(Cyclic) Term Graph Rewriting is adequate for Rational Parallel Term Rewriting

"Acyclic" Term Graphs are able to represent terms with sharing, and the relationship between Term Graph Rewriting (TGR) and Term Rewrtiting (TR) is now well understood. During the last years, some researchers considered the extension of TGR to possibly "cyclic" term graphs, which can represent possibly infinite, rational terms. In [Kennaway et.al.,1994] the authors formalize the classical relationship between TGR and TR as an "adequate mapping" between rewriting systems, and extend it by proving that unraveling is an adequate mapping from cyclic TGR to rational, infinitary term rewriting: In fact, a single graph reduction may correspond to an infinite sequence of term reductions. Using the same notions, we propose a different adequacy result, showing that unraveling is an adequate mapping from cyclic TGR to "rational parallel term rewriting", where at each reduction infinitely many rules can be applied in parallel. We also argue that our adequacy result is more natural than that proposed in [Kennaway et.al.,1994], because the length of the reduction sequences is preserved by unraveling, and collapsing rules are treated in a completely uniform way.