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

YES 0.487 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

((succ :: Char -> Char) :: Char -> Char)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((succ :: Char -> Char) :: Char -> Char)

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

          ↳ NumRed

mainModule Main

((succ :: Char -> Char) :: Char -> Char)

module Main where

import qualified Prelude

Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

mainModule Main

(succ :: Char -> Char)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="succ",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="succ vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="toEnum . (Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnum ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primIntToChar ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="primIntToChar (Pos (Succ Zero) + fromEnum vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="primIntToChar (primPlusInt (Pos (Succ Zero)) (fromEnum vx3))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="primIntToChar (primPlusInt (Pos (Succ Zero)) (primCharToInt vx3))",fontsize=16,color="burlywood",shape="box"];24[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];9 -> 24[label="",style="solid", color="burlywood", weight=9];
24 -> 10[label="",style="solid", color="burlywood", weight=3];
10[label="primIntToChar (primPlusInt (Pos (Succ Zero)) (primCharToInt (Char vx30)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="primIntToChar (primPlusInt (Pos (Succ Zero)) (Pos vx30))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="primIntToChar (Pos (primPlusNat (Succ Zero) vx30))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="Char (primPlusNat (Succ Zero) vx30)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3];
14[label="primPlusNat (Succ Zero) vx30",fontsize=16,color="burlywood",shape="box"];25[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];14 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 15[label="",style="solid", color="burlywood", weight=3];
26[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="primPlusNat (Succ Zero) (Succ vx300)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="Succ (Succ (primPlusNat Zero vx300))",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3];
18[label="Succ Zero",fontsize=16,color="green",shape="box"];19[label="primPlusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];27[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];19 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 20[label="",style="solid", color="burlywood", weight=3];
28[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 21[label="",style="solid", color="burlywood", weight=3];
20[label="primPlusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
21[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
22[label="Succ vx3000",fontsize=16,color="green",shape="box"];23[label="Zero",fontsize=16,color="green",shape="box"];}