self-examination vs rumination

self-examination and rumination both are nouns.

Word	Noun	Adjective	Verb	Adverb
self-examination	Yes	No	No	No
rumination	Yes	No	No	No

As nouns, rumination is a hypernym of self-examination; that is, rumination is a word with a broader meaning than self-examination:

self-examination: the contemplation of your own thoughts and desires and conduct
rumination: a calm, lengthy, intent consideration

Other hypernyms of self-examination include contemplation, musing, reflection, reflexion, thoughtfulness.

self-examination (noun)	rumination (noun)
the contemplation of your own thoughts and desires and conduct	regurgitation of small amounts of food; seen in some infants after feeding
	(of ruminants) chewing (the cud)
	a calm, lengthy, intent consideration