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

NO 1.409 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 disproven:

↳ HASKELL

  ↳ LR

mainModule Main

((blockIO :: ((a -> IOResult) -> IO ()) -> IO a) :: ((a -> IOResult) -> IO ()) -> IO a)

module Main where

import qualified Prelude

Lambda Reductions:
The following Lambda expression

\fs→Hugs_BlockThread (s . fromObj) m'

is transformed to

blockIO0 f s = Hugs_BlockThread (s . fromObj) m'

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

mainModule Main

((blockIO :: ((a -> IOResult) -> IO ()) -> IO a) :: ((a -> IOResult) -> IO ()) -> IO a)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Main

((blockIO :: ((a -> IOResult) -> IO ()) -> IO a) :: ((a -> IOResult) -> IO ()) -> IO a)

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

              ↳ LetRed

mainModule Main

((blockIO :: ((a -> IOResult) -> IO ()) -> IO a) :: ((a -> IOResult) -> IO ()) -> IO a)

module Main where

import qualified Prelude

Let/Where Reductions:
The bindings of the following Let/Where expression

IO blockIO0

where

blockIO0 f s = Hugs_BlockThread (s . fromObj) m'

m' k = threadToIOResult (m (k . toObj))

are unpacked to the following functions on top level

blockIOBlockIO0 vy f s = Hugs_BlockThread (s . fromObj) (blockIOM' vy)

blockIOM' vy k = threadToIOResult (vy (k . toObj))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

mainModule Main

(blockIO :: ((a -> IOResult) -> IO ()) -> IO a)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="blockIO",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="blockIO vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="IO (blockIOBlockIO0 vz3)",fontsize=16,color="green",shape="box"];4 -> 5[label="",style="dashed", color="green", weight=3];
5[label="blockIOBlockIO0 vz3",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="blockIOBlockIO0 vz3 vz4",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
7[label="blockIOBlockIO0 vz3 vz4 vz5",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="Hugs_BlockThread (vz5 . fromObj) (blockIOM' vz3)",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3];
8 -> 10[label="",style="dashed", color="green", weight=3];
9[label="vz5 . fromObj",fontsize=16,color="grey",shape="box"];9 -> 11[label="",style="dashed", color="grey", weight=3];
10[label="blockIOM' vz3",fontsize=16,color="grey",shape="box"];10 -> 12[label="",style="dashed", color="grey", weight=3];
11[label="vz5 . fromObj",fontsize=16,color="black",shape="triangle"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="blockIOM' vz3 vz7",fontsize=16,color="black",shape="triangle"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="vz5 (fromObj vz6)",fontsize=16,color="green",shape="box"];13 -> 15[label="",style="dashed", color="green", weight=3];
14 -> 16[label="",style="dashed", color="red", weight=0];
14[label="threadToIOResult (vz3 (vz7 . toObj))",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
15[label="fromObj vz6",fontsize=16,color="black",shape="triangle"];15 -> 18[label="",style="solid", color="black", weight=3];
17[label="vz3 (vz7 . toObj)",fontsize=16,color="green",shape="box"];17 -> 21[label="",style="dashed", color="green", weight=3];
16[label="threadToIOResult vz8",fontsize=16,color="burlywood",shape="triangle"];34[label="vz8/IO vz80",fontsize=10,color="white",style="solid",shape="box"];16 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 20[label="",style="solid", color="burlywood", weight=3];
18 -> 15[label="",style="dashed", color="red", weight=0];
18[label="fromObj vz6",fontsize=16,color="magenta"];21[label="vz7 . toObj",fontsize=16,color="grey",shape="box"];21 -> 24[label="",style="dashed", color="grey", weight=3];
20[label="threadToIOResult (IO vz80)",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
24 -> 22[label="",style="dashed", color="red", weight=0];
24[label="vz7 . toObj",fontsize=16,color="magenta"];24 -> 28[label="",style="dashed", color="magenta", weight=3];
23[label="vz80 Hugs_Error (const Hugs_DeadThread)",fontsize=16,color="green",shape="box"];23 -> 26[label="",style="dashed", color="green", weight=3];
23 -> 27[label="",style="dashed", color="green", weight=3];
28[label="vz10",fontsize=16,color="green",shape="box"];22[label="vz7 . toObj",fontsize=16,color="black",shape="triangle"];22 -> 25[label="",style="solid", color="black", weight=3];
26[label="Hugs_Error",fontsize=16,color="green",shape="box"];27[label="const Hugs_DeadThread",fontsize=16,color="grey",shape="box"];27 -> 30[label="",style="dashed", color="grey", weight=3];
25[label="vz7 (toObj vz9)",fontsize=16,color="green",shape="box"];25 -> 29[label="",style="dashed", color="green", weight=3];
30[label="const Hugs_DeadThread vz11",fontsize=16,color="black",shape="triangle"];30 -> 32[label="",style="solid", color="black", weight=3];
29[label="toObj vz9",fontsize=16,color="black",shape="triangle"];29 -> 31[label="",style="solid", color="black", weight=3];
32[label="Hugs_DeadThread",fontsize=16,color="green",shape="box"];31 -> 29[label="",style="dashed", color="red", weight=0];
31[label="toObj vz9",fontsize=16,color="magenta"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                        ↳ NonTerminationProof

                      ↳ QDP

                  ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_toObj(vz9, ba) → new_toObj(vz9, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

The TRS P consists of the following rules:

new_toObj(vz9, ba) → new_toObj(vz9, ba)

The TRS R consists of the following rules:none

s = new_toObj(vz9, ba) evaluates to t =new_toObj(vz9, ba)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_toObj(vz9, ba) to new_toObj(vz9, ba).

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                        ↳ NonTerminationProof

                  ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_fromObj(vz6, ba) → new_fromObj(vz6, ba)

The TRS R consists of the following rules:none

s = new_fromObj(vz6, ba) evaluates to t =new_fromObj(vz6, ba)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_fromObj(vz6, ba) to new_fromObj(vz6, ba).

Haskell To QDPs

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

                    ↳ QDP

                      ↳ NonTerminationProof

Q DP problem:
The TRS P consists of the following rules:

new_fromObj(vz6, ba, []) → new_fromObj(vz6, ba, [])

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

The TRS P consists of the following rules:

new_fromObj(vz6, ba, []) → new_fromObj(vz6, ba, [])

The TRS R consists of the following rules:none

s = new_fromObj(vz6, ba, []) evaluates to t =new_fromObj(vz6, ba, [])

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_fromObj(vz6, ba, []) to new_fromObj(vz6, ba, []).