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

YES 1.551 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

((isPrefixOf :: 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

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

((isPrefixOf :: 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

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

(isPrefixOf :: 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

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
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716 -> 5[label="",style="solid", color="burlywood", weight=3];
717[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="isPrefixOf (xy30 : xy31) xy4\n  Eq a",fontsize=16,color="burlywood",shape="box"];718[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 7[label="",style="solid", color="burlywood", weight=3];
719[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 8[label="",style="solid", color="burlywood", weight=3];
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7[label="isPrefixOf (xy30 : xy31) (xy40 : xy41)\n  Eq a",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
8[label="isPrefixOf (xy30 : xy31) []\n  Eq a",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9[label="True",fontsize=16,color="green",shape="box"];10 -> 107[label="",style="dashed", color="red", weight=0];
10[label="xy30 == xy40 && isPrefixOf xy31 xy41\n  Eq a",fontsize=16,color="magenta"];10 -> 108[label="",style="dashed", color="magenta", weight=3];
10 -> 109[label="",style="dashed", color="magenta", weight=3];
11[label="False",fontsize=16,color="green",shape="box"];108 -> 4[label="",style="dashed", color="red", weight=0];
108[label="isPrefixOf xy31 xy41\n  Eq a",fontsize=16,color="magenta"];108 -> 126[label="",style="dashed", color="magenta", weight=3];
108 -> 127[label="",style="dashed", color="magenta", weight=3];
109[label="xy30 == xy40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];722[label="xy30/xy300 : xy301",fontsize=10,color="white",style="solid",shape="box"];109 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 128[label="",style="solid", color="burlywood", weight=3];
723[label="xy30/[]",fontsize=10,color="white",style="solid",shape="box"];109 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 129[label="",style="solid", color="burlywood", weight=3];
107[label="xy18 && xy19",fontsize=16,color="burlywood",shape="triangle"];724[label="xy18/False",fontsize=10,color="white",style="solid",shape="box"];107 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 130[label="",style="solid", color="burlywood", weight=3];
725[label="xy18/True",fontsize=10,color="white",style="solid",shape="box"];107 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 131[label="",style="solid", color="burlywood", weight=3];
126[label="xy31\n  Eq a",fontsize=16,color="green",shape="box"];127[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];128[label="xy300 : xy301 == xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];726[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];128 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 132[label="",style="solid", color="burlywood", weight=3];
727[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];128 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 133[label="",style="solid", color="burlywood", weight=3];
129[label="[] == xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];728[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];129 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 134[label="",style="solid", color="burlywood", weight=3];
729[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];129 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 135[label="",style="solid", color="burlywood", weight=3];
130[label="False && xy19",fontsize=16,color="black",shape="box"];130 -> 136[label="",style="solid", color="black", weight=3];
131[label="True && xy19",fontsize=16,color="black",shape="box"];131 -> 137[label="",style="solid", color="black", weight=3];
132[label="xy300 : xy301 == xy400 : xy401\n  Eq a",fontsize=16,color="black",shape="box"];132 -> 138[label="",style="solid", color="black", weight=3];
133[label="xy300 : xy301 == []\n  Eq a",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3];
134[label="[] == xy400 : xy401\n  Eq a",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3];
135[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];135 -> 141[label="",style="solid", color="black", weight=3];
136[label="False",fontsize=16,color="green",shape="box"];137[label="xy19",fontsize=16,color="green",shape="box"];138 -> 107[label="",style="dashed", color="red", weight=0];
138[label="xy300 == xy400 && xy301 == xy401\n  Eq a",fontsize=16,color="magenta"];138 -> 142[label="",style="dashed", color="magenta", weight=3];
138 -> 143[label="",style="dashed", color="magenta", weight=3];
139[label="False",fontsize=16,color="green",shape="box"];140[label="False",fontsize=16,color="green",shape="box"];141[label="True",fontsize=16,color="green",shape="box"];142 -> 109[label="",style="dashed", color="red", weight=0];
142[label="xy301 == xy401\n  Eq a",fontsize=16,color="magenta"];142 -> 144[label="",style="dashed", color="magenta", weight=3];
142 -> 145[label="",style="dashed", color="magenta", weight=3];
143[label="xy300 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];732[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 732[label="",style="solid", color="blue", weight=9];
732 -> 146[label="",style="solid", color="blue", weight=3];
733[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 733[label="",style="solid", color="blue", weight=9];
733 -> 147[label="",style="solid", color="blue", weight=3];
734[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 734[label="",style="solid", color="blue", weight=9];
734 -> 148[label="",style="solid", color="blue", weight=3];
735[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 735[label="",style="solid", color="blue", weight=9];
735 -> 149[label="",style="solid", color="blue", weight=3];
736[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 736[label="",style="solid", color="blue", weight=9];
736 -> 150[label="",style="solid", color="blue", weight=3];
737[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 737[label="",style="solid", color="blue", weight=9];
737 -> 151[label="",style="solid", color="blue", weight=3];
738[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 738[label="",style="solid", color="blue", weight=9];
738 -> 152[label="",style="solid", color="blue", weight=3];
739[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 739[label="",style="solid", color="blue", weight=9];
739 -> 153[label="",style="solid", color="blue", weight=3];
740[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 740[label="",style="solid", color="blue", weight=9];
740 -> 154[label="",style="solid", color="blue", weight=3];
741[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 741[label="",style="solid", color="blue", weight=9];
741 -> 155[label="",style="solid", color="blue", weight=3];
742[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 742[label="",style="solid", color="blue", weight=9];
742 -> 156[label="",style="solid", color="blue", weight=3];
743[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 743[label="",style="solid", color="blue", weight=9];
743 -> 157[label="",style="solid", color="blue", weight=3];
744[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 744[label="",style="solid", color="blue", weight=9];
744 -> 158[label="",style="solid", color="blue", weight=3];
745[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];143 -> 745[label="",style="solid", color="blue", weight=9];
745 -> 159[label="",style="solid", color="blue", weight=3];
144[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];145[label="xy401\n  Eq a",fontsize=16,color="green",shape="box"];146[label="xy300 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];746[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];146 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 160[label="",style="solid", color="burlywood", weight=3];
147[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];747[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];147 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 161[label="",style="solid", color="burlywood", weight=3];
748[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];147 -> 748[label="",style="solid", color="burlywood", weight=9];
748 -> 162[label="",style="solid", color="burlywood", weight=3];
148[label="xy300 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];749[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];148 -> 749[label="",style="solid", color="burlywood", weight=9];
749 -> 163[label="",style="solid", color="burlywood", weight=3];
750[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];148 -> 750[label="",style="solid", color="burlywood", weight=9];
750 -> 164[label="",style="solid", color="burlywood", weight=3];
149[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];751[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];149 -> 751[label="",style="solid", color="burlywood", weight=9];
751 -> 165[label="",style="solid", color="burlywood", weight=3];
150[label="xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];752[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];150 -> 752[label="",style="solid", color="burlywood", weight=9];
752 -> 166[label="",style="solid", color="burlywood", weight=3];
753[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];150 -> 753[label="",style="solid", color="burlywood", weight=9];
753 -> 167[label="",style="solid", color="burlywood", weight=3];
151[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];754[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];151 -> 754[label="",style="solid", color="burlywood", weight=9];
754 -> 168[label="",style="solid", color="burlywood", weight=3];
152 -> 109[label="",style="dashed", color="red", weight=0];
152[label="xy300 == xy400\n  Eq a",fontsize=16,color="magenta"];152 -> 169[label="",style="dashed", color="magenta", weight=3];
152 -> 170[label="",style="dashed", color="magenta", weight=3];
153[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];153 -> 171[label="",style="solid", color="black", weight=3];
154[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];154 -> 172[label="",style="solid", color="black", weight=3];
155[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];756[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];155 -> 756[label="",style="solid", color="burlywood", weight=9];
756 -> 173[label="",style="solid", color="burlywood", weight=3];
757[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];155 -> 757[label="",style="solid", color="burlywood", weight=9];
757 -> 174[label="",style="solid", color="burlywood", weight=3];
758[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];155 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 175[label="",style="solid", color="burlywood", weight=3];
156[label="xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];759[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];156 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 176[label="",style="solid", color="burlywood", weight=3];
157[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];157 -> 177[label="",style="solid", color="black", weight=3];
158[label="xy300 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];760[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];158 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 178[label="",style="solid", color="burlywood", weight=3];
159[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];159 -> 179[label="",style="solid", color="black", weight=3];
160[label="xy3000 :% xy3001 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="box"];761[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];160 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 180[label="",style="solid", color="burlywood", weight=3];
161[label="False == xy400",fontsize=16,color="burlywood",shape="box"];762[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];161 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 181[label="",style="solid", color="burlywood", weight=3];
763[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];161 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 182[label="",style="solid", color="burlywood", weight=3];
162[label="True == xy400",fontsize=16,color="burlywood",shape="box"];764[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];162 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 183[label="",style="solid", color="burlywood", weight=3];
765[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];162 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 184[label="",style="solid", color="burlywood", weight=3];
163[label="Nothing == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];766[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];163 -> 766[label="",style="solid", color="burlywood", weight=9];
766 -> 185[label="",style="solid", color="burlywood", weight=3];
767[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];163 -> 767[label="",style="solid", color="burlywood", weight=9];
767 -> 186[label="",style="solid", color="burlywood", weight=3];
164[label="Just xy3000 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];768[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];164 -> 768[label="",style="solid", color="burlywood", weight=9];
768 -> 187[label="",style="solid", color="burlywood", weight=3];
769[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];164 -> 769[label="",style="solid", color="burlywood", weight=9];
769 -> 188[label="",style="solid", color="burlywood", weight=3];
165[label="() == xy400",fontsize=16,color="burlywood",shape="box"];770[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];165 -> 770[label="",style="solid", color="burlywood", weight=9];
770 -> 189[label="",style="solid", color="burlywood", weight=3];
166[label="Left xy3000 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];771[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];166 -> 771[label="",style="solid", color="burlywood", weight=9];
771 -> 190[label="",style="solid", color="burlywood", weight=3];
772[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];166 -> 772[label="",style="solid", color="burlywood", weight=9];
772 -> 191[label="",style="solid", color="burlywood", weight=3];
167[label="Right xy3000 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];773[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];167 -> 773[label="",style="solid", color="burlywood", weight=9];
773 -> 192[label="",style="solid", color="burlywood", weight=3];
774[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];167 -> 774[label="",style="solid", color="burlywood", weight=9];
774 -> 193[label="",style="solid", color="burlywood", weight=3];
168[label="Integer xy3000 == xy400",fontsize=16,color="burlywood",shape="box"];775[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];168 -> 775[label="",style="solid", color="burlywood", weight=9];
775 -> 194[label="",style="solid", color="burlywood", weight=3];
169[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];170[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];171[label="primEqInt xy300 xy400",fontsize=16,color="burlywood",shape="triangle"];776[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];171 -> 776[label="",style="solid", color="burlywood", weight=9];
776 -> 195[label="",style="solid", color="burlywood", weight=3];
777[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];171 -> 777[label="",style="solid", color="burlywood", weight=9];
777 -> 196[label="",style="solid", color="burlywood", weight=3];
172[label="primEqDouble xy300 xy400",fontsize=16,color="burlywood",shape="box"];778[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];172 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 197[label="",style="solid", color="burlywood", weight=3];
173[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];779[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];173 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 198[label="",style="solid", color="burlywood", weight=3];
780[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];173 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 199[label="",style="solid", color="burlywood", weight=3];
781[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];173 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 200[label="",style="solid", color="burlywood", weight=3];
174[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];782[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];174 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 201[label="",style="solid", color="burlywood", weight=3];
783[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];174 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 202[label="",style="solid", color="burlywood", weight=3];
784[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];174 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 203[label="",style="solid", color="burlywood", weight=3];
175[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];785[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];175 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 204[label="",style="solid", color="burlywood", weight=3];
786[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];175 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 205[label="",style="solid", color="burlywood", weight=3];
787[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];175 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 206[label="",style="solid", color="burlywood", weight=3];
176[label="(xy3000,xy3001) == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];788[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];176 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 207[label="",style="solid", color="burlywood", weight=3];
177[label="primEqFloat xy300 xy400",fontsize=16,color="burlywood",shape="box"];789[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];177 -> 789[label="",style="solid", color="burlywood", weight=9];
789 -> 208[label="",style="solid", color="burlywood", weight=3];
178[label="(xy3000,xy3001,xy3002) == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];790[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];178 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 209[label="",style="solid", color="burlywood", weight=3];
179[label="primEqChar xy300 xy400",fontsize=16,color="burlywood",shape="box"];791[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];179 -> 791[label="",style="solid", color="burlywood", weight=9];
791 -> 210[label="",style="solid", color="burlywood", weight=3];
180[label="xy3000 :% xy3001 == xy4000 :% xy4001\n  Integral a",fontsize=16,color="black",shape="box"];180 -> 211[label="",style="solid", color="black", weight=3];
181[label="False == False",fontsize=16,color="black",shape="box"];181 -> 212[label="",style="solid", color="black", weight=3];
182[label="False == True",fontsize=16,color="black",shape="box"];182 -> 213[label="",style="solid", color="black", weight=3];
183[label="True == False",fontsize=16,color="black",shape="box"];183 -> 214[label="",style="solid", color="black", weight=3];
184[label="True == True",fontsize=16,color="black",shape="box"];184 -> 215[label="",style="solid", color="black", weight=3];
185[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];185 -> 216[label="",style="solid", color="black", weight=3];
186[label="Nothing == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];186 -> 217[label="",style="solid", color="black", weight=3];
187[label="Just xy3000 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];187 -> 218[label="",style="solid", color="black", weight=3];
188[label="Just xy3000 == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];188 -> 219[label="",style="solid", color="black", weight=3];
189[label="() == ()",fontsize=16,color="black",shape="box"];189 -> 220[label="",style="solid", color="black", weight=3];
190[label="Left xy3000 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];190 -> 221[label="",style="solid", color="black", weight=3];
191[label="Left xy3000 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];191 -> 222[label="",style="solid", color="black", weight=3];
192[label="Right xy3000 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];192 -> 223[label="",style="solid", color="black", weight=3];
193[label="Right xy3000 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];193 -> 224[label="",style="solid", color="black", weight=3];
194[label="Integer xy3000 == Integer xy4000",fontsize=16,color="black",shape="box"];194 -> 225[label="",style="solid", color="black", weight=3];
195[label="primEqInt (Pos xy3000) xy400",fontsize=16,color="burlywood",shape="box"];792[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];195 -> 792[label="",style="solid", color="burlywood", weight=9];
792 -> 226[label="",style="solid", color="burlywood", weight=3];
793[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];195 -> 793[label="",style="solid", color="burlywood", weight=9];
793 -> 227[label="",style="solid", color="burlywood", weight=3];
196[label="primEqInt (Neg xy3000) xy400",fontsize=16,color="burlywood",shape="box"];794[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];196 -> 794[label="",style="solid", color="burlywood", weight=9];
794 -> 228[label="",style="solid", color="burlywood", weight=3];
795[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];196 -> 795[label="",style="solid", color="burlywood", weight=9];
795 -> 229[label="",style="solid", color="burlywood", weight=3];
197[label="primEqDouble (Double xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];796[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];197 -> 796[label="",style="solid", color="burlywood", weight=9];
796 -> 230[label="",style="solid", color="burlywood", weight=3];
198[label="LT == LT",fontsize=16,color="black",shape="box"];198 -> 231[label="",style="solid", color="black", weight=3];
199[label="LT == EQ",fontsize=16,color="black",shape="box"];199 -> 232[label="",style="solid", color="black", weight=3];
200[label="LT == GT",fontsize=16,color="black",shape="box"];200 -> 233[label="",style="solid", color="black", weight=3];
201[label="EQ == LT",fontsize=16,color="black",shape="box"];201 -> 234[label="",style="solid", color="black", weight=3];
202[label="EQ == EQ",fontsize=16,color="black",shape="box"];202 -> 235[label="",style="solid", color="black", weight=3];
203[label="EQ == GT",fontsize=16,color="black",shape="box"];203 -> 236[label="",style="solid", color="black", weight=3];
204[label="GT == LT",fontsize=16,color="black",shape="box"];204 -> 237[label="",style="solid", color="black", weight=3];
205[label="GT == EQ",fontsize=16,color="black",shape="box"];205 -> 238[label="",style="solid", color="black", weight=3];
206[label="GT == GT",fontsize=16,color="black",shape="box"];206 -> 239[label="",style="solid", color="black", weight=3];
207[label="(xy3000,xy3001) == (xy4000,xy4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];207 -> 240[label="",style="solid", color="black", weight=3];
208[label="primEqFloat (Float xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];797[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];208 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 241[label="",style="solid", color="burlywood", weight=3];
209[label="(xy3000,xy3001,xy3002) == (xy4000,xy4001,xy4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];209 -> 242[label="",style="solid", color="black", weight=3];
210[label="primEqChar (Char xy3000) xy400",fontsize=16,color="burlywood",shape="box"];798[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];210 -> 798[label="",style="solid", color="burlywood", weight=9];
798 -> 243[label="",style="solid", color="burlywood", weight=3];
211 -> 107[label="",style="dashed", color="red", weight=0];
211[label="xy3000 == xy4000 && xy3001 == xy4001\n  Integral a",fontsize=16,color="magenta"];211 -> 244[label="",style="dashed", color="magenta", weight=3];
211 -> 245[label="",style="dashed", color="magenta", weight=3];
212[label="True",fontsize=16,color="green",shape="box"];213[label="False",fontsize=16,color="green",shape="box"];214[label="False",fontsize=16,color="green",shape="box"];215[label="True",fontsize=16,color="green",shape="box"];216[label="True",fontsize=16,color="green",shape="box"];217[label="False",fontsize=16,color="green",shape="box"];218[label="False",fontsize=16,color="green",shape="box"];219[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];800[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 800[label="",style="solid", color="blue", weight=9];
800 -> 246[label="",style="solid", color="blue", weight=3];
801[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 801[label="",style="solid", color="blue", weight=9];
801 -> 247[label="",style="solid", color="blue", weight=3];
802[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 802[label="",style="solid", color="blue", weight=9];
802 -> 248[label="",style="solid", color="blue", weight=3];
803[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 803[label="",style="solid", color="blue", weight=9];
803 -> 249[label="",style="solid", color="blue", weight=3];
804[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 804[label="",style="solid", color="blue", weight=9];
804 -> 250[label="",style="solid", color="blue", weight=3];
805[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 805[label="",style="solid", color="blue", weight=9];
805 -> 251[label="",style="solid", color="blue", weight=3];
806[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 806[label="",style="solid", color="blue", weight=9];
806 -> 252[label="",style="solid", color="blue", weight=3];
807[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 807[label="",style="solid", color="blue", weight=9];
807 -> 253[label="",style="solid", color="blue", weight=3];
808[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 808[label="",style="solid", color="blue", weight=9];
808 -> 254[label="",style="solid", color="blue", weight=3];
809[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 809[label="",style="solid", color="blue", weight=9];
809 -> 255[label="",style="solid", color="blue", weight=3];
810[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 810[label="",style="solid", color="blue", weight=9];
810 -> 256[label="",style="solid", color="blue", weight=3];
811[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 811[label="",style="solid", color="blue", weight=9];
811 -> 257[label="",style="solid", color="blue", weight=3];
812[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 812[label="",style="solid", color="blue", weight=9];
812 -> 258[label="",style="solid", color="blue", weight=3];
813[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];219 -> 813[label="",style="solid", color="blue", weight=9];
813 -> 259[label="",style="solid", color="blue", weight=3];
220[label="True",fontsize=16,color="green",shape="box"];221[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];814[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 814[label="",style="solid", color="blue", weight=9];
814 -> 260[label="",style="solid", color="blue", weight=3];
815[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 815[label="",style="solid", color="blue", weight=9];
815 -> 261[label="",style="solid", color="blue", weight=3];
816[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 816[label="",style="solid", color="blue", weight=9];
816 -> 262[label="",style="solid", color="blue", weight=3];
817[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 817[label="",style="solid", color="blue", weight=9];
817 -> 263[label="",style="solid", color="blue", weight=3];
818[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 818[label="",style="solid", color="blue", weight=9];
818 -> 264[label="",style="solid", color="blue", weight=3];
819[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 819[label="",style="solid", color="blue", weight=9];
819 -> 265[label="",style="solid", color="blue", weight=3];
820[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 820[label="",style="solid", color="blue", weight=9];
820 -> 266[label="",style="solid", color="blue", weight=3];
821[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 821[label="",style="solid", color="blue", weight=9];
821 -> 267[label="",style="solid", color="blue", weight=3];
822[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 822[label="",style="solid", color="blue", weight=9];
822 -> 268[label="",style="solid", color="blue", weight=3];
823[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 823[label="",style="solid", color="blue", weight=9];
823 -> 269[label="",style="solid", color="blue", weight=3];
824[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 824[label="",style="solid", color="blue", weight=9];
824 -> 270[label="",style="solid", color="blue", weight=3];
825[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 825[label="",style="solid", color="blue", weight=9];
825 -> 271[label="",style="solid", color="blue", weight=3];
826[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 826[label="",style="solid", color="blue", weight=9];
826 -> 272[label="",style="solid", color="blue", weight=3];
827[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];221 -> 827[label="",style="solid", color="blue", weight=9];
827 -> 273[label="",style="solid", color="blue", weight=3];
222[label="False",fontsize=16,color="green",shape="box"];223[label="False",fontsize=16,color="green",shape="box"];224[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];828[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 828[label="",style="solid", color="blue", weight=9];
828 -> 274[label="",style="solid", color="blue", weight=3];
829[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 829[label="",style="solid", color="blue", weight=9];
829 -> 275[label="",style="solid", color="blue", weight=3];
830[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 830[label="",style="solid", color="blue", weight=9];
830 -> 276[label="",style="solid", color="blue", weight=3];
831[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 831[label="",style="solid", color="blue", weight=9];
831 -> 277[label="",style="solid", color="blue", weight=3];
832[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 832[label="",style="solid", color="blue", weight=9];
832 -> 278[label="",style="solid", color="blue", weight=3];
833[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 833[label="",style="solid", color="blue", weight=9];
833 -> 279[label="",style="solid", color="blue", weight=3];
834[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 834[label="",style="solid", color="blue", weight=9];
834 -> 280[label="",style="solid", color="blue", weight=3];
835[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 835[label="",style="solid", color="blue", weight=9];
835 -> 281[label="",style="solid", color="blue", weight=3];
836[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 836[label="",style="solid", color="blue", weight=9];
836 -> 282[label="",style="solid", color="blue", weight=3];
837[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 837[label="",style="solid", color="blue", weight=9];
837 -> 283[label="",style="solid", color="blue", weight=3];
838[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 838[label="",style="solid", color="blue", weight=9];
838 -> 284[label="",style="solid", color="blue", weight=3];
839[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 839[label="",style="solid", color="blue", weight=9];
839 -> 285[label="",style="solid", color="blue", weight=3];
840[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 840[label="",style="solid", color="blue", weight=9];
840 -> 286[label="",style="solid", color="blue", weight=3];
841[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];224 -> 841[label="",style="solid", color="blue", weight=9];
841 -> 287[label="",style="solid", color="blue", weight=3];
225 -> 171[label="",style="dashed", color="red", weight=0];
225[label="primEqInt xy3000 xy4000",fontsize=16,color="magenta"];225 -> 288[label="",style="dashed", color="magenta", weight=3];
225 -> 289[label="",style="dashed", color="magenta", weight=3];
226[label="primEqInt (Pos (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];843[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];226 -> 843[label="",style="solid", color="burlywood", weight=9];
843 -> 290[label="",style="solid", color="burlywood", weight=3];
844[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];226 -> 844[label="",style="solid", color="burlywood", weight=9];
844 -> 291[label="",style="solid", color="burlywood", weight=3];
227[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];845[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];227 -> 845[label="",style="solid", color="burlywood", weight=9];
845 -> 292[label="",style="solid", color="burlywood", weight=3];
846[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];227 -> 846[label="",style="solid", color="burlywood", weight=9];
846 -> 293[label="",style="solid", color="burlywood", weight=3];
228[label="primEqInt (Neg (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];847[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];228 -> 847[label="",style="solid", color="burlywood", weight=9];
847 -> 294[label="",style="solid", color="burlywood", weight=3];
848[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];228 -> 848[label="",style="solid", color="burlywood", weight=9];
848 -> 295[label="",style="solid", color="burlywood", weight=3];
229[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];849[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];229 -> 849[label="",style="solid", color="burlywood", weight=9];
849 -> 296[label="",style="solid", color="burlywood", weight=3];
850[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];229 -> 850[label="",style="solid", color="burlywood", weight=9];
850 -> 297[label="",style="solid", color="burlywood", weight=3];
230[label="primEqDouble (Double xy3000 xy3001) (Double xy4000 xy4001)",fontsize=16,color="black",shape="box"];230 -> 298[label="",style="solid", color="black", weight=3];
231[label="True",fontsize=16,color="green",shape="box"];232[label="False",fontsize=16,color="green",shape="box"];233[label="False",fontsize=16,color="green",shape="box"];234[label="False",fontsize=16,color="green",shape="box"];235[label="True",fontsize=16,color="green",shape="box"];236[label="False",fontsize=16,color="green",shape="box"];237[label="False",fontsize=16,color="green",shape="box"];238[label="False",fontsize=16,color="green",shape="box"];239[label="True",fontsize=16,color="green",shape="box"];240 -> 107[label="",style="dashed", color="red", weight=0];
240[label="xy3000 == xy4000 && xy3001 == xy4001\n  Eq a  Eq b",fontsize=16,color="magenta"];240 -> 299[label="",style="dashed", color="magenta", weight=3];
240 -> 300[label="",style="dashed", color="magenta", weight=3];
241[label="primEqFloat (Float xy3000 xy3001) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];241 -> 301[label="",style="solid", color="black", weight=3];
242 -> 107[label="",style="dashed", color="red", weight=0];
242[label="xy3000 == xy4000 && xy3001 == xy4001 && xy3002 == xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];242 -> 302[label="",style="dashed", color="magenta", weight=3];
242 -> 303[label="",style="dashed", color="magenta", weight=3];
243[label="primEqChar (Char xy3000) (Char xy4000)",fontsize=16,color="black",shape="box"];243 -> 304[label="",style="solid", color="black", weight=3];
244[label="xy3001 == xy4001\n  Integral a",fontsize=16,color="blue",shape="box"];853[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];244 -> 853[label="",style="solid", color="blue", weight=9];
853 -> 305[label="",style="solid", color="blue", weight=3];
854[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];244 -> 854[label="",style="solid", color="blue", weight=9];
854 -> 306[label="",style="solid", color="blue", weight=3];
245[label="xy3000 == xy4000\n  Integral a",fontsize=16,color="blue",shape="box"];855[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];245 -> 855[label="",style="solid", color="blue", weight=9];
855 -> 307[label="",style="solid", color="blue", weight=3];
856[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];245 -> 856[label="",style="solid", color="blue", weight=9];
856 -> 308[label="",style="solid", color="blue", weight=3];
246 -> 146[label="",style="dashed", color="red", weight=0];
246[label="xy3000 == xy4000\n  Integral a",fontsize=16,color="magenta"];246 -> 309[label="",style="dashed", color="magenta", weight=3];
246 -> 310[label="",style="dashed", color="magenta", weight=3];
247 -> 147[label="",style="dashed", color="red", weight=0];
247[label="xy3000 == xy4000",fontsize=16,color="magenta"];247 -> 311[label="",style="dashed", color="magenta", weight=3];
247 -> 312[label="",style="dashed", color="magenta", weight=3];
248 -> 148[label="",style="dashed", color="red", weight=0];
248[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="magenta"];248 -> 313[label="",style="dashed", color="magenta", weight=3];
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600[label="xy40000",fontsize=16,color="green",shape="box"];601[label="xy30000",fontsize=16,color="green",shape="box"];602[label="xy40000",fontsize=16,color="green",shape="box"];603[label="xy30000",fontsize=16,color="green",shape="box"];604[label="primMulInt (Pos xy30010) xy4001",fontsize=16,color="burlywood",shape="box"];1071[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];604 -> 1071[label="",style="solid", color="burlywood", weight=9];
1071 -> 666[label="",style="solid", color="burlywood", weight=3];
1072[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];604 -> 1072[label="",style="solid", color="burlywood", weight=9];
1072 -> 667[label="",style="solid", color="burlywood", weight=3];
605[label="primMulInt (Neg xy30010) xy4001",fontsize=16,color="burlywood",shape="box"];1073[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];605 -> 1073[label="",style="solid", color="burlywood", weight=9];
1073 -> 668[label="",style="solid", color="burlywood", weight=3];
1074[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];605 -> 1074[label="",style="solid", color="burlywood", weight=9];
1074 -> 669[label="",style="solid", color="burlywood", weight=3];
606[label="xy4002\n  Integral a",fontsize=16,color="green",shape="box"];607[label="xy3002\n  Integral a",fontsize=16,color="green",shape="box"];608[label="xy4002",fontsize=16,color="green",shape="box"];609[label="xy3002",fontsize=16,color="green",shape="box"];610[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];611[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];612[label="xy4002",fontsize=16,color="green",shape="box"];613[label="xy3002",fontsize=16,color="green",shape="box"];614[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];615[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];616[label="xy4002",fontsize=16,color="green",shape="box"];617[label="xy3002",fontsize=16,color="green",shape="box"];618[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];619[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];620[label="xy4002",fontsize=16,color="green",shape="box"];621[label="xy3002",fontsize=16,color="green",shape="box"];622[label="xy4002",fontsize=16,color="green",shape="box"];623[label="xy3002",fontsize=16,color="green",shape="box"];624[label="xy4002",fontsize=16,color="green",shape="box"];625[label="xy3002",fontsize=16,color="green",shape="box"];626[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];627[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];628[label="xy4002",fontsize=16,color="green",shape="box"];629[label="xy3002",fontsize=16,color="green",shape="box"];630[label="xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];631[label="xy3002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];632[label="xy4002",fontsize=16,color="green",shape="box"];633[label="xy3002",fontsize=16,color="green",shape="box"];634[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];635[label="xy3001\n  Integral a",fontsize=16,color="green",shape="box"];636[label="xy4001",fontsize=16,color="green",shape="box"];637[label="xy3001",fontsize=16,color="green",shape="box"];638[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];639[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];640[label="xy4001",fontsize=16,color="green",shape="box"];641[label="xy3001",fontsize=16,color="green",shape="box"];642[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];643[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];644[label="xy4001",fontsize=16,color="green",shape="box"];645[label="xy3001",fontsize=16,color="green",shape="box"];646[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];647[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];648[label="xy4001",fontsize=16,color="green",shape="box"];649[label="xy3001",fontsize=16,color="green",shape="box"];650[label="xy4001",fontsize=16,color="green",shape="box"];651[label="xy3001",fontsize=16,color="green",shape="box"];652[label="xy4001",fontsize=16,color="green",shape="box"];653[label="xy3001",fontsize=16,color="green",shape="box"];654[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];655[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];656[label="xy4001",fontsize=16,color="green",shape="box"];657[label="xy3001",fontsize=16,color="green",shape="box"];658[label="xy4001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];659[label="xy3001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];660[label="xy4001",fontsize=16,color="green",shape="box"];661[label="xy3001",fontsize=16,color="green",shape="box"];662 -> 304[label="",style="dashed", color="red", weight=0];
662[label="primEqNat xy30000 xy40000",fontsize=16,color="magenta"];662 -> 670[label="",style="dashed", color="magenta", weight=3];
662 -> 671[label="",style="dashed", color="magenta", weight=3];
663[label="False",fontsize=16,color="green",shape="box"];664[label="False",fontsize=16,color="green",shape="box"];665[label="True",fontsize=16,color="green",shape="box"];666[label="primMulInt (Pos xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];666 -> 672[label="",style="solid", color="black", weight=3];
667[label="primMulInt (Pos xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];667 -> 673[label="",style="solid", color="black", weight=3];
668[label="primMulInt (Neg xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];668 -> 674[label="",style="solid", color="black", weight=3];
669[label="primMulInt (Neg xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];669 -> 675[label="",style="solid", color="black", weight=3];
670[label="xy40000",fontsize=16,color="green",shape="box"];671[label="xy30000",fontsize=16,color="green",shape="box"];672[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];672 -> 676[label="",style="dashed", color="green", weight=3];
673[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];673 -> 677[label="",style="dashed", color="green", weight=3];
674[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];674 -> 678[label="",style="dashed", color="green", weight=3];
675[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];675 -> 679[label="",style="dashed", color="green", weight=3];
676[label="primMulNat xy30010 xy40010",fontsize=16,color="burlywood",shape="triangle"];1076[label="xy30010/Succ xy300100",fontsize=10,color="white",style="solid",shape="box"];676 -> 1076[label="",style="solid", color="burlywood", weight=9];
1076 -> 680[label="",style="solid", color="burlywood", weight=3];
1077[label="xy30010/Zero",fontsize=10,color="white",style="solid",shape="box"];676 -> 1077[label="",style="solid", color="burlywood", weight=9];
1077 -> 681[label="",style="solid", color="burlywood", weight=3];
677 -> 676[label="",style="dashed", color="red", weight=0];
677[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];677 -> 682[label="",style="dashed", color="magenta", weight=3];
678 -> 676[label="",style="dashed", color="red", weight=0];
678[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];678 -> 683[label="",style="dashed", color="magenta", weight=3];
679 -> 676[label="",style="dashed", color="red", weight=0];
679[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];679 -> 684[label="",style="dashed", color="magenta", weight=3];
679 -> 685[label="",style="dashed", color="magenta", weight=3];
680[label="primMulNat (Succ xy300100) xy40010",fontsize=16,color="burlywood",shape="box"];1081[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];680 -> 1081[label="",style="solid", color="burlywood", weight=9];
1081 -> 686[label="",style="solid", color="burlywood", weight=3];
1082[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];680 -> 1082[label="",style="solid", color="burlywood", weight=9];
1082 -> 687[label="",style="solid", color="burlywood", weight=3];
681[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];1083[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];681 -> 1083[label="",style="solid", color="burlywood", weight=9];
1083 -> 688[label="",style="solid", color="burlywood", weight=3];
1084[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 1084[label="",style="solid", color="burlywood", weight=9];
1084 -> 689[label="",style="solid", color="burlywood", weight=3];
682[label="xy40010",fontsize=16,color="green",shape="box"];683[label="xy30010",fontsize=16,color="green",shape="box"];684[label="xy30010",fontsize=16,color="green",shape="box"];685[label="xy40010",fontsize=16,color="green",shape="box"];686[label="primMulNat (Succ xy300100) (Succ xy400100)",fontsize=16,color="black",shape="box"];686 -> 690[label="",style="solid", color="black", weight=3];
687[label="primMulNat (Succ xy300100) Zero",fontsize=16,color="black",shape="box"];687 -> 691[label="",style="solid", color="black", weight=3];
688[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];688 -> 692[label="",style="solid", color="black", weight=3];
689[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];689 -> 693[label="",style="solid", color="black", weight=3];
690 -> 694[label="",style="dashed", color="red", weight=0];
690[label="primPlusNat (primMulNat xy300100 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];690 -> 695[label="",style="dashed", color="magenta", weight=3];
691[label="Zero",fontsize=16,color="green",shape="box"];692[label="Zero",fontsize=16,color="green",shape="box"];693[label="Zero",fontsize=16,color="green",shape="box"];695 -> 676[label="",style="dashed", color="red", weight=0];
695[label="primMulNat xy300100 (Succ xy400100)",fontsize=16,color="magenta"];695 -> 696[label="",style="dashed", color="magenta", weight=3];
695 -> 697[label="",style="dashed", color="magenta", weight=3];
694[label="primPlusNat xy20 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];1087[label="xy20/Succ xy200",fontsize=10,color="white",style="solid",shape="box"];694 -> 1087[label="",style="solid", color="burlywood", weight=9];
1087 -> 698[label="",style="solid", color="burlywood", weight=3];
1088[label="xy20/Zero",fontsize=10,color="white",style="solid",shape="box"];694 -> 1088[label="",style="solid", color="burlywood", weight=9];
1088 -> 699[label="",style="solid", color="burlywood", weight=3];
696[label="xy300100",fontsize=16,color="green",shape="box"];697[label="Succ xy400100",fontsize=16,color="green",shape="box"];698[label="primPlusNat (Succ xy200) (Succ xy400100)",fontsize=16,color="black",shape="box"];698 -> 700[label="",style="solid", color="black", weight=3];
699[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];699 -> 701[label="",style="solid", color="black", weight=3];
700[label="Succ (Succ (primPlusNat xy200 xy400100))",fontsize=16,color="green",shape="box"];700 -> 702[label="",style="dashed", color="green", weight=3];
701[label="Succ xy400100",fontsize=16,color="green",shape="box"];702[label="primPlusNat xy200 xy400100",fontsize=16,color="burlywood",shape="triangle"];1089[label="xy200/Succ xy2000",fontsize=10,color="white",style="solid",shape="box"];702 -> 1089[label="",style="solid", color="burlywood", weight=9];
1089 -> 703[label="",style="solid", color="burlywood", weight=3];
1090[label="xy200/Zero",fontsize=10,color="white",style="solid",shape="box"];702 -> 1090[label="",style="solid", color="burlywood", weight=9];
1090 -> 704[label="",style="solid", color="burlywood", weight=3];
703[label="primPlusNat (Succ xy2000) xy400100",fontsize=16,color="burlywood",shape="box"];1091[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];703 -> 1091[label="",style="solid", color="burlywood", weight=9];
1091 -> 705[label="",style="solid", color="burlywood", weight=3];
1092[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];703 -> 1092[label="",style="solid", color="burlywood", weight=9];
1092 -> 706[label="",style="solid", color="burlywood", weight=3];
704[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];1093[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];704 -> 1093[label="",style="solid", color="burlywood", weight=9];
1093 -> 707[label="",style="solid", color="burlywood", weight=3];
1094[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];704 -> 1094[label="",style="solid", color="burlywood", weight=9];
1094 -> 708[label="",style="solid", color="burlywood", weight=3];
705[label="primPlusNat (Succ xy2000) (Succ xy4001000)",fontsize=16,color="black",shape="box"];705 -> 709[label="",style="solid", color="black", weight=3];
706[label="primPlusNat (Succ xy2000) Zero",fontsize=16,color="black",shape="box"];706 -> 710[label="",style="solid", color="black", weight=3];
707[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];707 -> 711[label="",style="solid", color="black", weight=3];
708[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3];
709[label="Succ (Succ (primPlusNat xy2000 xy4001000))",fontsize=16,color="green",shape="box"];709 -> 713[label="",style="dashed", color="green", weight=3];
710[label="Succ xy2000",fontsize=16,color="green",shape="box"];711[label="Succ xy4001000",fontsize=16,color="green",shape="box"];712[label="Zero",fontsize=16,color="green",shape="box"];713 -> 702[label="",style="dashed", color="red", weight=0];
713[label="primPlusNat xy2000 xy4001000",fontsize=16,color="magenta"];713 -> 714[label="",style="dashed", color="magenta", weight=3];
713 -> 715[label="",style="dashed", color="magenta", weight=3];
714[label="xy2000",fontsize=16,color="green",shape="box"];715[label="xy4001000",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(xy2000), Succ(xy4001000)) → new_primPlusNat(xy2000, xy4001000)

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(xy2000), Succ(xy4001000)) → new_primPlusNat(xy2000, xy4001000)
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(xy300100), Succ(xy400100)) → new_primMulNat(xy300100, Succ(xy400100))

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

new_primMulNat(Succ(xy300100), Succ(xy400100)) → new_primMulNat(xy300100, Succ(xy400100))
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(xy30000), Succ(xy40000)) → new_primEqNat(xy30000, xy40000)

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

new_primEqNat(Succ(xy30000), Succ(xy40000)) → new_primEqNat(xy30000, xy40000)
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(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(ty_@2, bcg), bch)), hg), bbb)) → new_esEs2(xy3000, xy4000, bcg, bch)
new_esEs1(Right(xy3000), Right(xy4000), df, app(ty_Maybe, dg)) → new_esEs0(xy3000, xy4000, dg)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(ty_@2, bad), bae))) → new_esEs2(xy3002, xy4002, bad, bae)
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(ty_[], eb))) → new_esEs(xy3000, xy4000, eb)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(ty_Maybe, bba)), bbb)) → new_esEs0(xy3001, xy4001, bba)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(ty_Maybe, bba), bbb) → new_esEs0(xy3001, xy4001, bba)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(ty_[], gh)), ge)) → new_esEs(xy3000, xy4000, gh)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(app(ty_@3, hc), hd), he)), ge)) → new_esEs3(xy3000, xy4000, hc, hd, he)
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(ty_@2, ec), ed))) → new_esEs2(xy3000, xy4000, ec, ed)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(ty_Maybe, hh)) → new_esEs0(xy3002, xy4002, hh)
new_esEs0(Just(xy3000), Just(xy4000), app(ty_Maybe, bb)) → new_esEs0(xy3000, xy4000, bb)
new_esEs0(Just(xy3000), Just(xy4000), app(ty_[], be)) → new_esEs(xy3000, xy4000, be)
new_esEs1(Left(xy3000), Left(xy4000), app(app(ty_Either, ce), cf), cd) → new_esEs1(xy3000, xy4000, ce, cf)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(ty_Maybe, bcc)), hg), bbb)) → new_esEs0(xy3000, xy4000, bcc)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(app(ty_@3, ga), gb), gc)) → new_esEs3(xy3001, xy4001, ga, gb, gc)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(ty_[], bbe), bbb) → new_esEs(xy3001, xy4001, bbe)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(ty_[], ff))) → new_esEs(xy3001, xy4001, ff)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bcd), bce), hg, bbb) → new_esEs1(xy3000, xy4000, bcd, bce)
new_esEs1(Left(xy3000), Left(xy4000), app(app(ty_@2, da), db), cd) → new_esEs2(xy3000, xy4000, da, db)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(app(ty_@3, bda), bdb), bdc)), hg), bbb)) → new_esEs3(xy3000, xy4000, bda, bdb, bdc)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, gd), ge) → new_esEs0(xy3000, xy4000, gd)
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(ty_[], cg)), cd)) → new_esEs(xy3000, xy4000, cg)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(ty_Either, bbc), bbd), bbb) → new_esEs1(xy3001, xy4001, bbc, bbd)
new_esEs0(Just(xy3000), Just(xy4000), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(xy3000, xy4000, bh, ca, cb)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bcg), bch), hg, bbb) → new_esEs2(xy3000, xy4000, bcg, bch)
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(app(ty_@3, dc), dd), de)), cd)) → new_esEs3(xy3000, xy4000, dc, dd, de)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(ty_Either, fc), fd))) → new_esEs1(xy3001, xy4001, fc, fd)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(ty_Maybe, hh))) → new_esEs0(xy3002, xy4002, hh)
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(ty_@2, da), db)), cd)) → new_esEs2(xy3000, xy4000, da, db)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(ty_Either, gf), gg)), ge)) → new_esEs1(xy3000, xy4000, gf, gg)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bcc), hg, bbb) → new_esEs0(xy3000, xy4000, bcc)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(app(ty_@3, bbh), bca), bcb)), bbb)) → new_esEs3(xy3001, xy4001, bbh, bca, bcb)
new_esEs1(Right(xy3000), Right(xy4000), df, app(ty_[], eb)) → new_esEs(xy3000, xy4000, eb)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, gf), gg), ge) → new_esEs1(xy3000, xy4000, gf, gg)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(ty_[], bac))) → new_esEs(xy3002, xy4002, bac)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, hc), hd), he), ge) → new_esEs3(xy3000, xy4000, hc, hd, he)
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(ty_Maybe, dg))) → new_esEs0(xy3000, xy4000, dg)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(ty_[], bbe)), bbb)) → new_esEs(xy3001, xy4001, bbe)
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(ty_Either, ce), cf)), cd)) → new_esEs1(xy3000, xy4000, ce, cf)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(ty_@2, bbf), bbg)), bbb)) → new_esEs2(xy3001, xy4001, bbf, bbg)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(ty_@2, fg), fh))) → new_esEs2(xy3001, xy4001, fg, fh)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(app(ty_@3, baf), bag), bah)) → new_esEs3(xy3002, xy4002, baf, bag, bah)
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(ty_Maybe, cc)), cd)) → new_esEs0(xy3000, xy4000, cc)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(ty_[], bcf)), hg), bbb)) → new_esEs(xy3000, xy4000, bcf)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(ty_[], bac)) → new_esEs(xy3002, xy4002, bac)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(ty_@2, fg), fh)) → new_esEs2(xy3001, xy4001, fg, fh)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(ty_Either, bcd), bce)), hg), bbb)) → new_esEs1(xy3000, xy4000, bcd, bce)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(ty_Maybe, fb)) → new_esEs0(xy3001, xy4001, fb)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], bcf), hg, bbb) → new_esEs(xy3000, xy4000, bcf)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, ha), hb), ge) → new_esEs2(xy3000, xy4000, ha, hb)
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(ty_[], be))) → new_esEs(xy3000, xy4000, be)
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(ty_Either, dh), ea)) → new_esEs1(xy3000, xy4000, dh, ea)
new_esEs1(Left(xy3000), Left(xy4000), app(ty_Maybe, cc), cd) → new_esEs0(xy3000, xy4000, cc)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(app(ty_@3, baf), bag), bah))) → new_esEs3(xy3002, xy4002, baf, bag, bah)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(ty_Either, fc), fd)) → new_esEs1(xy3001, xy4001, fc, fd)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(app(ty_@3, bbh), bca), bcb), bbb) → new_esEs3(xy3001, xy4001, bbh, bca, bcb)
new_esEs0(Just(xy3000), Just(xy4000), app(app(ty_@2, bf), bg)) → new_esEs2(xy3000, xy4000, bf, bg)
new_esEs(:(xy300, xy301), :(xy400, xy401), ba) → new_esEs(xy301, xy401, ba)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(ty_[], ff)) → new_esEs(xy3001, xy4001, ff)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(ty_@2, bad), bae)) → new_esEs2(xy3002, xy4002, bad, bae)
new_esEs0(Just(xy3000), Just(xy4000), app(app(ty_Either, bc), bd)) → new_esEs1(xy3000, xy4000, bc, bd)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(ty_Either, baa), bab))) → new_esEs1(xy3002, xy4002, baa, bab)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(ty_@2, bbf), bbg), bbb) → new_esEs2(xy3001, xy4001, bbf, bbg)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(ty_Maybe, gd)), ge)) → new_esEs0(xy3000, xy4000, gd)
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(app(ty_@3, ee), ef), eg)) → new_esEs3(xy3000, xy4000, ee, ef, eg)
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(ty_@2, bf), bg))) → new_esEs2(xy3000, xy4000, bf, bg)
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(ty_Maybe, bb))) → new_esEs0(xy3000, xy4000, bb)
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(app(ty_@3, bh), ca), cb))) → new_esEs3(xy3000, xy4000, bh, ca, cb)
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(ty_@2, ec), ed)) → new_esEs2(xy3000, xy4000, ec, ed)
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(app(ty_@3, ee), ef), eg))) → new_esEs3(xy3000, xy4000, ee, ef, eg)
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(ty_Either, bc), bd))) → new_esEs1(xy3000, xy4000, bc, bd)
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], gh), ge) → new_esEs(xy3000, xy4000, gh)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(ty_@2, ha), hb)), ge)) → new_esEs2(xy3000, xy4000, ha, hb)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(ty_Either, baa), bab)) → new_esEs1(xy3002, xy4002, baa, bab)
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(ty_Either, dh), ea))) → new_esEs1(xy3000, xy4000, dh, ea)
new_esEs1(Left(xy3000), Left(xy4000), app(ty_[], cg), cd) → new_esEs(xy3000, xy4000, cg)
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(ty_Either, bbc), bbd)), bbb)) → new_esEs1(xy3001, xy4001, bbc, bbd)
new_esEs1(Left(xy3000), Left(xy4000), app(app(app(ty_@3, dc), dd), de), cd) → new_esEs3(xy3000, xy4000, dc, dd, de)
new_esEs(:(xy300, xy301), :(xy400, xy401), app(ty_[], eh)) → new_esEs(xy300, xy400, eh)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(ty_Maybe, fb))) → new_esEs0(xy3001, xy4001, fb)
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bda), bdb), bdc), hg, bbb) → new_esEs3(xy3000, xy4000, bda, bdb, bdc)
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(app(ty_@3, ga), gb), gc))) → new_esEs3(xy3001, xy4001, ga, gb, gc)

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

new_esEs0(Just(xy3000), Just(xy4000), app(ty_[], be)) → new_esEs(xy3000, xy4000, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Just(xy3000), Just(xy4000), app(app(ty_Either, bc), bd)) → new_esEs1(xy3000, xy4000, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xy3000), Just(xy4000), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(xy3000, xy4000, bh, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Just(xy3000), Just(xy4000), app(ty_Maybe, bb)) → new_esEs0(xy3000, xy4000, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Just(xy3000), Just(xy4000), app(app(ty_@2, bf), bg)) → new_esEs2(xy3000, xy4000, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(ty_[], ff)) → new_esEs(xy3001, xy4001, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], gh), ge) → new_esEs(xy3000, xy4000, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, gf), gg), ge) → new_esEs1(xy3000, xy4000, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(ty_Either, fc), fd)) → new_esEs1(xy3001, xy4001, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(app(ty_@3, ga), gb), gc)) → new_esEs3(xy3001, xy4001, ga, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, hc), hd), he), ge) → new_esEs3(xy3000, xy4000, hc, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, gd), ge) → new_esEs0(xy3000, xy4000, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(ty_Maybe, fb)) → new_esEs0(xy3001, xy4001, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), fa, app(app(ty_@2, fg), fh)) → new_esEs2(xy3001, xy4001, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, ha), hb), ge) → new_esEs2(xy3000, xy4000, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(ty_[], eb))) → new_esEs(xy3000, xy4000, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(ty_[], gh)), ge)) → new_esEs(xy3000, xy4000, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(ty_[], ff))) → new_esEs(xy3001, xy4001, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(ty_[], cg)), cd)) → new_esEs(xy3000, xy4000, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(ty_[], bac))) → new_esEs(xy3002, xy4002, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(ty_[], bbe)), bbb)) → new_esEs(xy3001, xy4001, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(ty_[], bcf)), hg), bbb)) → new_esEs(xy3000, xy4000, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(ty_[], be))) → new_esEs(xy3000, xy4000, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xy300, xy301), :(xy400, xy401), ba) → new_esEs(xy301, xy401, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(xy300, xy301), :(xy400, xy401), app(ty_[], eh)) → new_esEs(xy300, xy400, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(ty_[], bbe), bbb) → new_esEs(xy3001, xy4001, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(ty_[], bac)) → new_esEs(xy3002, xy4002, bac)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], bcf), hg, bbb) → new_esEs(xy3000, xy4000, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Right(xy3000), Right(xy4000), df, app(ty_[], eb)) → new_esEs(xy3000, xy4000, eb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Left(xy3000), Left(xy4000), app(ty_[], cg), cd) → new_esEs(xy3000, xy4000, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(ty_Either, fc), fd))) → new_esEs1(xy3001, xy4001, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(ty_Either, gf), gg)), ge)) → new_esEs1(xy3000, xy4000, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(ty_Either, ce), cf)), cd)) → new_esEs1(xy3000, xy4000, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(ty_Either, bcd), bce)), hg), bbb)) → new_esEs1(xy3000, xy4000, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(ty_Either, baa), bab))) → new_esEs1(xy3002, xy4002, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(ty_Either, bc), bd))) → new_esEs1(xy3000, xy4000, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(ty_Either, dh), ea))) → new_esEs1(xy3000, xy4000, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(ty_Either, bbc), bbd)), bbb)) → new_esEs1(xy3001, xy4001, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bcd), bce), hg, bbb) → new_esEs1(xy3000, xy4000, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(ty_Either, bbc), bbd), bbb) → new_esEs1(xy3001, xy4001, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(ty_Either, baa), bab)) → new_esEs1(xy3002, xy4002, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(Left(xy3000), Left(xy4000), app(app(ty_Either, ce), cf), cd) → new_esEs1(xy3000, xy4000, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(ty_Either, dh), ea)) → new_esEs1(xy3000, xy4000, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(app(ty_@3, hc), hd), he)), ge)) → new_esEs3(xy3000, xy4000, hc, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(app(ty_@3, bda), bdb), bdc)), hg), bbb)) → new_esEs3(xy3000, xy4000, bda, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(app(ty_@3, dc), dd), de)), cd)) → new_esEs3(xy3000, xy4000, dc, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(app(ty_@3, bbh), bca), bcb)), bbb)) → new_esEs3(xy3001, xy4001, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(app(ty_@3, baf), bag), bah))) → new_esEs3(xy3002, xy4002, baf, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(app(ty_@3, bh), ca), cb))) → new_esEs3(xy3000, xy4000, bh, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(app(ty_@3, ee), ef), eg))) → new_esEs3(xy3000, xy4000, ee, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(app(ty_@3, ga), gb), gc))) → new_esEs3(xy3001, xy4001, ga, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(ty_Maybe, bba)), bbb)) → new_esEs0(xy3001, xy4001, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(ty_Maybe, bcc)), hg), bbb)) → new_esEs0(xy3000, xy4000, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(ty_Maybe, hh))) → new_esEs0(xy3002, xy4002, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(ty_Maybe, dg))) → new_esEs0(xy3000, xy4000, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(ty_Maybe, cc)), cd)) → new_esEs0(xy3000, xy4000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(ty_Maybe, gd)), ge)) → new_esEs0(xy3000, xy4000, gd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(ty_Maybe, bb))) → new_esEs0(xy3000, xy4000, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(ty_Maybe, fb))) → new_esEs0(xy3001, xy4001, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, app(app(ty_@2, bcg), bch)), hg), bbb)) → new_esEs2(xy3000, xy4000, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), hg), app(app(ty_@2, bad), bae))) → new_esEs2(xy3002, xy4002, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Right(xy3000), xy301), :(Right(xy4000), xy401), app(app(ty_Either, df), app(app(ty_@2, ec), ed))) → new_esEs2(xy3000, xy4000, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Left(xy3000), xy301), :(Left(xy4000), xy401), app(app(ty_Either, app(app(ty_@2, da), db)), cd)) → new_esEs2(xy3000, xy4000, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@3(xy3000, xy3001, xy3002), xy301), :(@3(xy4000, xy4001, xy4002), xy401), app(app(app(ty_@3, hf), app(app(ty_@2, bbf), bbg)), bbb)) → new_esEs2(xy3001, xy4001, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, fa), app(app(ty_@2, fg), fh))) → new_esEs2(xy3001, xy4001, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(Just(xy3000), xy301), :(Just(xy4000), xy401), app(ty_Maybe, app(app(ty_@2, bf), bg))) → new_esEs2(xy3000, xy4000, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(@2(xy3000, xy3001), xy301), :(@2(xy4000, xy4001), xy401), app(app(ty_@2, app(app(ty_@2, ha), hb)), ge)) → new_esEs2(xy3000, xy4000, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(app(ty_@3, baf), bag), bah)) → new_esEs3(xy3002, xy4002, baf, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(app(ty_@3, bbh), bca), bcb), bbb) → new_esEs3(xy3001, xy4001, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bda), bdb), bdc), hg, bbb) → new_esEs3(xy3000, xy4000, bda, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(app(ty_@3, ee), ef), eg)) → new_esEs3(xy3000, xy4000, ee, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(Left(xy3000), Left(xy4000), app(app(app(ty_@3, dc), dd), de), cd) → new_esEs3(xy3000, xy4000, dc, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(ty_Maybe, bba), bbb) → new_esEs0(xy3001, xy4001, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(ty_Maybe, hh)) → new_esEs0(xy3002, xy4002, hh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bcc), hg, bbb) → new_esEs0(xy3000, xy4000, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bcg), bch), hg, bbb) → new_esEs2(xy3000, xy4000, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, hg, app(app(ty_@2, bad), bae)) → new_esEs2(xy3002, xy4002, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs3(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), hf, app(app(ty_@2, bbf), bbg), bbb) → new_esEs2(xy3001, xy4001, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(Right(xy3000), Right(xy4000), df, app(ty_Maybe, dg)) → new_esEs0(xy3000, xy4000, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Left(xy3000), Left(xy4000), app(ty_Maybe, cc), cd) → new_esEs0(xy3000, xy4000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Left(xy3000), Left(xy4000), app(app(ty_@2, da), db), cd) → new_esEs2(xy3000, xy4000, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Right(xy3000), Right(xy4000), df, app(app(ty_@2, ec), ed)) → new_esEs2(xy3000, xy4000, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4

↳ 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_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba) → new_isPrefixOf(xy31, xy41, ba)

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

new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba) → new_isPrefixOf(xy31, xy41, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3