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).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.

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'.