relation to each other. "I shall have much pleasure in accepting your
kind invitation" is wrong, unless you really mean that just now you
decline though by-and-by you intend to accept; or unless you mean that
you do accept now, though you have no pleasure in doing so, but look
forward to be more pleased by-and-by. In fact the sequence of the
compound tenses puzzle experienced writers. The best plan is to go back
in thought to the time in question and use the tense you would _then_
naturally use. Now in the sentence "I should have liked to have gone to
see the circus" the way to find out the proper sequence is to ask
yourself the question--what is it I "should have liked" to do? and the
plain answer is "to go to see the circus." I cannot answer--"To have gone
to see the circus" for that would imply that at a certain moment I would
have liked to be in the position of having gone to the circus. But I do
not mean this; I mean that at the moment at which I am speaking I wish I
had gone to see the circus. The verbal phrase _I should have liked_
carries me back to the time when there was a chance of seeing the circus
and once back at the time, the going to the circus is a thing of the
present. This whole explanation resolves itself into the simple
question,--what should I have liked _at that time_, and the answer is "to
go to see the circus," therefore this is the proper sequence, and the
expression should be "I should have liked to go to see the circus."

If we wish to speak of something relating to a time _prior_ to that
indicated in the past tense we must use the perfect tense of the
infinitive; as, "He appeared to have seen better days." We should say "I
expected to _meet him_," not "I expected _to have met him_." "We intended
_to visit you_," not "_to have visited_ you." "I hoped they _would_
arrive," not "I hoped they _would have_ arrived." "I thought I should
_catch_ the bird," not "I thought I should _have caught_ the bird." "I
had intended _to go_ to the meeting," not "I had intended to _have gone_