CAnIllustrativeExample WeprovideanillustrativecounterexampleforshowingthattheFS-WBPinEq.(10)isnotanMCF problemwhenm=3andn=3. ExampleC.1. Whenm=3andn=3,theconstraintmatrixis

When n = 2, the constraint matrixA has E = I2 1>2 and G = 1>2 I2. Now we simplify the matrixAby removing a specific set of redundantrows. Furthermore, the rows of A are categorized into a single set so that the criterion in Proposition 3.2 holds true (thedashed lineintheformulation of Aservesasapartition ofthissingle setintotwosets). We use the proof by contradiction. In particular, assume that problem(10) is a MCF problem whenm 3andn 3,Proposition 3.3 implies that the constraint matrixAisTU.