The most musically complex prog band(s)?

To me complex and avant garde can sound similar but come from a different place. Avant to me is throwing convention completely out the window and avoiding traditional structure, often introducing intentional chaos, which can inspired, mindblowing, complete noise, self-indulgent, useless, and often combinations of them all.

Complex involves multiple interconnecting parts, the more and more involved the connections the more "complex." This gain be inspired, mindblowing, sterile, boring, self-indulgent, useless.....you get the idea.

Mr. Bungle, Zappa, Crimson all used elements of both. Gentle Giant is more complex than avant garde, while they certainly redefined convention, nothing ever felt random, in fact, rarely even improvised.

Except GENTLE GIANT and YES of the TFTO album,try YEZDA URFA...you'll be blown,that's really complex but creative music!

This is all a bit of a t**ser. The only way you can judge complexity is at a playing level, not a listening level. That is- which grade would they be placed in at a music examination level: Grade 1 (easiest)  to Licentiate (most difficult, with a very small percentage of players being able to attain the skill needed to play them). Of course band music has the added problem of being group music, so there are other considerations of how to rate them such as contrapuntal problems (is it easy or extremely difficult for the group to play this together and keep the timing true). A good example of this may be certain Yes songs, which have 4 instruments playing completely different parts that come together as a whole in some strange magical meld, that are not that difficult to play as solos, but putting the four parts together and in time adds to the difficulty of the piece, astronomically.

So how do you judge music complexity?