Thue systems as rewriting systems
Proc. of the first international conference on Rewriting techniques and applications
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Sequentiality, monadic second-order logic and tree automata
Information and Computation
An algorithm for reasoning about equality
Communications of the ACM
Algorithms and reductions for rewriting problems. II
Information Processing Letters
Relative undecidability in term rewriting: II. the confluence hierarchy
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
Polynomial Time Termination and Constraint Satisfaction Tests
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Decidable Approximations of Term Rewriting Systems
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The Confluence of Ground Term Rewrite Systems is Decidable in Polynomial Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Equations and rewrite rules: a survey
Equations and rewrite rules: a survey
Characterizing Confluence by Rewrite Closure and Right Ground Term Rewrite Systems
Applicable Algebra in Engineering, Communication and Computing
A new decidability technique for ground term rewriting systems with applications
ACM Transactions on Computational Logic (TOCL)
Algorithms and Reductions for Rewriting Problems
Fundamenta Informaticae
Unique Normalization for Shallow TRS
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
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We present several new and some significantly improved polynomial-time reductions between basic decision problems of term rewriting systems. We prove two theorems that imply tighter upper bounds for deciding the uniqueness of normal forms (UN$^{=}$) and unique normalization (UN$^{→}$) properties under certain conditions. From these theorems we derive a new and simpler polynomial-time algorithm for the UN$^{=}$ property of ground rewrite systems, and explicit upper bounds for both UN$^{=}$ and UN$^{→}$ properties of left-linear right-ground systems. We also show that both properties are undecidable for right-ground systems. It was already known that these properties are undecidable for linear systems. Hence, in a sense the decidability results are "close" to optimal.