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

YES 0.462 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

  ↳ LR

mainModule Monad

((liftM :: (b -> a) -> Maybe b -> Maybe a) :: (b -> a) -> Maybe b -> Maybe a)

module Monad where

import qualified Maybe
import qualified Prelude

liftM :: Monad c => (b -> a) -> c b -> c a

liftM

f m1

m1 >>= (\x1 ->return (f x1))

module Maybe where

import qualified Monad
import qualified Prelude

Lambda Reductions:
The following Lambda expression

\x1→return (f x1)

is transformed to

liftM0 f x1 = return (f x1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

mainModule Monad

((liftM :: (a -> b) -> Maybe a -> Maybe b) :: (a -> b) -> Maybe a -> Maybe b)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM :: Monad a => (c -> b) -> a c -> a b

liftM

f m1

m1 >>= liftM0 f

liftM0

f x1

return (f x1)

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Monad

((liftM :: (b -> a) -> Maybe b -> Maybe a) :: (b -> a) -> Maybe b -> Maybe a)

module Monad where

import qualified Maybe
import qualified Prelude

liftM :: Monad c => (a -> b) -> c a -> c b

liftM

f m1

m1 >>= liftM0 f

liftM0

f x1

return (f x1)

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

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

mainModule Monad

(liftM :: (a -> b) -> Maybe a -> Maybe b)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM :: Monad b => (c -> a) -> b c -> b a

liftM

f m1

m1 >>= liftM0 f

liftM0

f x1

return (f x1)

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="liftM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="liftM vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="liftM vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="vy4 >>= liftM0 vy3",fontsize=16,color="burlywood",shape="box"];14[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
14 -> 6[label="",style="solid", color="burlywood", weight=3];
15[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="Nothing >>= liftM0 vy3",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="Just vy40 >>= liftM0 vy3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="Nothing",fontsize=16,color="green",shape="box"];9[label="liftM0 vy3 vy40",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="return (vy3 vy40)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="Just (vy3 vy40)",fontsize=16,color="green",shape="box"];11 -> 12[label="",style="dashed", color="green", weight=3];
12[label="vy3 vy40",fontsize=16,color="green",shape="box"];12 -> 13[label="",style="dashed", color="green", weight=3];
13[label="vy40",fontsize=16,color="green",shape="box"];}