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

YES 0.444 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

((join :: Maybe (Maybe a) -> Maybe a) :: Maybe (Maybe a) -> Maybe a)

module Monad where

import qualified Maybe
import qualified Prelude

join :: Monad b => b (b a) -> b a

join

x >>= id

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

((join :: Maybe (Maybe a) -> Maybe a) :: Maybe (Maybe a) -> Maybe a)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

join :: Monad b => b (b a) -> b a

join

x >>= id

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

(join :: Maybe (Maybe a) -> Maybe a)

module Monad where

import qualified Maybe
import qualified Prelude

join :: Monad a => a (a b) -> a b

join

x >>= id

module Maybe where

import qualified Monad
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="join",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="join vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="vy3 >>= id",fontsize=16,color="burlywood",shape="box"];10[label="vy3/Nothing",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
10 -> 5[label="",style="solid", color="burlywood", weight=3];
11[label="vy3/Just vy30",fontsize=10,color="white",style="solid",shape="box"];4 -> 11[label="",style="solid", color="burlywood", weight=9];
11 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="Nothing >>= id",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="Just vy30 >>= id",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="Nothing",fontsize=16,color="green",shape="box"];8[label="id vy30",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="vy30",fontsize=16,color="green",shape="box"];}