  Evolutionary scenarios displaying reticulation events are often represented
by rooted phylogenetic networks. Due to biological reasons, those events occur
very rarely, and, thus, networks containing a minimum number of such events,
so-called minimum hybridization networks, are of particular interest for
research. Moreover, to study reticulate evolution, biologist need not only a
subset but all of those networks. To achieve this goal, the less complex
concept of rooted phylogenetic trees can be used as building block. Here, as a
first important step, the trees are disjoint into common parts, so-called
maximum acyclic agreement forests, which can then be turned into minimum
hybridization networks by applying further network building algorithms. In this
paper, we present two modifications of the first non-naive algorithm --- called
allMAAFs --- computing all maximum acyclic agreement forests for two rooted
binary phylogenetic trees on the same set of taxa. By a simulation study, we
indicate that through these modifications the algorithm is on average 8 times
faster than the original algorithm making this algorithm accessible to larger
input trees and, thus, to a wider range of biological problems.
