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 term_order_PPO t1 t2 : term_order t1 t2 -> PPO rank t1 t2.