Thue systems as rewriting systems
Journal of Symbolic Computation
Theoretical Computer Science
Term rewriting and all that
Axiomatic Rewriting Theory VI Residual Theory Revisited
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Completion-Time Optimization of Rewrite-Time Goal Solving
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
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We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with an equational specification. These tools consist of introducing a monoid of partial maps, listing the monoid relations corresponding to the local confluence diagrams of the rewrite system, introducing the group presented by these relations, and, finally, replacing the initial rewrite system with an internal process entirely sitting in this group. When the approach can be completed, one typically obtains a practical method for constructing algebras satisfying prescribed equations and for solving the associated word problem. The above techniques have been developed by the first author in a context of general algebra. The goal of this paper is to bring them to the attention of the rewrite system community. We hope that these techniques may be useful for more general rewrite systems.