Left diagram presents a simple acyclic directed graph which edges derscribe obligations. Directed graph in the middle has cycles and, at the same time, is equivalent to the first graph in temrs of obligations' balances. Now cycle A-B-C-D may be reduced as shown on the right. Thus B and C get their receivables and payables redeemed by 50 units, and 50 units of A's payables are transferred from B to D.

The problem here is that both A and D must accept this new relationship generated by an upgraded ARMO System, even if those two entities did not know each other before. In the latter scenario A and D should exchange with each other some attributes required in their accounting systems (what is quite easy for an ARMO Programme with Recognition System).

With this extended functionality a Programme may generate posistive ARMO results even when initial graph of participants' obligations has no cycles.