by creating a boolen cleared you mean
boolean cleared() {
if (rings.size()==0) {
return true;
} else {
return false;
}
}
void display() {
if (cleared()) {
for (int i=rings.size()-1; i>0; i--) {
Ring r=rings.get(i);
r.update();
r.display();
if (r.isDead()) {
rings.remove(i);
}
}
}
}