The Church-Rosser property for ground term-rewriting systems is decidable
Theoretical Computer Science
On ground-confluence of term rewriting systems
Information and Computation
Information and Computation
Handbook of theoretical computer science (vol. B)
String-rewriting systems
Decidability and complexity analysis by basic paramodulation
Information and Computation
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Deciding Confluence of Certain Term Rewriting Systems in Polynomial Time
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
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 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
Confluence of right ground term rewriting systems is decidable
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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The confluence property of ground (i.e., variable-free) term rewrite systems (TRS) is well known to be decidable. This was proved independently in Dauchet et al. [1987, 1990] and in Oyamaguchi [1987] using tree automata techniques and ground tree transducer techniques (originated from this problem), yielding EXPTIME decision procedures (PSPACE for strings). Since then, and until last year, the optimality of this bound had been a well-known longstanding open question (see, e.g., RTA-LOOP [2001]).In Comon et al. [2001], we gave the first polynomial-time algorithm for deciding the confluence of ground TRS. Later in Tiwari [2002] this result was extended, using abstract congruent closure techniques, to linear shallow TRS, that is, TRS where no variable occurs twice in the same rule nor at depth greater than one. Here, we give a new and much simpler proof of the latter result.