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

YES 0.612 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

  ↳ LR

mainModule Main

((print :: () -> IO ()) :: () -> IO ())

module Main where

import qualified Prelude

Lambda Reductions:
The following Lambda expression

\_→q

is transformed to

gtGt0 q _ = q

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

mainModule Main

((print :: () -> IO ()) :: () -> IO ())

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Main

((print :: () -> IO ()) :: () -> IO ())

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

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ NumRed

mainModule Main

((print :: () -> IO ()) :: () -> IO ())

module Main where

import qualified Prelude

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ NumRed

                ↳ HASKELL

                  ↳ Narrow

mainModule Main

(print :: () -> IO ())

module Main where

import qualified Prelude

Haskell To QDPs

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90[label="[] ++ []",fontsize=16,color="black",shape="box"];90 -> 91[label="",style="solid", color="black", weight=3];
91[label="[]",fontsize=16,color="green",shape="box"];}