Use of The perfect infinitive
to have + past participle:
to have done , to have told, to have guessed, to have heard
He seems to have passed the examination.
It appears to have been completed.
The girl pretended to have read the book.
The girl pretended that she had read the book.
I happened to have driven such kind of car before.
It happened that I had driven such kind of car before.
The student seems to have been absent yesterday.
It seems that the boy was absent yesterday.
Use of The perfect infinitive continuous
to have been + present participle:
to have been doing , to have been playing, to have been reading
It is mainly used after auxiliary verbs and appear and seem, but it can also be used after happen, pretend and the passive voice of believe, know, report, say, understand:
Someone seems to have been waiting for you in the field.
It appears that someone has been waiting for you in the field.
She pretends to have been reading in the room.
She pretends that she has been reading in the room.
He seems to have been spying for both sides.
It seems that he has been spying for both sides.