Definition judgsize (p:cbv) := term_size (proj_left p) + value_size (proj_right p).

Lemma active_size_bound_max qic qif cs: forall i s p c f lv d v, valid_QI qic qif cs -> let t := (fapply f lv) in let pi := cbv_update i s p c t d v in let la := (activations pi) in let l:= (map (fun x=> mcs * (term_size t)) lv) in wf pi -> cache_bounded qic qif c -> forall la', incl la' la -> maxl (map judgsize la') <= (max_arity + 1) * qif f l + 1.