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

YES 1.252 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

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

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="notElem\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
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812 -> 10[label="",style="solid", color="burlywood", weight=3];
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817 -> 26[label="",style="solid", color="blue", weight=3];
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818 -> 27[label="",style="solid", color="blue", weight=3];
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819 -> 28[label="",style="solid", color="blue", weight=3];
820[label="/= :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 820[label="",style="solid", color="blue", weight=9];
820 -> 29[label="",style="solid", color="blue", weight=3];
821[label="/= :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 821[label="",style="solid", color="blue", weight=9];
821 -> 30[label="",style="solid", color="blue", weight=3];
822[label="/= :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 822[label="",style="solid", color="blue", weight=9];
822 -> 31[label="",style="solid", color="blue", weight=3];
823[label="/= :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 823[label="",style="solid", color="blue", weight=9];
823 -> 32[label="",style="solid", color="blue", weight=3];
824[label="/= :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 824[label="",style="solid", color="blue", weight=9];
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825[label="/= :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 825[label="",style="solid", color="blue", weight=9];
825 -> 34[label="",style="solid", color="blue", weight=3];
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826 -> 35[label="",style="solid", color="blue", weight=3];
827[label="/= :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 827[label="",style="solid", color="blue", weight=9];
827 -> 36[label="",style="solid", color="blue", weight=3];
828[label="/= :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 828[label="",style="solid", color="blue", weight=9];
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829[label="/= :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];21 -> 829[label="",style="solid", color="blue", weight=9];
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830 -> 39[label="",style="solid", color="burlywood", weight=3];
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846 -> 198[label="",style="solid", color="burlywood", weight=3];
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848 -> 200[label="",style="solid", color="burlywood", weight=3];
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850 -> 202[label="",style="solid", color="burlywood", weight=3];
152[label="xv3 == xv40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];851[label="xv3/xv30 : xv31",fontsize=10,color="white",style="solid",shape="box"];152 -> 851[label="",style="solid", color="burlywood", weight=9];
851 -> 203[label="",style="solid", color="burlywood", weight=3];
852[label="xv3/[]",fontsize=10,color="white",style="solid",shape="box"];152 -> 852[label="",style="solid", color="burlywood", weight=9];
852 -> 204[label="",style="solid", color="burlywood", weight=3];
153[label="xv3 == xv40",fontsize=16,color="burlywood",shape="triangle"];853[label="xv3/()",fontsize=10,color="white",style="solid",shape="box"];153 -> 853[label="",style="solid", color="burlywood", weight=9];
853 -> 205[label="",style="solid", color="burlywood", weight=3];
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855 -> 208[label="",style="solid", color="burlywood", weight=3];
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856 -> 209[label="",style="solid", color="burlywood", weight=3];
157[label="xv3 == xv40",fontsize=16,color="burlywood",shape="triangle"];857[label="xv3/LT",fontsize=10,color="white",style="solid",shape="box"];157 -> 857[label="",style="solid", color="burlywood", weight=9];
857 -> 210[label="",style="solid", color="burlywood", weight=3];
858[label="xv3/EQ",fontsize=10,color="white",style="solid",shape="box"];157 -> 858[label="",style="solid", color="burlywood", weight=9];
858 -> 211[label="",style="solid", color="burlywood", weight=3];
859[label="xv3/GT",fontsize=10,color="white",style="solid",shape="box"];157 -> 859[label="",style="solid", color="burlywood", weight=9];
859 -> 212[label="",style="solid", color="burlywood", weight=3];
158[label="xv3 == xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];860[label="xv3/(xv30,xv31)",fontsize=10,color="white",style="solid",shape="box"];158 -> 860[label="",style="solid", color="burlywood", weight=9];
860 -> 213[label="",style="solid", color="burlywood", weight=3];
159[label="xv3 == xv40",fontsize=16,color="black",shape="triangle"];159 -> 214[label="",style="solid", color="black", weight=3];
160[label="xv3 == xv40",fontsize=16,color="black",shape="triangle"];160 -> 215[label="",style="solid", color="black", weight=3];
161[label="xv3 == xv40",fontsize=16,color="black",shape="triangle"];161 -> 216[label="",style="solid", color="black", weight=3];
162[label="xv3 == xv40",fontsize=16,color="burlywood",shape="triangle"];861[label="xv3/Integer xv30",fontsize=10,color="white",style="solid",shape="box"];162 -> 861[label="",style="solid", color="burlywood", weight=9];
861 -> 217[label="",style="solid", color="burlywood", weight=3];
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863 -> 219[label="",style="solid", color="burlywood", weight=3];
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864 -> 220[label="",style="solid", color="burlywood", weight=3];
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865 -> 221[label="",style="solid", color="burlywood", weight=3];
199[label="Right xv30 == xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];866[label="xv40/Left xv400",fontsize=10,color="white",style="solid",shape="box"];199 -> 866[label="",style="solid", color="burlywood", weight=9];
866 -> 222[label="",style="solid", color="burlywood", weight=3];
867[label="xv40/Right xv400",fontsize=10,color="white",style="solid",shape="box"];199 -> 867[label="",style="solid", color="burlywood", weight=9];
867 -> 223[label="",style="solid", color="burlywood", weight=3];
200[label="not False",fontsize=16,color="black",shape="box"];200 -> 224[label="",style="solid", color="black", weight=3];
201[label="not True",fontsize=16,color="black",shape="box"];201 -> 225[label="",style="solid", color="black", weight=3];
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868 -> 226[label="",style="solid", color="burlywood", weight=3];
203[label="xv30 : xv31 == xv40\n  Eq a",fontsize=16,color="burlywood",shape="box"];869[label="xv40/xv400 : xv401",fontsize=10,color="white",style="solid",shape="box"];203 -> 869[label="",style="solid", color="burlywood", weight=9];
869 -> 227[label="",style="solid", color="burlywood", weight=3];
870[label="xv40/[]",fontsize=10,color="white",style="solid",shape="box"];203 -> 870[label="",style="solid", color="burlywood", weight=9];
870 -> 228[label="",style="solid", color="burlywood", weight=3];
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871 -> 229[label="",style="solid", color="burlywood", weight=3];
872[label="xv40/[]",fontsize=10,color="white",style="solid",shape="box"];204 -> 872[label="",style="solid", color="burlywood", weight=9];
872 -> 230[label="",style="solid", color="burlywood", weight=3];
205[label="() == xv40",fontsize=16,color="burlywood",shape="box"];873[label="xv40/()",fontsize=10,color="white",style="solid",shape="box"];205 -> 873[label="",style="solid", color="burlywood", weight=9];
873 -> 231[label="",style="solid", color="burlywood", weight=3];
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874 -> 232[label="",style="solid", color="burlywood", weight=3];
875[label="xv3/Neg xv30",fontsize=10,color="white",style="solid",shape="box"];206 -> 875[label="",style="solid", color="burlywood", weight=9];
875 -> 233[label="",style="solid", color="burlywood", weight=3];
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876 -> 234[label="",style="solid", color="burlywood", weight=3];
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878 -> 236[label="",style="solid", color="burlywood", weight=3];
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879 -> 237[label="",style="solid", color="burlywood", weight=3];
880[label="xv40/Just xv400",fontsize=10,color="white",style="solid",shape="box"];209 -> 880[label="",style="solid", color="burlywood", weight=9];
880 -> 238[label="",style="solid", color="burlywood", weight=3];
210[label="LT == xv40",fontsize=16,color="burlywood",shape="box"];881[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];210 -> 881[label="",style="solid", color="burlywood", weight=9];
881 -> 239[label="",style="solid", color="burlywood", weight=3];
882[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];210 -> 882[label="",style="solid", color="burlywood", weight=9];
882 -> 240[label="",style="solid", color="burlywood", weight=3];
883[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];210 -> 883[label="",style="solid", color="burlywood", weight=9];
883 -> 241[label="",style="solid", color="burlywood", weight=3];
211[label="EQ == xv40",fontsize=16,color="burlywood",shape="box"];884[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];211 -> 884[label="",style="solid", color="burlywood", weight=9];
884 -> 242[label="",style="solid", color="burlywood", weight=3];
885[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];211 -> 885[label="",style="solid", color="burlywood", weight=9];
885 -> 243[label="",style="solid", color="burlywood", weight=3];
886[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];211 -> 886[label="",style="solid", color="burlywood", weight=9];
886 -> 244[label="",style="solid", color="burlywood", weight=3];
212[label="GT == xv40",fontsize=16,color="burlywood",shape="box"];887[label="xv40/LT",fontsize=10,color="white",style="solid",shape="box"];212 -> 887[label="",style="solid", color="burlywood", weight=9];
887 -> 245[label="",style="solid", color="burlywood", weight=3];
888[label="xv40/EQ",fontsize=10,color="white",style="solid",shape="box"];212 -> 888[label="",style="solid", color="burlywood", weight=9];
888 -> 246[label="",style="solid", color="burlywood", weight=3];
889[label="xv40/GT",fontsize=10,color="white",style="solid",shape="box"];212 -> 889[label="",style="solid", color="burlywood", weight=9];
889 -> 247[label="",style="solid", color="burlywood", weight=3];
213[label="(xv30,xv31) == xv40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];890[label="xv40/(xv400,xv401)",fontsize=10,color="white",style="solid",shape="box"];213 -> 890[label="",style="solid", color="burlywood", weight=9];
890 -> 248[label="",style="solid", color="burlywood", weight=3];
214[label="primEqFloat xv3 xv40",fontsize=16,color="burlywood",shape="box"];891[label="xv3/Float xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];214 -> 891[label="",style="solid", color="burlywood", weight=9];
891 -> 249[label="",style="solid", color="burlywood", weight=3];
215[label="primEqDouble xv3 xv40",fontsize=16,color="burlywood",shape="box"];892[label="xv3/Double xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];215 -> 892[label="",style="solid", color="burlywood", weight=9];
892 -> 250[label="",style="solid", color="burlywood", weight=3];
216[label="primEqChar xv3 xv40",fontsize=16,color="burlywood",shape="box"];893[label="xv3/Char xv30",fontsize=10,color="white",style="solid",shape="box"];216 -> 893[label="",style="solid", color="burlywood", weight=9];
893 -> 251[label="",style="solid", color="burlywood", weight=3];
217[label="Integer xv30 == xv40",fontsize=16,color="burlywood",shape="box"];894[label="xv40/Integer xv400",fontsize=10,color="white",style="solid",shape="box"];217 -> 894[label="",style="solid", color="burlywood", weight=9];
894 -> 252[label="",style="solid", color="burlywood", weight=3];
218[label="False == xv40",fontsize=16,color="burlywood",shape="box"];895[label="xv40/False",fontsize=10,color="white",style="solid",shape="box"];218 -> 895[label="",style="solid", color="burlywood", weight=9];
895 -> 253[label="",style="solid", color="burlywood", weight=3];
896[label="xv40/True",fontsize=10,color="white",style="solid",shape="box"];218 -> 896[label="",style="solid", color="burlywood", weight=9];
896 -> 254[label="",style="solid", color="burlywood", weight=3];
219[label="True == xv40",fontsize=16,color="burlywood",shape="box"];897[label="xv40/False",fontsize=10,color="white",style="solid",shape="box"];219 -> 897[label="",style="solid", color="burlywood", weight=9];
897 -> 255[label="",style="solid", color="burlywood", weight=3];
898[label="xv40/True",fontsize=10,color="white",style="solid",shape="box"];219 -> 898[label="",style="solid", color="burlywood", weight=9];
898 -> 256[label="",style="solid", color="burlywood", weight=3];
220[label="Left xv30 == Left xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];220 -> 257[label="",style="solid", color="black", weight=3];
221[label="Left xv30 == Right xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];221 -> 258[label="",style="solid", color="black", weight=3];
222[label="Right xv30 == Left xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];222 -> 259[label="",style="solid", color="black", weight=3];
223[label="Right xv30 == Right xv400\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];223 -> 260[label="",style="solid", color="black", weight=3];
224[label="True",fontsize=16,color="green",shape="box"];225[label="False",fontsize=16,color="green",shape="box"];226[label="(xv30,xv31,xv32) == (xv400,xv401,xv402)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];226 -> 261[label="",style="solid", color="black", weight=3];
227[label="xv30 : xv31 == xv400 : xv401\n  Eq a",fontsize=16,color="black",shape="box"];227 -> 262[label="",style="solid", color="black", weight=3];
228[label="xv30 : xv31 == []\n  Eq a",fontsize=16,color="black",shape="box"];228 -> 263[label="",style="solid", color="black", weight=3];
229[label="[] == xv400 : xv401\n  Eq a",fontsize=16,color="black",shape="box"];229 -> 264[label="",style="solid", color="black", weight=3];
230[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];230 -> 265[label="",style="solid", color="black", weight=3];
231[label="() == ()",fontsize=16,color="black",shape="box"];231 -> 266[label="",style="solid", color="black", weight=3];
232[label="primEqInt (Pos xv30) xv40",fontsize=16,color="burlywood",shape="box"];899[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];232 -> 899[label="",style="solid", color="burlywood", weight=9];
899 -> 267[label="",style="solid", color="burlywood", weight=3];
900[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];232 -> 900[label="",style="solid", color="burlywood", weight=9];
900 -> 268[label="",style="solid", color="burlywood", weight=3];
233[label="primEqInt (Neg xv30) xv40",fontsize=16,color="burlywood",shape="box"];901[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];233 -> 901[label="",style="solid", color="burlywood", weight=9];
901 -> 269[label="",style="solid", color="burlywood", weight=3];
902[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];233 -> 902[label="",style="solid", color="burlywood", weight=9];
902 -> 270[label="",style="solid", color="burlywood", weight=3];
234[label="xv30 :% xv31 == xv400 :% xv401\n  Integral a",fontsize=16,color="black",shape="box"];234 -> 271[label="",style="solid", color="black", weight=3];
235[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];235 -> 272[label="",style="solid", color="black", weight=3];
236[label="Nothing == Just xv400\n  Eq a",fontsize=16,color="black",shape="box"];236 -> 273[label="",style="solid", color="black", weight=3];
237[label="Just xv30 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];237 -> 274[label="",style="solid", color="black", weight=3];
238[label="Just xv30 == Just xv400\n  Eq a",fontsize=16,color="black",shape="box"];238 -> 275[label="",style="solid", color="black", weight=3];
239[label="LT == LT",fontsize=16,color="black",shape="box"];239 -> 276[label="",style="solid", color="black", weight=3];
240[label="LT == EQ",fontsize=16,color="black",shape="box"];240 -> 277[label="",style="solid", color="black", weight=3];
241[label="LT == GT",fontsize=16,color="black",shape="box"];241 -> 278[label="",style="solid", color="black", weight=3];
242[label="EQ == LT",fontsize=16,color="black",shape="box"];242 -> 279[label="",style="solid", color="black", weight=3];
243[label="EQ == EQ",fontsize=16,color="black",shape="box"];243 -> 280[label="",style="solid", color="black", weight=3];
244[label="EQ == GT",fontsize=16,color="black",shape="box"];244 -> 281[label="",style="solid", color="black", weight=3];
245[label="GT == LT",fontsize=16,color="black",shape="box"];245 -> 282[label="",style="solid", color="black", weight=3];
246[label="GT == EQ",fontsize=16,color="black",shape="box"];246 -> 283[label="",style="solid", color="black", weight=3];
247[label="GT == GT",fontsize=16,color="black",shape="box"];247 -> 284[label="",style="solid", color="black", weight=3];
248[label="(xv30,xv31) == (xv400,xv401)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];248 -> 285[label="",style="solid", color="black", weight=3];
249[label="primEqFloat (Float xv30 xv31) xv40",fontsize=16,color="burlywood",shape="box"];903[label="xv40/Float xv400 xv401",fontsize=10,color="white",style="solid",shape="box"];249 -> 903[label="",style="solid", color="burlywood", weight=9];
903 -> 286[label="",style="solid", color="burlywood", weight=3];
250[label="primEqDouble (Double xv30 xv31) xv40",fontsize=16,color="burlywood",shape="box"];904[label="xv40/Double xv400 xv401",fontsize=10,color="white",style="solid",shape="box"];250 -> 904[label="",style="solid", color="burlywood", weight=9];
904 -> 287[label="",style="solid", color="burlywood", weight=3];
251[label="primEqChar (Char xv30) xv40",fontsize=16,color="burlywood",shape="box"];905[label="xv40/Char xv400",fontsize=10,color="white",style="solid",shape="box"];251 -> 905[label="",style="solid", color="burlywood", weight=9];
905 -> 288[label="",style="solid", color="burlywood", weight=3];
252[label="Integer xv30 == Integer xv400",fontsize=16,color="black",shape="box"];252 -> 289[label="",style="solid", color="black", weight=3];
253[label="False == False",fontsize=16,color="black",shape="box"];253 -> 290[label="",style="solid", color="black", weight=3];
254[label="False == True",fontsize=16,color="black",shape="box"];254 -> 291[label="",style="solid", color="black", weight=3];
255[label="True == False",fontsize=16,color="black",shape="box"];255 -> 292[label="",style="solid", color="black", weight=3];
256[label="True == True",fontsize=16,color="black",shape="box"];256 -> 293[label="",style="solid", color="black", weight=3];
257[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];906[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 906[label="",style="solid", color="blue", weight=9];
906 -> 294[label="",style="solid", color="blue", weight=3];
907[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 907[label="",style="solid", color="blue", weight=9];
907 -> 295[label="",style="solid", color="blue", weight=3];
908[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 908[label="",style="solid", color="blue", weight=9];
908 -> 296[label="",style="solid", color="blue", weight=3];
909[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 909[label="",style="solid", color="blue", weight=9];
909 -> 297[label="",style="solid", color="blue", weight=3];
910[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 910[label="",style="solid", color="blue", weight=9];
910 -> 298[label="",style="solid", color="blue", weight=3];
911[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 911[label="",style="solid", color="blue", weight=9];
911 -> 299[label="",style="solid", color="blue", weight=3];
912[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 912[label="",style="solid", color="blue", weight=9];
912 -> 300[label="",style="solid", color="blue", weight=3];
913[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 913[label="",style="solid", color="blue", weight=9];
913 -> 301[label="",style="solid", color="blue", weight=3];
914[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 914[label="",style="solid", color="blue", weight=9];
914 -> 302[label="",style="solid", color="blue", weight=3];
915[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 915[label="",style="solid", color="blue", weight=9];
915 -> 303[label="",style="solid", color="blue", weight=3];
916[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 916[label="",style="solid", color="blue", weight=9];
916 -> 304[label="",style="solid", color="blue", weight=3];
917[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 917[label="",style="solid", color="blue", weight=9];
917 -> 305[label="",style="solid", color="blue", weight=3];
918[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 918[label="",style="solid", color="blue", weight=9];
918 -> 306[label="",style="solid", color="blue", weight=3];
919[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];257 -> 919[label="",style="solid", color="blue", weight=9];
919 -> 307[label="",style="solid", color="blue", weight=3];
258[label="False",fontsize=16,color="green",shape="box"];259[label="False",fontsize=16,color="green",shape="box"];260[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];920[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 920[label="",style="solid", color="blue", weight=9];
920 -> 308[label="",style="solid", color="blue", weight=3];
921[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 921[label="",style="solid", color="blue", weight=9];
921 -> 309[label="",style="solid", color="blue", weight=3];
922[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 922[label="",style="solid", color="blue", weight=9];
922 -> 310[label="",style="solid", color="blue", weight=3];
923[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 923[label="",style="solid", color="blue", weight=9];
923 -> 311[label="",style="solid", color="blue", weight=3];
924[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 924[label="",style="solid", color="blue", weight=9];
924 -> 312[label="",style="solid", color="blue", weight=3];
925[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 925[label="",style="solid", color="blue", weight=9];
925 -> 313[label="",style="solid", color="blue", weight=3];
926[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 926[label="",style="solid", color="blue", weight=9];
926 -> 314[label="",style="solid", color="blue", weight=3];
927[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 927[label="",style="solid", color="blue", weight=9];
927 -> 315[label="",style="solid", color="blue", weight=3];
928[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 928[label="",style="solid", color="blue", weight=9];
928 -> 316[label="",style="solid", color="blue", weight=3];
929[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 929[label="",style="solid", color="blue", weight=9];
929 -> 317[label="",style="solid", color="blue", weight=3];
930[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 930[label="",style="solid", color="blue", weight=9];
930 -> 318[label="",style="solid", color="blue", weight=3];
931[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 931[label="",style="solid", color="blue", weight=9];
931 -> 319[label="",style="solid", color="blue", weight=3];
932[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 932[label="",style="solid", color="blue", weight=9];
932 -> 320[label="",style="solid", color="blue", weight=3];
933[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];260 -> 933[label="",style="solid", color="blue", weight=9];
933 -> 321[label="",style="solid", color="blue", weight=3];
261 -> 19[label="",style="dashed", color="red", weight=0];
261[label="xv30 == xv400 && xv31 == xv401 && xv32 == xv402\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];261 -> 322[label="",style="dashed", color="magenta", weight=3];
261 -> 323[label="",style="dashed", color="magenta", weight=3];
262 -> 19[label="",style="dashed", color="red", weight=0];
262[label="xv30 == xv400 && xv31 == xv401\n  Eq a",fontsize=16,color="magenta"];262 -> 324[label="",style="dashed", color="magenta", weight=3];
262 -> 325[label="",style="dashed", color="magenta", weight=3];
263[label="False",fontsize=16,color="green",shape="box"];264[label="False",fontsize=16,color="green",shape="box"];265[label="True",fontsize=16,color="green",shape="box"];266[label="True",fontsize=16,color="green",shape="box"];267[label="primEqInt (Pos (Succ xv300)) xv40",fontsize=16,color="burlywood",shape="box"];936[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];267 -> 936[label="",style="solid", color="burlywood", weight=9];
936 -> 326[label="",style="solid", color="burlywood", weight=3];
937[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];267 -> 937[label="",style="solid", color="burlywood", weight=9];
937 -> 327[label="",style="solid", color="burlywood", weight=3];
268[label="primEqInt (Pos Zero) xv40",fontsize=16,color="burlywood",shape="box"];938[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];268 -> 938[label="",style="solid", color="burlywood", weight=9];
938 -> 328[label="",style="solid", color="burlywood", weight=3];
939[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];268 -> 939[label="",style="solid", color="burlywood", weight=9];
939 -> 329[label="",style="solid", color="burlywood", weight=3];
269[label="primEqInt (Neg (Succ xv300)) xv40",fontsize=16,color="burlywood",shape="box"];940[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];269 -> 940[label="",style="solid", color="burlywood", weight=9];
940 -> 330[label="",style="solid", color="burlywood", weight=3];
941[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];269 -> 941[label="",style="solid", color="burlywood", weight=9];
941 -> 331[label="",style="solid", color="burlywood", weight=3];
270[label="primEqInt (Neg Zero) xv40",fontsize=16,color="burlywood",shape="box"];942[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];270 -> 942[label="",style="solid", color="burlywood", weight=9];
942 -> 332[label="",style="solid", color="burlywood", weight=3];
943[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];270 -> 943[label="",style="solid", color="burlywood", weight=9];
943 -> 333[label="",style="solid", color="burlywood", weight=3];
271 -> 19[label="",style="dashed", color="red", weight=0];
271[label="xv30 == xv400 && xv31 == xv401\n  Integral a",fontsize=16,color="magenta"];271 -> 334[label="",style="dashed", color="magenta", weight=3];
271 -> 335[label="",style="dashed", color="magenta", weight=3];
272[label="True",fontsize=16,color="green",shape="box"];273[label="False",fontsize=16,color="green",shape="box"];274[label="False",fontsize=16,color="green",shape="box"];275[label="xv30 == xv400\n  Eq a",fontsize=16,color="blue",shape="box"];945[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 945[label="",style="solid", color="blue", weight=9];
945 -> 336[label="",style="solid", color="blue", weight=3];
946[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 946[label="",style="solid", color="blue", weight=9];
946 -> 337[label="",style="solid", color="blue", weight=3];
947[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 947[label="",style="solid", color="blue", weight=9];
947 -> 338[label="",style="solid", color="blue", weight=3];
948[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 948[label="",style="solid", color="blue", weight=9];
948 -> 339[label="",style="solid", color="blue", weight=3];
949[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 949[label="",style="solid", color="blue", weight=9];
949 -> 340[label="",style="solid", color="blue", weight=3];
950[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 950[label="",style="solid", color="blue", weight=9];
950 -> 341[label="",style="solid", color="blue", weight=3];
951[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 951[label="",style="solid", color="blue", weight=9];
951 -> 342[label="",style="solid", color="blue", weight=3];
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776[label="primMulNat (Succ xv3100) xv4010",fontsize=16,color="burlywood",shape="box"];1218[label="xv4010/Succ xv40100",fontsize=10,color="white",style="solid",shape="box"];776 -> 1218[label="",style="solid", color="burlywood", weight=9];
1218 -> 782[label="",style="solid", color="burlywood", weight=3];
1219[label="xv4010/Zero",fontsize=10,color="white",style="solid",shape="box"];776 -> 1219[label="",style="solid", color="burlywood", weight=9];
1219 -> 783[label="",style="solid", color="burlywood", weight=3];
777[label="primMulNat Zero xv4010",fontsize=16,color="burlywood",shape="box"];1220[label="xv4010/Succ xv40100",fontsize=10,color="white",style="solid",shape="box"];777 -> 1220[label="",style="solid", color="burlywood", weight=9];
1220 -> 784[label="",style="solid", color="burlywood", weight=3];
1221[label="xv4010/Zero",fontsize=10,color="white",style="solid",shape="box"];777 -> 1221[label="",style="solid", color="burlywood", weight=9];
1221 -> 785[label="",style="solid", color="burlywood", weight=3];
778[label="xv4010",fontsize=16,color="green",shape="box"];779[label="xv310",fontsize=16,color="green",shape="box"];780[label="xv4010",fontsize=16,color="green",shape="box"];781[label="xv310",fontsize=16,color="green",shape="box"];782[label="primMulNat (Succ xv3100) (Succ xv40100)",fontsize=16,color="black",shape="box"];782 -> 786[label="",style="solid", color="black", weight=3];
783[label="primMulNat (Succ xv3100) Zero",fontsize=16,color="black",shape="box"];783 -> 787[label="",style="solid", color="black", weight=3];
784[label="primMulNat Zero (Succ xv40100)",fontsize=16,color="black",shape="box"];784 -> 788[label="",style="solid", color="black", weight=3];
785[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];785 -> 789[label="",style="solid", color="black", weight=3];
786 -> 790[label="",style="dashed", color="red", weight=0];
786[label="primPlusNat (primMulNat xv3100 (Succ xv40100)) (Succ xv40100)",fontsize=16,color="magenta"];786 -> 791[label="",style="dashed", color="magenta", weight=3];
787[label="Zero",fontsize=16,color="green",shape="box"];788[label="Zero",fontsize=16,color="green",shape="box"];789[label="Zero",fontsize=16,color="green",shape="box"];791 -> 772[label="",style="dashed", color="red", weight=0];
791[label="primMulNat xv3100 (Succ xv40100)",fontsize=16,color="magenta"];791 -> 792[label="",style="dashed", color="magenta", weight=3];
791 -> 793[label="",style="dashed", color="magenta", weight=3];
790[label="primPlusNat xv14 (Succ xv40100)",fontsize=16,color="burlywood",shape="triangle"];1224[label="xv14/Succ xv140",fontsize=10,color="white",style="solid",shape="box"];790 -> 1224[label="",style="solid", color="burlywood", weight=9];
1224 -> 794[label="",style="solid", color="burlywood", weight=3];
1225[label="xv14/Zero",fontsize=10,color="white",style="solid",shape="box"];790 -> 1225[label="",style="solid", color="burlywood", weight=9];
1225 -> 795[label="",style="solid", color="burlywood", weight=3];
792[label="Succ xv40100",fontsize=16,color="green",shape="box"];793[label="xv3100",fontsize=16,color="green",shape="box"];794[label="primPlusNat (Succ xv140) (Succ xv40100)",fontsize=16,color="black",shape="box"];794 -> 796[label="",style="solid", color="black", weight=3];
795[label="primPlusNat Zero (Succ xv40100)",fontsize=16,color="black",shape="box"];795 -> 797[label="",style="solid", color="black", weight=3];
796[label="Succ (Succ (primPlusNat xv140 xv40100))",fontsize=16,color="green",shape="box"];796 -> 798[label="",style="dashed", color="green", weight=3];
797[label="Succ xv40100",fontsize=16,color="green",shape="box"];798[label="primPlusNat xv140 xv40100",fontsize=16,color="burlywood",shape="triangle"];1226[label="xv140/Succ xv1400",fontsize=10,color="white",style="solid",shape="box"];798 -> 1226[label="",style="solid", color="burlywood", weight=9];
1226 -> 799[label="",style="solid", color="burlywood", weight=3];
1227[label="xv140/Zero",fontsize=10,color="white",style="solid",shape="box"];798 -> 1227[label="",style="solid", color="burlywood", weight=9];
1227 -> 800[label="",style="solid", color="burlywood", weight=3];
799[label="primPlusNat (Succ xv1400) xv40100",fontsize=16,color="burlywood",shape="box"];1228[label="xv40100/Succ xv401000",fontsize=10,color="white",style="solid",shape="box"];799 -> 1228[label="",style="solid", color="burlywood", weight=9];
1228 -> 801[label="",style="solid", color="burlywood", weight=3];
1229[label="xv40100/Zero",fontsize=10,color="white",style="solid",shape="box"];799 -> 1229[label="",style="solid", color="burlywood", weight=9];
1229 -> 802[label="",style="solid", color="burlywood", weight=3];
800[label="primPlusNat Zero xv40100",fontsize=16,color="burlywood",shape="box"];1230[label="xv40100/Succ xv401000",fontsize=10,color="white",style="solid",shape="box"];800 -> 1230[label="",style="solid", color="burlywood", weight=9];
1230 -> 803[label="",style="solid", color="burlywood", weight=3];
1231[label="xv40100/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 1231[label="",style="solid", color="burlywood", weight=9];
1231 -> 804[label="",style="solid", color="burlywood", weight=3];
801[label="primPlusNat (Succ xv1400) (Succ xv401000)",fontsize=16,color="black",shape="box"];801 -> 805[label="",style="solid", color="black", weight=3];
802[label="primPlusNat (Succ xv1400) Zero",fontsize=16,color="black",shape="box"];802 -> 806[label="",style="solid", color="black", weight=3];
803[label="primPlusNat Zero (Succ xv401000)",fontsize=16,color="black",shape="box"];803 -> 807[label="",style="solid", color="black", weight=3];
804[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];804 -> 808[label="",style="solid", color="black", weight=3];
805[label="Succ (Succ (primPlusNat xv1400 xv401000))",fontsize=16,color="green",shape="box"];805 -> 809[label="",style="dashed", color="green", weight=3];
806[label="Succ xv1400",fontsize=16,color="green",shape="box"];807[label="Succ xv401000",fontsize=16,color="green",shape="box"];808[label="Zero",fontsize=16,color="green",shape="box"];809 -> 798[label="",style="dashed", color="red", weight=0];
809[label="primPlusNat xv1400 xv401000",fontsize=16,color="magenta"];809 -> 810[label="",style="dashed", color="magenta", weight=3];
809 -> 811[label="",style="dashed", color="magenta", weight=3];
810[label="xv1400",fontsize=16,color="green",shape="box"];811[label="xv401000",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(xv1400), Succ(xv401000)) → new_primPlusNat(xv1400, xv401000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

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

new_primPlusNat(Succ(xv1400), Succ(xv401000)) → new_primPlusNat(xv1400, xv401000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

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

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

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

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

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

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

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

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

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

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

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

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