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

NO 1.5070000000000001 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

((catchHugsException :: IO a -> (HugsException -> IO a) -> IO a) :: IO a -> (HugsException -> IO a) -> IO a)

module Main where

import qualified Prelude

Lambda Reductions:
The following Lambda expression

\e→

case k e of
IO k' → k' f s

is transformed to

catchHugsException0 k f s e =

case k e of
IO k' → k' f s

The following Lambda expression

\fs→Hugs_Catch (m Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 k f s) f (s . fromObj)

is transformed to

catchHugsException1 m k f s = Hugs_Catch (m Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 k f s) f (s . fromObj)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

mainModule Main

((catchHugsException :: IO a -> (HugsException -> IO a) -> IO a) :: IO a -> (HugsException -> IO a) -> IO a)

module Main where

import qualified Prelude

Case Reductions:
The following Case expression

case k e of
IO k' → k' f s

is transformed to

catchHugsException00 f s (IO k') = k' f s

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

mainModule Main

((catchHugsException :: IO a -> (HugsException -> IO a) -> IO a) :: IO a -> (HugsException -> IO a) -> IO a)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

mainModule Main

((catchHugsException :: IO a -> (HugsException -> IO a) -> IO a) :: IO a -> (HugsException -> IO a) -> 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

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

mainModule Main

(catchHugsException :: IO a -> (HugsException -> IO a) -> IO a)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="catchHugsException",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="catchHugsException vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="catchHugsException vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];35[label="vx3/IO vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 5[label="",style="solid", color="burlywood", weight=3];
5[label="catchHugsException (IO vx30) vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="(IO $ catchHugsException1 vx30 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="IO (catchHugsException1 vx30 vx4)",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
8[label="catchHugsException1 vx30 vx4",fontsize=16,color="grey",shape="box"];8 -> 9[label="",style="dashed", color="grey", weight=3];
9[label="catchHugsException1 vx30 vx4 vx5",fontsize=16,color="grey",shape="box"];9 -> 10[label="",style="dashed", color="grey", weight=3];
10[label="catchHugsException1 vx30 vx4 vx5 vx6",fontsize=16,color="black",shape="triangle"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="Hugs_Catch (vx30 Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 vx4 vx5 vx6) vx5 (vx6 . fromObj)",fontsize=16,color="green",shape="box"];11 -> 12[label="",style="dashed", color="green", weight=3];
11 -> 13[label="",style="dashed", color="green", weight=3];
11 -> 14[label="",style="dashed", color="green", weight=3];
12[label="vx30 Hugs_Error (Hugs_Return . toObj)",fontsize=16,color="green",shape="box"];12 -> 15[label="",style="dashed", color="green", weight=3];
12 -> 16[label="",style="dashed", color="green", weight=3];
13[label="catchHugsException0 vx4 vx5 vx6",fontsize=16,color="grey",shape="box"];13 -> 17[label="",style="dashed", color="grey", weight=3];
14[label="vx6 . fromObj",fontsize=16,color="grey",shape="box"];14 -> 18[label="",style="dashed", color="grey", weight=3];
15[label="Hugs_Error",fontsize=16,color="green",shape="box"];16[label="Hugs_Return . toObj",fontsize=16,color="grey",shape="box"];16 -> 19[label="",style="dashed", color="grey", weight=3];
17[label="catchHugsException0 vx4 vx5 vx6 vx7",fontsize=16,color="black",shape="triangle"];17 -> 20[label="",style="solid", color="black", weight=3];
18[label="vx6 . fromObj",fontsize=16,color="black",shape="triangle"];18 -> 21[label="",style="solid", color="black", weight=3];
19[label="Hugs_Return . toObj",fontsize=16,color="black",shape="triangle"];19 -> 22[label="",style="solid", color="black", weight=3];
20 -> 23[label="",style="dashed", color="red", weight=0];
20[label="catchHugsException00 vx5 vx6 (vx4 vx7)",fontsize=16,color="magenta"];20 -> 24[label="",style="dashed", color="magenta", weight=3];
21[label="vx6 (fromObj vx8)",fontsize=16,color="green",shape="box"];21 -> 25[label="",style="dashed", color="green", weight=3];
22[label="Hugs_Return (toObj vx9)",fontsize=16,color="green",shape="box"];22 -> 26[label="",style="dashed", color="green", weight=3];
24[label="vx4 vx7",fontsize=16,color="green",shape="box"];24 -> 29[label="",style="dashed", color="green", weight=3];
23[label="catchHugsException00 vx5 vx6 vx10",fontsize=16,color="burlywood",shape="triangle"];37[label="vx10/IO vx100",fontsize=10,color="white",style="solid",shape="box"];23 -> 37[label="",style="solid", color="burlywood", weight=9];
37 -> 28[label="",style="solid", color="burlywood", weight=3];
25[label="fromObj vx8",fontsize=16,color="black",shape="triangle"];25 -> 30[label="",style="solid", color="black", weight=3];
26[label="toObj vx9",fontsize=16,color="black",shape="triangle"];26 -> 31[label="",style="solid", color="black", weight=3];
29[label="vx7",fontsize=16,color="green",shape="box"];28[label="catchHugsException00 vx5 vx6 (IO vx100)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
30 -> 25[label="",style="dashed", color="red", weight=0];
30[label="fromObj vx8",fontsize=16,color="magenta"];31 -> 26[label="",style="dashed", color="red", weight=0];
31[label="toObj vx9",fontsize=16,color="magenta"];32[label="vx100 vx5 vx6",fontsize=16,color="green",shape="box"];32 -> 33[label="",style="dashed", color="green", weight=3];
32 -> 34[label="",style="dashed", color="green", weight=3];
33[label="vx5",fontsize=16,color="green",shape="box"];34[label="vx6",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                        ↳ NonTerminationProof

                      ↳ QDP

                  ↳ Narrow

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

new_fromObj(vx8, ba) → new_fromObj(vx8, 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_fromObj(vx8, ba) → new_fromObj(vx8, ba)

The TRS R consists of the following rules:none

s = new_fromObj(vx8, ba) evaluates to t =new_fromObj(vx8, 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(vx8, ba) to new_fromObj(vx8, ba).

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                        ↳ NonTerminationProof

                  ↳ Narrow

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

new_toObj(vx9, ba) → new_toObj(vx9, ba)

The TRS R consists of the following rules:none

s = new_toObj(vx9, ba) evaluates to t =new_toObj(vx9, 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(vx9, ba) to new_toObj(vx9, ba).

Haskell To QDPs

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                        ↳ NonTerminationProof

                      ↳ QDP

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

new_fromObj(vx8, ba, []) → new_fromObj(vx8, 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(vx8, ba, []) → new_fromObj(vx8, ba, [])

The TRS R consists of the following rules:none

s = new_fromObj(vx8, ba, []) evaluates to t =new_fromObj(vx8, 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(vx8, ba, []) to new_fromObj(vx8, ba, []).

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

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

new_toObj(vx9, ba, []) → new_toObj(vx9, ba, [])

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.