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

YES 0.41300000000000003 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

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

((<=) :: Ordering -> Ordering -> 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"];26[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];4 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 5[label="",style="solid", color="burlywood", weight=3];
27[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];4 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 6[label="",style="solid", color="burlywood", weight=3];
28[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];4 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 7[label="",style="solid", color="burlywood", weight=3];
5[label="(<=) LT vx4",fontsize=16,color="burlywood",shape="box"];29[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 29[label="",style="solid", color="burlywood", weight=9];
29 -> 8[label="",style="solid", color="burlywood", weight=3];
30[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
30 -> 9[label="",style="solid", color="burlywood", weight=3];
31[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 10[label="",style="solid", color="burlywood", weight=3];
6[label="(<=) EQ vx4",fontsize=16,color="burlywood",shape="box"];32[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
32 -> 11[label="",style="solid", color="burlywood", weight=3];
33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
33 -> 12[label="",style="solid", color="burlywood", weight=3];
34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 13[label="",style="solid", color="burlywood", weight=3];
7[label="(<=) GT vx4",fontsize=16,color="burlywood",shape="box"];35[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 14[label="",style="solid", color="burlywood", weight=3];
36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 15[label="",style="solid", color="burlywood", weight=3];
37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
37 -> 16[label="",style="solid", color="burlywood", weight=3];
8[label="(<=) LT LT",fontsize=16,color="black",shape="box"];8 -> 17[label="",style="solid", color="black", weight=3];
9[label="(<=) LT EQ",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
10[label="(<=) LT GT",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
11[label="(<=) EQ LT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
12[label="(<=) EQ EQ",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
13[label="(<=) EQ GT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
14[label="(<=) GT LT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
15[label="(<=) GT EQ",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
16[label="(<=) GT GT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
17[label="True",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="True",fontsize=16,color="green",shape="box"];20[label="False",fontsize=16,color="green",shape="box"];21[label="True",fontsize=16,color="green",shape="box"];22[label="True",fontsize=16,color="green",shape="box"];23[label="False",fontsize=16,color="green",shape="box"];24[label="False",fontsize=16,color="green",shape="box"];25[label="True",fontsize=16,color="green",shape="box"];}