Searching a sorted array is a very classical textbook problem. In some special circumstances, such as searching a regression in a version control system, it is necessary to search in a partially ordered set. The problem can then be seen as trying to identify a faulty vertex in a directed acyclic graph where each step consists in querying a vertex and asking whether the searched vertex is an ancestor of the current vertex. Though the problem is known to be NP-complete in general, we put more focus on the more interesting setting when the indegree of each vertex is bounded, and in particular when it is bounded by two. We show that with the degree 2 restrictions, all directed acyclic graphs on n vertices can be searched in no more than logφ(n) + 1 queries, where φ stands for the golden ratio. On the other hand, we also show that there exists directed trees which require at least ⌈logφ(n)⌉ − 2 queries. Expectedly, the later proof expectedly involves Fibonnaci related trees. We will also discuss how the NP-completeness proof of the problem can be extended to this setting. Based on joint work with Julien Courtiel and Romain Lecoq