Lambda the Ultimate

People like blowing stuff up, explosions are great! I started wondering about type bombs, small expressions which have large type terms. Is there anything known about that, in particular for Haskell/ML since these are popular?

The small bomb I know of employs 'dup' and is relatively well known. I.e., take `dup`

dup x = (x,x)

The repeated application gives back a type term which grows exponentially in the size of the expression.

(dup . dup . dup . dup . dup) 0

(It depends on the type checker, of course, whether the type actually is represented exponentially.)

You can lift `dup` further but can you grow faster? I tried `let t = (\f -> f . f) in let d = (\x -> (x,x)) in (t.t.t.t) d 0` which doesn't type check in ghci as a first order approximation. But I thought I would ask you, people.

What is the fastest growing type term you can come up with? Or what term will keep a type checker really, really busy?