Consider a very simple economy with two agents (A, B) and two goods ($x$, $y$). Agent A has utility $u_a = \min \{x_a, 2y_a\}$; agent B symmetrically has utility $u_b = \min \{2x_b, y_b\}$. Suppose that there are 3 units of $x$ and 3 units of $y$ in total.
It seems that, if $x_a = 2y_a$ and endowments are exhausted, then the allocation is efficient. In addition, if $2x_b = y_b$ and endowments are exhausted, i.e. $2(3 - x_a) = 3 - y_a$, then the allocation is also efficient. Finally, there seem to be some efficient allocations on the boundary of the feasible set. Plotting these yields
Can I confirm that the red lines do indeed depict the set of efficient allocations? I'm not looking for a formal proof, but just a confirmation that I haven't overlooked anything in this problem.