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

YES 0.42 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

(((>>) :: IO a -> IO b -> IO b) :: IO a -> IO b -> IO b)

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

(((>>) :: IO a -> IO b -> IO b) :: IO a -> IO b -> IO b)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Main

(((>>) :: IO b -> IO a -> IO a) :: IO b -> IO a -> IO a)

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

              ↳ Narrow

mainModule Main

((>>) :: IO b -> IO a -> IO a)

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="(>>) vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="(>>) vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="vy3 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primbindIO vy3 (gtGt0 vy4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="terminator vy3 (gtGt0 vy4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="ter0m vy3 (gtGt0 vy4)",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3];
8 -> 10[label="",style="dashed", color="green", weight=3];
9[label="vy3",fontsize=16,color="green",shape="box"];10[label="gtGt0 vy4",fontsize=16,color="grey",shape="box"];10 -> 11[label="",style="dashed", color="grey", weight=3];
11[label="gtGt0 vy4 vy5",fontsize=16,color="black",shape="triangle"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="vy4",fontsize=16,color="green",shape="box"];}