What is the test for a demurrer based on a statute of limitations?

Where, as here, the defendant demurs on the primary ground that the action is time-barred under the affirmative defense of the statute of limitations, we apply the following standard: " ' "A demurrer based on a statute of limitations will not lie where the action may be, but is not necessarily, barred. [Citation.] In order for the bar . . . to be raised by demurrer, the defect must clearly and affirmatively appear on the face of the complaint [and matters subject to judicial notice]; it is not enough that the complaint shows that the action may be barred. [Citation.]" [Citation.]' [Citation.]" (Committee for Green Foothills v. Santa Clara County Bd. of Supervisors (2010) 48 Cal.4th 32, 42; accord, 430.30, subd. (a).)