  In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its
automorphism group is not commensurable with an arithmetic group, answering a
question of Mazur. We give examples of rational surfaces with the same
property. Our examples $Y$ are log Calabi--Yau surfaces, i.e., there is a
reduced normal crossing divisor $D \subset Y$ such that $K_{Y} + D = 0$.
