Parallelism in AGREE transformations

The AGREE approach to graph transformation allows to specify rules that clone items of the host graph, controlling in a finegrained way how to deal with the edges that are incident, but not matched, to the rewritten part of the graph. Here, we investigate in which ways cloning (with controlled embedding) may affect the dependencies between two rules applied to the same graph. We extend to AGREE the classical notion of parallel independence between the matches of two rules to the same graph, identifying sufficient conditions that guarantee that two rules can be applied in any order leading to the same result.