The authors present a local variant of k-WL-equivalent provably expressive graph neural networks. - the reviewers appreciated the importance and timeliness of the topic, in particular the theoretical expressive power of graph neural networks - the paper proposes a novel way of reducing the complexity of k-WL - impressive experimental results The rebuttal was read and discussed by the reviewers. The rebuttal addressed most concerns raised, yet, some concern still remained about the gap between theory and practice. Overall the reviewers are positive and our recommendation is to accept the paper.