I sometimes worry that I get too enthusiastic with derivational morphology. Then I read things like this, from The Navajo Verb System: an Overview, by Robert W. Young, and I feel like a derivational slacker. It's a long quotation (pp. 57-59), but it's worth it.
Note that in Athabascan linguistics, a "classifier" has nothing to do with the usual linguistic sense of that word, but has to do with transitivity. The null classifier is noted with Ø.
The "run" verbs provide classic examples of crystalized metaphor.
"Singular-run" verbs are derived from a root WOD (Perfective Stem), the base meaning of which is "flex, bend." With Ø-Classifier the Verb Theme ØWOD is produced and this Theme, in combination with adverbial 'ahá-: apart, derives the Verb Base 'ahá-øwod with the meaning "bend apart, become disjointed," as in shigaan 'ahááwod: my arm became disjointed (bent apart). With Ł-Classifier the "bend" theme is transitivized to acquire the meaning "cause to bend," and again in combination with 'ahá-: apart, the Verb Base 'ahá-̵łhod is generated, with the meaning "cause to bend or flex apart, break by flexing apart" as in béésh 'áłts'ózí 'ahááłhod: I bent or flexed the wire apart.
With L-Classifier the causative-transitive Theme becomes mediopassive, serving to derive constructions in which the subject and object are the same. LWOD and its Stem variants produce lexical constructions that describe the subject as "self-flexing" and this came to be used as a metaphor for "run," an action performed by flexing the legs. Thus 'ashkii 'ólta'dę́ę́' ch'élwod: the boy ran ("self-flexed") out of the school; 'ashkii 'ólta'di yílwod: the boy ran ("arrived self-flexing") to school, 'ashkii 'atiin góyaa yilwoł: the boy is running ("self-flexing") down the road.
The concept involved in running carries a connotation of "swift movement," a feature that opens the way to further extension of what began as a metaphoric mediopassive Theme. With the meaning "go swiftly" the "singular-run" verbs are applied to inanimate objects - contexts in which "Self-flex" plays no part, asi n chidí (dzi'izí, nááts'ó'oołdísii, kǫ' na'ałbąąsii) yilwoł: the care (bicycle, whirlwind, locomotive) is running along; k'aa' shighálwod: the arrow went through me.
Applied to conveyances, in Verb Bases that include the postposition P-ił: in company with P, the "transportation by fast vehicle" verbs are generated. Here the subject is the vehicle and the person transported is represented by the pronoun object of the postposition P-. Thus, chidí shił yilwoł: I'm riding along in the car (i.e., the car is running along with me; kintahdę́ę́' shił ná'oolwoł: I'm returning from town by (unspecified) fast moving vehicle (car, motorcycle) (literally, something unspecified is running back with me); Yootóodi shił 'ílwod, I arrived in Santa Fe (by unspecified fast moving vehicle). Other modes of travel are distinguished by other verbal roots, as P-ił (d)t'a: fly; P-ił Ø'éél: go by boat; P-ił idloosh: go by quadruped (horse, burro); P-ił (d)'na': go by slow-moving (crawling) vehicle (tractor, army tank, heavy truck).
"Run" is used idiomatically in expressions of the type: Pí-ka 'a--lwod: help P (literally "run away out of sight after P") as in shimá bíká 'eeshwod: I helped (ran away after) my mother; Pí-lák'ee ha--lwod: escape from P, as in 'awáalyaaí shílák'ee haalwod: the prisoner escaped from me (literally "ran out of my hand"), 'éé' biih --lwod: dress hurriedly, as in 'éé' biih yishwod: I dressed quickly (literally "ran into my clothes").
And finally, the "singular-run" Theme appears as a calque from English, functioning with the meaning "operate," as in naalyéhé bá hooghan yiyoołwoł: he runs a trading post, he runs a store (literally: he causes it to be running along).
The "run" verbs employ three distinct Stems, distinguishing number as singular, dual and plural (1, 2 and 3+ subjects).
"Dual-run," like "singular-run," is derived somewhat deviously as a metaphor - but here one in which the two subjects are described literally as "chasing each other."
An intransitive Verb Theme NI-ØCHĄ́Ą́' (Perfective Stem) and its modal variants carry the meaning "flee." as in tsé'ą́ą́ góne' yah 'anííchą́ą́': I fled into the cave; siláo yik'ee noochéé̵ł: he's fleeing from the police. Ł-Classifier produces a causative-transitive Theme NI-ŁCHĄ́Ą́': chase (cause to flee), as in łééchąą'í shinoołchééł: the dog is chasing me (i.e., causing me to flee).
When the direct object of the causative-transitive Theme is recoprical 'ahi-: each other, L-Classifier replaces Ł-, and the theme takes the shape 'ahi-NI-LCHĄ́Ą́': chase each other. It is this Theme that carries the figurative meaning "dual-run," as in 'ashiiké 'atiin góyaa 'ahinoolchééł: the two boys are running (chasing each other) down the road.
(Skipping some morphological trickiness not relevant here. —Wm)
Again, the connotation "swift movement" permits an extension of the "dual-run" verbs to include inanimate objects, as in chidí 'atiin góyaa 'ahinoolchééł: the two cars are running down the road; k'aa' naakigo shigháhi'neelchą́ą́;: two arrows went through me (literally "chased each other through me"). And "dual-run" verbs are used idiomatically in contexts of the type 'at'ééké bimá yíká 'ahi'noolchą́ą́': the two girls helped their mother (literally "they ran away out of sight after her"), 'awáalyaaí shílák'ee hahi'noolchą́ą́': they two prisoners escaped from me (literally "they chased each other out of my hand").