  We study resource similarity and resource bisimilarity -- congruent
restrictions of the bisimulation equivalence for the (P,P)-class of Process
Rewrite Systems (PRS). Both these equivalences coincide with the bisimulation
equivalence for (1,P)-subclass of (P,P)-PRS, which is known to be decidable.
While it has been shown in the literature that resource similarity is
undecidable for (P,P)-PRS, decidability of resource bisimilarity for (P,P)-PRS
remained an open question.
  In this paper, we present an algorithm for checking resource bisimilarity for
(P,P)-PRS. We show that although both resource similarity and resource
bisimilarity are congruences and have a finite semi-linear basis, only the
latter is decidable.
