  The relationship between Term Graph Rewriting and Term Rewriting is well
understood: a single term graph reduction may correspond to several term
reductions, due to sharing. It is also known that if term graphs are allowed to
contain cycles, then one term graph reduction may correspond to infinitely many
term reductions. We stress that this fact can be interpreted in two ways.
According to the "sequential interpretation", a term graph reduction
corresponds to an infinite sequence of term reductions, as formalized by
Kennaway et.al. using strongly converging derivations over the complete metric
space of infinite terms. Instead according to the "parallel interpretation" a
term graph reduction corresponds to the parallel reduction of an infinite set
of redexes in a rational term. We formalize the latter notion by exploiting the
complete partial order of infinite and possibly partial terms, and we stress
that this interpretation allows to explain the result of reducing circular
redexes in several approaches to term graph rewriting.
