Confluence of Shallow Right-Linear Rewrite Systems
We show that confluence of shallow and right-linear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving, which implies that its reachability and joinability problems are decidable. The new decidability result is obtained by building upon our prior work for the class of ground term rewriting systems and shallow linear term rewriting systems. The proof relies on the concept of extracting more general rewrite derivations from a given rewrite derivation.
KeywordsInduction Hypothesis Congruence Relation Ground Term Tree Automaton Joinability Problem
Unable to display preview. Download preview PDF.
- 3.Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (1997), Available on http://www.grappa.univ-lille3.fr/tata
- 5.Dershowitz, N., Jouannaud, J.P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Amsterdam. Formal Models and Semantics, vol. B, pp. 243–320. North-Holland, Amsterdam (1990)Google Scholar