H-Termination proof of ../tpdb/FP/full_haskell/Prelude_succ

YES H-Termination proof of ../tpdb/FP/full_haskell/Prelude_succ_4.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

((succ :: Int -> Int) :: Int -> Int)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ NumRed

mainModule Main

((succ :: Int -> Int) :: Int -> Int)

module Main where

import qualified Prelude

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ NumRed

        ↳ HASKELL

          ↳ Narrow

mainModule Main

(succ :: Int -> Int)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="succ\n",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="succ vx3\n",fontsize=16,color="burlywood",shape="triangle"];14[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 14[label="",style="solid", color="burlywood", weight=9];
14 -> 4[label="",style="solid", color="burlywood", weight=3];
15[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="succ (Pos vx30)\n",fontsize=16,color="burlywood",shape="box"];16[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 6[label="",style="solid", color="burlywood", weight=3];
17[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 7[label="",style="solid", color="burlywood", weight=3];
5[label="succ (Neg vx30)\n",fontsize=16,color="burlywood",shape="box"];18[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
18 -> 8[label="",style="solid", color="burlywood", weight=3];
19[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 9[label="",style="solid", color="burlywood", weight=3];
6[label="succ (Pos (Succ vx300))\n",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3];
7[label="succ (Pos Zero)\n",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
8[label="succ (Neg (Succ vx300))\n",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="succ (Neg Zero)\n",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="Pos (Succ (Succ vx300))\n",fontsize=16,color="green",shape="box"];11[label="Pos (Succ Zero)\n",fontsize=16,color="green",shape="box"];12[label="Neg vx300\n",fontsize=16,color="green",shape="box"];13[label="Pos (Succ Zero)\n",fontsize=16,color="green",shape="box"];}