Show that splitting an edge in a flow network yields an equivalent network. More formally, suppose that flow network G contains edge (u, v), and we create a new flow network G by creating a new vertex x and replacing (u, v) by new edges (u,x) and (x, v) with c(u, x) -c(x, v) - c(u, v). Show that a maximum flow in G' has the same value as a maximum flow in G. (If you are presenting a constructive proof, don't forget to show that the flow you construct preserves the flow conservation and the capacity constraints.)