"Mary is trying to improve the condition of her
house."
There seems to be confusions of forms and functions
in the discussion of this example.
Any intelligent definition of the form of a verb
phrase must recognize that a VP structure is finite. An infinitive is not a part
of a true verb phrase except, as Bruce mentioned, as a modal equivalent
["have to" = "must," "be going to" = "will," etc.]. The confusion comes from
catenative verbs, as Martha mentioned, where the semantics mixes stickily with
the structures. Since an infinitive phrase can function nominally, adjectivally,
or adverbially, the problems of putting a functional label on the infinitive
form for a given example is not always just "a very basic exercise in
part-of-speech recognition."
Perhaps the confusion in the example is owing to
the idiomaticness of "trying." In the example, a fair paraphrase of the verb "to
try" seems to be "to attempt":
Mary is attempting to improve
the condition of her house.
In that case, the infinitive phrase is seen more
clearly in its function as a nominal/direct object, similar to using a
noun phrase in its place:
Mary is attempting an
improvement to her house.
Using "to try" with an infinitive phrase following
(whether you consider it catenative or not) is far more idiomatic, obviously,
but the underlying structures are the same.