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

YES H-Termination proof of ../tpdb/FP/full_haskell/Prelude_realToFrac_8.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

((realToFrac :: Ratio Int -> Ratio Int) :: Ratio Int -> Ratio Int)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ NumRed

mainModule Main

((realToFrac :: Ratio Int -> Ratio Int) :: Ratio Int -> Ratio 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

(realToFrac :: Ratio Int -> Ratio Int)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="realToFrac\n",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="realToFrac vx3\n",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="fromRational . toRational\n",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fromRational (toRational vx3)\n",fontsize=16,color="burlywood",shape="box"];15[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="fromRational (toRational (vx30 :% vx31))\n",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="fromRational (toInteger vx30 :% toInteger vx31)\n",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="fromRational (Integer vx30 :% toInteger vx31)\n",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="fromRational (Integer vx30 :% Integer vx31)\n",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="fromInteger (Integer vx30) :% fromInteger (Integer vx31)\n",fontsize=16,color="green",shape="box"];10 -> 11[label="",style="dashed", color="green", weight=3];
10 -> 12[label="",style="dashed", color="green", weight=3];
11[label="fromInteger (Integer vx30)\n",fontsize=16,color="black",shape="triangle"];11 -> 13[label="",style="solid", color="black", weight=3];
12 -> 11[label="",style="dashed", color="red", weight=0];
12[label="fromInteger (Integer vx31)\n",fontsize=16,color="magenta"];12 -> 14[label="",style="dashed", color="magenta", weight=3];
13[label="vx30\n",fontsize=16,color="green",shape="box"];14[label="vx31\n",fontsize=16,color="green",shape="box"];}