GHC's simplifier can go into a loop if you use fixpoints in a funny way, as documented here http://www.haskell.org/ghc/docs/latest/html/users_guide/bugs.html\#bugs-ghc (12.2.1, third bullet). But GADTs provide new opportunities. This ticket records one, thanks to Ryan Ingram and Matthieu Sozeau:

{-# LANGUAGE GADTs #-}
module Contr where

newtype I f = I (f ())
data R o a where R :: (a (I a) -> o) -> R o (I a)

run :: R o (I (R o)) -> R o (I (R o)) -> o
run x (R f) = f x
rir :: (R o) (I (R o))
rir = R (\x -> run x x)

absurd :: a
absurd = run rir rir

Now the simplifier can loop. Look:

run rir rir

= {inline run}
  case rir of R f -> f rir

= {case of known constructor}
  let { f = \x -> run x x } in f rir

= {inline f}
  run rir rir