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

YES 1.596 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 b, Eq a) => [(a,b)] -> [(a,b)] -> Bool) :: (Eq a, Eq b) => [(a,b)] -> [(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 a, Eq b) => [(b,a)] -> [(b,a)] -> Bool) :: (Eq b, Eq a) => [(b,a)] -> [(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) => [(a,b)] -> [(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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149 -> 198[label="",style="dashed", color="magenta", weight=3];
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771 -> 200[label="",style="solid", color="burlywood", weight=3];
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776[label="xy401/Just xy4010",fontsize=10,color="white",style="solid",shape="box"];153 -> 776[label="",style="solid", color="burlywood", weight=9];
776 -> 205[label="",style="solid", color="burlywood", weight=3];
154[label="Just xy3010 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];777[label="xy401/Nothing",fontsize=10,color="white",style="solid",shape="box"];154 -> 777[label="",style="solid", color="burlywood", weight=9];
777 -> 206[label="",style="solid", color="burlywood", weight=3];
778[label="xy401/Just xy4010",fontsize=10,color="white",style="solid",shape="box"];154 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 207[label="",style="solid", color="burlywood", weight=3];
155[label="False == xy401",fontsize=16,color="burlywood",shape="box"];779[label="xy401/False",fontsize=10,color="white",style="solid",shape="box"];155 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 208[label="",style="solid", color="burlywood", weight=3];
780[label="xy401/True",fontsize=10,color="white",style="solid",shape="box"];155 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 209[label="",style="solid", color="burlywood", weight=3];
156[label="True == xy401",fontsize=16,color="burlywood",shape="box"];781[label="xy401/False",fontsize=10,color="white",style="solid",shape="box"];156 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 210[label="",style="solid", color="burlywood", weight=3];
782[label="xy401/True",fontsize=10,color="white",style="solid",shape="box"];156 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 211[label="",style="solid", color="burlywood", weight=3];
157[label="xy401\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];158[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];159[label="primEqInt xy301 xy401",fontsize=16,color="burlywood",shape="triangle"];783[label="xy301/Pos xy3010",fontsize=10,color="white",style="solid",shape="box"];159 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 212[label="",style="solid", color="burlywood", weight=3];
784[label="xy301/Neg xy3010",fontsize=10,color="white",style="solid",shape="box"];159 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 213[label="",style="solid", color="burlywood", weight=3];
160[label="primEqFloat xy301 xy401",fontsize=16,color="burlywood",shape="box"];785[label="xy301/Float xy3010 xy3011",fontsize=10,color="white",style="solid",shape="box"];160 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 214[label="",style="solid", color="burlywood", weight=3];
161[label="(xy3010,xy3011,xy3012) == xy401\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];786[label="xy401/(xy4010,xy4011,xy4012)",fontsize=10,color="white",style="solid",shape="box"];161 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 215[label="",style="solid", color="burlywood", weight=3];
162[label="xy3010 :% xy3011 == xy401\n  Integral a",fontsize=16,color="burlywood",shape="box"];787[label="xy401/xy4010 :% xy4011",fontsize=10,color="white",style="solid",shape="box"];162 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 216[label="",style="solid", color="burlywood", weight=3];
163[label="Integer xy3010 == xy401",fontsize=16,color="burlywood",shape="box"];788[label="xy401/Integer xy4010",fontsize=10,color="white",style="solid",shape="box"];163 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 217[label="",style="solid", color="burlywood", weight=3];
164[label="primEqChar xy301 xy401",fontsize=16,color="burlywood",shape="box"];789[label="xy301/Char xy3010",fontsize=10,color="white",style="solid",shape="box"];164 -> 789[label="",style="solid", color="burlywood", weight=9];
789 -> 218[label="",style="solid", color="burlywood", weight=3];
165[label="xy3010 : xy3011 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];790[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];165 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 219[label="",style="solid", color="burlywood", weight=3];
791[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];165 -> 791[label="",style="solid", color="burlywood", weight=9];
791 -> 220[label="",style="solid", color="burlywood", weight=3];
166[label="[] == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];792[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];166 -> 792[label="",style="solid", color="burlywood", weight=9];
792 -> 221[label="",style="solid", color="burlywood", weight=3];
793[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];166 -> 793[label="",style="solid", color="burlywood", weight=9];
793 -> 222[label="",style="solid", color="burlywood", weight=3];
167[label="LT == xy401",fontsize=16,color="burlywood",shape="box"];794[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];167 -> 794[label="",style="solid", color="burlywood", weight=9];
794 -> 223[label="",style="solid", color="burlywood", weight=3];
795[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];167 -> 795[label="",style="solid", color="burlywood", weight=9];
795 -> 224[label="",style="solid", color="burlywood", weight=3];
796[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];167 -> 796[label="",style="solid", color="burlywood", weight=9];
796 -> 225[label="",style="solid", color="burlywood", weight=3];
168[label="EQ == xy401",fontsize=16,color="burlywood",shape="box"];797[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];168 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 226[label="",style="solid", color="burlywood", weight=3];
798[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];168 -> 798[label="",style="solid", color="burlywood", weight=9];
798 -> 227[label="",style="solid", color="burlywood", weight=3];
799[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];168 -> 799[label="",style="solid", color="burlywood", weight=9];
799 -> 228[label="",style="solid", color="burlywood", weight=3];
169[label="GT == xy401",fontsize=16,color="burlywood",shape="box"];800[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];169 -> 800[label="",style="solid", color="burlywood", weight=9];
800 -> 229[label="",style="solid", color="burlywood", weight=3];
801[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];169 -> 801[label="",style="solid", color="burlywood", weight=9];
801 -> 230[label="",style="solid", color="burlywood", weight=3];
802[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];169 -> 802[label="",style="solid", color="burlywood", weight=9];
802 -> 231[label="",style="solid", color="burlywood", weight=3];
170[label="primEqDouble xy301 xy401",fontsize=16,color="burlywood",shape="box"];803[label="xy301/Double xy3010 xy3011",fontsize=10,color="white",style="solid",shape="box"];170 -> 803[label="",style="solid", color="burlywood", weight=9];
803 -> 232[label="",style="solid", color="burlywood", weight=3];
171[label="xy400",fontsize=16,color="green",shape="box"];172[label="xy300",fontsize=16,color="green",shape="box"];173[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];174[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];175[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];176[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];177[label="xy400",fontsize=16,color="green",shape="box"];178[label="xy300",fontsize=16,color="green",shape="box"];179[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];180[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];181[label="xy400",fontsize=16,color="green",shape="box"];182[label="xy300",fontsize=16,color="green",shape="box"];183[label="xy400",fontsize=16,color="green",shape="box"];184[label="xy300",fontsize=16,color="green",shape="box"];185[label="xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];186[label="xy300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];187[label="xy400\n  Integral a",fontsize=16,color="green",shape="box"];188[label="xy300\n  Integral a",fontsize=16,color="green",shape="box"];189[label="xy400",fontsize=16,color="green",shape="box"];190[label="xy300",fontsize=16,color="green",shape="box"];191[label="xy400",fontsize=16,color="green",shape="box"];192[label="xy300",fontsize=16,color="green",shape="box"];193[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];194[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];195[label="xy400",fontsize=16,color="green",shape="box"];196[label="xy300",fontsize=16,color="green",shape="box"];197[label="xy400",fontsize=16,color="green",shape="box"];198[label="xy300",fontsize=16,color="green",shape="box"];199[label="() == ()",fontsize=16,color="black",shape="box"];199 -> 233[label="",style="solid", color="black", weight=3];
200[label="Left xy3010 == Left xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];200 -> 234[label="",style="solid", color="black", weight=3];
201[label="Left xy3010 == Right xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];201 -> 235[label="",style="solid", color="black", weight=3];
202[label="Right xy3010 == Left xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];202 -> 236[label="",style="solid", color="black", weight=3];
203[label="Right xy3010 == Right xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];203 -> 237[label="",style="solid", color="black", weight=3];
204[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];204 -> 238[label="",style="solid", color="black", weight=3];
205[label="Nothing == Just xy4010\n  Eq a",fontsize=16,color="black",shape="box"];205 -> 239[label="",style="solid", color="black", weight=3];
206[label="Just xy3010 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];206 -> 240[label="",style="solid", color="black", weight=3];
207[label="Just xy3010 == Just xy4010\n  Eq a",fontsize=16,color="black",shape="box"];207 -> 241[label="",style="solid", color="black", weight=3];
208[label="False == False",fontsize=16,color="black",shape="box"];208 -> 242[label="",style="solid", color="black", weight=3];
209[label="False == True",fontsize=16,color="black",shape="box"];209 -> 243[label="",style="solid", color="black", weight=3];
210[label="True == False",fontsize=16,color="black",shape="box"];210 -> 244[label="",style="solid", color="black", weight=3];
211[label="True == True",fontsize=16,color="black",shape="box"];211 -> 245[label="",style="solid", color="black", weight=3];
212[label="primEqInt (Pos xy3010) xy401",fontsize=16,color="burlywood",shape="box"];804[label="xy3010/Succ xy30100",fontsize=10,color="white",style="solid",shape="box"];212 -> 804[label="",style="solid", color="burlywood", weight=9];
804 -> 246[label="",style="solid", color="burlywood", weight=3];
805[label="xy3010/Zero",fontsize=10,color="white",style="solid",shape="box"];212 -> 805[label="",style="solid", color="burlywood", weight=9];
805 -> 247[label="",style="solid", color="burlywood", weight=3];
213[label="primEqInt (Neg xy3010) xy401",fontsize=16,color="burlywood",shape="box"];806[label="xy3010/Succ xy30100",fontsize=10,color="white",style="solid",shape="box"];213 -> 806[label="",style="solid", color="burlywood", weight=9];
806 -> 248[label="",style="solid", color="burlywood", weight=3];
807[label="xy3010/Zero",fontsize=10,color="white",style="solid",shape="box"];213 -> 807[label="",style="solid", color="burlywood", weight=9];
807 -> 249[label="",style="solid", color="burlywood", weight=3];
214[label="primEqFloat (Float xy3010 xy3011) xy401",fontsize=16,color="burlywood",shape="box"];808[label="xy401/Float xy4010 xy4011",fontsize=10,color="white",style="solid",shape="box"];214 -> 808[label="",style="solid", color="burlywood", weight=9];
808 -> 250[label="",style="solid", color="burlywood", weight=3];
215[label="(xy3010,xy3011,xy3012) == (xy4010,xy4011,xy4012)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];215 -> 251[label="",style="solid", color="black", weight=3];
216[label="xy3010 :% xy3011 == xy4010 :% xy4011\n  Integral a",fontsize=16,color="black",shape="box"];216 -> 252[label="",style="solid", color="black", weight=3];
217[label="Integer xy3010 == Integer xy4010",fontsize=16,color="black",shape="box"];217 -> 253[label="",style="solid", color="black", weight=3];
218[label="primEqChar (Char xy3010) xy401",fontsize=16,color="burlywood",shape="box"];809[label="xy401/Char xy4010",fontsize=10,color="white",style="solid",shape="box"];218 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 254[label="",style="solid", color="burlywood", weight=3];
219[label="xy3010 : xy3011 == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];219 -> 255[label="",style="solid", color="black", weight=3];
220[label="xy3010 : xy3011 == []\n  Eq a",fontsize=16,color="black",shape="box"];220 -> 256[label="",style="solid", color="black", weight=3];
221[label="[] == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];221 -> 257[label="",style="solid", color="black", weight=3];
222[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];222 -> 258[label="",style="solid", color="black", weight=3];
223[label="LT == LT",fontsize=16,color="black",shape="box"];223 -> 259[label="",style="solid", color="black", weight=3];
224[label="LT == EQ",fontsize=16,color="black",shape="box"];224 -> 260[label="",style="solid", color="black", weight=3];
225[label="LT == GT",fontsize=16,color="black",shape="box"];225 -> 261[label="",style="solid", color="black", weight=3];
226[label="EQ == LT",fontsize=16,color="black",shape="box"];226 -> 262[label="",style="solid", color="black", weight=3];
227[label="EQ == EQ",fontsize=16,color="black",shape="box"];227 -> 263[label="",style="solid", color="black", weight=3];
228[label="EQ == GT",fontsize=16,color="black",shape="box"];228 -> 264[label="",style="solid", color="black", weight=3];
229[label="GT == LT",fontsize=16,color="black",shape="box"];229 -> 265[label="",style="solid", color="black", weight=3];
230[label="GT == EQ",fontsize=16,color="black",shape="box"];230 -> 266[label="",style="solid", color="black", weight=3];
231[label="GT == GT",fontsize=16,color="black",shape="box"];231 -> 267[label="",style="solid", color="black", weight=3];
232[label="primEqDouble (Double xy3010 xy3011) xy401",fontsize=16,color="burlywood",shape="box"];810[label="xy401/Double xy4010 xy4011",fontsize=10,color="white",style="solid",shape="box"];232 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 268[label="",style="solid", color="burlywood", weight=3];
233[label="True",fontsize=16,color="green",shape="box"];234[label="xy3010 == xy4010\n  Eq a",fontsize=16,color="blue",shape="box"];811[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 811[label="",style="solid", color="blue", weight=9];
811 -> 269[label="",style="solid", color="blue", weight=3];
812[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 812[label="",style="solid", color="blue", weight=9];
812 -> 270[label="",style="solid", color="blue", weight=3];
813[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 813[label="",style="solid", color="blue", weight=9];
813 -> 271[label="",style="solid", color="blue", weight=3];
814[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 814[label="",style="solid", color="blue", weight=9];
814 -> 272[label="",style="solid", color="blue", weight=3];
815[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 815[label="",style="solid", color="blue", weight=9];
815 -> 273[label="",style="solid", color="blue", weight=3];
816[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 816[label="",style="solid", color="blue", weight=9];
816 -> 274[label="",style="solid", color="blue", weight=3];
817[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 817[label="",style="solid", color="blue", weight=9];
817 -> 275[label="",style="solid", color="blue", weight=3];
818[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 818[label="",style="solid", color="blue", weight=9];
818 -> 276[label="",style="solid", color="blue", weight=3];
819[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 819[label="",style="solid", color="blue", weight=9];
819 -> 277[label="",style="solid", color="blue", weight=3];
820[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 820[label="",style="solid", color="blue", weight=9];
820 -> 278[label="",style="solid", color="blue", weight=3];
821[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 821[label="",style="solid", color="blue", weight=9];
821 -> 279[label="",style="solid", color="blue", weight=3];
822[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 822[label="",style="solid", color="blue", weight=9];
822 -> 280[label="",style="solid", color="blue", weight=3];
823[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 823[label="",style="solid", color="blue", weight=9];
823 -> 281[label="",style="solid", color="blue", weight=3];
824[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 824[label="",style="solid", color="blue", weight=9];
824 -> 282[label="",style="solid", color="blue", weight=3];
235[label="False",fontsize=16,color="green",shape="box"];236[label="False",fontsize=16,color="green",shape="box"];237[label="xy3010 == xy4010\n  Eq a",fontsize=16,color="blue",shape="box"];825[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 825[label="",style="solid", color="blue", weight=9];
825 -> 283[label="",style="solid", color="blue", weight=3];
826[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 826[label="",style="solid", color="blue", weight=9];
826 -> 284[label="",style="solid", color="blue", weight=3];
827[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 827[label="",style="solid", color="blue", weight=9];
827 -> 285[label="",style="solid", color="blue", weight=3];
828[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 828[label="",style="solid", color="blue", weight=9];
828 -> 286[label="",style="solid", color="blue", weight=3];
829[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 829[label="",style="solid", color="blue", weight=9];
829 -> 287[label="",style="solid", color="blue", weight=3];
830[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 830[label="",style="solid", color="blue", weight=9];
830 -> 288[label="",style="solid", color="blue", weight=3];
831[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 831[label="",style="solid", color="blue", weight=9];
831 -> 289[label="",style="solid", color="blue", weight=3];
832[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 832[label="",style="solid", color="blue", weight=9];
832 -> 290[label="",style="solid", color="blue", weight=3];
833[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 833[label="",style="solid", color="blue", weight=9];
833 -> 291[label="",style="solid", color="blue", weight=3];
834[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 834[label="",style="solid", color="blue", weight=9];
834 -> 292[label="",style="solid", color="blue", weight=3];
835[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 835[label="",style="solid", color="blue", weight=9];
835 -> 293[label="",style="solid", color="blue", weight=3];
836[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 836[label="",style="solid", color="blue", weight=9];
836 -> 294[label="",style="solid", color="blue", weight=3];
837[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 837[label="",style="solid", color="blue", weight=9];
837 -> 295[label="",style="solid", color="blue", weight=3];
838[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];237 -> 838[label="",style="solid", color="blue", weight=9];
838 -> 296[label="",style="solid", color="blue", weight=3];
238[label="True",fontsize=16,color="green",shape="box"];239[label="False",fontsize=16,color="green",shape="box"];240[label="False",fontsize=16,color="green",shape="box"];241[label="xy3010 == xy4010\n  Eq a",fontsize=16,color="blue",shape="box"];839[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];241 -> 839[label="",style="solid", color="blue", weight=9];
839 -> 297[label="",style="solid", color="blue", weight=3];
840[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];241 -> 840[label="",style="solid", color="blue", weight=9];
840 -> 298[label="",style="solid", color="blue", weight=3];
841[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];241 -> 841[label="",style="solid", color="blue", weight=9];
841 -> 299[label="",style="solid", color="blue", weight=3];
842[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];241 -> 842[label="",style="solid", color="blue", weight=9];
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963[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];430 -> 963[label="",style="solid", color="blue", weight=9];
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967[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];430 -> 967[label="",style="solid", color="blue", weight=9];
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552[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];552 -> 650[label="",style="solid", color="black", weight=3];
553[label="xy4010",fontsize=16,color="green",shape="box"];554[label="xy3010",fontsize=16,color="green",shape="box"];555[label="xy4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];556[label="xy3010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];557[label="xy4010\n  Eq a",fontsize=16,color="green",shape="box"];558[label="xy3010\n  Eq a",fontsize=16,color="green",shape="box"];559[label="xy4010",fontsize=16,color="green",shape="box"];560[label="xy3010",fontsize=16,color="green",shape="box"];561[label="xy4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];562[label="xy3010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];563[label="xy4010",fontsize=16,color="green",shape="box"];564[label="xy3010",fontsize=16,color="green",shape="box"];565[label="xy4010",fontsize=16,color="green",shape="box"];566[label="xy3010",fontsize=16,color="green",shape="box"];567[label="xy4010\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];568[label="xy3010\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];569[label="xy4010\n  Integral a",fontsize=16,color="green",shape="box"];570[label="xy3010\n  Integral a",fontsize=16,color="green",shape="box"];571[label="xy4010",fontsize=16,color="green",shape="box"];572[label="xy3010",fontsize=16,color="green",shape="box"];573[label="xy4010",fontsize=16,color="green",shape="box"];574[label="xy3010",fontsize=16,color="green",shape="box"];575[label="xy4010\n  Eq a",fontsize=16,color="green",shape="box"];576[label="xy3010\n  Eq a",fontsize=16,color="green",shape="box"];577[label="xy4010",fontsize=16,color="green",shape="box"];578[label="xy3010",fontsize=16,color="green",shape="box"];579[label="xy4010",fontsize=16,color="green",shape="box"];580[label="xy3010",fontsize=16,color="green",shape="box"];581[label="xy3011",fontsize=16,color="green",shape="box"];582[label="xy4011",fontsize=16,color="green",shape="box"];583[label="xy3010",fontsize=16,color="green",shape="box"];584[label="xy4010",fontsize=16,color="green",shape="box"];585[label="xy30100",fontsize=16,color="green",shape="box"];586[label="xy40100",fontsize=16,color="green",shape="box"];587[label="xy30100",fontsize=16,color="green",shape="box"];588[label="xy40100",fontsize=16,color="green",shape="box"];589[label="primMulInt (Pos xy30110) xy4011",fontsize=16,color="burlywood",shape="box"];1056[label="xy4011/Pos xy40110",fontsize=10,color="white",style="solid",shape="box"];589 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 651[label="",style="solid", color="burlywood", weight=3];
1057[label="xy4011/Neg xy40110",fontsize=10,color="white",style="solid",shape="box"];589 -> 1057[label="",style="solid", color="burlywood", weight=9];
1057 -> 652[label="",style="solid", color="burlywood", weight=3];
590[label="primMulInt (Neg xy30110) xy4011",fontsize=16,color="burlywood",shape="box"];1058[label="xy4011/Pos xy40110",fontsize=10,color="white",style="solid",shape="box"];590 -> 1058[label="",style="solid", color="burlywood", weight=9];
1058 -> 653[label="",style="solid", color="burlywood", weight=3];
1059[label="xy4011/Neg xy40110",fontsize=10,color="white",style="solid",shape="box"];590 -> 1059[label="",style="solid", color="burlywood", weight=9];
1059 -> 654[label="",style="solid", color="burlywood", weight=3];
591[label="xy4012",fontsize=16,color="green",shape="box"];592[label="xy3012",fontsize=16,color="green",shape="box"];593[label="xy4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];594[label="xy3012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];595[label="xy4012\n  Eq a",fontsize=16,color="green",shape="box"];596[label="xy3012\n  Eq a",fontsize=16,color="green",shape="box"];597[label="xy4012",fontsize=16,color="green",shape="box"];598[label="xy3012",fontsize=16,color="green",shape="box"];599[label="xy4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];600[label="xy3012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];601[label="xy4012",fontsize=16,color="green",shape="box"];602[label="xy3012",fontsize=16,color="green",shape="box"];603[label="xy4012",fontsize=16,color="green",shape="box"];604[label="xy3012",fontsize=16,color="green",shape="box"];605[label="xy4012\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];606[label="xy3012\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];607[label="xy4012\n  Integral a",fontsize=16,color="green",shape="box"];608[label="xy3012\n  Integral a",fontsize=16,color="green",shape="box"];609[label="xy4012",fontsize=16,color="green",shape="box"];610[label="xy3012",fontsize=16,color="green",shape="box"];611[label="xy4012",fontsize=16,color="green",shape="box"];612[label="xy3012",fontsize=16,color="green",shape="box"];613[label="xy4012\n  Eq a",fontsize=16,color="green",shape="box"];614[label="xy3012\n  Eq a",fontsize=16,color="green",shape="box"];615[label="xy4012",fontsize=16,color="green",shape="box"];616[label="xy3012",fontsize=16,color="green",shape="box"];617[label="xy4012",fontsize=16,color="green",shape="box"];618[label="xy3012",fontsize=16,color="green",shape="box"];619[label="xy4011",fontsize=16,color="green",shape="box"];620[label="xy3011",fontsize=16,color="green",shape="box"];621[label="xy4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];622[label="xy3011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];623[label="xy4011\n  Eq a",fontsize=16,color="green",shape="box"];624[label="xy3011\n  Eq a",fontsize=16,color="green",shape="box"];625[label="xy4011",fontsize=16,color="green",shape="box"];626[label="xy3011",fontsize=16,color="green",shape="box"];627[label="xy4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];628[label="xy3011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];629[label="xy4011",fontsize=16,color="green",shape="box"];630[label="xy3011",fontsize=16,color="green",shape="box"];631[label="xy4011",fontsize=16,color="green",shape="box"];632[label="xy3011",fontsize=16,color="green",shape="box"];633[label="xy4011\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];634[label="xy3011\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];635[label="xy4011\n  Integral a",fontsize=16,color="green",shape="box"];636[label="xy3011\n  Integral a",fontsize=16,color="green",shape="box"];637[label="xy4011",fontsize=16,color="green",shape="box"];638[label="xy3011",fontsize=16,color="green",shape="box"];639[label="xy4011",fontsize=16,color="green",shape="box"];640[label="xy3011",fontsize=16,color="green",shape="box"];641[label="xy4011\n  Eq a",fontsize=16,color="green",shape="box"];642[label="xy3011\n  Eq a",fontsize=16,color="green",shape="box"];643[label="xy4011",fontsize=16,color="green",shape="box"];644[label="xy3011",fontsize=16,color="green",shape="box"];645[label="xy4011",fontsize=16,color="green",shape="box"];646[label="xy3011",fontsize=16,color="green",shape="box"];647 -> 326[label="",style="dashed", color="red", weight=0];
647[label="primEqNat xy30100 xy40100",fontsize=16,color="magenta"];647 -> 655[label="",style="dashed", color="magenta", weight=3];
647 -> 656[label="",style="dashed", color="magenta", weight=3];
648[label="False",fontsize=16,color="green",shape="box"];649[label="False",fontsize=16,color="green",shape="box"];650[label="True",fontsize=16,color="green",shape="box"];651[label="primMulInt (Pos xy30110) (Pos xy40110)",fontsize=16,color="black",shape="box"];651 -> 657[label="",style="solid", color="black", weight=3];
652[label="primMulInt (Pos xy30110) (Neg xy40110)",fontsize=16,color="black",shape="box"];652 -> 658[label="",style="solid", color="black", weight=3];
653[label="primMulInt (Neg xy30110) (Pos xy40110)",fontsize=16,color="black",shape="box"];653 -> 659[label="",style="solid", color="black", weight=3];
654[label="primMulInt (Neg xy30110) (Neg xy40110)",fontsize=16,color="black",shape="box"];654 -> 660[label="",style="solid", color="black", weight=3];
655[label="xy30100",fontsize=16,color="green",shape="box"];656[label="xy40100",fontsize=16,color="green",shape="box"];657[label="Pos (primMulNat xy30110 xy40110)",fontsize=16,color="green",shape="box"];657 -> 661[label="",style="dashed", color="green", weight=3];
658[label="Neg (primMulNat xy30110 xy40110)",fontsize=16,color="green",shape="box"];658 -> 662[label="",style="dashed", color="green", weight=3];
659[label="Neg (primMulNat xy30110 xy40110)",fontsize=16,color="green",shape="box"];659 -> 663[label="",style="dashed", color="green", weight=3];
660[label="Pos (primMulNat xy30110 xy40110)",fontsize=16,color="green",shape="box"];660 -> 664[label="",style="dashed", color="green", weight=3];
661[label="primMulNat xy30110 xy40110",fontsize=16,color="burlywood",shape="triangle"];1061[label="xy30110/Succ xy301100",fontsize=10,color="white",style="solid",shape="box"];661 -> 1061[label="",style="solid", color="burlywood", weight=9];
1061 -> 665[label="",style="solid", color="burlywood", weight=3];
1062[label="xy30110/Zero",fontsize=10,color="white",style="solid",shape="box"];661 -> 1062[label="",style="solid", color="burlywood", weight=9];
1062 -> 666[label="",style="solid", color="burlywood", weight=3];
662 -> 661[label="",style="dashed", color="red", weight=0];
662[label="primMulNat xy30110 xy40110",fontsize=16,color="magenta"];662 -> 667[label="",style="dashed", color="magenta", weight=3];
663 -> 661[label="",style="dashed", color="red", weight=0];
663[label="primMulNat xy30110 xy40110",fontsize=16,color="magenta"];663 -> 668[label="",style="dashed", color="magenta", weight=3];
664 -> 661[label="",style="dashed", color="red", weight=0];
664[label="primMulNat xy30110 xy40110",fontsize=16,color="magenta"];664 -> 669[label="",style="dashed", color="magenta", weight=3];
664 -> 670[label="",style="dashed", color="magenta", weight=3];
665[label="primMulNat (Succ xy301100) xy40110",fontsize=16,color="burlywood",shape="box"];1066[label="xy40110/Succ xy401100",fontsize=10,color="white",style="solid",shape="box"];665 -> 1066[label="",style="solid", color="burlywood", weight=9];
1066 -> 671[label="",style="solid", color="burlywood", weight=3];
1067[label="xy40110/Zero",fontsize=10,color="white",style="solid",shape="box"];665 -> 1067[label="",style="solid", color="burlywood", weight=9];
1067 -> 672[label="",style="solid", color="burlywood", weight=3];
666[label="primMulNat Zero xy40110",fontsize=16,color="burlywood",shape="box"];1068[label="xy40110/Succ xy401100",fontsize=10,color="white",style="solid",shape="box"];666 -> 1068[label="",style="solid", color="burlywood", weight=9];
1068 -> 673[label="",style="solid", color="burlywood", weight=3];
1069[label="xy40110/Zero",fontsize=10,color="white",style="solid",shape="box"];666 -> 1069[label="",style="solid", color="burlywood", weight=9];
1069 -> 674[label="",style="solid", color="burlywood", weight=3];
667[label="xy40110",fontsize=16,color="green",shape="box"];668[label="xy30110",fontsize=16,color="green",shape="box"];669[label="xy30110",fontsize=16,color="green",shape="box"];670[label="xy40110",fontsize=16,color="green",shape="box"];671[label="primMulNat (Succ xy301100) (Succ xy401100)",fontsize=16,color="black",shape="box"];671 -> 675[label="",style="solid", color="black", weight=3];
672[label="primMulNat (Succ xy301100) Zero",fontsize=16,color="black",shape="box"];672 -> 676[label="",style="solid", color="black", weight=3];
673[label="primMulNat Zero (Succ xy401100)",fontsize=16,color="black",shape="box"];673 -> 677[label="",style="solid", color="black", weight=3];
674[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];674 -> 678[label="",style="solid", color="black", weight=3];
675 -> 679[label="",style="dashed", color="red", weight=0];
675[label="primPlusNat (primMulNat xy301100 (Succ xy401100)) (Succ xy401100)",fontsize=16,color="magenta"];675 -> 680[label="",style="dashed", color="magenta", weight=3];
676[label="Zero",fontsize=16,color="green",shape="box"];677[label="Zero",fontsize=16,color="green",shape="box"];678[label="Zero",fontsize=16,color="green",shape="box"];680 -> 661[label="",style="dashed", color="red", weight=0];
680[label="primMulNat xy301100 (Succ xy401100)",fontsize=16,color="magenta"];680 -> 681[label="",style="dashed", color="magenta", weight=3];
680 -> 682[label="",style="dashed", color="magenta", weight=3];
679[label="primPlusNat xy20 (Succ xy401100)",fontsize=16,color="burlywood",shape="triangle"];1072[label="xy20/Succ xy200",fontsize=10,color="white",style="solid",shape="box"];679 -> 1072[label="",style="solid", color="burlywood", weight=9];
1072 -> 683[label="",style="solid", color="burlywood", weight=3];
1073[label="xy20/Zero",fontsize=10,color="white",style="solid",shape="box"];679 -> 1073[label="",style="solid", color="burlywood", weight=9];
1073 -> 684[label="",style="solid", color="burlywood", weight=3];
681[label="xy301100",fontsize=16,color="green",shape="box"];682[label="Succ xy401100",fontsize=16,color="green",shape="box"];683[label="primPlusNat (Succ xy200) (Succ xy401100)",fontsize=16,color="black",shape="box"];683 -> 685[label="",style="solid", color="black", weight=3];
684[label="primPlusNat Zero (Succ xy401100)",fontsize=16,color="black",shape="box"];684 -> 686[label="",style="solid", color="black", weight=3];
685[label="Succ (Succ (primPlusNat xy200 xy401100))",fontsize=16,color="green",shape="box"];685 -> 687[label="",style="dashed", color="green", weight=3];
686[label="Succ xy401100",fontsize=16,color="green",shape="box"];687[label="primPlusNat xy200 xy401100",fontsize=16,color="burlywood",shape="triangle"];1074[label="xy200/Succ xy2000",fontsize=10,color="white",style="solid",shape="box"];687 -> 1074[label="",style="solid", color="burlywood", weight=9];
1074 -> 688[label="",style="solid", color="burlywood", weight=3];
1075[label="xy200/Zero",fontsize=10,color="white",style="solid",shape="box"];687 -> 1075[label="",style="solid", color="burlywood", weight=9];
1075 -> 689[label="",style="solid", color="burlywood", weight=3];
688[label="primPlusNat (Succ xy2000) xy401100",fontsize=16,color="burlywood",shape="box"];1076[label="xy401100/Succ xy4011000",fontsize=10,color="white",style="solid",shape="box"];688 -> 1076[label="",style="solid", color="burlywood", weight=9];
1076 -> 690[label="",style="solid", color="burlywood", weight=3];
1077[label="xy401100/Zero",fontsize=10,color="white",style="solid",shape="box"];688 -> 1077[label="",style="solid", color="burlywood", weight=9];
1077 -> 691[label="",style="solid", color="burlywood", weight=3];
689[label="primPlusNat Zero xy401100",fontsize=16,color="burlywood",shape="box"];1078[label="xy401100/Succ xy4011000",fontsize=10,color="white",style="solid",shape="box"];689 -> 1078[label="",style="solid", color="burlywood", weight=9];
1078 -> 692[label="",style="solid", color="burlywood", weight=3];
1079[label="xy401100/Zero",fontsize=10,color="white",style="solid",shape="box"];689 -> 1079[label="",style="solid", color="burlywood", weight=9];
1079 -> 693[label="",style="solid", color="burlywood", weight=3];
690[label="primPlusNat (Succ xy2000) (Succ xy4011000)",fontsize=16,color="black",shape="box"];690 -> 694[label="",style="solid", color="black", weight=3];
691[label="primPlusNat (Succ xy2000) Zero",fontsize=16,color="black",shape="box"];691 -> 695[label="",style="solid", color="black", weight=3];
692[label="primPlusNat Zero (Succ xy4011000)",fontsize=16,color="black",shape="box"];692 -> 696[label="",style="solid", color="black", weight=3];
693[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];693 -> 697[label="",style="solid", color="black", weight=3];
694[label="Succ (Succ (primPlusNat xy2000 xy4011000))",fontsize=16,color="green",shape="box"];694 -> 698[label="",style="dashed", color="green", weight=3];
695[label="Succ xy2000",fontsize=16,color="green",shape="box"];696[label="Succ xy4011000",fontsize=16,color="green",shape="box"];697[label="Zero",fontsize=16,color="green",shape="box"];698 -> 687[label="",style="dashed", color="red", weight=0];
698[label="primPlusNat xy2000 xy4011000",fontsize=16,color="magenta"];698 -> 699[label="",style="dashed", color="magenta", weight=3];
698 -> 700[label="",style="dashed", color="magenta", weight=3];
699[label="xy2000",fontsize=16,color="green",shape="box"];700[label="xy4011000",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(xy4011000)) → new_primPlusNat(xy2000, xy4011000)

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(xy4011000)) → new_primPlusNat(xy2000, xy4011000)
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(xy301100), Succ(xy401100)) → new_primMulNat(xy301100, Succ(xy401100))

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

new_primMulNat(Succ(xy301100), Succ(xy401100)) → new_primMulNat(xy301100, Succ(xy401100))
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(xy30100), Succ(xy40100)) → new_primEqNat(xy30100, xy40100)

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

new_primEqNat(Succ(xy30100), Succ(xy40100)) → new_primEqNat(xy30100, xy40100)
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_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(ty_Either, ba), bb)), bc)) → new_esEs(xy3010, xy4010, ba, bb)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(ty_Either, bcc), bcd), bce) → new_esEs(xy300, xy400, bcc, bcd)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(ty_[], bcb)) → new_esEs3(xy3010, xy4010, bcb)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(ty_Maybe, bbd)) → new_esEs0(xy3010, xy4010, bbd)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(ty_@2, fh), ga)) → new_esEs1(xy3012, xy4012, fh, ga)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(ty_[], bdd), bce) → new_esEs3(xy300, xy400, bdd)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(ty_[], hg)), gh)) → new_esEs3(xy3011, xy4011, hg)
new_esEs0(Just(xy3010), Just(xy4010), app(ty_Maybe, dh)) → new_esEs0(xy3010, xy4010, dh)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(ty_Maybe, bbd))) → new_esEs0(xy3010, xy4010, bbd)
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(ty_Maybe, cf))) → new_esEs0(xy3010, xy4010, cf)
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(ty_Either, df), dg))) → new_esEs(xy3010, xy4010, df, dg)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(ty_Maybe, fg)) → new_esEs0(xy3012, xy4012, fg)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(ty_Maybe, ha)), gh)) → new_esEs0(xy3011, xy4011, ha)
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(ty_Maybe, bd)), bc)) → new_esEs0(xy3010, xy4010, bd)
new_esEs(Left(xy3010), Left(xy4010), app(ty_Maybe, bd), bc) → new_esEs0(xy3010, xy4010, bd)
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(app(ty_@3, db), dc), dd))) → new_esEs2(xy3010, xy4010, db, dc, dd)
new_esEs(Left(xy3010), Left(xy4010), app(ty_[], cb), bc) → new_esEs3(xy3010, xy4010, cb)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), bba) → new_esEs3(xy3011, xy4011, bba)
new_esEs0(Just(xy3010), Just(xy4010), app(app(ty_Either, df), dg)) → new_esEs(xy3010, xy4010, df, dg)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(ty_[], bcb))) → new_esEs3(xy3010, xy4010, bcb)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(ty_@2, bac), bad), fc, gh) → new_esEs1(xy3010, xy4010, bac, bad)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(ty_@2, hb), hc)), gh)) → new_esEs1(xy3011, xy4011, hb, hc)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), eg, app(app(ty_@2, eh), fa)) → new_esEs1(xy301, xy401, eh, fa)
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(ty_Either, cd), ce))) → new_esEs(xy3010, xy4010, cd, ce)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(ty_Either, fd), ff)) → new_esEs(xy3012, xy4012, fd, ff)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs2(xy3010, xy4010, bbg, bbh, bca)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(ty_@2, hb), hc), gh) → new_esEs1(xy3011, xy4011, hb, hc)
new_esEs0(Just(xy3010), Just(xy4010), app(ty_[], ef)) → new_esEs3(xy3010, xy4010, ef)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(ty_Either, hh), baa)), fc), gh)) → new_esEs(xy3010, xy4010, hh, baa)
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(ty_@2, cg), da)) → new_esEs1(xy3010, xy4010, cg, da)
new_esEs(Right(xy3010), Right(xy4010), cc, app(ty_Maybe, cf)) → new_esEs0(xy3010, xy4010, cf)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(ty_Either, fd), ff))) → new_esEs(xy3012, xy4012, fd, ff)
new_esEs0(Just(xy3010), Just(xy4010), app(app(ty_@2, ea), eb)) → new_esEs1(xy3010, xy4010, ea, eb)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(xy3012, xy4012, gb, gc, gd)
new_esEs(Left(xy3010), Left(xy4010), app(app(ty_Either, ba), bb), bc) → new_esEs(xy3010, xy4010, ba, bb)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(ty_Either, bbb), bbc)) → new_esEs(xy3010, xy4010, bbb, bbc)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(ty_Maybe, bcf), bce) → new_esEs0(xy300, xy400, bcf)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(app(ty_@3, bae), baf), bag), fc, gh) → new_esEs2(xy3010, xy4010, bae, baf, bag)
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(app(ty_@3, bg), bh), ca)), bc)) → new_esEs2(xy3010, xy4010, bg, bh, ca)
new_esEs0(Just(xy3010), Just(xy4010), app(app(app(ty_@3, ec), ed), ee)) → new_esEs2(xy3010, xy4010, ec, ed, ee)
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(ty_Maybe, dh))) → new_esEs0(xy3010, xy4010, dh)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(ty_Either, gf), gg)), gh)) → new_esEs(xy3011, xy4011, gf, gg)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(ty_Either, hh), baa), fc, gh) → new_esEs(xy3010, xy4010, hh, baa)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(ty_[], ge))) → new_esEs3(xy3012, xy4012, ge)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(ty_[], hg), gh) → new_esEs3(xy3011, xy4011, hg)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(ty_@2, bbe), bbf))) → new_esEs1(xy3010, xy4010, bbe, bbf)
new_esEs(Left(xy3010), Left(xy4010), app(app(ty_@2, be), bf), bc) → new_esEs1(xy3010, xy4010, be, bf)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(ty_[], bah)), fc), gh)) → new_esEs3(xy3010, xy4010, bah)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], bba)) → new_esEs3(xy3011, xy4011, bba)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(app(ty_@3, gb), gc), gd))) → new_esEs2(xy3012, xy4012, gb, gc, gd)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(ty_Maybe, ha), gh) → new_esEs0(xy3011, xy4011, ha)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(ty_Maybe, fg))) → new_esEs0(xy3012, xy4012, fg)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(app(ty_@3, bbg), bbh), bca))) → new_esEs2(xy3010, xy4010, bbg, bbh, bca)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(app(ty_@3, bae), baf), bag)), fc), gh)) → new_esEs2(xy3010, xy4010, bae, baf, bag)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(ty_Maybe, bab), fc, gh) → new_esEs0(xy3010, xy4010, bab)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(ty_Either, gf), gg), gh) → new_esEs(xy3011, xy4011, gf, gg)
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(ty_@2, cg), da))) → new_esEs1(xy3010, xy4010, cg, da)
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(ty_Either, bbb), bbc))) → new_esEs(xy3010, xy4010, bbb, bbc)
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(ty_Either, cd), ce)) → new_esEs(xy3010, xy4010, cd, ce)
new_esEs(Right(xy3010), Right(xy4010), cc, app(ty_[], de)) → new_esEs3(xy3010, xy4010, de)
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(ty_@2, bbe), bbf)) → new_esEs1(xy3010, xy4010, bbe, bbf)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(ty_[], ge)) → new_esEs3(xy3012, xy4012, ge)
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(ty_@2, ea), eb))) → new_esEs1(xy3010, xy4010, ea, eb)
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(ty_[], cb)), bc)) → new_esEs3(xy3010, xy4010, cb)
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(ty_[], de))) → new_esEs3(xy3010, xy4010, de)
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(app(ty_@3, ec), ed), ee))) → new_esEs2(xy3010, xy4010, ec, ed, ee)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(app(ty_@3, hd), he), hf), gh) → new_esEs2(xy3011, xy4011, hd, he, hf)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(ty_@2, bac), bad)), fc), gh)) → new_esEs1(xy3010, xy4010, bac, bad)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(ty_@2, bcg), bch), bce) → new_esEs1(xy300, xy400, bcg, bch)
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(ty_[], bah), fc, gh) → new_esEs3(xy3010, xy4010, bah)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(app(ty_@3, hd), he), hf)), gh)) → new_esEs2(xy3011, xy4011, hd, he, hf)
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(ty_@2, be), bf)), bc)) → new_esEs1(xy3010, xy4010, be, bf)
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(app(ty_@3, db), dc), dd)) → new_esEs2(xy3010, xy4010, db, dc, dd)
new_esEs(Left(xy3010), Left(xy4010), app(app(app(ty_@3, bg), bh), ca), bc) → new_esEs2(xy3010, xy4010, bg, bh, ca)
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(ty_[], ef))) → new_esEs3(xy3010, xy4010, ef)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(ty_@2, fh), ga))) → new_esEs1(xy3012, xy4012, fh, ga)
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(ty_Maybe, bab)), fc), gh)) → new_esEs0(xy3010, xy4010, bab)
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(app(ty_@3, bda), bdb), bdc), bce) → new_esEs2(xy300, xy400, bda, bdb, bdc)

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

new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(ty_@2, bbe), bbf)) → new_esEs1(xy3010, xy4010, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xy3010), Just(xy4010), app(app(ty_@2, ea), eb)) → new_esEs1(xy3010, xy4010, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xy3010), Just(xy4010), app(ty_[], ef)) → new_esEs3(xy3010, xy4010, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs2(xy3010, xy4010, bbg, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Just(xy3010), Just(xy4010), app(app(app(ty_@3, ec), ed), ee)) → new_esEs2(xy3010, xy4010, ec, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(ty_Maybe, bbd)) → new_esEs0(xy3010, xy4010, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(app(ty_Either, bbb), bbc)) → new_esEs(xy3010, xy4010, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Just(xy3010), Just(xy4010), app(ty_Maybe, dh)) → new_esEs0(xy3010, xy4010, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Just(xy3010), Just(xy4010), app(app(ty_Either, df), dg)) → new_esEs(xy3010, xy4010, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(ty_@2, cg), da)) → new_esEs1(xy3010, xy4010, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Left(xy3010), Left(xy4010), app(app(ty_@2, be), bf), bc) → new_esEs1(xy3010, xy4010, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Left(xy3010), Left(xy4010), app(ty_[], cb), bc) → new_esEs3(xy3010, xy4010, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(xy3010), Right(xy4010), cc, app(ty_[], de)) → new_esEs3(xy3010, xy4010, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Left(xy3010), Left(xy4010), app(app(app(ty_@3, bg), bh), ca), bc) → new_esEs2(xy3010, xy4010, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(app(ty_@3, db), dc), dd)) → new_esEs2(xy3010, xy4010, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(Left(xy3010), Left(xy4010), app(ty_Maybe, bd), bc) → new_esEs0(xy3010, xy4010, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(xy3010), Right(xy4010), cc, app(ty_Maybe, cf)) → new_esEs0(xy3010, xy4010, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Left(xy3010), Left(xy4010), app(app(ty_Either, ba), bb), bc) → new_esEs(xy3010, xy4010, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Right(xy3010), Right(xy4010), cc, app(app(ty_Either, cd), ce)) → new_esEs(xy3010, xy4010, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), eg, app(app(ty_@2, eh), fa)) → new_esEs1(xy301, xy401, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(ty_@2, hb), hc)), gh)) → new_esEs1(xy3011, xy4011, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(ty_@2, bbe), bbf))) → new_esEs1(xy3010, xy4010, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(ty_@2, cg), da))) → new_esEs1(xy3010, xy4010, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(ty_@2, ea), eb))) → new_esEs1(xy3010, xy4010, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(ty_@2, bcg), bch), bce) → new_esEs1(xy300, xy400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(ty_@2, bac), bad)), fc), gh)) → new_esEs1(xy3010, xy4010, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(ty_@2, be), bf)), bc)) → new_esEs1(xy3010, xy4010, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(ty_@2, fh), ga))) → new_esEs1(xy3012, xy4012, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(ty_@2, fh), ga)) → new_esEs1(xy3012, xy4012, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(ty_@2, bac), bad), fc, gh) → new_esEs1(xy3010, xy4010, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(ty_@2, hb), hc), gh) → new_esEs1(xy3011, xy4011, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), app(ty_[], bcb)) → new_esEs3(xy3010, xy4010, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xy3010, xy3011), :(xy4010, xy4011), bba) → new_esEs3(xy3011, xy4011, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(ty_[], bdd), bce) → new_esEs3(xy300, xy400, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(ty_[], hg)), gh)) → new_esEs3(xy3011, xy4011, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(ty_[], bcb))) → new_esEs3(xy3010, xy4010, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(ty_[], ge))) → new_esEs3(xy3012, xy4012, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(ty_[], bah)), fc), gh)) → new_esEs3(xy3010, xy4010, bah)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], bba)) → new_esEs3(xy3011, xy4011, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(ty_[], cb)), bc)) → new_esEs3(xy3010, xy4010, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(ty_[], de))) → new_esEs3(xy3010, xy4010, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(ty_[], ef))) → new_esEs3(xy3010, xy4010, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(ty_[], hg), gh) → new_esEs3(xy3011, xy4011, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(ty_[], ge)) → new_esEs3(xy3012, xy4012, ge)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(ty_[], bah), fc, gh) → new_esEs3(xy3010, xy4010, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(app(ty_@3, db), dc), dd))) → new_esEs2(xy3010, xy4010, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(app(ty_@3, bg), bh), ca)), bc)) → new_esEs2(xy3010, xy4010, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(app(ty_@3, gb), gc), gd))) → new_esEs2(xy3012, xy4012, gb, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(app(ty_@3, bbg), bbh), bca))) → new_esEs2(xy3010, xy4010, bbg, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(app(ty_@3, bae), baf), bag)), fc), gh)) → new_esEs2(xy3010, xy4010, bae, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(app(ty_@3, ec), ed), ee))) → new_esEs2(xy3010, xy4010, ec, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(app(ty_@3, hd), he), hf)), gh)) → new_esEs2(xy3011, xy4011, hd, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(app(ty_@3, bda), bdb), bdc), bce) → new_esEs2(xy300, xy400, bda, bdb, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(ty_Maybe, bbd))) → new_esEs0(xy3010, xy4010, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(ty_Maybe, cf))) → new_esEs0(xy3010, xy4010, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(ty_Maybe, bd)), bc)) → new_esEs0(xy3010, xy4010, bd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(ty_Maybe, ha)), gh)) → new_esEs0(xy3011, xy4011, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(ty_Maybe, bcf), bce) → new_esEs0(xy300, xy400, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(ty_Maybe, dh))) → new_esEs0(xy3010, xy4010, dh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(ty_Maybe, fg))) → new_esEs0(xy3012, xy4012, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(ty_Maybe, bab)), fc), gh)) → new_esEs0(xy3010, xy4010, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, Left(xy3010)), @2(xy400, Left(xy4010)), eg, app(app(ty_Either, app(app(ty_Either, ba), bb)), bc)) → new_esEs(xy3010, xy4010, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy400, xy401), app(app(ty_Either, bcc), bcd), bce) → new_esEs(xy300, xy400, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, Just(xy3010)), @2(xy400, Just(xy4010)), eg, app(ty_Maybe, app(app(ty_Either, df), dg))) → new_esEs(xy3010, xy4010, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, Right(xy3010)), @2(xy400, Right(xy4010)), eg, app(app(ty_Either, cc), app(app(ty_Either, cd), ce))) → new_esEs(xy3010, xy4010, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, app(app(ty_Either, hh), baa)), fc), gh)) → new_esEs(xy3010, xy4010, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), fc), app(app(ty_Either, fd), ff))) → new_esEs(xy3012, xy4012, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, @3(xy3010, xy3011, xy3012)), @2(xy400, @3(xy4010, xy4011, xy4012)), eg, app(app(app(ty_@3, fb), app(app(ty_Either, gf), gg)), gh)) → new_esEs(xy3011, xy4011, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, :(xy3010, xy3011)), @2(xy400, :(xy4010, xy4011)), eg, app(ty_[], app(app(ty_Either, bbb), bbc))) → new_esEs(xy3010, xy4010, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(app(ty_@3, gb), gc), gd)) → new_esEs2(xy3012, xy4012, gb, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(app(ty_@3, bae), baf), bag), fc, gh) → new_esEs2(xy3010, xy4010, bae, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(app(ty_@3, hd), he), hf), gh) → new_esEs2(xy3011, xy4011, hd, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(ty_Maybe, fg)) → new_esEs0(xy3012, xy4012, fg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(ty_Maybe, ha), gh) → new_esEs0(xy3011, xy4011, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(ty_Maybe, bab), fc, gh) → new_esEs0(xy3010, xy4010, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, fc, app(app(ty_Either, fd), ff)) → new_esEs(xy3012, xy4012, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), app(app(ty_Either, hh), baa), fc, gh) → new_esEs(xy3010, xy4010, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(xy3010, xy3011, xy3012), @3(xy4010, xy4011, xy4012), fb, app(app(ty_Either, gf), gg), gh) → new_esEs(xy3011, xy4011, gf, gg)
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, 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