Based on my reading, the simple predicate only includes the verb or verb phrase, while the complete predicate includes the verb or verb phrase plus all of its modifiers. With that in mind, would "just saw" count as a simple predicate, or would it just be the word "saw"? My own understanding says "just saw her" is the complete predicate, while "saw" is the simple predicate.
I bring this up because of an example on this page: What Is a Predicate? — Your Dictionary
It also indicates that simple predicates can include adjectives, as in "I was late," with "was late" being considered the simple predicate. My understanding is that "was" would be the simple predicate here, while "was late" would be the complete predicate, with "late" being considered a predicate adjective. Is that not the case with linking verbs and adjectives? And if this is the case, does this extend to complements in general? Could I also say that in the case of "Jimi Hendrix was a great guitar player" that the simple predicate is "was a great guitar player"? Or is this a case where I shouldn't believe everything I read on the internet in regard to the link above? :)
I would appreciate any insight into this topic from more seasoned linguistic minds.