YES 0.498 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ IFR

mainModule Main
  ((showParen :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char]) :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char])

module Main where
  import qualified Prelude


If Reductions:
The following If expression
if b then (showChar '(') . p . showChar ')' else p

is transformed to
showParen0 p True = (showChar '(') . p . showChar ')'
showParen0 p False = p



↳ HASKELL
  ↳ IFR
    ↳ HASKELL
      ↳ BR

mainModule Main
  ((showParen :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char]) :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char])

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ IFR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR

mainModule Main
  ((showParen :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char]) :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char])

module Main where
  import qualified Prelude


Cond Reductions:
The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



↳ HASKELL
  ↳ IFR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ NumRed

mainModule Main
  ((showParen :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char]) :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char])

module Main where
  import qualified Prelude


Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL
  ↳ IFR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ NumRed
                ↳ HASKELL
                  ↳ Narrow

mainModule Main
  (showParen :: Bool  ->  ([Char]  ->  [Char])  ->  [Char]  ->  [Char])

module Main where
  import qualified Prelude


Haskell To QDPs