The problems of cyclic equality and conjugacy for finite complete rewriting systems
Theoretical Computer Science
Journal of Symbolic Computation
Confluent string rewriting
String-rewriting systems
On termination of confluent one-rule string-rewriting systems
Information Processing Letters
On normalizing non-terminating one-rule string rewriting systems
Theoretical Computer Science
Termination and derivational complexity of confluent one-rule string-rewriting systems
Theoretical Computer Science
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Decidability of Termination of Grid String Rewriting Rules
SIAM Journal on Computing
Semi-Thue Systems with an Inhibitor
Journal of Automated Reasoning
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
On the Termination Problem for One-Rule Semi-Thue System
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Decision Problems for Semi-Thue Systems with a Few Rules
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Termination of string rewriting rules that have one pair of overlaps
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
On One-Rule Grid Semi-Thue Systems
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
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Loops are the most frequent cause of non-termination in string rewriting. In the general case, non-terminating, nonlooping string rewriting systems exist, and the uniform termination problem is undecidable. For rewriting with only one string rewriting rule, it is unknown whether non-terminating, non-looping systems exist and whether uniform termination is decidable. If in the one-rule case, non-termination is equivalent to the existence of loops, as McNaughton conjectures, then a decision procedure for the existence of loops also solves the uniform termination problem. As the existence of loops of bounded lengths is decidable, the question is raised how long shortest loops may be. We show that string rewriting rules exist whose shortest loops have superexponential lengths in the size of the rule.