Definition compatible_rule (r:rule) : Prop :=
match r with
| rule_intro f _ t => forall f', In f' (functions_of_term t) -> rank f' <= rank f
end.
Definition compatible_prog : Prop :=
forall r, In r prog -> compatible_rule r.

Lemma PPO_is_compatible_rule:
forall r, PPO_rule rank r -> compatible_rule r.