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

YES 1.933 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

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] _	=	True
isPrefixOf	_ []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

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

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

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

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

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1516 -> 821[label="",style="solid", color="burlywood", weight=3];
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1517 -> 822[label="",style="solid", color="burlywood", weight=3];
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1519 -> 826[label="",style="solid", color="burlywood", weight=3];
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1525 -> 832[label="",style="solid", color="burlywood", weight=3];
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1526 -> 833[label="",style="solid", color="burlywood", weight=3];
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1530 -> 838[label="",style="solid", color="burlywood", weight=3];
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1533 -> 842[label="",style="solid", color="burlywood", weight=3];
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1534 -> 843[label="",style="solid", color="burlywood", weight=3];
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823[label="isPrefixOf (xy530 : xy531) []\n  Eq a",fontsize=16,color="black",shape="box"];823 -> 848[label="",style="solid", color="black", weight=3];
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1535 -> 849[label="",style="solid", color="burlywood", weight=3];
826[label="LT == xy570",fontsize=16,color="burlywood",shape="box"];1536[label="xy570/LT",fontsize=10,color="white",style="solid",shape="box"];826 -> 1536[label="",style="solid", color="burlywood", weight=9];
1536 -> 850[label="",style="solid", color="burlywood", weight=3];
1537[label="xy570/EQ",fontsize=10,color="white",style="solid",shape="box"];826 -> 1537[label="",style="solid", color="burlywood", weight=9];
1537 -> 851[label="",style="solid", color="burlywood", weight=3];
1538[label="xy570/GT",fontsize=10,color="white",style="solid",shape="box"];826 -> 1538[label="",style="solid", color="burlywood", weight=9];
1538 -> 852[label="",style="solid", color="burlywood", weight=3];
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1539 -> 853[label="",style="solid", color="burlywood", weight=3];
1540[label="xy570/EQ",fontsize=10,color="white",style="solid",shape="box"];827 -> 1540[label="",style="solid", color="burlywood", weight=9];
1540 -> 854[label="",style="solid", color="burlywood", weight=3];
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1541 -> 855[label="",style="solid", color="burlywood", weight=3];
828[label="GT == xy570",fontsize=16,color="burlywood",shape="box"];1542[label="xy570/LT",fontsize=10,color="white",style="solid",shape="box"];828 -> 1542[label="",style="solid", color="burlywood", weight=9];
1542 -> 856[label="",style="solid", color="burlywood", weight=3];
1543[label="xy570/EQ",fontsize=10,color="white",style="solid",shape="box"];828 -> 1543[label="",style="solid", color="burlywood", weight=9];
1543 -> 857[label="",style="solid", color="burlywood", weight=3];
1544[label="xy570/GT",fontsize=10,color="white",style="solid",shape="box"];828 -> 1544[label="",style="solid", color="burlywood", weight=9];
1544 -> 858[label="",style="solid", color="burlywood", weight=3];
829[label="Integer xy540 == xy570",fontsize=16,color="burlywood",shape="box"];1545[label="xy570/Integer xy5700",fontsize=10,color="white",style="solid",shape="box"];829 -> 1545[label="",style="solid", color="burlywood", weight=9];
1545 -> 859[label="",style="solid", color="burlywood", weight=3];
830[label="() == xy570",fontsize=16,color="burlywood",shape="box"];1546[label="xy570/()",fontsize=10,color="white",style="solid",shape="box"];830 -> 1546[label="",style="solid", color="burlywood", weight=9];
1546 -> 860[label="",style="solid", color="burlywood", weight=3];
831[label="(xy540,xy541) == xy570\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1547[label="xy570/(xy5700,xy5701)",fontsize=10,color="white",style="solid",shape="box"];831 -> 1547[label="",style="solid", color="burlywood", weight=9];
1547 -> 861[label="",style="solid", color="burlywood", weight=3];
832[label="False == xy570",fontsize=16,color="burlywood",shape="box"];1548[label="xy570/False",fontsize=10,color="white",style="solid",shape="box"];832 -> 1548[label="",style="solid", color="burlywood", weight=9];
1548 -> 862[label="",style="solid", color="burlywood", weight=3];
1549[label="xy570/True",fontsize=10,color="white",style="solid",shape="box"];832 -> 1549[label="",style="solid", color="burlywood", weight=9];
1549 -> 863[label="",style="solid", color="burlywood", weight=3];
833[label="True == xy570",fontsize=16,color="burlywood",shape="box"];1550[label="xy570/False",fontsize=10,color="white",style="solid",shape="box"];833 -> 1550[label="",style="solid", color="burlywood", weight=9];
1550 -> 864[label="",style="solid", color="burlywood", weight=3];
1551[label="xy570/True",fontsize=10,color="white",style="solid",shape="box"];833 -> 1551[label="",style="solid", color="burlywood", weight=9];
1551 -> 865[label="",style="solid", color="burlywood", weight=3];
834[label="primEqDouble xy54 xy570",fontsize=16,color="burlywood",shape="box"];1552[label="xy54/Double xy540 xy541",fontsize=10,color="white",style="solid",shape="box"];834 -> 1552[label="",style="solid", color="burlywood", weight=9];
1552 -> 866[label="",style="solid", color="burlywood", weight=3];
835[label="xy540 : xy541 == xy570\n  Eq a",fontsize=16,color="burlywood",shape="box"];1553[label="xy570/xy5700 : xy5701",fontsize=10,color="white",style="solid",shape="box"];835 -> 1553[label="",style="solid", color="burlywood", weight=9];
1553 -> 867[label="",style="solid", color="burlywood", weight=3];
1554[label="xy570/[]",fontsize=10,color="white",style="solid",shape="box"];835 -> 1554[label="",style="solid", color="burlywood", weight=9];
1554 -> 868[label="",style="solid", color="burlywood", weight=3];
836[label="[] == xy570\n  Eq a",fontsize=16,color="burlywood",shape="box"];1555[label="xy570/xy5700 : xy5701",fontsize=10,color="white",style="solid",shape="box"];836 -> 1555[label="",style="solid", color="burlywood", weight=9];
1555 -> 869[label="",style="solid", color="burlywood", weight=3];
1556[label="xy570/[]",fontsize=10,color="white",style="solid",shape="box"];836 -> 1556[label="",style="solid", color="burlywood", weight=9];
1556 -> 870[label="",style="solid", color="burlywood", weight=3];
837[label="(xy540,xy541,xy542) == xy570\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1557[label="xy570/(xy5700,xy5701,xy5702)",fontsize=10,color="white",style="solid",shape="box"];837 -> 1557[label="",style="solid", color="burlywood", weight=9];
1557 -> 871[label="",style="solid", color="burlywood", weight=3];
838[label="Nothing == xy570\n  Eq a",fontsize=16,color="burlywood",shape="box"];1558[label="xy570/Nothing",fontsize=10,color="white",style="solid",shape="box"];838 -> 1558[label="",style="solid", color="burlywood", weight=9];
1558 -> 872[label="",style="solid", color="burlywood", weight=3];
1559[label="xy570/Just xy5700",fontsize=10,color="white",style="solid",shape="box"];838 -> 1559[label="",style="solid", color="burlywood", weight=9];
1559 -> 873[label="",style="solid", color="burlywood", weight=3];
839[label="Just xy540 == xy570\n  Eq a",fontsize=16,color="burlywood",shape="box"];1560[label="xy570/Nothing",fontsize=10,color="white",style="solid",shape="box"];839 -> 1560[label="",style="solid", color="burlywood", weight=9];
1560 -> 874[label="",style="solid", color="burlywood", weight=3];
1561[label="xy570/Just xy5700",fontsize=10,color="white",style="solid",shape="box"];839 -> 1561[label="",style="solid", color="burlywood", weight=9];
1561 -> 875[label="",style="solid", color="burlywood", weight=3];
840[label="xy540 :% xy541 == xy570\n  Integral a",fontsize=16,color="burlywood",shape="box"];1562[label="xy570/xy5700 :% xy5701",fontsize=10,color="white",style="solid",shape="box"];840 -> 1562[label="",style="solid", color="burlywood", weight=9];
1562 -> 876[label="",style="solid", color="burlywood", weight=3];
841[label="primEqChar xy54 xy570",fontsize=16,color="burlywood",shape="box"];1563[label="xy54/Char xy540",fontsize=10,color="white",style="solid",shape="box"];841 -> 1563[label="",style="solid", color="burlywood", weight=9];
1563 -> 877[label="",style="solid", color="burlywood", weight=3];
842[label="Left xy540 == xy570\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1564[label="xy570/Left xy5700",fontsize=10,color="white",style="solid",shape="box"];842 -> 1564[label="",style="solid", color="burlywood", weight=9];
1564 -> 878[label="",style="solid", color="burlywood", weight=3];
1565[label="xy570/Right xy5700",fontsize=10,color="white",style="solid",shape="box"];842 -> 1565[label="",style="solid", color="burlywood", weight=9];
1565 -> 879[label="",style="solid", color="burlywood", weight=3];
843[label="Right xy540 == xy570\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1566[label="xy570/Left xy5700",fontsize=10,color="white",style="solid",shape="box"];843 -> 1566[label="",style="solid", color="burlywood", weight=9];
1566 -> 880[label="",style="solid", color="burlywood", weight=3];
1567[label="xy570/Right xy5700",fontsize=10,color="white",style="solid",shape="box"];843 -> 1567[label="",style="solid", color="burlywood", weight=9];
1567 -> 881[label="",style="solid", color="burlywood", weight=3];
844[label="primEqInt xy54 xy570",fontsize=16,color="burlywood",shape="triangle"];1568[label="xy54/Pos xy540",fontsize=10,color="white",style="solid",shape="box"];844 -> 1568[label="",style="solid", color="burlywood", weight=9];
1568 -> 882[label="",style="solid", color="burlywood", weight=3];
1569[label="xy54/Neg xy540",fontsize=10,color="white",style="solid",shape="box"];844 -> 1569[label="",style="solid", color="burlywood", weight=9];
1569 -> 883[label="",style="solid", color="burlywood", weight=3];
845[label="False",fontsize=16,color="green",shape="box"];846[label="xy77",fontsize=16,color="green",shape="box"];847 -> 799[label="",style="dashed", color="red", weight=0];
847[label="xy530 == xy5710 && isPrefixOf xy531 xy5711\n  Eq a",fontsize=16,color="magenta"];847 -> 884[label="",style="dashed", color="magenta", weight=3];
847 -> 885[label="",style="dashed", color="magenta", weight=3];
848[label="False",fontsize=16,color="green",shape="box"];849[label="primEqFloat (Float xy540 xy541) xy570",fontsize=16,color="burlywood",shape="box"];1571[label="xy570/Float xy5700 xy5701",fontsize=10,color="white",style="solid",shape="box"];849 -> 1571[label="",style="solid", color="burlywood", weight=9];
1571 -> 886[label="",style="solid", color="burlywood", weight=3];
850[label="LT == LT",fontsize=16,color="black",shape="box"];850 -> 887[label="",style="solid", color="black", weight=3];
851[label="LT == EQ",fontsize=16,color="black",shape="box"];851 -> 888[label="",style="solid", color="black", weight=3];
852[label="LT == GT",fontsize=16,color="black",shape="box"];852 -> 889[label="",style="solid", color="black", weight=3];
853[label="EQ == LT",fontsize=16,color="black",shape="box"];853 -> 890[label="",style="solid", color="black", weight=3];
854[label="EQ == EQ",fontsize=16,color="black",shape="box"];854 -> 891[label="",style="solid", color="black", weight=3];
855[label="EQ == GT",fontsize=16,color="black",shape="box"];855 -> 892[label="",style="solid", color="black", weight=3];
856[label="GT == LT",fontsize=16,color="black",shape="box"];856 -> 893[label="",style="solid", color="black", weight=3];
857[label="GT == EQ",fontsize=16,color="black",shape="box"];857 -> 894[label="",style="solid", color="black", weight=3];
858[label="GT == GT",fontsize=16,color="black",shape="box"];858 -> 895[label="",style="solid", color="black", weight=3];
859[label="Integer xy540 == Integer xy5700",fontsize=16,color="black",shape="box"];859 -> 896[label="",style="solid", color="black", weight=3];
860[label="() == ()",fontsize=16,color="black",shape="box"];860 -> 897[label="",style="solid", color="black", weight=3];
861[label="(xy540,xy541) == (xy5700,xy5701)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];861 -> 898[label="",style="solid", color="black", weight=3];
862[label="False == False",fontsize=16,color="black",shape="box"];862 -> 899[label="",style="solid", color="black", weight=3];
863[label="False == True",fontsize=16,color="black",shape="box"];863 -> 900[label="",style="solid", color="black", weight=3];
864[label="True == False",fontsize=16,color="black",shape="box"];864 -> 901[label="",style="solid", color="black", weight=3];
865[label="True == True",fontsize=16,color="black",shape="box"];865 -> 902[label="",style="solid", color="black", weight=3];
866[label="primEqDouble (Double xy540 xy541) xy570",fontsize=16,color="burlywood",shape="box"];1572[label="xy570/Double xy5700 xy5701",fontsize=10,color="white",style="solid",shape="box"];866 -> 1572[label="",style="solid", color="burlywood", weight=9];
1572 -> 903[label="",style="solid", color="burlywood", weight=3];
867[label="xy540 : xy541 == xy5700 : xy5701\n  Eq a",fontsize=16,color="black",shape="box"];867 -> 904[label="",style="solid", color="black", weight=3];
868[label="xy540 : xy541 == []\n  Eq a",fontsize=16,color="black",shape="box"];868 -> 905[label="",style="solid", color="black", weight=3];
869[label="[] == xy5700 : xy5701\n  Eq a",fontsize=16,color="black",shape="box"];869 -> 906[label="",style="solid", color="black", weight=3];
870[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];870 -> 907[label="",style="solid", color="black", weight=3];
871[label="(xy540,xy541,xy542) == (xy5700,xy5701,xy5702)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];871 -> 908[label="",style="solid", color="black", weight=3];
872[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];872 -> 909[label="",style="solid", color="black", weight=3];
873[label="Nothing == Just xy5700\n  Eq a",fontsize=16,color="black",shape="box"];873 -> 910[label="",style="solid", color="black", weight=3];
874[label="Just xy540 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];874 -> 911[label="",style="solid", color="black", weight=3];
875[label="Just xy540 == Just xy5700\n  Eq a",fontsize=16,color="black",shape="box"];875 -> 912[label="",style="solid", color="black", weight=3];
876[label="xy540 :% xy541 == xy5700 :% xy5701\n  Integral a",fontsize=16,color="black",shape="box"];876 -> 913[label="",style="solid", color="black", weight=3];
877[label="primEqChar (Char xy540) xy570",fontsize=16,color="burlywood",shape="box"];1573[label="xy570/Char xy5700",fontsize=10,color="white",style="solid",shape="box"];877 -> 1573[label="",style="solid", color="burlywood", weight=9];
1573 -> 914[label="",style="solid", color="burlywood", weight=3];
878[label="Left xy540 == Left xy5700\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];878 -> 915[label="",style="solid", color="black", weight=3];
879[label="Left xy540 == Right xy5700\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];879 -> 916[label="",style="solid", color="black", weight=3];
880[label="Right xy540 == Left xy5700\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];880 -> 917[label="",style="solid", color="black", weight=3];
881[label="Right xy540 == Right xy5700\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];881 -> 918[label="",style="solid", color="black", weight=3];
882[label="primEqInt (Pos xy540) xy570",fontsize=16,color="burlywood",shape="box"];1574[label="xy540/Succ xy5400",fontsize=10,color="white",style="solid",shape="box"];882 -> 1574[label="",style="solid", color="burlywood", weight=9];
1574 -> 919[label="",style="solid", color="burlywood", weight=3];
1575[label="xy540/Zero",fontsize=10,color="white",style="solid",shape="box"];882 -> 1575[label="",style="solid", color="burlywood", weight=9];
1575 -> 920[label="",style="solid", color="burlywood", weight=3];
883[label="primEqInt (Neg xy540) xy570",fontsize=16,color="burlywood",shape="box"];1576[label="xy540/Succ xy5400",fontsize=10,color="white",style="solid",shape="box"];883 -> 1576[label="",style="solid", color="burlywood", weight=9];
1576 -> 921[label="",style="solid", color="burlywood", weight=3];
1577[label="xy540/Zero",fontsize=10,color="white",style="solid",shape="box"];883 -> 1577[label="",style="solid", color="burlywood", weight=9];
1577 -> 922[label="",style="solid", color="burlywood", weight=3];
884 -> 800[label="",style="dashed", color="red", weight=0];
884[label="isPrefixOf xy531 xy5711\n  Eq a",fontsize=16,color="magenta"];884 -> 923[label="",style="dashed", color="magenta", weight=3];
884 -> 924[label="",style="dashed", color="magenta", weight=3];
885[label="xy530 == xy5710\n  Eq a",fontsize=16,color="blue",shape="box"];1579[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1579[label="",style="solid", color="blue", weight=9];
1579 -> 925[label="",style="solid", color="blue", weight=3];
1580[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1580[label="",style="solid", color="blue", weight=9];
1580 -> 926[label="",style="solid", color="blue", weight=3];
1581[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1581[label="",style="solid", color="blue", weight=9];
1581 -> 927[label="",style="solid", color="blue", weight=3];
1582[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1582[label="",style="solid", color="blue", weight=9];
1582 -> 928[label="",style="solid", color="blue", weight=3];
1583[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1583[label="",style="solid", color="blue", weight=9];
1583 -> 929[label="",style="solid", color="blue", weight=3];
1584[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1584[label="",style="solid", color="blue", weight=9];
1584 -> 930[label="",style="solid", color="blue", weight=3];
1585[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1585[label="",style="solid", color="blue", weight=9];
1585 -> 931[label="",style="solid", color="blue", weight=3];
1586[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1586[label="",style="solid", color="blue", weight=9];
1586 -> 932[label="",style="solid", color="blue", weight=3];
1587[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1587[label="",style="solid", color="blue", weight=9];
1587 -> 933[label="",style="solid", color="blue", weight=3];
1588[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1588[label="",style="solid", color="blue", weight=9];
1588 -> 934[label="",style="solid", color="blue", weight=3];
1589[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1589[label="",style="solid", color="blue", weight=9];
1589 -> 935[label="",style="solid", color="blue", weight=3];
1590[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1590[label="",style="solid", color="blue", weight=9];
1590 -> 936[label="",style="solid", color="blue", weight=3];
1591[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1591[label="",style="solid", color="blue", weight=9];
1591 -> 937[label="",style="solid", color="blue", weight=3];
1592[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];885 -> 1592[label="",style="solid", color="blue", weight=9];
1592 -> 938[label="",style="solid", color="blue", weight=3];
886[label="primEqFloat (Float xy540 xy541) (Float xy5700 xy5701)",fontsize=16,color="black",shape="box"];886 -> 939[label="",style="solid", color="black", weight=3];
887[label="True",fontsize=16,color="green",shape="box"];888[label="False",fontsize=16,color="green",shape="box"];889[label="False",fontsize=16,color="green",shape="box"];890[label="False",fontsize=16,color="green",shape="box"];891[label="True",fontsize=16,color="green",shape="box"];892[label="False",fontsize=16,color="green",shape="box"];893[label="False",fontsize=16,color="green",shape="box"];894[label="False",fontsize=16,color="green",shape="box"];895[label="True",fontsize=16,color="green",shape="box"];896 -> 844[label="",style="dashed", color="red", weight=0];
896[label="primEqInt xy540 xy5700",fontsize=16,color="magenta"];896 -> 940[label="",style="dashed", color="magenta", weight=3];
896 -> 941[label="",style="dashed", color="magenta", weight=3];
897[label="True",fontsize=16,color="green",shape="box"];898 -> 799[label="",style="dashed", color="red", weight=0];
898[label="xy540 == xy5700 && xy541 == xy5701\n  Eq a  Eq b",fontsize=16,color="magenta"];898 -> 942[label="",style="dashed", color="magenta", weight=3];
898 -> 943[label="",style="dashed", color="magenta", weight=3];
899[label="True",fontsize=16,color="green",shape="box"];900[label="False",fontsize=16,color="green",shape="box"];901[label="False",fontsize=16,color="green",shape="box"];902[label="True",fontsize=16,color="green",shape="box"];903[label="primEqDouble (Double xy540 xy541) (Double xy5700 xy5701)",fontsize=16,color="black",shape="box"];903 -> 944[label="",style="solid", color="black", weight=3];
904 -> 799[label="",style="dashed", color="red", weight=0];
904[label="xy540 == xy5700 && xy541 == xy5701\n  Eq a",fontsize=16,color="magenta"];904 -> 945[label="",style="dashed", color="magenta", weight=3];
904 -> 946[label="",style="dashed", color="magenta", weight=3];
905[label="False",fontsize=16,color="green",shape="box"];906[label="False",fontsize=16,color="green",shape="box"];907[label="True",fontsize=16,color="green",shape="box"];908 -> 799[label="",style="dashed", color="red", weight=0];
908[label="xy540 == xy5700 && xy541 == xy5701 && xy542 == xy5702\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];908 -> 947[label="",style="dashed", color="magenta", weight=3];
908 -> 948[label="",style="dashed", color="magenta", weight=3];
909[label="True",fontsize=16,color="green",shape="box"];910[label="False",fontsize=16,color="green",shape="box"];911[label="False",fontsize=16,color="green",shape="box"];912[label="xy540 == xy5700\n  Eq a",fontsize=16,color="blue",shape="box"];1597[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1597[label="",style="solid", color="blue", weight=9];
1597 -> 949[label="",style="solid", color="blue", weight=3];
1598[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1598[label="",style="solid", color="blue", weight=9];
1598 -> 950[label="",style="solid", color="blue", weight=3];
1599[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1599[label="",style="solid", color="blue", weight=9];
1599 -> 951[label="",style="solid", color="blue", weight=3];
1600[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1600[label="",style="solid", color="blue", weight=9];
1600 -> 952[label="",style="solid", color="blue", weight=3];
1601[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1601[label="",style="solid", color="blue", weight=9];
1601 -> 953[label="",style="solid", color="blue", weight=3];
1602[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1602[label="",style="solid", color="blue", weight=9];
1602 -> 954[label="",style="solid", color="blue", weight=3];
1603[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1603[label="",style="solid", color="blue", weight=9];
1603 -> 955[label="",style="solid", color="blue", weight=3];
1604[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1604[label="",style="solid", color="blue", weight=9];
1604 -> 956[label="",style="solid", color="blue", weight=3];
1605[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1605[label="",style="solid", color="blue", weight=9];
1605 -> 957[label="",style="solid", color="blue", weight=3];
1606[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1606[label="",style="solid", color="blue", weight=9];
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1607[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1607[label="",style="solid", color="blue", weight=9];
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1608[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1608[label="",style="solid", color="blue", weight=9];
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1610[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];912 -> 1610[label="",style="solid", color="blue", weight=9];
1610 -> 962[label="",style="solid", color="blue", weight=3];
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1614[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1614[label="",style="solid", color="blue", weight=9];
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1615[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1615[label="",style="solid", color="blue", weight=9];
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1616[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1616[label="",style="solid", color="blue", weight=9];
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1617[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1617[label="",style="solid", color="blue", weight=9];
1617 -> 971[label="",style="solid", color="blue", weight=3];
1618[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1618[label="",style="solid", color="blue", weight=9];
1618 -> 972[label="",style="solid", color="blue", weight=3];
1619[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1619[label="",style="solid", color="blue", weight=9];
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1621[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1621[label="",style="solid", color="blue", weight=9];
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1622[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1622[label="",style="solid", color="blue", weight=9];
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1624[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1624[label="",style="solid", color="blue", weight=9];
1624 -> 978[label="",style="solid", color="blue", weight=3];
1625[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];915 -> 1625[label="",style="solid", color="blue", weight=9];
1625 -> 979[label="",style="solid", color="blue", weight=3];
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1628[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1628[label="",style="solid", color="blue", weight=9];
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1629[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1629[label="",style="solid", color="blue", weight=9];
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1630 -> 984[label="",style="solid", color="blue", weight=3];
1631[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1631[label="",style="solid", color="blue", weight=9];
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1632[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1632[label="",style="solid", color="blue", weight=9];
1632 -> 986[label="",style="solid", color="blue", weight=3];
1633[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1633[label="",style="solid", color="blue", weight=9];
1633 -> 987[label="",style="solid", color="blue", weight=3];
1634[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1634[label="",style="solid", color="blue", weight=9];
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1635[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1635[label="",style="solid", color="blue", weight=9];
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1636[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1636[label="",style="solid", color="blue", weight=9];
1636 -> 990[label="",style="solid", color="blue", weight=3];
1637[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1637[label="",style="solid", color="blue", weight=9];
1637 -> 991[label="",style="solid", color="blue", weight=3];
1638[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1638[label="",style="solid", color="blue", weight=9];
1638 -> 992[label="",style="solid", color="blue", weight=3];
1639[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];918 -> 1639[label="",style="solid", color="blue", weight=9];
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1643[label="xy570/Neg xy5700",fontsize=10,color="white",style="solid",shape="box"];920 -> 1643[label="",style="solid", color="burlywood", weight=9];
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1647 -> 1001[label="",style="solid", color="burlywood", weight=3];
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925[label="xy530 == xy5710",fontsize=16,color="magenta"];925 -> 1002[label="",style="dashed", color="magenta", weight=3];
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930 -> 1013[label="",style="dashed", color="magenta", weight=3];
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932 -> 813[label="",style="dashed", color="red", weight=0];
932[label="xy530 == xy5710\n  Eq a",fontsize=16,color="magenta"];932 -> 1016[label="",style="dashed", color="magenta", weight=3];
932 -> 1017[label="",style="dashed", color="magenta", weight=3];
933 -> 814[label="",style="dashed", color="red", weight=0];
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934 -> 815[label="",style="dashed", color="red", weight=0];
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934 -> 1021[label="",style="dashed", color="magenta", weight=3];
935 -> 816[label="",style="dashed", color="red", weight=0];
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937 -> 1027[label="",style="dashed", color="magenta", weight=3];
938 -> 819[label="",style="dashed", color="red", weight=0];
938[label="xy530 == xy5710",fontsize=16,color="magenta"];938 -> 1028[label="",style="dashed", color="magenta", weight=3];
938 -> 1029[label="",style="dashed", color="magenta", weight=3];
939 -> 819[label="",style="dashed", color="red", weight=0];
939[label="xy540 * xy5700 == xy541 * xy5701",fontsize=16,color="magenta"];939 -> 1030[label="",style="dashed", color="magenta", weight=3];
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1665[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1665[label="",style="solid", color="blue", weight=9];
1665 -> 1034[label="",style="solid", color="blue", weight=3];
1666[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1666[label="",style="solid", color="blue", weight=9];
1666 -> 1035[label="",style="solid", color="blue", weight=3];
1667[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1667[label="",style="solid", color="blue", weight=9];
1667 -> 1036[label="",style="solid", color="blue", weight=3];
1668[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1668[label="",style="solid", color="blue", weight=9];
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1669[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1669[label="",style="solid", color="blue", weight=9];
1669 -> 1038[label="",style="solid", color="blue", weight=3];
1670[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1670[label="",style="solid", color="blue", weight=9];
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1672[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1672[label="",style="solid", color="blue", weight=9];
1672 -> 1041[label="",style="solid", color="blue", weight=3];
1673[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1673[label="",style="solid", color="blue", weight=9];
1673 -> 1042[label="",style="solid", color="blue", weight=3];
1674[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1674[label="",style="solid", color="blue", weight=9];
1674 -> 1043[label="",style="solid", color="blue", weight=3];
1675[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1675[label="",style="solid", color="blue", weight=9];
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1676[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];942 -> 1676[label="",style="solid", color="blue", weight=9];
1676 -> 1045[label="",style="solid", color="blue", weight=3];
943[label="xy540 == xy5700\n  Eq a",fontsize=16,color="blue",shape="box"];1677[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1677[label="",style="solid", color="blue", weight=9];
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1678[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1678[label="",style="solid", color="blue", weight=9];
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1679[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1679[label="",style="solid", color="blue", weight=9];
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1680[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1680[label="",style="solid", color="blue", weight=9];
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1681[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1681[label="",style="solid", color="blue", weight=9];
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1682[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1682[label="",style="solid", color="blue", weight=9];
1682 -> 1051[label="",style="solid", color="blue", weight=3];
1683[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1683[label="",style="solid", color="blue", weight=9];
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1684[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1684[label="",style="solid", color="blue", weight=9];
1684 -> 1053[label="",style="solid", color="blue", weight=3];
1685[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1685[label="",style="solid", color="blue", weight=9];
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1686[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1686[label="",style="solid", color="blue", weight=9];
1686 -> 1055[label="",style="solid", color="blue", weight=3];
1687[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1687[label="",style="solid", color="blue", weight=9];
1687 -> 1056[label="",style="solid", color="blue", weight=3];
1688[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1688[label="",style="solid", color="blue", weight=9];
1688 -> 1057[label="",style="solid", color="blue", weight=3];
1689[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1689[label="",style="solid", color="blue", weight=9];
1689 -> 1058[label="",style="solid", color="blue", weight=3];
1690[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];943 -> 1690[label="",style="solid", color="blue", weight=9];
1690 -> 1059[label="",style="solid", color="blue", weight=3];
944 -> 819[label="",style="dashed", color="red", weight=0];
944[label="xy540 * xy5700 == xy541 * xy5701",fontsize=16,color="magenta"];944 -> 1060[label="",style="dashed", color="magenta", weight=3];
944 -> 1061[label="",style="dashed", color="magenta", weight=3];
945 -> 813[label="",style="dashed", color="red", weight=0];
945[label="xy541 == xy5701\n  Eq a",fontsize=16,color="magenta"];945 -> 1062[label="",style="dashed", color="magenta", weight=3];
945 -> 1063[label="",style="dashed", color="magenta", weight=3];
946[label="xy540 == xy5700\n  Eq a",fontsize=16,color="blue",shape="box"];1693[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];946 -> 1693[label="",style="solid", color="blue", weight=9];
1693 -> 1064[label="",style="solid", color="blue", weight=3];
1694[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];946 -> 1694[label="",style="solid", color="blue", weight=9];
1694 -> 1065[label="",style="solid", color="blue", weight=3];
1695[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];946 -> 1695[label="",style="solid", color="blue", weight=9];
1695 -> 1066[label="",style="solid", color="blue", weight=3];
1696[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];946 -> 1696[label="",style="solid", color="blue", weight=9];
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1002[label="xy530",fontsize=16,color="green",shape="box"];1003[label="xy5710",fontsize=16,color="green",shape="box"];1004[label="xy530",fontsize=16,color="green",shape="box"];1005[label="xy5710",fontsize=16,color="green",shape="box"];1006[label="xy530",fontsize=16,color="green",shape="box"];1007[label="xy5710",fontsize=16,color="green",shape="box"];1008[label="xy530",fontsize=16,color="green",shape="box"];1009[label="xy5710",fontsize=16,color="green",shape="box"];1010[label="xy530\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1011[label="xy5710\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1012[label="xy530",fontsize=16,color="green",shape="box"];1013[label="xy5710",fontsize=16,color="green",shape="box"];1014[label="xy530",fontsize=16,color="green",shape="box"];1015[label="xy5710",fontsize=16,color="green",shape="box"];1016[label="xy530\n  Eq a",fontsize=16,color="green",shape="box"];1017[label="xy5710\n  Eq a",fontsize=16,color="green",shape="box"];1018[label="xy530\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1019[label="xy5710\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1020[label="xy530\n  Eq a",fontsize=16,color="green",shape="box"];1021[label="xy5710\n  Eq a",fontsize=16,color="green",shape="box"];1022[label="xy530\n  Integral a",fontsize=16,color="green",shape="box"];1023[label="xy5710\n  Integral a",fontsize=16,color="green",shape="box"];1024[label="xy530",fontsize=16,color="green",shape="box"];1025[label="xy5710",fontsize=16,color="green",shape="box"];1026[label="xy530\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1027[label="xy5710\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1028[label="xy530",fontsize=16,color="green",shape="box"];1029[label="xy5710",fontsize=16,color="green",shape="box"];1030[label="xy540 * xy5700",fontsize=16,color="black",shape="triangle"];1030 -> 1198[label="",style="solid", color="black", weight=3];
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1031[label="xy541 * xy5701",fontsize=16,color="magenta"];1031 -> 1199[label="",style="dashed", color="magenta", weight=3];
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1036 -> 810[label="",style="dashed", color="red", weight=0];
1036[label="xy541 == xy5701\n  Eq a  Eq b",fontsize=16,color="magenta"];1036 -> 1209[label="",style="dashed", color="magenta", weight=3];
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1038[label="xy541 == xy5701",fontsize=16,color="magenta"];1038 -> 1213[label="",style="dashed", color="magenta", weight=3];
1038 -> 1214[label="",style="dashed", color="magenta", weight=3];
1039 -> 813[label="",style="dashed", color="red", weight=0];
1039[label="xy541 == xy5701\n  Eq a",fontsize=16,color="magenta"];1039 -> 1215[label="",style="dashed", color="magenta", weight=3];
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1040 -> 814[label="",style="dashed", color="red", weight=0];
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1041 -> 815[label="",style="dashed", color="red", weight=0];
1041[label="xy541 == xy5701\n  Eq a",fontsize=16,color="magenta"];1041 -> 1219[label="",style="dashed", color="magenta", weight=3];
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1042 -> 816[label="",style="dashed", color="red", weight=0];
1042[label="xy541 == xy5701\n  Integral a",fontsize=16,color="magenta"];1042 -> 1221[label="",style="dashed", color="magenta", weight=3];
1042 -> 1222[label="",style="dashed", color="magenta", weight=3];
1043 -> 817[label="",style="dashed", color="red", weight=0];
1043[label="xy541 == xy5701",fontsize=16,color="magenta"];1043 -> 1223[label="",style="dashed", color="magenta", weight=3];
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1044 -> 818[label="",style="dashed", color="red", weight=0];
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1052 -> 1242[label="",style="dashed", color="magenta", weight=3];
1053 -> 813[label="",style="dashed", color="red", weight=0];
1053[label="xy540 == xy5700\n  Eq a",fontsize=16,color="magenta"];1053 -> 1243[label="",style="dashed", color="magenta", weight=3];
1053 -> 1244[label="",style="dashed", color="magenta", weight=3];
1054 -> 814[label="",style="dashed", color="red", weight=0];
1054[label="xy540 == xy5700\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];1054 -> 1245[label="",style="dashed", color="magenta", weight=3];
1054 -> 1246[label="",style="dashed", color="magenta", weight=3];
1055 -> 815[label="",style="dashed", color="red", weight=0];
1055[label="xy540 == xy5700\n  Eq a",fontsize=16,color="magenta"];1055 -> 1247[label="",style="dashed", color="magenta", weight=3];
1055 -> 1248[label="",style="dashed", color="magenta", weight=3];
1056 -> 816[label="",style="dashed", color="red", weight=0];
1056[label="xy540 == xy5700\n  Integral a",fontsize=16,color="magenta"];1056 -> 1249[label="",style="dashed", color="magenta", weight=3];
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1057 -> 817[label="",style="dashed", color="red", weight=0];
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1188[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1188 -> 1360[label="",style="solid", color="black", weight=3];
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1190[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1190 -> 1362[label="",style="solid", color="black", weight=3];
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1197[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1197 -> 1368[label="",style="solid", color="black", weight=3];
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1199[label="xy541",fontsize=16,color="green",shape="box"];1200[label="xy5701",fontsize=16,color="green",shape="box"];1201[label="xy541",fontsize=16,color="green",shape="box"];1202[label="xy5701",fontsize=16,color="green",shape="box"];1203[label="xy541",fontsize=16,color="green",shape="box"];1204[label="xy5701",fontsize=16,color="green",shape="box"];1205[label="xy541",fontsize=16,color="green",shape="box"];1206[label="xy5701",fontsize=16,color="green",shape="box"];1207[label="xy541",fontsize=16,color="green",shape="box"];1208[label="xy5701",fontsize=16,color="green",shape="box"];1209[label="xy541\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1210[label="xy5701\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1211[label="xy541",fontsize=16,color="green",shape="box"];1212[label="xy5701",fontsize=16,color="green",shape="box"];1213[label="xy541",fontsize=16,color="green",shape="box"];1214[label="xy5701",fontsize=16,color="green",shape="box"];1215[label="xy541\n  Eq 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1299 -> 816[label="",style="dashed", color="red", weight=0];
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1300 -> 817[label="",style="dashed", color="red", weight=0];
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1310 -> 813[label="",style="dashed", color="red", weight=0];
1310[label="xy541 == xy5701\n  Eq a",fontsize=16,color="magenta"];1310 -> 1413[label="",style="dashed", color="magenta", weight=3];
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1311 -> 814[label="",style="dashed", color="red", weight=0];
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1355[label="primEqNat Zero (Succ xy57000)",fontsize=16,color="black",shape="box"];1355 -> 1429[label="",style="solid", color="black", weight=3];
1356[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];1356 -> 1430[label="",style="solid", color="black", weight=3];
1357 -> 965[label="",style="dashed", color="red", weight=0];
1357[label="primEqNat xy5400 xy57000",fontsize=16,color="magenta"];1357 -> 1431[label="",style="dashed", color="magenta", weight=3];
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1909 -> 1435[label="",style="solid", color="burlywood", weight=3];
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1912 -> 1438[label="",style="solid", color="burlywood", weight=3];
1371[label="xy542",fontsize=16,color="green",shape="box"];1372[label="xy5702",fontsize=16,color="green",shape="box"];1373[label="xy542",fontsize=16,color="green",shape="box"];1374[label="xy5702",fontsize=16,color="green",shape="box"];1375[label="xy542",fontsize=16,color="green",shape="box"];1376[label="xy5702",fontsize=16,color="green",shape="box"];1377[label="xy542",fontsize=16,color="green",shape="box"];1378[label="xy5702",fontsize=16,color="green",shape="box"];1379[label="xy542\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1380[label="xy5702\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1381[label="xy542",fontsize=16,color="green",shape="box"];1382[label="xy5702",fontsize=16,color="green",shape="box"];1383[label="xy542",fontsize=16,color="green",shape="box"];1384[label="xy5702",fontsize=16,color="green",shape="box"];1385[label="xy542\n  Eq a",fontsize=16,color="green",shape="box"];1386[label="xy5702\n  Eq a",fontsize=16,color="green",shape="box"];1387[label="xy542\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1388[label="xy5702\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1389[label="xy542\n  Eq a",fontsize=16,color="green",shape="box"];1390[label="xy5702\n  Eq a",fontsize=16,color="green",shape="box"];1391[label="xy542\n  Integral a",fontsize=16,color="green",shape="box"];1392[label="xy5702\n  Integral a",fontsize=16,color="green",shape="box"];1393[label="xy542",fontsize=16,color="green",shape="box"];1394[label="xy5702",fontsize=16,color="green",shape="box"];1395[label="xy542\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1396[label="xy5702\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1397[label="xy542",fontsize=16,color="green",shape="box"];1398[label="xy5702",fontsize=16,color="green",shape="box"];1399[label="xy541",fontsize=16,color="green",shape="box"];1400[label="xy5701",fontsize=16,color="green",shape="box"];1401[label="xy541",fontsize=16,color="green",shape="box"];1402[label="xy5701",fontsize=16,color="green",shape="box"];1403[label="xy541",fontsize=16,color="green",shape="box"];1404[label="xy5701",fontsize=16,color="green",shape="box"];1405[label="xy541",fontsize=16,color="green",shape="box"];1406[label="xy5701",fontsize=16,color="green",shape="box"];1407[label="xy541\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1408[label="xy5701\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1409[label="xy541",fontsize=16,color="green",shape="box"];1410[label="xy5701",fontsize=16,color="green",shape="box"];1411[label="xy541",fontsize=16,color="green",shape="box"];1412[label="xy5701",fontsize=16,color="green",shape="box"];1413[label="xy541\n  Eq a",fontsize=16,color="green",shape="box"];1414[label="xy5701\n  Eq a",fontsize=16,color="green",shape="box"];1415[label="xy541\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1416[label="xy5701\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1417[label="xy541\n  Eq a",fontsize=16,color="green",shape="box"];1418[label="xy5701\n  Eq a",fontsize=16,color="green",shape="box"];1419[label="xy541\n  Integral a",fontsize=16,color="green",shape="box"];1420[label="xy5701\n  Integral a",fontsize=16,color="green",shape="box"];1421[label="xy541",fontsize=16,color="green",shape="box"];1422[label="xy5701",fontsize=16,color="green",shape="box"];1423[label="xy541\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1424[label="xy5701\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1425[label="xy541",fontsize=16,color="green",shape="box"];1426[label="xy5701",fontsize=16,color="green",shape="box"];1427 -> 965[label="",style="dashed", color="red", weight=0];
1427[label="primEqNat xy5400 xy57000",fontsize=16,color="magenta"];1427 -> 1439[label="",style="dashed", color="magenta", weight=3];
1427 -> 1440[label="",style="dashed", color="magenta", weight=3];
1428[label="False",fontsize=16,color="green",shape="box"];1429[label="False",fontsize=16,color="green",shape="box"];1430[label="True",fontsize=16,color="green",shape="box"];1431[label="xy57000",fontsize=16,color="green",shape="box"];1432[label="xy5400",fontsize=16,color="green",shape="box"];1433[label="xy57000",fontsize=16,color="green",shape="box"];1434[label="xy5400",fontsize=16,color="green",shape="box"];1435[label="primMulInt (Pos xy5400) (Pos xy57000)",fontsize=16,color="black",shape="box"];1435 -> 1441[label="",style="solid", color="black", weight=3];
1436[label="primMulInt (Pos xy5400) (Neg xy57000)",fontsize=16,color="black",shape="box"];1436 -> 1442[label="",style="solid", color="black", weight=3];
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1438[label="primMulInt (Neg xy5400) (Neg xy57000)",fontsize=16,color="black",shape="box"];1438 -> 1444[label="",style="solid", color="black", weight=3];
1439[label="xy57000",fontsize=16,color="green",shape="box"];1440[label="xy5400",fontsize=16,color="green",shape="box"];1441[label="Pos (primMulNat xy5400 xy57000)",fontsize=16,color="green",shape="box"];1441 -> 1445[label="",style="dashed", color="green", weight=3];
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1448[label="primMulNat xy5400 xy57000",fontsize=16,color="magenta"];1448 -> 1453[label="",style="dashed", color="magenta", weight=3];
1448 -> 1454[label="",style="dashed", color="magenta", weight=3];
1449[label="primMulNat (Succ xy54000) xy57000",fontsize=16,color="burlywood",shape="box"];1919[label="xy57000/Succ xy570000",fontsize=10,color="white",style="solid",shape="box"];1449 -> 1919[label="",style="solid", color="burlywood", weight=9];
1919 -> 1455[label="",style="solid", color="burlywood", weight=3];
1920[label="xy57000/Zero",fontsize=10,color="white",style="solid",shape="box"];1449 -> 1920[label="",style="solid", color="burlywood", weight=9];
1920 -> 1456[label="",style="solid", color="burlywood", weight=3];
1450[label="primMulNat Zero xy57000",fontsize=16,color="burlywood",shape="box"];1921[label="xy57000/Succ xy570000",fontsize=10,color="white",style="solid",shape="box"];1450 -> 1921[label="",style="solid", color="burlywood", weight=9];
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1922[label="xy57000/Zero",fontsize=10,color="white",style="solid",shape="box"];1450 -> 1922[label="",style="solid", color="burlywood", weight=9];
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1457[label="primMulNat Zero (Succ xy570000)",fontsize=16,color="black",shape="box"];1457 -> 1461[label="",style="solid", color="black", weight=3];
1458[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1458 -> 1462[label="",style="solid", color="black", weight=3];
1459 -> 1463[label="",style="dashed", color="red", weight=0];
1459[label="primPlusNat (primMulNat xy54000 (Succ xy570000)) (Succ xy570000)",fontsize=16,color="magenta"];1459 -> 1464[label="",style="dashed", color="magenta", weight=3];
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1926 -> 1468[label="",style="solid", color="burlywood", weight=3];
1465[label="xy54000",fontsize=16,color="green",shape="box"];1466[label="Succ xy570000",fontsize=16,color="green",shape="box"];1467[label="primPlusNat (Succ xy780) (Succ xy570000)",fontsize=16,color="black",shape="box"];1467 -> 1469[label="",style="solid", color="black", weight=3];
1468[label="primPlusNat Zero (Succ xy570000)",fontsize=16,color="black",shape="box"];1468 -> 1470[label="",style="solid", color="black", weight=3];
1469[label="Succ (Succ (primPlusNat xy780 xy570000))",fontsize=16,color="green",shape="box"];1469 -> 1471[label="",style="dashed", color="green", weight=3];
1470[label="Succ xy570000",fontsize=16,color="green",shape="box"];1471[label="primPlusNat xy780 xy570000",fontsize=16,color="burlywood",shape="triangle"];1927[label="xy780/Succ xy7800",fontsize=10,color="white",style="solid",shape="box"];1471 -> 1927[label="",style="solid", color="burlywood", weight=9];
1927 -> 1472[label="",style="solid", color="burlywood", weight=3];
1928[label="xy780/Zero",fontsize=10,color="white",style="solid",shape="box"];1471 -> 1928[label="",style="solid", color="burlywood", weight=9];
1928 -> 1473[label="",style="solid", color="burlywood", weight=3];
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1929 -> 1474[label="",style="solid", color="burlywood", weight=3];
1930[label="xy570000/Zero",fontsize=10,color="white",style="solid",shape="box"];1472 -> 1930[label="",style="solid", color="burlywood", weight=9];
1930 -> 1475[label="",style="solid", color="burlywood", weight=3];
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1932[label="xy570000/Zero",fontsize=10,color="white",style="solid",shape="box"];1473 -> 1932[label="",style="solid", color="burlywood", weight=9];
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1475[label="primPlusNat (Succ xy7800) Zero",fontsize=16,color="black",shape="box"];1475 -> 1479[label="",style="solid", color="black", weight=3];
1476[label="primPlusNat Zero (Succ xy5700000)",fontsize=16,color="black",shape="box"];1476 -> 1480[label="",style="solid", color="black", weight=3];
1477[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1477 -> 1481[label="",style="solid", color="black", weight=3];
1478[label="Succ (Succ (primPlusNat xy7800 xy5700000))",fontsize=16,color="green",shape="box"];1478 -> 1482[label="",style="dashed", color="green", weight=3];
1479[label="Succ xy7800",fontsize=16,color="green",shape="box"];1480[label="Succ xy5700000",fontsize=16,color="green",shape="box"];1481[label="Zero",fontsize=16,color="green",shape="box"];1482 -> 1471[label="",style="dashed", color="red", weight=0];
1482[label="primPlusNat xy7800 xy5700000",fontsize=16,color="magenta"];1482 -> 1483[label="",style="dashed", color="magenta", weight=3];
1482 -> 1484[label="",style="dashed", color="magenta", weight=3];
1483[label="xy7800",fontsize=16,color="green",shape="box"];1484[label="xy5700000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xy7800), Succ(xy5700000)) → new_primPlusNat(xy7800, xy5700000)

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(xy7800), Succ(xy5700000)) → new_primPlusNat(xy7800, xy5700000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xy54000), Succ(xy570000)) → new_primMulNat(xy54000, Succ(xy570000))

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

new_primMulNat(Succ(xy54000), Succ(xy570000)) → new_primMulNat(xy54000, Succ(xy570000))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(xy5400), Succ(xy57000)) → new_primEqNat(xy5400, xy57000)

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

new_primEqNat(Succ(xy5400), Succ(xy57000)) → new_primEqNat(xy5400, xy57000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(ty_@2, cc), cd), ce) → new_esEs(xy540, xy5700, cc, cd)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(ty_[], cf), ce) → new_esEs0(xy540, xy5700, cf)
new_esEs2(Just(xy540), Just(xy5700), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs1(xy540, xy5700, bbb, bbc, bbd)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(app(ty_@3, gh), ha), hb), gf) → new_esEs1(xy541, xy5701, gh, ha, hb)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(ty_Maybe, bh)) → new_esEs2(xy541, xy5701, bh)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(ty_Either, hd), he), gf) → new_esEs3(xy541, xy5701, hd, he)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(ty_@2, gd), ge), gf) → new_esEs(xy541, xy5701, gd, ge)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(ty_Either, gb), gc)) → new_esEs3(xy542, xy5702, gb, gc)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(ty_[], hh), fa, gf) → new_esEs0(xy540, xy5700, hh)
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy540, xy5700, beb, bec)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(app(ty_@3, ff), fg), fh)) → new_esEs1(xy542, xy5702, ff, fg, fh)
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(xy540, xy5700, bdf, bdg, bdh)
new_esEs3(Left(xy540), Left(xy5700), app(app(app(ty_@3, bcd), bce), bcf), bcb) → new_esEs1(xy540, xy5700, bcd, bce, bcf)
new_esEs2(Just(xy540), Just(xy5700), app(ty_Maybe, bbe)) → new_esEs2(xy540, xy5700, bbe)
new_esEs3(Left(xy540), Left(xy5700), app(app(ty_Either, bch), bda), bcb) → new_esEs3(xy540, xy5700, bch, bda)
new_esEs3(Left(xy540), Left(xy5700), app(app(ty_@2, bbh), bca), bcb) → new_esEs(xy540, xy5700, bbh, bca)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(ty_Either, ef), eg)) → new_esEs3(xy540, xy5700, ef, eg)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(ty_@2, fb), fc)) → new_esEs(xy542, xy5702, fb, fc)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(app(ty_@3, be), bf), bg)) → new_esEs1(xy541, xy5701, be, bf, bg)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(ty_[], fd)) → new_esEs0(xy542, xy5702, fd)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(app(ty_@3, baa), bab), bac), fa, gf) → new_esEs1(xy540, xy5700, baa, bab, bac)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(ty_Either, dd), de), ce) → new_esEs3(xy540, xy5700, dd, de)
new_esEs3(Left(xy540), Left(xy5700), app(ty_Maybe, bcg), bcb) → new_esEs2(xy540, xy5700, bcg)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(ty_Maybe, hc), gf) → new_esEs2(xy541, xy5701, hc)
new_esEs3(Left(xy540), Left(xy5700), app(ty_[], bcc), bcb) → new_esEs0(xy540, xy5700, bcc)
new_esEs2(Just(xy540), Just(xy5700), app(app(ty_@2, bag), bah)) → new_esEs(xy540, xy5700, bag, bah)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(ty_Either, ca), cb)) → new_esEs3(xy541, xy5701, ca, cb)
new_esEs3(Right(xy540), Right(xy5700), bdb, app(ty_[], bde)) → new_esEs0(xy540, xy5700, bde)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(app(ty_@3, eb), ec), ed)) → new_esEs1(xy540, xy5700, eb, ec, ed)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(ty_[], gg), gf) → new_esEs0(xy541, xy5701, gg)
new_esEs2(Just(xy540), Just(xy5700), app(ty_[], bba)) → new_esEs0(xy540, xy5700, bba)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(ty_Maybe, ga)) → new_esEs2(xy542, xy5702, ga)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(ty_[], bd)) → new_esEs0(xy541, xy5701, bd)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(ty_Maybe, dc), ce) → new_esEs2(xy540, xy5700, dc)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy541, xy5701, bb, bc)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(ty_Maybe, ee)) → new_esEs2(xy540, xy5700, ee)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(ty_Maybe, bad), fa, gf) → new_esEs2(xy540, xy5700, bad)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(ty_Either, bae), baf), fa, gf) → new_esEs3(xy540, xy5700, bae, baf)
new_esEs3(Right(xy540), Right(xy5700), bdb, app(ty_Maybe, bea)) → new_esEs2(xy540, xy5700, bea)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(ty_@2, dg), dh)) → new_esEs(xy540, xy5700, dg, dh)
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(app(ty_@3, cg), da), db), ce) → new_esEs1(xy540, xy5700, cg, da, db)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(ty_[], ea)) → new_esEs0(xy540, xy5700, ea)
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(ty_@2, hf), hg), fa, gf) → new_esEs(xy540, xy5700, hf, hg)
new_esEs2(Just(xy540), Just(xy5700), app(app(ty_Either, bbf), bbg)) → new_esEs3(xy540, xy5700, bbf, bbg)
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), df) → new_esEs0(xy541, xy5701, df)
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(ty_@2, bdc), bdd)) → new_esEs(xy540, xy5700, bdc, bdd)

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

new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(ty_Maybe, ee)) → new_esEs2(xy540, xy5700, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(ty_@2, dg), dh)) → new_esEs(xy540, xy5700, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(app(ty_@3, eb), ec), ed)) → new_esEs1(xy540, xy5700, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(xy540), Just(xy5700), app(ty_Maybe, bbe)) → new_esEs2(xy540, xy5700, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(xy540), Just(xy5700), app(app(ty_@2, bag), bah)) → new_esEs(xy540, xy5700, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy540), Just(xy5700), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs1(xy540, xy5700, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(app(ty_Either, ef), eg)) → new_esEs3(xy540, xy5700, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy540), Just(xy5700), app(app(ty_Either, bbf), bbg)) → new_esEs3(xy540, xy5700, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy540), Just(xy5700), app(ty_[], bba)) → new_esEs0(xy540, xy5700, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(ty_Maybe, hc), gf) → new_esEs2(xy541, xy5701, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(ty_Maybe, ga)) → new_esEs2(xy542, xy5702, ga)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(ty_Maybe, bad), fa, gf) → new_esEs2(xy540, xy5700, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(ty_@2, gd), ge), gf) → new_esEs(xy541, xy5701, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(ty_@2, fb), fc)) → new_esEs(xy542, xy5702, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(ty_@2, hf), hg), fa, gf) → new_esEs(xy540, xy5700, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(app(ty_@3, gh), ha), hb), gf) → new_esEs1(xy541, xy5701, gh, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(app(ty_@3, ff), fg), fh)) → new_esEs1(xy542, xy5702, ff, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(app(ty_@3, baa), bab), bac), fa, gf) → new_esEs1(xy540, xy5700, baa, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(app(ty_Either, hd), he), gf) → new_esEs3(xy541, xy5701, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(app(ty_Either, gb), gc)) → new_esEs3(xy542, xy5702, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(app(ty_Either, bae), baf), fa, gf) → new_esEs3(xy540, xy5700, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), app(ty_[], hh), fa, gf) → new_esEs0(xy540, xy5700, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, fa, app(ty_[], fd)) → new_esEs0(xy542, xy5702, fd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(xy540, xy541, xy542), @3(xy5700, xy5701, xy5702), eh, app(ty_[], gg), gf) → new_esEs0(xy541, xy5701, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(ty_Maybe, bh)) → new_esEs2(xy541, xy5701, bh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(ty_Maybe, dc), ce) → new_esEs2(xy540, xy5700, dc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Left(xy540), Left(xy5700), app(ty_Maybe, bcg), bcb) → new_esEs2(xy540, xy5700, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy540), Right(xy5700), bdb, app(ty_Maybe, bea)) → new_esEs2(xy540, xy5700, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), app(ty_[], ea)) → new_esEs0(xy540, xy5700, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(:(xy540, xy541), :(xy5700, xy5701), df) → new_esEs0(xy541, xy5701, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(ty_@2, cc), cd), ce) → new_esEs(xy540, xy5700, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy541, xy5701, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Left(xy540), Left(xy5700), app(app(ty_@2, bbh), bca), bcb) → new_esEs(xy540, xy5700, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(ty_@2, bdc), bdd)) → new_esEs(xy540, xy5700, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(app(ty_@3, be), bf), bg)) → new_esEs1(xy541, xy5701, be, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(app(ty_@3, cg), da), db), ce) → new_esEs1(xy540, xy5700, cg, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(app(ty_Either, dd), de), ce) → new_esEs3(xy540, xy5700, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(app(ty_Either, ca), cb)) → new_esEs3(xy541, xy5701, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), app(ty_[], cf), ce) → new_esEs0(xy540, xy5700, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy540, xy541), @2(xy5700, xy5701), ba, app(ty_[], bd)) → new_esEs0(xy541, xy5701, bd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(xy540, xy5700, bdf, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(Left(xy540), Left(xy5700), app(app(app(ty_@3, bcd), bce), bcf), bcb) → new_esEs1(xy540, xy5700, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Right(xy540), Right(xy5700), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy540, xy5700, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Left(xy540), Left(xy5700), app(app(ty_Either, bch), bda), bcb) → new_esEs3(xy540, xy5700, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Left(xy540), Left(xy5700), app(ty_[], bcc), bcb) → new_esEs0(xy540, xy5700, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy540), Right(xy5700), bdb, app(ty_[], bde)) → new_esEs0(xy540, xy5700, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_isPrefixOf(:(xy530, xy531), :(xy5710, xy5711), ba) → new_isPrefixOf(xy531, xy5711, ba)

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

new_isPrefixOf(:(xy530, xy531), :(xy5710, xy5711), ba) → new_isPrefixOf(xy531, xy5711, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_isPrefixOf0(xy54, xy53, xy57, :(xy5610, xy5611), ba) → new_isPrefixOf0(xy54, xy53, new_flip(xy57, xy5610, ba), xy5611, ba)

The TRS R consists of the following rules:

new_flip(xy53, xy54, ba) → :(xy54, xy53)

The set Q consists of the following terms:

new_flip(x0, x1, x2)

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_isPrefixOf0(xy54, xy53, xy57, :(xy5610, xy5611), ba) → new_isPrefixOf0(xy54, xy53, new_flip(xy57, xy5610, ba), xy5611, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_isPrefixOf1(xy53, xy54, :(xy550, xy551), xy56, ba) → new_isPrefixOf1(new_flip(xy53, xy54, ba), xy550, xy551, xy56, ba)

The TRS R consists of the following rules:

new_flip(xy53, xy54, ba) → :(xy54, xy53)

The set Q consists of the following terms:

new_flip(x0, x1, x2)

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_isPrefixOf1(xy53, xy54, :(xy550, xy551), xy56, ba) → new_isPrefixOf1(new_flip(xy53, xy54, ba), xy550, xy551, xy56, ba)
The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5