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

YES 0.465 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

  ↳ IFR

mainModule Monad

((when :: Monad a => Bool -> a () -> a ()) :: Monad a => Bool -> a () -> a ())

module Monad where

import qualified Maybe
import qualified Prelude

when :: Monad a => Bool -> a () -> a ()

when

p s

if p then s else return ()

module Maybe where

import qualified Monad
import qualified Prelude

If Reductions:
The following If expression

if p then s else return ()

is transformed to

when0 s True = s

when0 s False = return ()

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

mainModule Monad

((when :: Monad a => Bool -> a () -> a ()) :: Monad a => Bool -> a () -> a ())

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

when :: Monad a => Bool -> a () -> a ()

when

p s

when0 s p

when0	s True	=	s
when0	s False	=	return ()

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Monad

((when :: Monad a => Bool -> a () -> a ()) :: Monad a => Bool -> a () -> a ())

module Monad where

import qualified Maybe
import qualified Prelude

when :: Monad a => Bool -> a () -> a ()

when

p s

when0 s p

when0	s True	=	s
when0	s False	=	return ()

module Maybe where

import qualified Monad
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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

mainModule Monad

(when :: Monad a => Bool -> a () -> a ())

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

when :: Monad a => Bool -> a () -> a ()

when

p s

when0 s p

when0	s True	=	s
when0	s False	=	return ()

Haskell To QDPs

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15[label="() : []",fontsize=16,color="green",shape="box"];16[label="terminator ()",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
17[label="ter0m ()",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3];
18[label="()",fontsize=16,color="green",shape="box"];}