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In PLDI'20, Lee et al. introduced the \emph{promising } semantics PS 2.0 of the C++ concurrency that captures most of the common program transformations while satisfying the DRF guarantee. The reachability problem for finite-state programs under PS 2.0 with only release-acquire accesses is already known to be undecidable. Therefore, we address, in this paper, the reachability problem for programs running under PS 2.0 with relaxed accesses together with promises. We show that this problem is undecidable even in the case where the input program has finite state. Given this undecidability result, we consider the fragment of PS 2.0 with only relaxed accesses allowing bounded number of promises. We show that under this restriction, the reachability is decidable, albeit very expensive: it is non-primitive recursive. Given this high complexity with bounded number of promises and the undecidability result for the RA fragment of PS 2.0, we consider a bounded version of the reachability problem. To this end, we bound both the number of promises and the "view-switches", i.e, the number of times the processes may switch their local views of the global memory. We provide a code-to-code translation from an input program under PS 2.0, with relaxed and release-acquire memory accesses along with promises, to a program under SC. This leads to a reduction of the bounded reachability problem under PS 2.0 to the bounded context-switching problem under SC. We have implemented a prototype tool and tested it on a set of benchmarks, demonstrating that many bugs in programs can be found using a small bound.