This paper presents a greedy sequential algorithm for decomposing a Boolean Nth-order tensor into a Boolean sum of rank 1 components, using Left-Triangular-like and geometric considerations. The paper includes detailed theory, algorithm development and some experiments. This makes the exposition rather dense but the authors have clearly invested a lot time and effort in the work. The task is interesting and the rank-1 pattern revealing algorithm looks nice and intriguing. The work received divergent scores with the main points of disagreement being the difficulty of following the exposition, the practical need for special methods dedicated to Boolean tensors, and the lack of comparative experiments with other algorithms and with (NP hard) exact minimal decompositions. However, in our opinion the method is interesting enough and potentially-useful enough, and the experiments are illustrative enough, for acceptance. The final paper should do its best to address the clarity / reader accessibility issues and to reinforce the experimental comparisons.