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

YES 1.655 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, Eq b) => [Either a b] -> [Either a b] -> Bool) :: (Eq a, Eq b) => [Either a b] -> [Either a b] -> 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 b, Eq a) => [Either b a] -> [Either b a] -> Bool) :: (Eq a, Eq b) => [Either b a] -> [Either b 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 b, Eq a) => [Either a b] -> [Either a b] -> 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

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703[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];84 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 134[label="",style="solid", color="burlywood", weight=3];
85[label="(xy3000,xy3001,xy3002) == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];704[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];85 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 135[label="",style="solid", color="burlywood", weight=3];
86[label="xy3000 : xy3001 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];705[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];86 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 136[label="",style="solid", color="burlywood", weight=3];
706[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];86 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 137[label="",style="solid", color="burlywood", weight=3];
87[label="[] == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];707[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];87 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 138[label="",style="solid", color="burlywood", weight=3];
708[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];87 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 139[label="",style="solid", color="burlywood", weight=3];
88[label="(xy3000,xy3001) == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];709[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];88 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 140[label="",style="solid", color="burlywood", weight=3];
89[label="primEqFloat xy300 xy400",fontsize=16,color="burlywood",shape="box"];710[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];89 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 141[label="",style="solid", color="burlywood", weight=3];
90[label="primEqChar xy300 xy400",fontsize=16,color="burlywood",shape="box"];711[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];90 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 142[label="",style="solid", color="burlywood", weight=3];
91[label="primEqDouble xy300 xy400",fontsize=16,color="burlywood",shape="box"];712[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];91 -> 712[label="",style="solid", color="burlywood", weight=9];
712 -> 143[label="",style="solid", color="burlywood", weight=3];
92[label="primEqInt xy300 xy400",fontsize=16,color="burlywood",shape="triangle"];713[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];92 -> 713[label="",style="solid", color="burlywood", weight=9];
713 -> 144[label="",style="solid", color="burlywood", weight=3];
714[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];92 -> 714[label="",style="solid", color="burlywood", weight=9];
714 -> 145[label="",style="solid", color="burlywood", weight=3];
93[label="Nothing == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];715[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];93 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 146[label="",style="solid", color="burlywood", weight=3];
716[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];93 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 147[label="",style="solid", color="burlywood", weight=3];
94[label="Just xy3000 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];717[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];94 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 148[label="",style="solid", color="burlywood", weight=3];
718[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];94 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 149[label="",style="solid", color="burlywood", weight=3];
95[label="() == xy400",fontsize=16,color="burlywood",shape="box"];719[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];95 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 150[label="",style="solid", color="burlywood", weight=3];
96[label="xy3000 :% xy3001 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="box"];720[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];96 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 151[label="",style="solid", color="burlywood", weight=3];
97[label="Integer xy3000 == xy400",fontsize=16,color="burlywood",shape="box"];721[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];97 -> 721[label="",style="solid", color="burlywood", weight=9];
721 -> 152[label="",style="solid", color="burlywood", weight=3];
98[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];99[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];100[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];722[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];100 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 153[label="",style="solid", color="burlywood", weight=3];
723[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];100 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 154[label="",style="solid", color="burlywood", weight=3];
724[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];100 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 155[label="",style="solid", color="burlywood", weight=3];
101[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];725[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];101 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 156[label="",style="solid", color="burlywood", weight=3];
726[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];101 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 157[label="",style="solid", color="burlywood", weight=3];
727[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];101 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 158[label="",style="solid", color="burlywood", weight=3];
102[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];728[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];102 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 159[label="",style="solid", color="burlywood", weight=3];
729[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];102 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 160[label="",style="solid", color="burlywood", weight=3];
730[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];102 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 161[label="",style="solid", color="burlywood", weight=3];
103[label="xy400",fontsize=16,color="green",shape="box"];104[label="xy300",fontsize=16,color="green",shape="box"];105[label="xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];106[label="xy300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];107[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];108[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];109[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];110[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];111[label="xy400",fontsize=16,color="green",shape="box"];112[label="xy300",fontsize=16,color="green",shape="box"];113[label="xy400",fontsize=16,color="green",shape="box"];114[label="xy300",fontsize=16,color="green",shape="box"];115[label="xy400",fontsize=16,color="green",shape="box"];116[label="xy300",fontsize=16,color="green",shape="box"];117[label="xy400",fontsize=16,color="green",shape="box"];118[label="xy300",fontsize=16,color="green",shape="box"];119[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];120[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];121[label="xy400",fontsize=16,color="green",shape="box"];122[label="xy300",fontsize=16,color="green",shape="box"];123[label="xy400\n  Integral a",fontsize=16,color="green",shape="box"];124[label="xy300\n  Integral a",fontsize=16,color="green",shape="box"];125[label="xy400",fontsize=16,color="green",shape="box"];126[label="xy300",fontsize=16,color="green",shape="box"];127[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];128[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];129[label="xy400",fontsize=16,color="green",shape="box"];130[label="xy300",fontsize=16,color="green",shape="box"];131[label="False == False",fontsize=16,color="black",shape="box"];131 -> 162[label="",style="solid", color="black", weight=3];
132[label="False == True",fontsize=16,color="black",shape="box"];132 -> 163[label="",style="solid", color="black", weight=3];
133[label="True == False",fontsize=16,color="black",shape="box"];133 -> 164[label="",style="solid", color="black", weight=3];
134[label="True == True",fontsize=16,color="black",shape="box"];134 -> 165[label="",style="solid", color="black", weight=3];
135[label="(xy3000,xy3001,xy3002) == (xy4000,xy4001,xy4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];135 -> 166[label="",style="solid", color="black", weight=3];
136[label="xy3000 : xy3001 == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];136 -> 167[label="",style="solid", color="black", weight=3];
137[label="xy3000 : xy3001 == []\n  Eq a",fontsize=16,color="black",shape="box"];137 -> 168[label="",style="solid", color="black", weight=3];
138[label="[] == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];138 -> 169[label="",style="solid", color="black", weight=3];
139[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];139 -> 170[label="",style="solid", color="black", weight=3];
140[label="(xy3000,xy3001) == (xy4000,xy4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];140 -> 171[label="",style="solid", color="black", weight=3];
141[label="primEqFloat (Float xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];731[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];141 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 172[label="",style="solid", color="burlywood", weight=3];
142[label="primEqChar (Char xy3000) xy400",fontsize=16,color="burlywood",shape="box"];732[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];142 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 173[label="",style="solid", color="burlywood", weight=3];
143[label="primEqDouble (Double xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];733[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];143 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 174[label="",style="solid", color="burlywood", weight=3];
144[label="primEqInt (Pos xy3000) xy400",fontsize=16,color="burlywood",shape="box"];734[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];144 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 175[label="",style="solid", color="burlywood", weight=3];
735[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];144 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 176[label="",style="solid", color="burlywood", weight=3];
145[label="primEqInt (Neg xy3000) xy400",fontsize=16,color="burlywood",shape="box"];736[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];145 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 177[label="",style="solid", color="burlywood", weight=3];
737[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];145 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 178[label="",style="solid", color="burlywood", weight=3];
146[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];146 -> 179[label="",style="solid", color="black", weight=3];
147[label="Nothing == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];147 -> 180[label="",style="solid", color="black", weight=3];
148[label="Just xy3000 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];148 -> 181[label="",style="solid", color="black", weight=3];
149[label="Just xy3000 == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];149 -> 182[label="",style="solid", color="black", weight=3];
150[label="() == ()",fontsize=16,color="black",shape="box"];150 -> 183[label="",style="solid", color="black", weight=3];
151[label="xy3000 :% xy3001 == xy4000 :% xy4001\n  Integral a",fontsize=16,color="black",shape="box"];151 -> 184[label="",style="solid", color="black", weight=3];
152[label="Integer xy3000 == Integer xy4000",fontsize=16,color="black",shape="box"];152 -> 185[label="",style="solid", color="black", weight=3];
153[label="LT == LT",fontsize=16,color="black",shape="box"];153 -> 186[label="",style="solid", color="black", weight=3];
154[label="LT == EQ",fontsize=16,color="black",shape="box"];154 -> 187[label="",style="solid", color="black", weight=3];
155[label="LT == GT",fontsize=16,color="black",shape="box"];155 -> 188[label="",style="solid", color="black", weight=3];
156[label="EQ == LT",fontsize=16,color="black",shape="box"];156 -> 189[label="",style="solid", color="black", weight=3];
157[label="EQ == EQ",fontsize=16,color="black",shape="box"];157 -> 190[label="",style="solid", color="black", weight=3];
158[label="EQ == GT",fontsize=16,color="black",shape="box"];158 -> 191[label="",style="solid", color="black", weight=3];
159[label="GT == LT",fontsize=16,color="black",shape="box"];159 -> 192[label="",style="solid", color="black", weight=3];
160[label="GT == EQ",fontsize=16,color="black",shape="box"];160 -> 193[label="",style="solid", color="black", weight=3];
161[label="GT == GT",fontsize=16,color="black",shape="box"];161 -> 194[label="",style="solid", color="black", weight=3];
162[label="True",fontsize=16,color="green",shape="box"];163[label="False",fontsize=16,color="green",shape="box"];164[label="False",fontsize=16,color="green",shape="box"];165[label="True",fontsize=16,color="green",shape="box"];166 -> 26[label="",style="dashed", color="red", weight=0];
166[label="xy3000 == xy4000 && xy3001 == xy4001 && xy3002 == xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];166 -> 195[label="",style="dashed", color="magenta", weight=3];
166 -> 196[label="",style="dashed", color="magenta", weight=3];
167 -> 26[label="",style="dashed", color="red", weight=0];
167[label="xy3000 == xy4000 && xy3001 == xy4001\n  Eq a",fontsize=16,color="magenta"];167 -> 197[label="",style="dashed", color="magenta", weight=3];
167 -> 198[label="",style="dashed", color="magenta", weight=3];
168[label="False",fontsize=16,color="green",shape="box"];169[label="False",fontsize=16,color="green",shape="box"];170[label="True",fontsize=16,color="green",shape="box"];171 -> 26[label="",style="dashed", color="red", weight=0];
171[label="xy3000 == xy4000 && xy3001 == xy4001\n  Eq a  Eq b",fontsize=16,color="magenta"];171 -> 199[label="",style="dashed", color="magenta", weight=3];
171 -> 200[label="",style="dashed", color="magenta", weight=3];
172[label="primEqFloat (Float xy3000 xy3001) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];172 -> 201[label="",style="solid", color="black", weight=3];
173[label="primEqChar (Char xy3000) (Char xy4000)",fontsize=16,color="black",shape="box"];173 -> 202[label="",style="solid", color="black", weight=3];
174[label="primEqDouble (Double xy3000 xy3001) (Double xy4000 xy4001)",fontsize=16,color="black",shape="box"];174 -> 203[label="",style="solid", color="black", weight=3];
175[label="primEqInt (Pos (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];741[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];175 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 204[label="",style="solid", color="burlywood", weight=3];
742[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];175 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 205[label="",style="solid", color="burlywood", weight=3];
176[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];743[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];176 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 206[label="",style="solid", color="burlywood", weight=3];
744[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];176 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 207[label="",style="solid", color="burlywood", weight=3];
177[label="primEqInt (Neg (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];745[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];177 -> 745[label="",style="solid", color="burlywood", weight=9];
745 -> 208[label="",style="solid", color="burlywood", weight=3];
746[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];177 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 209[label="",style="solid", color="burlywood", weight=3];
178[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];747[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];178 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 210[label="",style="solid", color="burlywood", weight=3];
748[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];178 -> 748[label="",style="solid", color="burlywood", weight=9];
748 -> 211[label="",style="solid", color="burlywood", weight=3];
179[label="True",fontsize=16,color="green",shape="box"];180[label="False",fontsize=16,color="green",shape="box"];181[label="False",fontsize=16,color="green",shape="box"];182[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];749[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 749[label="",style="solid", color="blue", weight=9];
749 -> 212[label="",style="solid", color="blue", weight=3];
750[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 750[label="",style="solid", color="blue", weight=9];
750 -> 213[label="",style="solid", color="blue", weight=3];
751[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 751[label="",style="solid", color="blue", weight=9];
751 -> 214[label="",style="solid", color="blue", weight=3];
752[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 752[label="",style="solid", color="blue", weight=9];
752 -> 215[label="",style="solid", color="blue", weight=3];
753[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 753[label="",style="solid", color="blue", weight=9];
753 -> 216[label="",style="solid", color="blue", weight=3];
754[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 754[label="",style="solid", color="blue", weight=9];
754 -> 217[label="",style="solid", color="blue", weight=3];
755[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 755[label="",style="solid", color="blue", weight=9];
755 -> 218[label="",style="solid", color="blue", weight=3];
756[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 756[label="",style="solid", color="blue", weight=9];
756 -> 219[label="",style="solid", color="blue", weight=3];
757[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 757[label="",style="solid", color="blue", weight=9];
757 -> 220[label="",style="solid", color="blue", weight=3];
758[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 758[label="",style="solid", color="blue", weight=9];
758 -> 221[label="",style="solid", color="blue", weight=3];
759[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 759[label="",style="solid", color="blue", weight=9];
759 -> 222[label="",style="solid", color="blue", weight=3];
760[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 760[label="",style="solid", color="blue", weight=9];
760 -> 223[label="",style="solid", color="blue", weight=3];
761[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 761[label="",style="solid", color="blue", weight=9];
761 -> 224[label="",style="solid", color="blue", weight=3];
762[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 762[label="",style="solid", color="blue", weight=9];
762 -> 225[label="",style="solid", color="blue", weight=3];
183[label="True",fontsize=16,color="green",shape="box"];184 -> 26[label="",style="dashed", color="red", weight=0];
184[label="xy3000 == xy4000 && xy3001 == xy4001\n  Integral a",fontsize=16,color="magenta"];184 -> 226[label="",style="dashed", color="magenta", weight=3];
184 -> 227[label="",style="dashed", color="magenta", weight=3];
185 -> 92[label="",style="dashed", color="red", weight=0];
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500[label="False",fontsize=16,color="green",shape="box"];501[label="False",fontsize=16,color="green",shape="box"];502[label="True",fontsize=16,color="green",shape="box"];503[label="False",fontsize=16,color="green",shape="box"];504[label="True",fontsize=16,color="green",shape="box"];505[label="xy4000",fontsize=16,color="green",shape="box"];506[label="xy3000",fontsize=16,color="green",shape="box"];507[label="xy4000",fontsize=16,color="green",shape="box"];508[label="xy3000",fontsize=16,color="green",shape="box"];509[label="xy4001",fontsize=16,color="green",shape="box"];510[label="xy3001",fontsize=16,color="green",shape="box"];511[label="xy4001",fontsize=16,color="green",shape="box"];512[label="xy3001",fontsize=16,color="green",shape="box"];513[label="xy4001",fontsize=16,color="green",shape="box"];514[label="xy3001",fontsize=16,color="green",shape="box"];515[label="xy4001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];516[label="xy3001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];517[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];518[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];519[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];520[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];521[label="xy4001",fontsize=16,color="green",shape="box"];522[label="xy3001",fontsize=16,color="green",shape="box"];523[label="xy4001",fontsize=16,color="green",shape="box"];524[label="xy3001",fontsize=16,color="green",shape="box"];525[label="xy4001",fontsize=16,color="green",shape="box"];526[label="xy3001",fontsize=16,color="green",shape="box"];527[label="xy4001",fontsize=16,color="green",shape="box"];528[label="xy3001",fontsize=16,color="green",shape="box"];529[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];530[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];531[label="xy4001",fontsize=16,color="green",shape="box"];532[label="xy3001",fontsize=16,color="green",shape="box"];533[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];534[label="xy3001\n  Integral a",fontsize=16,color="green",shape="box"];535[label="xy4001",fontsize=16,color="green",shape="box"];536[label="xy3001",fontsize=16,color="green",shape="box"];537[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];538[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];539[label="xy4001",fontsize=16,color="green",shape="box"];540[label="xy3001",fontsize=16,color="green",shape="box"];541[label="xy4002",fontsize=16,color="green",shape="box"];542[label="xy3002",fontsize=16,color="green",shape="box"];543[label="xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];544[label="xy3002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];545[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];546[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];547[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];548[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];549[label="xy4002",fontsize=16,color="green",shape="box"];550[label="xy3002",fontsize=16,color="green",shape="box"];551[label="xy4002",fontsize=16,color="green",shape="box"];552[label="xy3002",fontsize=16,color="green",shape="box"];553[label="xy4002",fontsize=16,color="green",shape="box"];554[label="xy3002",fontsize=16,color="green",shape="box"];555[label="xy4002",fontsize=16,color="green",shape="box"];556[label="xy3002",fontsize=16,color="green",shape="box"];557[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];558[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];559[label="xy4002",fontsize=16,color="green",shape="box"];560[label="xy3002",fontsize=16,color="green",shape="box"];561[label="xy4002\n  Integral a",fontsize=16,color="green",shape="box"];562[label="xy3002\n  Integral a",fontsize=16,color="green",shape="box"];563[label="xy4002",fontsize=16,color="green",shape="box"];564[label="xy3002",fontsize=16,color="green",shape="box"];565[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];566[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];567[label="xy4002",fontsize=16,color="green",shape="box"];568[label="xy3002",fontsize=16,color="green",shape="box"];569[label="primMulInt (Pos xy30010) xy4001",fontsize=16,color="burlywood",shape="box"];984[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];569 -> 984[label="",style="solid", color="burlywood", weight=9];
984 -> 579[label="",style="solid", color="burlywood", weight=3];
985[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];569 -> 985[label="",style="solid", color="burlywood", weight=9];
985 -> 580[label="",style="solid", color="burlywood", weight=3];
570[label="primMulInt (Neg xy30010) xy4001",fontsize=16,color="burlywood",shape="box"];986[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];570 -> 986[label="",style="solid", color="burlywood", weight=9];
986 -> 581[label="",style="solid", color="burlywood", weight=3];
987[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];570 -> 987[label="",style="solid", color="burlywood", weight=9];
987 -> 582[label="",style="solid", color="burlywood", weight=3];
571 -> 202[label="",style="dashed", color="red", weight=0];
571[label="primEqNat xy30000 xy40000",fontsize=16,color="magenta"];571 -> 583[label="",style="dashed", color="magenta", weight=3];
571 -> 584[label="",style="dashed", color="magenta", weight=3];
572[label="False",fontsize=16,color="green",shape="box"];573[label="False",fontsize=16,color="green",shape="box"];574[label="True",fontsize=16,color="green",shape="box"];575[label="xy30000",fontsize=16,color="green",shape="box"];576[label="xy40000",fontsize=16,color="green",shape="box"];577[label="xy30000",fontsize=16,color="green",shape="box"];578[label="xy40000",fontsize=16,color="green",shape="box"];579[label="primMulInt (Pos xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];579 -> 585[label="",style="solid", color="black", weight=3];
580[label="primMulInt (Pos xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];580 -> 586[label="",style="solid", color="black", weight=3];
581[label="primMulInt (Neg xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];581 -> 587[label="",style="solid", color="black", weight=3];
582[label="primMulInt (Neg xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];582 -> 588[label="",style="solid", color="black", weight=3];
583[label="xy30000",fontsize=16,color="green",shape="box"];584[label="xy40000",fontsize=16,color="green",shape="box"];585[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];585 -> 589[label="",style="dashed", color="green", weight=3];
586[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];586 -> 590[label="",style="dashed", color="green", weight=3];
587[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];587 -> 591[label="",style="dashed", color="green", weight=3];
588[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];588 -> 592[label="",style="dashed", color="green", weight=3];
589[label="primMulNat xy30010 xy40010",fontsize=16,color="burlywood",shape="triangle"];989[label="xy30010/Succ xy300100",fontsize=10,color="white",style="solid",shape="box"];589 -> 989[label="",style="solid", color="burlywood", weight=9];
989 -> 593[label="",style="solid", color="burlywood", weight=3];
990[label="xy30010/Zero",fontsize=10,color="white",style="solid",shape="box"];589 -> 990[label="",style="solid", color="burlywood", weight=9];
990 -> 594[label="",style="solid", color="burlywood", weight=3];
590 -> 589[label="",style="dashed", color="red", weight=0];
590[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];590 -> 595[label="",style="dashed", color="magenta", weight=3];
591 -> 589[label="",style="dashed", color="red", weight=0];
591[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];591 -> 596[label="",style="dashed", color="magenta", weight=3];
592 -> 589[label="",style="dashed", color="red", weight=0];
592[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];592 -> 597[label="",style="dashed", color="magenta", weight=3];
592 -> 598[label="",style="dashed", color="magenta", weight=3];
593[label="primMulNat (Succ xy300100) xy40010",fontsize=16,color="burlywood",shape="box"];994[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];593 -> 994[label="",style="solid", color="burlywood", weight=9];
994 -> 599[label="",style="solid", color="burlywood", weight=3];
995[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];593 -> 995[label="",style="solid", color="burlywood", weight=9];
995 -> 600[label="",style="solid", color="burlywood", weight=3];
594[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];996[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];594 -> 996[label="",style="solid", color="burlywood", weight=9];
996 -> 601[label="",style="solid", color="burlywood", weight=3];
997[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];594 -> 997[label="",style="solid", color="burlywood", weight=9];
997 -> 602[label="",style="solid", color="burlywood", weight=3];
595[label="xy40010",fontsize=16,color="green",shape="box"];596[label="xy30010",fontsize=16,color="green",shape="box"];597[label="xy30010",fontsize=16,color="green",shape="box"];598[label="xy40010",fontsize=16,color="green",shape="box"];599[label="primMulNat (Succ xy300100) (Succ xy400100)",fontsize=16,color="black",shape="box"];599 -> 603[label="",style="solid", color="black", weight=3];
600[label="primMulNat (Succ xy300100) Zero",fontsize=16,color="black",shape="box"];600 -> 604[label="",style="solid", color="black", weight=3];
601[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];601 -> 605[label="",style="solid", color="black", weight=3];
602[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];602 -> 606[label="",style="solid", color="black", weight=3];
603 -> 607[label="",style="dashed", color="red", weight=0];
603[label="primPlusNat (primMulNat xy300100 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];603 -> 608[label="",style="dashed", color="magenta", weight=3];
604[label="Zero",fontsize=16,color="green",shape="box"];605[label="Zero",fontsize=16,color="green",shape="box"];606[label="Zero",fontsize=16,color="green",shape="box"];608 -> 589[label="",style="dashed", color="red", weight=0];
608[label="primMulNat xy300100 (Succ xy400100)",fontsize=16,color="magenta"];608 -> 609[label="",style="dashed", color="magenta", weight=3];
608 -> 610[label="",style="dashed", color="magenta", weight=3];
607[label="primPlusNat xy11 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];1000[label="xy11/Succ xy110",fontsize=10,color="white",style="solid",shape="box"];607 -> 1000[label="",style="solid", color="burlywood", weight=9];
1000 -> 611[label="",style="solid", color="burlywood", weight=3];
1001[label="xy11/Zero",fontsize=10,color="white",style="solid",shape="box"];607 -> 1001[label="",style="solid", color="burlywood", weight=9];
1001 -> 612[label="",style="solid", color="burlywood", weight=3];
609[label="xy300100",fontsize=16,color="green",shape="box"];610[label="Succ xy400100",fontsize=16,color="green",shape="box"];611[label="primPlusNat (Succ xy110) (Succ xy400100)",fontsize=16,color="black",shape="box"];611 -> 613[label="",style="solid", color="black", weight=3];
612[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];612 -> 614[label="",style="solid", color="black", weight=3];
613[label="Succ (Succ (primPlusNat xy110 xy400100))",fontsize=16,color="green",shape="box"];613 -> 615[label="",style="dashed", color="green", weight=3];
614[label="Succ xy400100",fontsize=16,color="green",shape="box"];615[label="primPlusNat xy110 xy400100",fontsize=16,color="burlywood",shape="triangle"];1002[label="xy110/Succ xy1100",fontsize=10,color="white",style="solid",shape="box"];615 -> 1002[label="",style="solid", color="burlywood", weight=9];
1002 -> 616[label="",style="solid", color="burlywood", weight=3];
1003[label="xy110/Zero",fontsize=10,color="white",style="solid",shape="box"];615 -> 1003[label="",style="solid", color="burlywood", weight=9];
1003 -> 617[label="",style="solid", color="burlywood", weight=3];
616[label="primPlusNat (Succ xy1100) xy400100",fontsize=16,color="burlywood",shape="box"];1004[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];616 -> 1004[label="",style="solid", color="burlywood", weight=9];
1004 -> 618[label="",style="solid", color="burlywood", weight=3];
1005[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];616 -> 1005[label="",style="solid", color="burlywood", weight=9];
1005 -> 619[label="",style="solid", color="burlywood", weight=3];
617[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];1006[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];617 -> 1006[label="",style="solid", color="burlywood", weight=9];
1006 -> 620[label="",style="solid", color="burlywood", weight=3];
1007[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];617 -> 1007[label="",style="solid", color="burlywood", weight=9];
1007 -> 621[label="",style="solid", color="burlywood", weight=3];
618[label="primPlusNat (Succ xy1100) (Succ xy4001000)",fontsize=16,color="black",shape="box"];618 -> 622[label="",style="solid", color="black", weight=3];
619[label="primPlusNat (Succ xy1100) Zero",fontsize=16,color="black",shape="box"];619 -> 623[label="",style="solid", color="black", weight=3];
620[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];620 -> 624[label="",style="solid", color="black", weight=3];
621[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];621 -> 625[label="",style="solid", color="black", weight=3];
622[label="Succ (Succ (primPlusNat xy1100 xy4001000))",fontsize=16,color="green",shape="box"];622 -> 626[label="",style="dashed", color="green", weight=3];
623[label="Succ xy1100",fontsize=16,color="green",shape="box"];624[label="Succ xy4001000",fontsize=16,color="green",shape="box"];625[label="Zero",fontsize=16,color="green",shape="box"];626 -> 615[label="",style="dashed", color="red", weight=0];
626[label="primPlusNat xy1100 xy4001000",fontsize=16,color="magenta"];626 -> 627[label="",style="dashed", color="magenta", weight=3];
626 -> 628[label="",style="dashed", color="magenta", weight=3];
627[label="xy4001000",fontsize=16,color="green",shape="box"];628[label="xy1100",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(xy1100), Succ(xy4001000)) → new_primPlusNat(xy1100, 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(xy1100), Succ(xy4001000)) → new_primPlusNat(xy1100, 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_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_Maybe, bbe)), bbh) → new_esEs2(xy3000, xy4000, bbe)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), bd), app(app(app(ty_@3, dg), dh), ea)), bbh) → new_esEs(xy3002, xy4002, dg, dh, ea)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_[], gg)), gf), bbh) → new_esEs0(xy3000, xy4000, gg)
new_esEs2(Just(xy3000), Just(xy4000), app(app(app(ty_@3, bag), bah), bba)) → new_esEs(xy3000, xy4000, bag, bah, bba)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, cb), cc), bd, be) → new_esEs3(xy3000, xy4000, cb, cc)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, bd, app(ty_[], eb)) → new_esEs0(xy3002, xy4002, eb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], gg), gf) → new_esEs0(xy3000, xy4000, gg)
new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_Either, bdc), bdd)) → new_esEs3(xy300, xy400, bdc, bdd)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, app(ty_Maybe, dd), be) → new_esEs2(xy3001, xy4001, dd)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, he), app(app(ty_Either, bae), baf)), bbh) → new_esEs3(xy3001, xy4001, bae, baf)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), bd), app(ty_Maybe, ee)), bbh) → new_esEs2(xy3002, xy4002, ee)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(app(ty_@3, eh), fa), fb)) → new_esEs(xy3000, xy4000, eh, fa, fb)
new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_@2, bbc), bbd)), bbh) → new_esEs1(xy3000, xy4000, bbc, bbd)
new_esEs2(Just(xy3000), Just(xy4000), app(ty_Maybe, bbe)) → new_esEs2(xy3000, xy4000, bbe)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), he, app(ty_[], baa)) → new_esEs0(xy3001, xy4001, baa)
new_esEs3(Left(xy300), Left(xy400), app(app(ty_Either, bca), bcb), bbh) → new_esEs3(xy300, xy400, bca, bcb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, hb), gf) → new_esEs2(xy3000, xy4000, hb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), he, app(app(ty_Either, bae), baf)) → new_esEs3(xy3001, xy4001, bae, baf)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), bd), app(ty_[], eb)), bbh) → new_esEs0(xy3002, xy4002, eb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), he, app(app(ty_@2, bab), bac)) → new_esEs1(xy3001, xy4001, bab, bac)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_@2, gh), ha)), gf), bbh) → new_esEs1(xy3000, xy4000, gh, ha)
new_esEs3(Right(xy300), Right(xy400), bcc, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs(xy300, xy400, bcd, bce, bcf)
new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_Either, bbf), bbg)), bbh) → new_esEs3(xy3000, xy4000, bbf, bbg)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), app(ty_[], da)), be), bbh) → new_esEs0(xy3001, xy4001, da)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_@2, fd), ff)), bbh) → new_esEs1(xy3000, xy4000, fd, ff)
new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_[], bcg)) → new_esEs0(xy300, xy400, bcg)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_@2, fd), ff)) → new_esEs1(xy3000, xy4000, fd, ff)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_Either, cb), cc)), bd), be), bbh) → new_esEs3(xy3000, xy4000, cb, cc)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), app(app(app(ty_@3, ce), cf), cg)), be), bbh) → new_esEs(xy3001, xy4001, ce, cf, cg)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_Maybe, ca)), bd), be), bbh) → new_esEs2(xy3000, xy4000, ca)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_Maybe, fg)) → new_esEs2(xy3000, xy4000, fg)
new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_Maybe, bdb)) → new_esEs2(xy300, xy400, bdb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, hc), hd), gf) → new_esEs3(xy3000, xy4000, hc, hd)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), he, app(ty_Maybe, bad)) → new_esEs2(xy3001, xy4001, bad)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bg), bh), bd, be) → new_esEs1(xy3000, xy4000, bg, bh)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, app(app(ty_Either, de), df), be) → new_esEs3(xy3001, xy4001, de, df)
new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_Either, bbf), bbg)) → new_esEs3(xy3000, xy4000, bbf, bbg)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, he), app(ty_[], baa)), bbh) → new_esEs0(xy3001, xy4001, baa)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, he), app(app(ty_@2, bab), bac)), bbh) → new_esEs1(xy3001, xy4001, bab, bac)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), gb) → new_esEs0(xy3001, xy4001, gb)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, bd, app(app(ty_Either, ef), eg)) → new_esEs3(xy3002, xy4002, ef, eg)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(app(ty_@3, gc), gd), ge)), gf), bbh) → new_esEs(xy3000, xy4000, gc, gd, ge)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, app(ty_[], da), be) → new_esEs0(xy3001, xy4001, da)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, app(app(ty_@2, db), dc), be) → new_esEs1(xy3001, xy4001, db, dc)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_[], bf)), bd), be), bbh) → new_esEs0(xy3000, xy4000, bf)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, ca), bd, be) → new_esEs2(xy3000, xy4000, ca)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, he), app(app(app(ty_@3, hf), hg), hh)), bbh) → new_esEs(xy3001, xy4001, hf, hg, hh)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, bd, app(ty_Maybe, ee)) → new_esEs2(xy3002, xy4002, ee)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_Maybe, hb)), gf), bbh) → new_esEs2(xy3000, xy4000, hb)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(app(ty_@3, eh), fa), fb)), bbh) → new_esEs(xy3000, xy4000, eh, fa, fb)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], gb), bbh) → new_esEs0(xy3001, xy4001, gb)
new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(app(ty_@3, bag), bah), bba)), bbh) → new_esEs(xy3000, xy4000, bag, bah, bba)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_Maybe, fg)), bbh) → new_esEs2(xy3000, xy4000, fg)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, ba), bb), bc), bd, be) → new_esEs(xy3000, xy4000, ba, bb, bc)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_Either, hc), hd)), gf), bbh) → new_esEs3(xy3000, xy4000, hc, hd)
new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_[], bbb)), bbh) → new_esEs0(xy3000, xy4000, bbb)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, bd, app(app(ty_@2, ec), ed)) → new_esEs1(xy3002, xy4002, ec, ed)
new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_@2, bbc), bbd)) → new_esEs1(xy3000, xy4000, bbc, bbd)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_Either, fh), ga)) → new_esEs3(xy3000, xy4000, fh, ga)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_[], fc)), bbh) → new_esEs0(xy3000, xy4000, fc)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), bd), app(app(ty_@2, ec), ed)), bbh) → new_esEs1(xy3002, xy4002, ec, ed)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), app(app(ty_Either, de), df)), be), bbh) → new_esEs3(xy3001, xy4001, de, df)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), bd), app(app(ty_Either, ef), eg)), bbh) → new_esEs3(xy3002, xy4002, ef, eg)
new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_Either, fh), ga)), bbh) → new_esEs3(xy3000, xy4000, fh, ga)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), app(app(ty_@2, db), dc)), be), bbh) → new_esEs1(xy3001, xy4001, db, dc)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(app(ty_@3, ba), bb), bc)), bd), be), bbh) → new_esEs(xy3000, xy4000, ba, bb, bc)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, app(app(app(ty_@3, ce), cf), cg), be) → new_esEs(xy3001, xy4001, ce, cf, cg)
new_esEs2(Just(xy3000), Just(xy4000), app(ty_[], bbb)) → new_esEs0(xy3000, xy4000, bbb)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, gh), ha), gf) → new_esEs1(xy3000, xy4000, gh, ha)
new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, he), app(ty_Maybe, bad)), bbh) → new_esEs2(xy3001, xy4001, bad)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], bf), bd, be) → new_esEs0(xy3000, xy4000, bf)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_@2, bg), bh)), bd), be), bbh) → new_esEs1(xy3000, xy4000, bg, bh)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), he, app(app(app(ty_@3, hf), hg), hh)) → new_esEs(xy3001, xy4001, hf, hg, hh)
new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_[], fc)) → new_esEs0(xy3000, xy4000, fc)
new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_@2, bch), bda)) → new_esEs1(xy300, xy400, bch, bda)
new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, cd), app(ty_Maybe, dd)), be), bbh) → new_esEs2(xy3001, xy4001, dd)
new_esEs1(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, gc), gd), ge), gf) → new_esEs(xy3000, xy4000, gc, gd, ge)
new_esEs(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), cd, bd, app(app(app(ty_@3, dg), dh), ea)) → new_esEs(xy3002, xy4002, dg, dh, ea)

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

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

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

new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba, bb) → new_isPrefixOf(xy31, xy41, ba, bb)

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

new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba, bb) → new_isPrefixOf(xy31, xy41, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4