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

MAYBE 1.811 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could not be shown:

↳ HASKELL

  ↳ BR

mainModule Main

((minBound :: Bounded a => a) :: Bounded a => a)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((minBound :: Bounded a => a) :: Bounded a => 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

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

mainModule Main

((minBound :: Bounded a => a) :: Bounded a => a)

module Main where

import qualified Prelude

Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

              ↳ Narrow

mainModule Main

(minBound :: Bounded a => a)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="minBound\n  Bounded a",fontsize=16,color="blue",shape="box"];14[label="minBound :: Ordering",fontsize=10,color="white",style="solid",shape="box"];1 -> 14[label="",style="solid", color="blue", weight=9];
14 -> 3[label="",style="solid", color="blue", weight=3];
15[label="minBound :: ()",fontsize=10,color="white",style="solid",shape="box"];1 -> 15[label="",style="solid", color="blue", weight=9];
15 -> 4[label="",style="solid", color="blue", weight=3];
16[label="minBound :: Char",fontsize=10,color="white",style="solid",shape="box"];1 -> 16[label="",style="solid", color="blue", weight=9];
16 -> 5[label="",style="solid", color="blue", weight=3];
17[label="minBound :: Int",fontsize=10,color="white",style="solid",shape="box"];1 -> 17[label="",style="solid", color="blue", weight=9];
17 -> 6[label="",style="solid", color="blue", weight=3];
18[label="minBound :: Bool",fontsize=10,color="white",style="solid",shape="box"];1 -> 18[label="",style="solid", color="blue", weight=9];
18 -> 7[label="",style="solid", color="blue", weight=3];
3[label="minBound",fontsize=16,color="black",shape="box"];3 -> 8[label="",style="solid", color="black", weight=3];
4[label="minBound",fontsize=16,color="black",shape="box"];4 -> 9[label="",style="solid", color="black", weight=3];
5[label="minBound",fontsize=16,color="black",shape="box"];5 -> 10[label="",style="solid", color="black", weight=3];
6[label="minBound",fontsize=16,color="black",shape="box"];6 -> 11[label="",style="solid", color="black", weight=3];
7[label="minBound",fontsize=16,color="black",shape="box"];7 -> 12[label="",style="solid", color="black", weight=3];
8[label="LT",fontsize=16,color="green",shape="box"];9[label="()",fontsize=16,color="green",shape="box"];10[label="Char Zero",fontsize=16,color="green",shape="box"];11[label="primMinInt",fontsize=16,color="black",shape="triangle"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="False",fontsize=16,color="green",shape="box"];13 -> 11[label="",style="dashed", color="red", weight=0];
13[label="primMinInt",fontsize=16,color="magenta"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ QDP

                  ↳ NonTerminationProof

              ↳ Narrow

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

new_primMinInt → new_primMinInt

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_primMinInt → new_primMinInt

The TRS R consists of the following rules:none

s = new_primMinInt evaluates to t =new_primMinInt

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_primMinInt to new_primMinInt.

Haskell To QDPs

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

              ↳ Narrow

                ↳ QDP

                  ↳ NonTerminationProof

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

new_primMinInt([]) → new_primMinInt([])

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_primMinInt([]) → new_primMinInt([])

The TRS R consists of the following rules:none

s = new_primMinInt([]) evaluates to t =new_primMinInt([])

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_primMinInt([]) to new_primMinInt([]).