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

YES 0.487 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/Monad.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Monad

((guard :: MonadPlus a => Bool -> a ()) :: MonadPlus a => Bool -> a ())

module Monad where

import qualified Maybe
import qualified Prelude

class Monad a => MonadPlus a where

mzero :: MonadPlus a => a b

instance MonadPlus Maybe where

mzero

Nothing

instance MonadPlus [] where

mzero

[]

guard :: MonadPlus a => Bool -> a ()

guard	True	=	return ()
guard	False	=	mzero

module Maybe where

import qualified Monad
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Monad

((guard :: MonadPlus a => Bool -> a ()) :: MonadPlus a => Bool -> a ())

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

class Monad a => MonadPlus a where

mzero :: MonadPlus a => a b

instance MonadPlus Maybe where

mzero

Nothing

instance MonadPlus [] where

mzero

[]

guard :: MonadPlus a => Bool -> a ()

guard	True	=	return ()
guard	False	=	mzero

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

          ↳ Narrow

mainModule Monad

(guard :: MonadPlus a => Bool -> a ())

module Monad where

import qualified Maybe
import qualified Prelude

class Monad a => MonadPlus a where

mzero :: MonadPlus a => a b

instance MonadPlus Maybe where

mzero

Nothing

instance MonadPlus [] where

mzero

[]

guard :: MonadPlus a => Bool -> a ()

guard	True	=	return ()
guard	False	=	mzero

module Maybe where

import qualified Monad
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="guard\n  MonadPlus a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="guard vy3\n  MonadPlus a",fontsize=16,color="burlywood",shape="triangle"];16[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];3 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 4[label="",style="solid", color="burlywood", weight=3];
17[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];3 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="guard False\n  MonadPlus a",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
5[label="guard True\n  MonadPlus a",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="mzero\n  MonadPlus a",fontsize=16,color="blue",shape="box"];18[label="mzero :: Maybe ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 18[label="",style="solid", color="blue", weight=9];
18 -> 8[label="",style="solid", color="blue", weight=3];
19[label="mzero :: [] ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="blue", weight=9];
19 -> 9[label="",style="solid", color="blue", weight=3];
7[label="return ()\n  MonadPlus a",fontsize=16,color="blue",shape="box"];20[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 20[label="",style="solid", color="blue", weight=9];
20 -> 10[label="",style="solid", color="blue", weight=3];
21[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 21[label="",style="solid", color="blue", weight=9];
21 -> 11[label="",style="solid", color="blue", weight=3];
8[label="mzero",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="mzero",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="return ()",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="return ()",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="Nothing",fontsize=16,color="green",shape="box"];13[label="[]",fontsize=16,color="green",shape="box"];14[label="Just ()",fontsize=16,color="green",shape="box"];15[label="() : []",fontsize=16,color="green",shape="box"];}