YES 1.573 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
  ↳ LR

mainModule Main
  ((range :: (Ordering,Ordering ->  [Ordering]) :: (Ordering,Ordering ->  [Ordering])

module Main where
  import qualified Prelude



Lambda Reductions:
The following Lambda expression
\z→if y >= z && z >= x then z : [] else []

is transformed to
range0 y x z = if y >= z && z >= x then z : [] else []



↳ HASKELL
  ↳ LR
HASKELL
      ↳ IFR

mainModule Main
  ((range :: (Ordering,Ordering ->  [Ordering]) :: (Ordering,Ordering ->  [Ordering])

module Main where
  import qualified Prelude



If Reductions:
The following If expression
if y >= z && z >= x then z : [] else []

is transformed to
range00 z True = z : []
range00 z False = []



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ IFR
HASKELL
          ↳ BR

mainModule Main
  ((range :: (Ordering,Ordering ->  [Ordering]) :: (Ordering,Ordering ->  [Ordering])

module Main where
  import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule Main
  ((range :: (Ordering,Ordering ->  [Ordering]) :: (Ordering,Ordering ->  [Ordering])

module Main where
  import qualified Prelude



Cond Reductions:
The following Function with conditions
compare x y
 | x == y
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

compare2 x y True = EQ
compare2 x y False = compare1 x y (x <= y)

compare1 x y True = LT
compare1 x y False = compare0 x y otherwise

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
HASKELL
                  ↳ Narrow

mainModule Main
  (range :: (Ordering,Ordering ->  [Ordering])

module Main where
  import qualified Prelude



Haskell To QDPs