Learn English – Seem having vs Seem to have

You don't normally use Present Perfect with stative verbs (have, be, like, seem, prefer, understand, doubt, know, etc.) Here's a longer list - in general, they apply to states that last for some time.

In some contexts, such as "How long have you had/been having these symptoms?", there's no real difference. Arguably, been having calls more attention to the fact that you're still having the symptoms, but I doubt many people would consciously either make or hear that distinction.

A "rule of thumb" for to have is: when it means to experience, you might want to use Present Perfect; when it means to own, you almost certainly don't.

Here's an example for to be using the "slightly unusual" Present Perfect in a construction which is perfectly valid, and is probably the most succinct way of expressing the intended meaning...

By now the new cook will have been being introduced to her duties for several weeks.

Cambridge University Press's online English dictionary has this example: "She is usually acknowledged to be one of our best artists" and OUP's online dictionary has this example: "He is widely acknowledged to be the best player in the world".

From this, one can extrapolate that the people doing the acknowledging can say "I acknowledge him to be the best player in the world".

I haven't found a form with to+infinitive other than "to be". I can imagine "I acknowledge him to play chess better than Kasparov", but it sounds very stilted, compared with "I acknowledge that he plays ...".