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

((min :: 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

((min :: Bool -> Bool -> Bool) :: Bool -> Bool -> Bool)

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

min x y

| x <= y

= x

| otherwise

= y

is transformed to

min x y = min2 x y

min1 x y True = x

min1 x y False = min0 x y otherwise

min0 x y True = y

min2 x y = min1 x y (x <= y)

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

(min :: Bool -> Bool -> Bool)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="min",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="min vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="min vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="min1 vx3 vx4 (vx3 <= vx4)",fontsize=16,color="burlywood",shape="box"];23[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9];
23 -> 7[label="",style="solid", color="burlywood", weight=3];
24[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9];
24 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="min1 False vx4 (False <= vx4)",fontsize=16,color="burlywood",shape="box"];25[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 9[label="",style="solid", color="burlywood", weight=3];
26[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 10[label="",style="solid", color="burlywood", weight=3];
8[label="min1 True vx4 (True <= vx4)",fontsize=16,color="burlywood",shape="box"];27[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 11[label="",style="solid", color="burlywood", weight=3];
28[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 12[label="",style="solid", color="burlywood", weight=3];
9[label="min1 False False (False <= False)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="min1 False True (False <= True)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="min1 True False (True <= False)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="min1 True True (True <= True)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="min1 False False True",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="min1 False True True",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="min1 True False False",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="min1 True True True",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="False",fontsize=16,color="green",shape="box"];18[label="False",fontsize=16,color="green",shape="box"];19[label="min0 True False otherwise",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="True",fontsize=16,color="green",shape="box"];21[label="min0 True False True",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="False",fontsize=16,color="green",shape="box"];}