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

YES 0.919 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

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

module List where

import qualified Maybe
import qualified Prelude

tails :: [a] -> [[a]]

tails	[]	=	[] : []
tails	xxs@(_ : xs)	=	xxs : tails xs

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.
Binding Reductions:
The bind variable of the following binding Pattern

xxs@(vx : vy)

is replaced by the following term

vx : vy

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

tails :: [a] -> [[a]]

tails	[]	=	[] : []
tails	(vx : vy)	=	(vx : vy) : tails vy

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

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

module List where

import qualified Maybe
import qualified Prelude

tails :: [a] -> [[a]]

tails	[]	=	[] : []
tails	(vx : vy)	=	(vx : vy) : tails vy

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="tails",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="tails wv3",fontsize=16,color="burlywood",shape="triangle"];10[label="wv3/wv30 : wv31",fontsize=10,color="white",style="solid",shape="box"];3 -> 10[label="",style="solid", color="burlywood", weight=9];
10 -> 4[label="",style="solid", color="burlywood", weight=3];
11[label="wv3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 11[label="",style="solid", color="burlywood", weight=9];
11 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="tails (wv30 : wv31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
5[label="tails []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="(wv30 : wv31) : tails wv31",fontsize=16,color="green",shape="box"];6 -> 8[label="",style="dashed", color="green", weight=3];
7[label="[] : []",fontsize=16,color="green",shape="box"];8 -> 3[label="",style="dashed", color="red", weight=0];
8[label="tails wv31",fontsize=16,color="magenta"];8 -> 9[label="",style="dashed", color="magenta", weight=3];
9[label="wv31",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_tails(:(wv30, wv31), ba) → new_tails(wv31, 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_tails(:(wv30, wv31), ba) → new_tails(wv31, ba)
The graph contains the following edges 1 > 1, 2 >= 2