Incorrect usage of overlapping instances and data families sends GHC into loop

Sorry for the lack of descriptive title as I can't nail down the source of the bug. This is the minimal example to trigger the loop:

{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}

module Main where

data Tagged t a = Tagged a

type family Tag a where
  Tag (Tagged t a) = Tagged t a
  Tag a = Tagged Int a

class (r ~ Tag a) => TagImpl a r | a -> r where
  tag :: a -> r

instance {-# OVERLAPPING #-} (r ~ Tag (Tagged t a)) => TagImpl (Tagged t a) r where
  tag = id

#ifdef WRONG
instance {-# OVERLAPPING #-} (r ~ Tagged t a, r ~ Tag a) => TagImpl a r where
#else
instance {-# OVERLAPPING #-} (r ~ Tagged Int a, r ~ Tag a) => TagImpl a r where
#endif
  tag = Tagged @Int

data family   DF x
data instance DF (Tagged t a) = DF (Tagged t a)

class ToDF a b | a -> b where
  df :: a -> b

#ifdef WRONG
instance (TagImpl a a', b ~ DF a') => ToDF a b where
#else
instance (TagImpl a (Tagged t a'), b ~ DF (Tagged t a')) => ToDF a b where
#endif
  df = DF . tag

main :: IO ()
main = pure ()

When compiled with -DWRONG, it causes GHC (both 8.0.1 and HEAD@20160823) to loop:

$ ghc --version && ghc -fno-code Main.hs -DWRONG
The Glorious Glasgow Haskell Compilation System, version 8.1.20160823
[1 of 1] Compiling Main             ( Main.hs, nothing )
(loops indefinitely...)