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

YES 0.434 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

(((<=) :: Bool -> Bool -> Bool) :: Bool -> Bool -> Bool)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

(((<=) :: Bool -> Bool -> Bool) :: Bool -> Bool -> Bool)

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

((<=) :: Bool -> Bool -> Bool)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="(<=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="(<=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="(<=) vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];15[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 5[label="",style="solid", color="burlywood", weight=3];
16[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="(<=) False vx4",fontsize=16,color="burlywood",shape="box"];17[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 7[label="",style="solid", color="burlywood", weight=3];
18[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
18 -> 8[label="",style="solid", color="burlywood", weight=3];
6[label="(<=) True vx4",fontsize=16,color="burlywood",shape="box"];19[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 9[label="",style="solid", color="burlywood", weight=3];
20[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
20 -> 10[label="",style="solid", color="burlywood", weight=3];
7[label="(<=) False False",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
8[label="(<=) False True",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="(<=) True False",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="(<=) True True",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="True",fontsize=16,color="green",shape="box"];12[label="True",fontsize=16,color="green",shape="box"];13[label="False",fontsize=16,color="green",shape="box"];14[label="True",fontsize=16,color="green",shape="box"];}