Inductive list_order {A : Type} (R : A -> A -> Prop) : list A -> list A -> Prop :=
| lo_cons:  forall l1 l2 h, Forall (fun x => R x h) l1 -> list_order R (l1 ++ l2) (h :: l2).
Definition W {A : Type} (R : A -> A -> Prop) (l : list A) : Prop :=
Acc (list_order R) l.
(*  forall l', list_order R l' l -> Acc (list_order R) l'. *)

Lemma PPO_active_term_order_superset act act' :
PPO rank (term_from_active_term act) (term_from_active_term act') ->
active_term_order_superset act act'.