What is the type of an adjective "fed up"

Solution 1:

A phrasal verb can be described as an action, such as I don't want to see him because he will (look down on) me. whereas you would never say I don't want to see him because he will (feed me up).

The phrasal verb focuses on the process regardless of the result, but the compound adjective is wholly concerned with the current condition, regardless of the process by which that condition was achieved. There is certainly some grey area involved in the distinction. "Fed up" is an interesting clear case in which it would never be used as a verb. To turn that phrase into a verb would require a statement such as "He always gets me fed up" which requires a completely separate verb.

Another way to look at it is that a phrasal verb, whether used passively or actively, automatically leads the statement to an implied or stated subject. (He was looked down on) has no subject doing the looking, but implies that a specific subject did exist that did indeed look down on him, and therefore is a phrasal verb in past participle form.

(He was pooped out) also has no subject doing the pooping, but contrary to the first example, no subject is needed. The fact is that he had no energy, whether or not anything could be identified to have made him that way. This is therefore a compound adjective.