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

YES 0.448 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

((putStrLn :: [Char] -> IO ()) :: [Char] -> 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

((putStrLn :: [Char] -> IO ()) :: [Char] -> 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

((putStrLn :: [Char] -> IO ()) :: [Char] -> 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

((putStrLn :: [Char] -> IO ()) :: [Char] -> 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

(putStrLn :: [Char] -> IO ())

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="putStrLn",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="putStrLn vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4 -> 5[label="",style="dashed", color="red", weight=0];
4[label="putStr vy3 >> putChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];4 -> 6[label="",style="dashed", color="magenta", weight=3];
4 -> 7[label="",style="dashed", color="magenta", weight=3];
6[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];7[label="vy3",fontsize=16,color="green",shape="box"];5[label="putStr vy5 >> putChar (Char (Succ vy6))",fontsize=16,color="black",shape="triangle"];5 -> 8[label="",style="solid", color="black", weight=3];
8[label="putStr vy5 >>= gtGt0 (putChar (Char (Succ vy6)))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="primbindIO (putStr vy5) (gtGt0 (putChar (Char (Succ vy6))))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="terminator (putStr vy5) (gtGt0 (putChar (Char (Succ vy6))))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="ter0m (putStr vy5) (gtGt0 (putChar (Char (Succ vy6))))",fontsize=16,color="green",shape="box"];11 -> 12[label="",style="dashed", color="green", weight=3];
11 -> 13[label="",style="dashed", color="green", weight=3];
12[label="putStr vy5",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="gtGt0 (putChar (Char (Succ vy6)))",fontsize=16,color="grey",shape="box"];13 -> 15[label="",style="dashed", color="grey", weight=3];
14[label="terminator vy5",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="gtGt0 (putChar (Char (Succ vy6))) vy7",fontsize=16,color="black",shape="triangle"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="ter1m vy5",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3];
17[label="putChar (Char (Succ vy6))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
18[label="vy5",fontsize=16,color="green",shape="box"];19[label="terminator (Char (Succ vy6))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
20[label="ter2m (Char (Succ vy6))",fontsize=16,color="green",shape="box"];20 -> 21[label="",style="dashed", color="green", weight=3];
21[label="Char (Succ vy6)",fontsize=16,color="green",shape="box"];}