context-Sensitive Rewriting Using Dependency Pairs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Termination of rewriting under strategies
ACM Transactions on Computational Logic (TOCL)
Proving Confluence of Term Rewriting Systems Automatically
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Termination Analysis by Dependency Pairs and Inductive Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Innermost termination of context-sensitive rewriting
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Harnessing first order termination provers using higher order dependency pairs
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Generalized innermost rewriting
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Modularity in term rewriting revisited
Theoretical Computer Science
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We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination, weak innermost termination, (strong) innermost termination, (strong) termination, and their interrelations. New criteria are provided which are sufficient for the equivalence of these properties. These criteria provide interesting possibilities to infer completeness, i.e. termination plus confluence, from restricted termination and confluence properties. Our main result states that any (strongly) innermost terminating, locally confluent overlay system is terminating, and hence confluent and complete. Using these basic results we are also able to prove some new results about modular termination of rewriting. In particular, we show that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for non-overlapping and even for overlay systems. As an easy consequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of constructor systems. Similarly, a combined overlay system with shared constructors is complete if and only if its component sytems are complete overlay systems. Interestingly, these modularity results are obtained by means of a proof technique which itself constitutes a modular approach.