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.
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