The perfect continuous infinitive is used to express a continuing but now completed action after a verb which must be followed by the infinitive. The perfect infinitive is formed:
to have been + present participle
As with the present infinitive, there are situations where the zero form of the perfect continuous infinitive is required, so the word to is omitted. This happens after most modal auxiliaries, and in other places where zero infinitives are used.
- The woman seemed to have been crying.
- He pretended to have been painting all day.
- I would have preferred to have been sleeping all afternoon.
- You must have been waiting for hours!
- They might have been talking before you came in.
- You should have been studying for your test.