, the upper bound is attained when, for every variable x i , we can open either S(x i ) or S(x i ) so that, for every clause gadget C j , there is an open gate gadget creating a way from the departure gadget G(C j ) towards an arrival gadget A(x i , C j ) or A(x i , C j ) By considering that opening S(x i ) (resp. S(x i )) simulates the affectation of value true (resp. false) to x i , and that performing a pair of (= k)-augmentations from G(C j ) to A(x i , C j ) (or A(x i, C j )) simulates the fact that x i (resp. x i ) brings value true to C j , the equivalence with satisfying ? follows
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