We give the first *local* characterization of safe paths for flow decompositions in directed acyclic graphs (DAGs), leading to a practical algorithm for finding the *complete* set of safe paths. Additionally, we evaluate our algorithm on RNA transcript datasets against a trivial safe algorithm (extended unitigs), the recently proposed safe paths for path covers [TCBB 2021] and the popular heuristic *greedy-width*. Our safe and complete algorithm outperforms (by $\approx 20\%$) greedy-width on a unified metric (F-Score) considering both coverage and precision when the evaluated dataset has a significant number of complex graphs.