I don’t know if I’m simply imagining things, but is there some set connection between -ru and -su verbs that are very similar? e.g. 治す (naosu; to cure, to heal) and 治る (naoru; to be cured, to be healed); 返す (kaesu; to return (something), to restore) and 返る (kaeru: to return, to come back); 出す (dasu; to take out, to go out) and 出る (deru; to leave, to exit).
In the examples above the -su are transitive and the -ru are intransitive; is there a similar relation as is seen in, e.g. -まる and -める, where -eru denotes the transitive verb and -aru denotes the intransitive? That -su denotes the transitive and -ru denotes the/a related intransitive?
Or am I just barking up the wrong tree?