H-Termination proof of /home/matraf/haskell/eval_FullyBlown

YES 0.485 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

  ↳ BR

mainModule Main

((range :: ((),()) -> [()]) :: ((),()) -> [()])

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((range :: ((),()) -> [()]) :: ((),()) -> [()])

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

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

(range :: ((),()) -> [()])

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="range",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="range vx3",fontsize=16,color="burlywood",shape="triangle"];8[label="vx3/(vx30,vx31)",fontsize=10,color="white",style="solid",shape="box"];3 -> 8[label="",style="solid", color="burlywood", weight=9];
8 -> 4[label="",style="solid", color="burlywood", weight=3];
4[label="range (vx30,vx31)",fontsize=16,color="burlywood",shape="box"];9[label="vx30/()",fontsize=10,color="white",style="solid",shape="box"];4 -> 9[label="",style="solid", color="burlywood", weight=9];
9 -> 5[label="",style="solid", color="burlywood", weight=3];
5[label="range ((),vx31)",fontsize=16,color="burlywood",shape="box"];10[label="vx31/()",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9];
10 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="range ((),())",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="() : []",fontsize=16,color="green",shape="box"];}