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

YES 1.306 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

((elem :: Eq a => a -> [a] -> Bool) :: Eq a => a -> [a] -> Bool)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((elem :: Eq a => a -> [a] -> Bool) :: Eq a => a -> [a] -> Bool)

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

          ↳ Narrow

mainModule Main

(elem :: Eq a => a -> [a] -> Bool)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="elem\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="elem xv3\n  Eq a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="elem xv3 xv4\n  Eq a",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="any . (==)\n  Eq a",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="any ((==) xv3) xv4\n  Eq a",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="or . map ((==) xv3)\n  Eq a",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="or (map ((==) xv3) xv4)\n  Eq a",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="foldr (||) False (map ((==) xv3) xv4)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];697[label="xv4/xv40 : xv41",fontsize=10,color="white",style="solid",shape="box"];9 -> 697[label="",style="solid", color="burlywood", weight=9];
697 -> 10[label="",style="solid", color="burlywood", weight=3];
698[label="xv4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 698[label="",style="solid", color="burlywood", weight=9];
698 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="foldr (||) False (map ((==) xv3) (xv40 : xv41))\n  Eq a",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="foldr (||) False (map ((==) xv3) [])\n  Eq a",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="foldr (||) False (((==) xv3 xv40) : map ((==) xv3) xv41)\n  Eq a",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="foldr (||) False []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14 -> 19[label="",style="dashed", color="red", weight=0];
14[label="(||) (==) xv3 xv40 foldr (||) False (map ((==) xv3) xv41)\n  Eq a",fontsize=16,color="magenta"];14 -> 20[label="",style="dashed", color="magenta", weight=3];
14 -> 21[label="",style="dashed", color="magenta", weight=3];
15[label="False",fontsize=16,color="green",shape="box"];20 -> 9[label="",style="dashed", color="red", weight=0];
20[label="foldr (||) False (map ((==) xv3) xv41)\n  Eq a",fontsize=16,color="magenta"];20 -> 24[label="",style="dashed", color="magenta", weight=3];
21[label="(==) xv3 xv40\n  Eq a",fontsize=16,color="blue",shape="box"];701[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 701[label="",style="solid", color="blue", weight=9];
701 -> 25[label="",style="solid", color="blue", weight=3];
702[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 702[label="",style="solid", color="blue", weight=9];
702 -> 26[label="",style="solid", color="blue", weight=3];
703[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 703[label="",style="solid", color="blue", weight=9];
703 -> 27[label="",style="solid", color="blue", weight=3];
704[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 704[label="",style="solid", color="blue", weight=9];
704 -> 28[label="",style="solid", color="blue", weight=3];
705[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 705[label="",style="solid", color="blue", weight=9];
705 -> 29[label="",style="solid", color="blue", weight=3];
706[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 706[label="",style="solid", color="blue", weight=9];
706 -> 30[label="",style="solid", color="blue", weight=3];
707[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 707[label="",style="solid", color="blue", weight=9];
707 -> 31[label="",style="solid", color="blue", weight=3];
708[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 708[label="",style="solid", color="blue", weight=9];
708 -> 32[label="",style="solid", color="blue", weight=3];
709[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 709[label="",style="solid", color="blue", weight=9];
709 -> 33[label="",style="solid", color="blue", weight=3];
710[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 710[label="",style="solid", color="blue", weight=9];
710 -> 34[label="",style="solid", color="blue", weight=3];
711[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 711[label="",style="solid", color="blue", weight=9];
711 -> 35[label="",style="solid", color="blue", weight=3];
712[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 712[label="",style="solid", color="blue", weight=9];
712 -> 36[label="",style="solid", color="blue", weight=3];
713[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 713[label="",style="solid", color="blue", weight=9];
713 -> 37[label="",style="solid", color="blue", weight=3];
714[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 714[label="",style="solid", color="blue", weight=9];
714 -> 38[label="",style="solid", color="blue", weight=3];
19[label="(||) xv9 xv10",fontsize=16,color="burlywood",shape="triangle"];715[label="xv9/False",fontsize=10,color="white",style="solid",shape="box"];19 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 39[label="",style="solid", color="burlywood", weight=3];
716[label="xv9/True",fontsize=10,color="white",style="solid",shape="box"];19 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 40[label="",style="solid", color="burlywood", weight=3];
24[label="xv41\n  Eq a",fontsize=16,color="green",shape="box"];25[label="(==) xv3 xv40",fontsize=16,color="black",shape="triangle"];25 -> 41[label="",style="solid", color="black", weight=3];
26[label="(==) xv3 xv40",fontsize=16,color="burlywood",shape="triangle"];717[label="xv3/()",fontsize=10,color="white",style="solid",shape="box"];26 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 42[label="",style="solid", color="burlywood", weight=3];
27[label="(==) xv3 xv40",fontsize=16,color="burlywood",shape="triangle"];718[label="xv3/Integer xv30",fontsize=10,color="white",style="solid",shape="box"];27 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 43[label="",style="solid", color="burlywood", weight=3];
28[label="(==) xv3 xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];719[label="xv3/(xv30,xv31)",fontsize=10,color="white",style="solid",shape="box"];28 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 44[label="",style="solid", color="burlywood", weight=3];
29[label="(==) xv3 xv40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];720[label="xv3/Nothing",fontsize=10,color="white",style="solid",shape="box"];29 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 45[label="",style="solid", color="burlywood", weight=3];
721[label="xv3/Just xv30",fontsize=10,color="white",style="solid",shape="box"];29 -> 721[label="",style="solid", color="burlywood", weight=9];
721 -> 46[label="",style="solid", color="burlywood", weight=3];
30[label="(==) xv3 xv40",fontsize=16,color="black",shape="triangle"];30 -> 47[label="",style="solid", color="black", weight=3];
31[label="(==) xv3 xv40\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];722[label="xv3/(xv30,xv31,xv32)",fontsize=10,color="white",style="solid",shape="box"];31 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 48[label="",style="solid", color="burlywood", weight=3];
32[label="(==) xv3 xv40",fontsize=16,color="burlywood",shape="triangle"];723[label="xv3/LT",fontsize=10,color="white",style="solid",shape="box"];32 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 49[label="",style="solid", color="burlywood", weight=3];
724[label="xv3/EQ",fontsize=10,color="white",style="solid",shape="box"];32 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 50[label="",style="solid", color="burlywood", weight=3];
725[label="xv3/GT",fontsize=10,color="white",style="solid",shape="box"];32 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 51[label="",style="solid", color="burlywood", weight=3];
33[label="(==) xv3 xv40",fontsize=16,color="black",shape="triangle"];33 -> 52[label="",style="solid", color="black", weight=3];
34[label="(==) xv3 xv40",fontsize=16,color="burlywood",shape="triangle"];726[label="xv3/False",fontsize=10,color="white",style="solid",shape="box"];34 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 53[label="",style="solid", color="burlywood", weight=3];
727[label="xv3/True",fontsize=10,color="white",style="solid",shape="box"];34 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 54[label="",style="solid", color="burlywood", weight=3];
35[label="(==) xv3 xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];728[label="xv3/Left xv30",fontsize=10,color="white",style="solid",shape="box"];35 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 55[label="",style="solid", color="burlywood", weight=3];
729[label="xv3/Right xv30",fontsize=10,color="white",style="solid",shape="box"];35 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 56[label="",style="solid", color="burlywood", weight=3];
36[label="(==) xv3 xv40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];730[label="xv3/xv30 : xv31",fontsize=10,color="white",style="solid",shape="box"];36 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 57[label="",style="solid", color="burlywood", weight=3];
731[label="xv3/[]",fontsize=10,color="white",style="solid",shape="box"];36 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 58[label="",style="solid", color="burlywood", weight=3];
37[label="(==) xv3 xv40",fontsize=16,color="black",shape="triangle"];37 -> 59[label="",style="solid", color="black", weight=3];
38[label="(==) xv3 xv40\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];732[label="xv3/xv30 :% xv31",fontsize=10,color="white",style="solid",shape="box"];38 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 60[label="",style="solid", color="burlywood", weight=3];
39[label="(||) False xv10",fontsize=16,color="black",shape="box"];39 -> 61[label="",style="solid", color="black", weight=3];
40[label="(||) True xv10",fontsize=16,color="black",shape="box"];40 -> 62[label="",style="solid", color="black", weight=3];
41[label="primEqInt xv3 xv40",fontsize=16,color="burlywood",shape="triangle"];733[label="xv3/Pos xv30",fontsize=10,color="white",style="solid",shape="box"];41 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 63[label="",style="solid", color="burlywood", weight=3];
734[label="xv3/Neg xv30",fontsize=10,color="white",style="solid",shape="box"];41 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 64[label="",style="solid", color="burlywood", weight=3];
42[label="(==) () xv40",fontsize=16,color="burlywood",shape="box"];735[label="xv40/()",fontsize=10,color="white",style="solid",shape="box"];42 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 65[label="",style="solid", color="burlywood", weight=3];
43[label="(==) Integer xv30 xv40",fontsize=16,color="burlywood",shape="box"];736[label="xv40/Integer xv400",fontsize=10,color="white",style="solid",shape="box"];43 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 66[label="",style="solid", color="burlywood", weight=3];
44[label="(==) (xv30,xv31) xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];737[label="xv40/(xv400,xv401)",fontsize=10,color="white",style="solid",shape="box"];44 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 67[label="",style="solid", color="burlywood", weight=3];
45[label="(==) Nothing xv40\n  Eq a",fontsize=16,color="burlywood",shape="box"];738[label="xv40/Nothing",fontsize=10,color="white",style="solid",shape="box"];45 -> 738[label="",style="solid", color="burlywood", weight=9];
738 -> 68[label="",style="solid", color="burlywood", weight=3];
739[label="xv40/Just xv400",fontsize=10,color="white",style="solid",shape="box"];45 -> 739[label="",style="solid", color="burlywood", weight=9];
739 -> 69[label="",style="solid", color="burlywood", weight=3];
46[label="(==) Just xv30 xv40\n  Eq a",fontsize=16,color="burlywood",shape="box"];740[label="xv40/Nothing",fontsize=10,color="white",style="solid",shape="box"];46 -> 740[label="",style="solid", color="burlywood", weight=9];
740 -> 70[label="",style="solid", color="burlywood", weight=3];
741[label="xv40/Just xv400",fontsize=10,color="white",style="solid",shape="box"];46 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 71[label="",style="solid", color="burlywood", weight=3];
47[label="primEqChar xv3 xv40",fontsize=16,color="burlywood",shape="box"];742[label="xv3/Char xv30",fontsize=10,color="white",style="solid",shape="box"];47 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 72[label="",style="solid", color="burlywood", weight=3];
48[label="(==) (xv30,xv31,xv32) xv40\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];743[label="xv40/(xv400,xv401,xv402)",fontsize=10,color="white",style="solid",shape="box"];48 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 73[label="",style="solid", color="burlywood", weight=3];
49[label="(==) LT xv40",fontsize=16,color="burlywood",shape="box"];744[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];49 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 74[label="",style="solid", color="burlywood", weight=3];
745[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];49 -> 745[label="",style="solid", color="burlywood", weight=9];
745 -> 75[label="",style="solid", color="burlywood", weight=3];
746[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];49 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 76[label="",style="solid", color="burlywood", weight=3];
50[label="(==) EQ xv40",fontsize=16,color="burlywood",shape="box"];747[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];50 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 77[label="",style="solid", color="burlywood", weight=3];
748[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];50 -> 748[label="",style="solid", color="burlywood", weight=9];
748 -> 78[label="",style="solid", color="burlywood", weight=3];
749[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];50 -> 749[label="",style="solid", color="burlywood", weight=9];
749 -> 79[label="",style="solid", color="burlywood", weight=3];
51[label="(==) GT xv40",fontsize=16,color="burlywood",shape="box"];750[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];51 -> 750[label="",style="solid", color="burlywood", weight=9];
750 -> 80[label="",style="solid", color="burlywood", weight=3];
751[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];51 -> 751[label="",style="solid", color="burlywood", weight=9];
751 -> 81[label="",style="solid", color="burlywood", weight=3];
752[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];51 -> 752[label="",style="solid", color="burlywood", weight=9];
752 -> 82[label="",style="solid", color="burlywood", weight=3];
52[label="primEqDouble xv3 xv40",fontsize=16,color="burlywood",shape="box"];753[label="xv3/Double xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];52 -> 753[label="",style="solid", color="burlywood", weight=9];
753 -> 83[label="",style="solid", color="burlywood", weight=3];
53[label="(==) False xv40",fontsize=16,color="burlywood",shape="box"];754[label="xv40/False",fontsize=10,color="white",style="solid",shape="box"];53 -> 754[label="",style="solid", color="burlywood", weight=9];
754 -> 84[label="",style="solid", color="burlywood", weight=3];
755[label="xv40/True",fontsize=10,color="white",style="solid",shape="box"];53 -> 755[label="",style="solid", color="burlywood", weight=9];
755 -> 85[label="",style="solid", color="burlywood", weight=3];
54[label="(==) True xv40",fontsize=16,color="burlywood",shape="box"];756[label="xv40/False",fontsize=10,color="white",style="solid",shape="box"];54 -> 756[label="",style="solid", color="burlywood", weight=9];
756 -> 86[label="",style="solid", color="burlywood", weight=3];
757[label="xv40/True",fontsize=10,color="white",style="solid",shape="box"];54 -> 757[label="",style="solid", color="burlywood", weight=9];
757 -> 87[label="",style="solid", color="burlywood", weight=3];
55[label="(==) Left xv30 xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];758[label="xv40/Left xv400",fontsize=10,color="white",style="solid",shape="box"];55 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 88[label="",style="solid", color="burlywood", weight=3];
759[label="xv40/Right xv400",fontsize=10,color="white",style="solid",shape="box"];55 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 89[label="",style="solid", color="burlywood", weight=3];
56[label="(==) Right xv30 xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];760[label="xv40/Left xv400",fontsize=10,color="white",style="solid",shape="box"];56 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 90[label="",style="solid", color="burlywood", weight=3];
761[label="xv40/Right xv400",fontsize=10,color="white",style="solid",shape="box"];56 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 91[label="",style="solid", color="burlywood", weight=3];
57[label="(==) xv30 : xv31 xv40\n  Eq a",fontsize=16,color="burlywood",shape="box"];762[label="xv40/xv400 : xv401",fontsize=10,color="white",style="solid",shape="box"];57 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 92[label="",style="solid", color="burlywood", weight=3];
763[label="xv40/[]",fontsize=10,color="white",style="solid",shape="box"];57 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 93[label="",style="solid", color="burlywood", weight=3];
58[label="(==) [] xv40\n  Eq a",fontsize=16,color="burlywood",shape="box"];764[label="xv40/xv400 : xv401",fontsize=10,color="white",style="solid",shape="box"];58 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 94[label="",style="solid", color="burlywood", weight=3];
765[label="xv40/[]",fontsize=10,color="white",style="solid",shape="box"];58 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 95[label="",style="solid", color="burlywood", weight=3];
59[label="primEqFloat xv3 xv40",fontsize=16,color="burlywood",shape="box"];766[label="xv3/Float xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];59 -> 766[label="",style="solid", color="burlywood", weight=9];
766 -> 96[label="",style="solid", color="burlywood", weight=3];
60[label="(==) xv30 :% xv31 xv40\n  Integral a",fontsize=16,color="burlywood",shape="box"];767[label="xv40/xv400 :% xv401",fontsize=10,color="white",style="solid",shape="box"];60 -> 767[label="",style="solid", color="burlywood", weight=9];
767 -> 97[label="",style="solid", color="burlywood", weight=3];
61[label="xv10",fontsize=16,color="green",shape="box"];62[label="True",fontsize=16,color="green",shape="box"];63[label="primEqInt (Pos xv30) xv40",fontsize=16,color="burlywood",shape="box"];768[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];63 -> 768[label="",style="solid", color="burlywood", weight=9];
768 -> 98[label="",style="solid", color="burlywood", weight=3];
769[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 769[label="",style="solid", color="burlywood", weight=9];
769 -> 99[label="",style="solid", color="burlywood", weight=3];
64[label="primEqInt (Neg xv30) xv40",fontsize=16,color="burlywood",shape="box"];770[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];64 -> 770[label="",style="solid", color="burlywood", weight=9];
770 -> 100[label="",style="solid", color="burlywood", weight=3];
771[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 771[label="",style="solid", color="burlywood", weight=9];
771 -> 101[label="",style="solid", color="burlywood", weight=3];
65[label="(==) () ()",fontsize=16,color="black",shape="box"];65 -> 102[label="",style="solid", color="black", weight=3];
66[label="(==) Integer xv30 Integer xv400",fontsize=16,color="black",shape="box"];66 -> 103[label="",style="solid", color="black", weight=3];
67[label="(==) (xv30,xv31) (xv400,xv401)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];67 -> 104[label="",style="solid", color="black", weight=3];
68[label="(==) Nothing Nothing\n  Eq a",fontsize=16,color="black",shape="box"];68 -> 105[label="",style="solid", color="black", weight=3];
69[label="(==) Nothing Just xv400\n  Eq a",fontsize=16,color="black",shape="box"];69 -> 106[label="",style="solid", color="black", weight=3];
70[label="(==) Just xv30 Nothing\n  Eq a",fontsize=16,color="black",shape="box"];70 -> 107[label="",style="solid", color="black", weight=3];
71[label="(==) Just xv30 Just xv400\n  Eq a",fontsize=16,color="black",shape="box"];71 -> 108[label="",style="solid", color="black", weight=3];
72[label="primEqChar (Char xv30) xv40",fontsize=16,color="burlywood",shape="box"];772[label="xv40/Char xv400",fontsize=10,color="white",style="solid",shape="box"];72 -> 772[label="",style="solid", color="burlywood", weight=9];
772 -> 109[label="",style="solid", color="burlywood", weight=3];
73[label="(==) (xv30,xv31,xv32) (xv400,xv401,xv402)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];73 -> 110[label="",style="solid", color="black", weight=3];
74[label="(==) LT LT",fontsize=16,color="black",shape="box"];74 -> 111[label="",style="solid", color="black", weight=3];
75[label="(==) LT EQ",fontsize=16,color="black",shape="box"];75 -> 112[label="",style="solid", color="black", weight=3];
76[label="(==) LT GT",fontsize=16,color="black",shape="box"];76 -> 113[label="",style="solid", color="black", weight=3];
77[label="(==) EQ LT",fontsize=16,color="black",shape="box"];77 -> 114[label="",style="solid", color="black", weight=3];
78[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];78 -> 115[label="",style="solid", color="black", weight=3];
79[label="(==) EQ GT",fontsize=16,color="black",shape="box"];79 -> 116[label="",style="solid", color="black", weight=3];
80[label="(==) GT LT",fontsize=16,color="black",shape="box"];80 -> 117[label="",style="solid", color="black", weight=3];
81[label="(==) GT EQ",fontsize=16,color="black",shape="box"];81 -> 118[label="",style="solid", color="black", weight=3];
82[label="(==) GT GT",fontsize=16,color="black",shape="box"];82 -> 119[label="",style="solid", color="black", weight=3];
83[label="primEqDouble (Double xv30 xv31) xv40",fontsize=16,color="burlywood",shape="box"];773[label="xv40/Double xv400 xv401",fontsize=10,color="white",style="solid",shape="box"];83 -> 773[label="",style="solid", color="burlywood", weight=9];
773 -> 120[label="",style="solid", color="burlywood", weight=3];
84[label="(==) False False",fontsize=16,color="black",shape="box"];84 -> 121[label="",style="solid", color="black", weight=3];
85[label="(==) False True",fontsize=16,color="black",shape="box"];85 -> 122[label="",style="solid", color="black", weight=3];
86[label="(==) True False",fontsize=16,color="black",shape="box"];86 -> 123[label="",style="solid", color="black", weight=3];
87[label="(==) True True",fontsize=16,color="black",shape="box"];87 -> 124[label="",style="solid", color="black", weight=3];
88[label="(==) Left xv30 Left xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];88 -> 125[label="",style="solid", color="black", weight=3];
89[label="(==) Left xv30 Right xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];89 -> 126[label="",style="solid", color="black", weight=3];
90[label="(==) Right xv30 Left xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];90 -> 127[label="",style="solid", color="black", weight=3];
91[label="(==) Right xv30 Right xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];91 -> 128[label="",style="solid", color="black", weight=3];
92[label="(==) xv30 : xv31 xv400 : xv401\n  Eq a",fontsize=16,color="black",shape="box"];92 -> 129[label="",style="solid", color="black", weight=3];
93[label="(==) xv30 : xv31 []\n  Eq a",fontsize=16,color="black",shape="box"];93 -> 130[label="",style="solid", color="black", weight=3];
94[label="(==) [] xv400 : xv401\n  Eq a",fontsize=16,color="black",shape="box"];94 -> 131[label="",style="solid", color="black", weight=3];
95[label="(==) [] []\n  Eq a",fontsize=16,color="black",shape="box"];95 -> 132[label="",style="solid", color="black", weight=3];
96[label="primEqFloat (Float xv30 xv31) xv40",fontsize=16,color="burlywood",shape="box"];774[label="xv40/Float xv400 xv401",fontsize=10,color="white",style="solid",shape="box"];96 -> 774[label="",style="solid", color="burlywood", weight=9];
774 -> 133[label="",style="solid", color="burlywood", weight=3];
97[label="(==) xv30 :% xv31 xv400 :% xv401\n  Integral a",fontsize=16,color="black",shape="box"];97 -> 134[label="",style="solid", color="black", weight=3];
98[label="primEqInt (Pos (Succ xv300)) xv40",fontsize=16,color="burlywood",shape="box"];775[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];98 -> 775[label="",style="solid", color="burlywood", weight=9];
775 -> 135[label="",style="solid", color="burlywood", weight=3];
776[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];98 -> 776[label="",style="solid", color="burlywood", weight=9];
776 -> 136[label="",style="solid", color="burlywood", weight=3];
99[label="primEqInt (Pos Zero) xv40",fontsize=16,color="burlywood",shape="box"];777[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];99 -> 777[label="",style="solid", color="burlywood", weight=9];
777 -> 137[label="",style="solid", color="burlywood", weight=3];
778[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];99 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 138[label="",style="solid", color="burlywood", weight=3];
100[label="primEqInt (Neg (Succ xv300)) xv40",fontsize=16,color="burlywood",shape="box"];779[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];100 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 139[label="",style="solid", color="burlywood", weight=3];
780[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];100 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 140[label="",style="solid", color="burlywood", weight=3];
101[label="primEqInt (Neg Zero) xv40",fontsize=16,color="burlywood",shape="box"];781[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];101 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 141[label="",style="solid", color="burlywood", weight=3];
782[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];101 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 142[label="",style="solid", color="burlywood", weight=3];
102[label="True",fontsize=16,color="green",shape="box"];103 -> 41[label="",style="dashed", color="red", weight=0];
103[label="primEqInt xv30 xv400",fontsize=16,color="magenta"];103 -> 143[label="",style="dashed", color="magenta", weight=3];
103 -> 144[label="",style="dashed", color="magenta", weight=3];
104 -> 239[label="",style="dashed", color="red", weight=0];
104[label="xv30 == xv400 && xv31 == xv401\n  Eq a  Eq b",fontsize=16,color="magenta"];104 -> 240[label="",style="dashed", color="magenta", weight=3];
104 -> 241[label="",style="dashed", color="magenta", weight=3];
105[label="True",fontsize=16,color="green",shape="box"];106[label="False",fontsize=16,color="green",shape="box"];107[label="False",fontsize=16,color="green",shape="box"];108[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];785[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 785[label="",style="solid", color="blue", weight=9];
785 -> 155[label="",style="solid", color="blue", weight=3];
786[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 786[label="",style="solid", color="blue", weight=9];
786 -> 156[label="",style="solid", color="blue", weight=3];
787[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 787[label="",style="solid", color="blue", weight=9];
787 -> 157[label="",style="solid", color="blue", weight=3];
788[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 788[label="",style="solid", color="blue", weight=9];
788 -> 158[label="",style="solid", color="blue", weight=3];
789[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 789[label="",style="solid", color="blue", weight=9];
789 -> 159[label="",style="solid", color="blue", weight=3];
790[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 790[label="",style="solid", color="blue", weight=9];
790 -> 160[label="",style="solid", color="blue", weight=3];
791[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 791[label="",style="solid", color="blue", weight=9];
791 -> 161[label="",style="solid", color="blue", weight=3];
792[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 792[label="",style="solid", color="blue", weight=9];
792 -> 162[label="",style="solid", color="blue", weight=3];
793[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 793[label="",style="solid", color="blue", weight=9];
793 -> 163[label="",style="solid", color="blue", weight=3];
794[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 794[label="",style="solid", color="blue", weight=9];
794 -> 164[label="",style="solid", color="blue", weight=3];
795[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 795[label="",style="solid", color="blue", weight=9];
795 -> 165[label="",style="solid", color="blue", weight=3];
796[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 796[label="",style="solid", color="blue", weight=9];
796 -> 166[label="",style="solid", color="blue", weight=3];
797[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 797[label="",style="solid", color="blue", weight=9];
797 -> 167[label="",style="solid", color="blue", weight=3];
798[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];108 -> 798[label="",style="solid", color="blue", weight=9];
798 -> 168[label="",style="solid", color="blue", weight=3];
109[label="primEqChar (Char xv30) (Char xv400)",fontsize=16,color="black",shape="box"];109 -> 169[label="",style="solid", color="black", weight=3];
110 -> 239[label="",style="dashed", color="red", weight=0];
110[label="xv30 == xv400 && xv31 == xv401 && xv32 == xv402\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];110 -> 242[label="",style="dashed", color="magenta", weight=3];
110 -> 243[label="",style="dashed", color="magenta", weight=3];
111[label="True",fontsize=16,color="green",shape="box"];112[label="False",fontsize=16,color="green",shape="box"];113[label="False",fontsize=16,color="green",shape="box"];114[label="False",fontsize=16,color="green",shape="box"];115[label="True",fontsize=16,color="green",shape="box"];116[label="False",fontsize=16,color="green",shape="box"];117[label="False",fontsize=16,color="green",shape="box"];118[label="False",fontsize=16,color="green",shape="box"];119[label="True",fontsize=16,color="green",shape="box"];120[label="primEqDouble (Double xv30 xv31) (Double xv400 xv401)",fontsize=16,color="black",shape="box"];120 -> 181[label="",style="solid", color="black", weight=3];
121[label="True",fontsize=16,color="green",shape="box"];122[label="False",fontsize=16,color="green",shape="box"];123[label="False",fontsize=16,color="green",shape="box"];124[label="True",fontsize=16,color="green",shape="box"];125[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];800[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 800[label="",style="solid", color="blue", weight=9];
800 -> 182[label="",style="solid", color="blue", weight=3];
801[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 801[label="",style="solid", color="blue", weight=9];
801 -> 183[label="",style="solid", color="blue", weight=3];
802[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 802[label="",style="solid", color="blue", weight=9];
802 -> 184[label="",style="solid", color="blue", weight=3];
803[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 803[label="",style="solid", color="blue", weight=9];
803 -> 185[label="",style="solid", color="blue", weight=3];
804[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 804[label="",style="solid", color="blue", weight=9];
804 -> 186[label="",style="solid", color="blue", weight=3];
805[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 805[label="",style="solid", color="blue", weight=9];
805 -> 187[label="",style="solid", color="blue", weight=3];
806[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 806[label="",style="solid", color="blue", weight=9];
806 -> 188[label="",style="solid", color="blue", weight=3];
807[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 807[label="",style="solid", color="blue", weight=9];
807 -> 189[label="",style="solid", color="blue", weight=3];
808[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 808[label="",style="solid", color="blue", weight=9];
808 -> 190[label="",style="solid", color="blue", weight=3];
809[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 809[label="",style="solid", color="blue", weight=9];
809 -> 191[label="",style="solid", color="blue", weight=3];
810[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 810[label="",style="solid", color="blue", weight=9];
810 -> 192[label="",style="solid", color="blue", weight=3];
811[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 811[label="",style="solid", color="blue", weight=9];
811 -> 193[label="",style="solid", color="blue", weight=3];
812[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 812[label="",style="solid", color="blue", weight=9];
812 -> 194[label="",style="solid", color="blue", weight=3];
813[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 813[label="",style="solid", color="blue", weight=9];
813 -> 195[label="",style="solid", color="blue", weight=3];
126[label="False",fontsize=16,color="green",shape="box"];127[label="False",fontsize=16,color="green",shape="box"];128[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];814[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 814[label="",style="solid", color="blue", weight=9];
814 -> 196[label="",style="solid", color="blue", weight=3];
815[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 815[label="",style="solid", color="blue", weight=9];
815 -> 197[label="",style="solid", color="blue", weight=3];
816[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 816[label="",style="solid", color="blue", weight=9];
816 -> 198[label="",style="solid", color="blue", weight=3];
817[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 817[label="",style="solid", color="blue", weight=9];
817 -> 199[label="",style="solid", color="blue", weight=3];
818[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 818[label="",style="solid", color="blue", weight=9];
818 -> 200[label="",style="solid", color="blue", weight=3];
819[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 819[label="",style="solid", color="blue", weight=9];
819 -> 201[label="",style="solid", color="blue", weight=3];
820[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 820[label="",style="solid", color="blue", weight=9];
820 -> 202[label="",style="solid", color="blue", weight=3];
821[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 821[label="",style="solid", color="blue", weight=9];
821 -> 203[label="",style="solid", color="blue", weight=3];
822[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 822[label="",style="solid", color="blue", weight=9];
822 -> 204[label="",style="solid", color="blue", weight=3];
823[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 823[label="",style="solid", color="blue", weight=9];
823 -> 205[label="",style="solid", color="blue", weight=3];
824[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 824[label="",style="solid", color="blue", weight=9];
824 -> 206[label="",style="solid", color="blue", weight=3];
825[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 825[label="",style="solid", color="blue", weight=9];
825 -> 207[label="",style="solid", color="blue", weight=3];
826[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 826[label="",style="solid", color="blue", weight=9];
826 -> 208[label="",style="solid", color="blue", weight=3];
827[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 827[label="",style="solid", color="blue", weight=9];
827 -> 209[label="",style="solid", color="blue", weight=3];
129 -> 239[label="",style="dashed", color="red", weight=0];
129[label="xv30 == xv400 && xv31 == xv401\n  Eq a",fontsize=16,color="magenta"];129 -> 244[label="",style="dashed", color="magenta", weight=3];
129 -> 245[label="",style="dashed", color="magenta", weight=3];
130[label="False",fontsize=16,color="green",shape="box"];131[label="False",fontsize=16,color="green",shape="box"];132[label="True",fontsize=16,color="green",shape="box"];133[label="primEqFloat (Float xv30 xv31) (Float xv400 xv401)",fontsize=16,color="black",shape="box"];133 -> 210[label="",style="solid", color="black", weight=3];
134 -> 239[label="",style="dashed", color="red", weight=0];
134[label="xv30 == xv400 && xv31 == xv401\n  Integral a",fontsize=16,color="magenta"];134 -> 246[label="",style="dashed", color="magenta", weight=3];
134 -> 247[label="",style="dashed", color="magenta", weight=3];
135[label="primEqInt (Pos (Succ xv300)) (Pos xv400)",fontsize=16,color="burlywood",shape="box"];830[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];135 -> 830[label="",style="solid", color="burlywood", weight=9];
830 -> 211[label="",style="solid", color="burlywood", weight=3];
831[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];135 -> 831[label="",style="solid", color="burlywood", weight=9];
831 -> 212[label="",style="solid", color="burlywood", weight=3];
136[label="primEqInt (Pos (Succ xv300)) (Neg xv400)",fontsize=16,color="black",shape="box"];136 -> 213[label="",style="solid", color="black", weight=3];
137[label="primEqInt (Pos Zero) (Pos xv400)",fontsize=16,color="burlywood",shape="box"];832[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];137 -> 832[label="",style="solid", color="burlywood", weight=9];
832 -> 214[label="",style="solid", color="burlywood", weight=3];
833[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];137 -> 833[label="",style="solid", color="burlywood", weight=9];
833 -> 215[label="",style="solid", color="burlywood", weight=3];
138[label="primEqInt (Pos Zero) (Neg xv400)",fontsize=16,color="burlywood",shape="box"];834[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];138 -> 834[label="",style="solid", color="burlywood", weight=9];
834 -> 216[label="",style="solid", color="burlywood", weight=3];
835[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 835[label="",style="solid", color="burlywood", weight=9];
835 -> 217[label="",style="solid", color="burlywood", weight=3];
139[label="primEqInt (Neg (Succ xv300)) (Pos xv400)",fontsize=16,color="black",shape="box"];139 -> 218[label="",style="solid", color="black", weight=3];
140[label="primEqInt (Neg (Succ xv300)) (Neg xv400)",fontsize=16,color="burlywood",shape="box"];836[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];140 -> 836[label="",style="solid", color="burlywood", weight=9];
836 -> 219[label="",style="solid", color="burlywood", weight=3];
837[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 837[label="",style="solid", color="burlywood", weight=9];
837 -> 220[label="",style="solid", color="burlywood", weight=3];
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495 -> 38[label="",style="dashed", color="red", weight=0];
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585 -> 648[label="",style="dashed", color="magenta", weight=3];
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1102[label="xv40100/Zero",fontsize=10,color="white",style="solid",shape="box"];685 -> 1102[label="",style="solid", color="burlywood", weight=9];
1102 -> 689[label="",style="solid", color="burlywood", weight=3];
686[label="primPlusNat (Succ xv2400) (Succ xv401000)",fontsize=16,color="black",shape="box"];686 -> 690[label="",style="solid", color="black", weight=3];
687[label="primPlusNat (Succ xv2400) Zero",fontsize=16,color="black",shape="box"];687 -> 691[label="",style="solid", color="black", weight=3];
688[label="primPlusNat Zero (Succ xv401000)",fontsize=16,color="black",shape="box"];688 -> 692[label="",style="solid", color="black", weight=3];
689[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];689 -> 693[label="",style="solid", color="black", weight=3];
690[label="Succ (Succ (primPlusNat xv2400 xv401000))",fontsize=16,color="green",shape="box"];690 -> 694[label="",style="dashed", color="green", weight=3];
691[label="Succ xv2400",fontsize=16,color="green",shape="box"];692[label="Succ xv401000",fontsize=16,color="green",shape="box"];693[label="Zero",fontsize=16,color="green",shape="box"];694 -> 683[label="",style="dashed", color="red", weight=0];
694[label="primPlusNat xv2400 xv401000",fontsize=16,color="magenta"];694 -> 695[label="",style="dashed", color="magenta", weight=3];
694 -> 696[label="",style="dashed", color="magenta", weight=3];
695[label="xv401000",fontsize=16,color="green",shape="box"];696[label="xv2400",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xv2400), Succ(xv401000)) → new_primPlusNat(xv2400, xv401000)

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_primPlusNat(Succ(xv2400), Succ(xv401000)) → new_primPlusNat(xv2400, xv401000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xv3100), Succ(xv40100)) → new_primMulNat(xv3100, Succ(xv40100))

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

new_primMulNat(Succ(xv3100), Succ(xv40100)) → new_primMulNat(xv3100, Succ(xv40100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(xv300), Succ(xv4000)) → new_primEqNat(xv300, xv4000)

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

new_primEqNat(Succ(xv300), Succ(xv4000)) → new_primEqNat(xv300, xv4000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_@2, cc), cd), ce) → new_esEs(xv30, xv400, cc, cd)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(app(ty_@3, gg), gh), ha), ge) → new_esEs1(xv31, xv401, gg, gh, ha)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(ty_Either, fh), ga)) → new_esEs2(xv32, xv402, fh, ga)
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(ty_Maybe, bde)) → new_esEs0(xv30, xv400, bde)
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(ty_[], bec)) → new_esEs3(xv30, xv400, bec)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(ty_@2, gc), gd), ge) → new_esEs(xv31, xv401, gc, gd)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(ty_Either, bac), bad), eh, ge) → new_esEs2(xv30, xv400, bac, bad)
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(ty_@2, bdc), bdd)) → new_esEs(xv30, xv400, bdc, bdd)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(ty_[], gb)) → new_esEs3(xv32, xv402, gb)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(ty_Maybe, gf), ge) → new_esEs0(xv31, xv401, gf)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(app(ty_@3, fd), ff), fg)) → new_esEs1(xv32, xv402, fd, ff, fg)
new_esEs0(Just(xv30), Just(xv400), app(ty_Maybe, dh)) → new_esEs0(xv30, xv400, dh)
new_esEs2(Left(xv30), Left(xv400), app(app(ty_Either, bbe), bbf), bah) → new_esEs2(xv30, xv400, bbe, bbf)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(ty_Maybe, bd)) → new_esEs0(xv31, xv401, bd)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(ty_Either, hb), hc), ge) → new_esEs2(xv31, xv401, hb, hc)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(ty_Maybe, fc)) → new_esEs0(xv32, xv402, fc)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(ty_@2, fa), fb)) → new_esEs(xv32, xv402, fa, fb)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(ty_[], bae), eh, ge) → new_esEs3(xv30, xv400, bae)
new_esEs3(:(xv30, xv31), :(xv400, xv401), bdb) → new_esEs3(xv31, xv401, bdb)
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(xv30, xv400, bcd, bce, bcf)
new_esEs2(Left(xv30), Left(xv400), app(ty_[], bbg), bah) → new_esEs3(xv30, xv400, bbg)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(app(ty_@3, be), bf), bg)) → new_esEs1(xv31, xv401, be, bf, bg)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(app(ty_@3, hh), baa), bab), eh, ge) → new_esEs1(xv30, xv400, hh, baa, bab)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(ty_[], hd), ge) → new_esEs3(xv31, xv401, hd)
new_esEs0(Just(xv30), Just(xv400), app(app(ty_@2, df), dg)) → new_esEs(xv30, xv400, df, dg)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(ty_Maybe, cf), ce) → new_esEs0(xv30, xv400, cf)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(ty_[], cb)) → new_esEs3(xv31, xv401, cb)
new_esEs2(Left(xv30), Left(xv400), app(app(app(ty_@3, bbb), bbc), bbd), bah) → new_esEs1(xv30, xv400, bbb, bbc, bbd)
new_esEs0(Just(xv30), Just(xv400), app(ty_[], ef)) → new_esEs3(xv30, xv400, ef)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(ty_Either, bh), ca)) → new_esEs2(xv31, xv401, bh, ca)
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(ty_@2, bca), bcb)) → new_esEs(xv30, xv400, bca, bcb)
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(xv30, xv400, bcg, bch)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(ty_@2, bb), bc)) → new_esEs(xv31, xv401, bb, bc)
new_esEs2(Left(xv30), Left(xv400), app(app(ty_@2, baf), bag), bah) → new_esEs(xv30, xv400, baf, bag)
new_esEs2(Right(xv30), Right(xv400), bbh, app(ty_[], bda)) → new_esEs3(xv30, xv400, bda)
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(ty_Either, bea), beb)) → new_esEs2(xv30, xv400, bea, beb)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_Either, dc), dd), ce) → new_esEs2(xv30, xv400, dc, dd)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(ty_Maybe, hg), eh, ge) → new_esEs0(xv30, xv400, hg)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(app(ty_@3, cg), da), db), ce) → new_esEs1(xv30, xv400, cg, da, db)
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(ty_@2, he), hf), eh, ge) → new_esEs(xv30, xv400, he, hf)
new_esEs2(Left(xv30), Left(xv400), app(ty_Maybe, bba), bah) → new_esEs0(xv30, xv400, bba)
new_esEs2(Right(xv30), Right(xv400), bbh, app(ty_Maybe, bcc)) → new_esEs0(xv30, xv400, bcc)
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(ty_[], de), ce) → new_esEs3(xv30, xv400, de)
new_esEs0(Just(xv30), Just(xv400), app(app(ty_Either, ed), ee)) → new_esEs2(xv30, xv400, ed, ee)
new_esEs0(Just(xv30), Just(xv400), app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(xv30, xv400, ea, eb, ec)
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(xv30, xv400, bdf, bdg, bdh)

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

new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(ty_@2, bdc), bdd)) → new_esEs(xv30, xv400, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xv30), Just(xv400), app(app(ty_@2, df), dg)) → new_esEs(xv30, xv400, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(xv30, xv400, bdf, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Just(xv30), Just(xv400), app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(xv30, xv400, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Just(xv30), Just(xv400), app(ty_[], ef)) → new_esEs3(xv30, xv400, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(ty_Maybe, bde)) → new_esEs0(xv30, xv400, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(app(ty_Either, bea), beb)) → new_esEs2(xv30, xv400, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xv30), Just(xv400), app(ty_Maybe, dh)) → new_esEs0(xv30, xv400, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Just(xv30), Just(xv400), app(app(ty_Either, ed), ee)) → new_esEs2(xv30, xv400, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_@2, cc), cd), ce) → new_esEs(xv30, xv400, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(ty_@2, bb), bc)) → new_esEs(xv31, xv401, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(app(ty_@3, be), bf), bg)) → new_esEs1(xv31, xv401, be, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(app(ty_@3, cg), da), db), ce) → new_esEs1(xv30, xv400, cg, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(ty_[], cb)) → new_esEs3(xv31, xv401, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(ty_[], de), ce) → new_esEs3(xv30, xv400, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(ty_Maybe, bd)) → new_esEs0(xv31, xv401, bd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(ty_Maybe, cf), ce) → new_esEs0(xv30, xv400, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xv30, xv31), @2(xv400, xv401), ba, app(app(ty_Either, bh), ca)) → new_esEs2(xv31, xv401, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_Either, dc), dd), ce) → new_esEs2(xv30, xv400, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(ty_@2, gc), gd), ge) → new_esEs(xv31, xv401, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(ty_@2, fa), fb)) → new_esEs(xv32, xv402, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(ty_@2, he), hf), eh, ge) → new_esEs(xv30, xv400, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(ty_@2, bca), bcb)) → new_esEs(xv30, xv400, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Left(xv30), Left(xv400), app(app(ty_@2, baf), bag), bah) → new_esEs(xv30, xv400, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(app(ty_@3, gg), gh), ha), ge) → new_esEs1(xv31, xv401, gg, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(app(ty_@3, fd), ff), fg)) → new_esEs1(xv32, xv402, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(app(ty_@3, hh), baa), bab), eh, ge) → new_esEs1(xv30, xv400, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(ty_[], gb)) → new_esEs3(xv32, xv402, gb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(ty_[], bae), eh, ge) → new_esEs3(xv30, xv400, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(ty_[], hd), ge) → new_esEs3(xv31, xv401, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(ty_Maybe, gf), ge) → new_esEs0(xv31, xv401, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(ty_Maybe, fc)) → new_esEs0(xv32, xv402, fc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(ty_Maybe, hg), eh, ge) → new_esEs0(xv30, xv400, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, eh, app(app(ty_Either, fh), ga)) → new_esEs2(xv32, xv402, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), app(app(ty_Either, bac), bad), eh, ge) → new_esEs2(xv30, xv400, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(xv30, xv31, xv32), @3(xv400, xv401, xv402), eg, app(app(ty_Either, hb), hc), ge) → new_esEs2(xv31, xv401, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(xv30, xv400, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(Left(xv30), Left(xv400), app(app(app(ty_@3, bbb), bbc), bbd), bah) → new_esEs1(xv30, xv400, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Left(xv30), Left(xv400), app(ty_[], bbg), bah) → new_esEs3(xv30, xv400, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(xv30), Right(xv400), bbh, app(ty_[], bda)) → new_esEs3(xv30, xv400, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(xv30), Left(xv400), app(ty_Maybe, bba), bah) → new_esEs0(xv30, xv400, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(xv30), Right(xv400), bbh, app(ty_Maybe, bcc)) → new_esEs0(xv30, xv400, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(xv30), Left(xv400), app(app(ty_Either, bbe), bbf), bah) → new_esEs2(xv30, xv400, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(xv30), Right(xv400), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(xv30, xv400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(:(xv30, xv31), :(xv400, xv401), app(ty_[], bec)) → new_esEs3(xv30, xv400, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv30, xv31), :(xv400, xv401), bdb) → new_esEs3(xv31, xv401, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_foldr(xv3, :(xv40, xv41), ba) → new_foldr(xv3, xv41, ba)

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

new_foldr(xv3, :(xv40, xv41), ba) → new_foldr(xv3, xv41, ba)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3