An illustration of the depth-first search algorithm. Implementation of the forward-tracking and the backtracking routine for five reactions. Starting from rxn i, Forward-tracking A found two (rxn i + 1 and i + 3) downstream IFF. Backtracking A only found rxn i + 1 being the terminal IFF that can be converted into FAF. Forward-tracking B only found rxn i + 4 as an IFF. Backtracking B moved upstream beyond rxn i, and was unable to find among these reactions any one IFF that can be converted to FAF.