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Comparison of upYup arc and an arc that remains on N (hence u ≡ up) between the points [S(τ1), R(τ1)] and [S(τ2), R(τ2)], assuming that up remains feasible (that is, up ∈ [0, M]). Note that γ < 0 in the area of interest, and that a switching of a Y to an X arc is prohibited via the Maximum Principle. Thus, the only possibility is the curve illustrated, which leaves the boundary N for a Y arc before up becomes infeasible.
