The Church-Rosser property for ground term-rewriting systems is decidable
Theoretical Computer Science
Deciding equivalence of finite tree automata
SIAM Journal on Computing
Information and Computation
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Algorithms and reductions for rewriting problems. II
Information Processing Letters
Deciding Confluence of Certain Term Rewriting Systems in Polynomial Time
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Polynomial Time Termination and Constraint Satisfaction Tests
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
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
On the Normalization and Unique Normalization Properties of Term Rewrite Systems
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Unique Normalization for Shallow TRS
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Levels of undecidability in rewriting
Information and Computation
New Undecidability Results for Properties of Term Rewrite Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
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Programming language interpreters, proving equations (e.g. x3 = x implies the ring is Abelian), abstract data types, program transformation and optimization, and even computation itself (e.g., turing machine) can all be specified by a set of rules, called a rewrite system. Two fundamental properties of a rewrite system are the confluence or Church--Rosser property and the unique normalization property. In this article, we develop a standard form for ground rewrite systems and the concept of standard rewriting. These concepts are then used to: prove a pumping lemma for them, and to derive a new and direct decidability technique for decision problems of ground rewrite systems. To illustrate the usefulness of these concepts, we apply them to prove: (i) polynomial size bounds for witnesses to violations of unique normalization and confluence for ground rewrite systems containing unary symbols and constants, and (ii) polynomial height bounds for witnesses to violations of unique normalization and confluence for arbitrary ground systems. Apart from the fact that our technique is direct in contrast to previous decidability results for both problems, which were indirectly obtained using tree automata techniques, this approach also yields tighter bounds for rewrite systems with unary symbols than the ones that can be derived with the indirect approach. Finally, as part of our results, we give a polynomial-time algorithm for checking whether a rewrite system has the unique normalization property for all subterms in the rules of the system.