|U(c, t G )| + n pc (A ∪ I(c, t G )), where "pc" stands for problematic cycles, is a closer upper bound to the loss (c) and the following holds: As mentioned before, unlike the monotonic approach, a node can have a different head in A than in I(c, t G ) and, as a consequence, the resulting graph A ∪ I(c, t G ) has maximum in-degree 2 rather than 1, and there can be overlapping cycles.
the computation of the non-monotonic terms n c (A ∪ I(c, t G )) and n pc (A ∪ I(c, t G )) requires an algorithm such as the one by Johnson (1975) to find all elementary cycles in a directed graph.