Confluence of indirection reductions in graph rewrite systems (Q1113692)

The aim of this paper is to show that the indirection graph rewrite systems are confluent, i.e., if G \(\Rightarrow^* G_ 1\) and G \(\Rightarrow^* G_ 2\) for some indirection graphs G, \(G_ 1\) and \(G_ 2\), then there exist isomorphic indirection graphs \(G_ 1'\) and \(G_ 2'\) such that \(G_ 1 \Rightarrow^* G_ 1'\) and \(G_ 2 \Rightarrow^* G_ 2'.\) To show this, in Section 3 the author introduces equivalence relations on the sets of nodes and arcs of an indirection graph and derives a number of properties of these. The results of Section 3 are used in Section 4 in order to show that the indirection graph rewrite systems are confluent.