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

YES 0.807 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule List

((intersperse :: a -> [a] -> [a]) :: a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

intersperse :: a -> [a] -> [a]

intersperse	_ []	=	[]
intersperse	_ (x : [])	=	x : []
intersperse	sep (x : xs)	=	x : sep : intersperse sep xs

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule List

((intersperse :: a -> [a] -> [a]) :: a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

intersperse :: a -> [a] -> [a]

intersperse	vw []	=	[]
intersperse	vx (x : [])	=	x : []
intersperse	sep (x : xs)	=	x : sep : intersperse sep xs

module Maybe where

import qualified List
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

          ↳ Narrow

mainModule List

(intersperse :: a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

intersperse :: a -> [a] -> [a]

intersperse	vw []	=	[]
intersperse	vx (x : [])	=	x : []
intersperse	sep (x : xs)	=	x : sep : intersperse sep xs

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="intersperse",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="intersperse wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="intersperse wu3 wu4",fontsize=16,color="burlywood",shape="triangle"];14[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 14[label="",style="solid", color="burlywood", weight=9];
14 -> 5[label="",style="solid", color="burlywood", weight=3];
15[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="intersperse wu3 (wu40 : wu41)",fontsize=16,color="burlywood",shape="box"];16[label="wu41/wu410 : wu411",fontsize=10,color="white",style="solid",shape="box"];5 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 7[label="",style="solid", color="burlywood", weight=3];
17[label="wu41/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 8[label="",style="solid", color="burlywood", weight=3];
6[label="intersperse wu3 []",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3];
7[label="intersperse wu3 (wu40 : wu410 : wu411)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
8[label="intersperse wu3 (wu40 : [])",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9[label="[]",fontsize=16,color="green",shape="box"];10[label="wu40 : wu3 : intersperse wu3 (wu410 : wu411)",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="green", weight=3];
11[label="wu40 : []",fontsize=16,color="green",shape="box"];12 -> 4[label="",style="dashed", color="red", weight=0];
12[label="intersperse wu3 (wu410 : wu411)",fontsize=16,color="magenta"];12 -> 13[label="",style="dashed", color="magenta", weight=3];
13[label="wu410 : wu411",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ QDPSizeChangeProof

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

new_intersperse(wu3, :(wu40, :(wu410, wu411)), ba) → new_intersperse(wu3, :(wu410, wu411), ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

new_intersperse(wu3, :(wu40, :(wu410, wu411)), ba) → new_intersperse(wu3, :(wu410, wu411), ba)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3