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

YES 0.40900000000000003 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

((toEnum :: Int -> Ratio Int) :: Int -> Ratio Int)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((toEnum :: Int -> Ratio Int) :: Int -> Ratio Int)

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

((toEnum :: Int -> Ratio Int) :: Int -> Ratio Int)

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

(toEnum :: Int -> Ratio Int)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="toEnum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="toEnum vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="fromInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="intToRatio vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="fromInt vx3 :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
6 -> 8[label="",style="dashed", color="green", weight=3];
7[label="fromInt vx3",fontsize=16,color="black",shape="triangle"];7 -> 9[label="",style="solid", color="black", weight=3];
8 -> 7[label="",style="dashed", color="red", weight=0];
8[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];8 -> 10[label="",style="dashed", color="magenta", weight=3];
9[label="vx3",fontsize=16,color="green",shape="box"];10[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];}