On Android, does SQLite trigger triggers?

Consider this SQL in SQLite:

CREATE TABLE X (Xid INTEGER PRIMARY KEY);
CREATE TABLE Y (Yid INTEGER PRIMARY KEY, Xid INTEGER NOT NULL);
CREATE TABLE Z (Yid INTEGER PRIMARY KEY, Blah INTEGER NOT NULL);

CREATE TRIGGER IF NOT EXISTS OnDeleteX
    BEFORE DELETE ON X
    FOR EACH ROW BEGIN
        DELETE FROM Y WHERE Xid = OLD.Xid;
    END;

CREATE TRIGGER IF NOT EXISTS OnDeleteY
    BEFORE DELETE ON Y
    FOR EACH ROW BEGIN
        DELETE FROM Z WHERE Yid = OLD.Yid;
    END;

When I delete a line in X, I expect that its related elements in Y and Z will also be deleted. I tested this behavior on my PC using SQLite 3.7.11. In Android 4.0.4, this does not work.

Q: Does SQLite on Android support cascading triggers? That is, triggers that trigger other triggers.

In addition, it may be that some transaction may interfere with the operation of the trigger?