On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Rewrite, rewrite, rewrite, rewrite, rewrite, …
Selected papers of the 16th international colloquium on Automata, languages, and programming
Handbook of logic in computer science (vol. 2)
Modularity of confluence: a simplified proof
Information Processing Letters
Confluence by decreasing diagrams
Theoretical Computer Science
Transfinite reductions in orthogonal term rewriting systems
Information and Computation
Modular properties of composable term rewriting systems
Journal of Symbolic Computation
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Term rewriting and all that
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Operational and Semantic Equivalence Between Recursive Programs
Journal of the ACM (JACM)
Term Rewriting Systems
Modular termination of context-sensitive rewriting
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Context-sensitive rewriting strategies
Information and Computation
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Simultaneous Critical Pairs and Church-Rosser Property
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Transfinite Rewriting Semantics for Term Rewriting Systems
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Confluence without Termination via Parallel Critical Pairs
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Recursive Path Orderings Can Be Context-Sensitive
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Church-Rosser Property and Unique Normal Form Property of Non-Duplicating Term Rewriting Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
A New Parallel Closed Condition for Church-Rossser of Left-Linear Term Rewriting Systems
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Transformation techniques for context-sensitive rewrite systems
Journal of Functional Programming
Confluence of shallow right-linear rewrite systems
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Confluence by Decreasing Diagrams
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Decreasing Diagrams and Relative Termination
Journal of Automated Reasoning
Decreasing diagrams and relative termination
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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Confluence criteria for non-terminating rewrite systems are known to be rare and notoriously difficult to obtain. Here we prove a new result in this direction. Our main result is a generalized version of Newman's Lemma for left-linear term rewriting systems that does not need a full termination assumption. We discuss its relationships to previous confluence criteria, its restrictions, examples of application as well as open problems. The whole approach is developed in the (more general) framework of context-sensitive rewriting which thus turns out to be useful also for ordinary (context-free) rewriting.