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

YES 1.241 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

(((/=) :: 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

(((/=) :: 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

((/=) :: Eq a => a -> a -> Bool)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="(/=)\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
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836 -> 5[label="",style="solid", color="blue", weight=3];
837[label="/= :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 837[label="",style="solid", color="blue", weight=9];
837 -> 6[label="",style="solid", color="blue", weight=3];
838[label="/= :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 838[label="",style="solid", color="blue", weight=9];
838 -> 7[label="",style="solid", color="blue", weight=3];
839[label="/= :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 839[label="",style="solid", color="blue", weight=9];
839 -> 8[label="",style="solid", color="blue", weight=3];
840[label="/= :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 840[label="",style="solid", color="blue", weight=9];
840 -> 9[label="",style="solid", color="blue", weight=3];
841[label="/= :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 841[label="",style="solid", color="blue", weight=9];
841 -> 10[label="",style="solid", color="blue", weight=3];
842[label="/= :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 842[label="",style="solid", color="blue", weight=9];
842 -> 11[label="",style="solid", color="blue", weight=3];
843[label="/= :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 843[label="",style="solid", color="blue", weight=9];
843 -> 12[label="",style="solid", color="blue", weight=3];
844[label="/= :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 844[label="",style="solid", color="blue", weight=9];
844 -> 13[label="",style="solid", color="blue", weight=3];
845[label="/= :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 845[label="",style="solid", color="blue", weight=9];
845 -> 14[label="",style="solid", color="blue", weight=3];
846[label="/= :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 846[label="",style="solid", color="blue", weight=9];
846 -> 15[label="",style="solid", color="blue", weight=3];
847[label="/= :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 847[label="",style="solid", color="blue", weight=9];
847 -> 16[label="",style="solid", color="blue", weight=3];
848[label="/= :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 848[label="",style="solid", color="blue", weight=9];
848 -> 17[label="",style="solid", color="blue", weight=3];
849[label="/= :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 849[label="",style="solid", color="blue", weight=9];
849 -> 18[label="",style="solid", color="blue", weight=3];
5[label="(/=) xv3 xv4\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];5 -> 19[label="",style="solid", color="black", weight=3];
6[label="(/=) xv3 xv4",fontsize=16,color="black",shape="box"];6 -> 20[label="",style="solid", color="black", weight=3];
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8[label="(/=) xv3 xv4",fontsize=16,color="black",shape="box"];8 -> 22[label="",style="solid", color="black", weight=3];
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11[label="(/=) xv3 xv4\n  Eq a",fontsize=16,color="black",shape="box"];11 -> 25[label="",style="solid", color="black", weight=3];
12[label="(/=) xv3 xv4",fontsize=16,color="black",shape="box"];12 -> 26[label="",style="solid", color="black", weight=3];
13[label="(/=) xv3 xv4",fontsize=16,color="black",shape="box"];13 -> 27[label="",style="solid", color="black", weight=3];
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32[label="not (xv3 == xv4)",fontsize=16,color="magenta"];32 -> 156[label="",style="dashed", color="magenta", weight=3];
143[label="xv3 == xv4\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];864[label="xv3/(xv30,xv31,xv32)",fontsize=10,color="white",style="solid",shape="box"];143 -> 864[label="",style="solid", color="burlywood", weight=9];
864 -> 193[label="",style="solid", color="burlywood", weight=3];
142[label="not xv18",fontsize=16,color="burlywood",shape="triangle"];865[label="xv18/False",fontsize=10,color="white",style="solid",shape="box"];142 -> 865[label="",style="solid", color="burlywood", weight=9];
865 -> 194[label="",style="solid", color="burlywood", weight=3];
866[label="xv18/True",fontsize=10,color="white",style="solid",shape="box"];142 -> 866[label="",style="solid", color="burlywood", weight=9];
866 -> 195[label="",style="solid", color="burlywood", weight=3];
144[label="xv3 == xv4",fontsize=16,color="burlywood",shape="triangle"];867[label="xv3/LT",fontsize=10,color="white",style="solid",shape="box"];144 -> 867[label="",style="solid", color="burlywood", weight=9];
867 -> 196[label="",style="solid", color="burlywood", weight=3];
868[label="xv3/EQ",fontsize=10,color="white",style="solid",shape="box"];144 -> 868[label="",style="solid", color="burlywood", weight=9];
868 -> 197[label="",style="solid", color="burlywood", weight=3];
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870 -> 201[label="",style="solid", color="burlywood", weight=3];
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871 -> 202[label="",style="solid", color="burlywood", weight=3];
148[label="xv3 == xv4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];872[label="xv3/Nothing",fontsize=10,color="white",style="solid",shape="box"];148 -> 872[label="",style="solid", color="burlywood", weight=9];
872 -> 203[label="",style="solid", color="burlywood", weight=3];
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874 -> 205[label="",style="solid", color="burlywood", weight=3];
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875 -> 206[label="",style="solid", color="burlywood", weight=3];
150[label="xv3 == xv4",fontsize=16,color="burlywood",shape="triangle"];876[label="xv3/()",fontsize=10,color="white",style="solid",shape="box"];150 -> 876[label="",style="solid", color="burlywood", weight=9];
876 -> 207[label="",style="solid", color="burlywood", weight=3];
151[label="xv3 == xv4",fontsize=16,color="black",shape="triangle"];151 -> 208[label="",style="solid", color="black", weight=3];
152[label="xv3 == xv4",fontsize=16,color="burlywood",shape="triangle"];877[label="xv3/Integer xv30",fontsize=10,color="white",style="solid",shape="box"];152 -> 877[label="",style="solid", color="burlywood", weight=9];
877 -> 209[label="",style="solid", color="burlywood", weight=3];
153[label="xv3 == xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];878[label="xv3/(xv30,xv31)",fontsize=10,color="white",style="solid",shape="box"];153 -> 878[label="",style="solid", color="burlywood", weight=9];
878 -> 210[label="",style="solid", color="burlywood", weight=3];
154[label="xv3 == xv4\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];879[label="xv3/xv30 :% xv31",fontsize=10,color="white",style="solid",shape="box"];154 -> 879[label="",style="solid", color="burlywood", weight=9];
879 -> 211[label="",style="solid", color="burlywood", weight=3];
155[label="xv3 == xv4",fontsize=16,color="burlywood",shape="triangle"];880[label="xv3/False",fontsize=10,color="white",style="solid",shape="box"];155 -> 880[label="",style="solid", color="burlywood", weight=9];
880 -> 212[label="",style="solid", color="burlywood", weight=3];
881[label="xv3/True",fontsize=10,color="white",style="solid",shape="box"];155 -> 881[label="",style="solid", color="burlywood", weight=9];
881 -> 213[label="",style="solid", color="burlywood", weight=3];
156[label="xv3 == xv4",fontsize=16,color="black",shape="triangle"];156 -> 214[label="",style="solid", color="black", weight=3];
193[label="(xv30,xv31,xv32) == xv4\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];882[label="xv4/(xv40,xv41,xv42)",fontsize=10,color="white",style="solid",shape="box"];193 -> 882[label="",style="solid", color="burlywood", weight=9];
882 -> 215[label="",style="solid", color="burlywood", weight=3];
194[label="not False",fontsize=16,color="black",shape="box"];194 -> 216[label="",style="solid", color="black", weight=3];
195[label="not True",fontsize=16,color="black",shape="box"];195 -> 217[label="",style="solid", color="black", weight=3];
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883 -> 218[label="",style="solid", color="burlywood", weight=3];
884[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];196 -> 884[label="",style="solid", color="burlywood", weight=9];
884 -> 219[label="",style="solid", color="burlywood", weight=3];
885[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];196 -> 885[label="",style="solid", color="burlywood", weight=9];
885 -> 220[label="",style="solid", color="burlywood", weight=3];
197[label="EQ == xv4",fontsize=16,color="burlywood",shape="box"];886[label="xv4/LT",fontsize=10,color="white",style="solid",shape="box"];197 -> 886[label="",style="solid", color="burlywood", weight=9];
886 -> 221[label="",style="solid", color="burlywood", weight=3];
887[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];197 -> 887[label="",style="solid", color="burlywood", weight=9];
887 -> 222[label="",style="solid", color="burlywood", weight=3];
888[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];197 -> 888[label="",style="solid", color="burlywood", weight=9];
888 -> 223[label="",style="solid", color="burlywood", weight=3];
198[label="GT == xv4",fontsize=16,color="burlywood",shape="box"];889[label="xv4/LT",fontsize=10,color="white",style="solid",shape="box"];198 -> 889[label="",style="solid", color="burlywood", weight=9];
889 -> 224[label="",style="solid", color="burlywood", weight=3];
890[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];198 -> 890[label="",style="solid", color="burlywood", weight=9];
890 -> 225[label="",style="solid", color="burlywood", weight=3];
891[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];198 -> 891[label="",style="solid", color="burlywood", weight=9];
891 -> 226[label="",style="solid", color="burlywood", weight=3];
199[label="primEqChar xv3 xv4",fontsize=16,color="burlywood",shape="box"];892[label="xv3/Char xv30",fontsize=10,color="white",style="solid",shape="box"];199 -> 892[label="",style="solid", color="burlywood", weight=9];
892 -> 227[label="",style="solid", color="burlywood", weight=3];
200[label="primEqInt xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];893[label="xv3/Pos xv30",fontsize=10,color="white",style="solid",shape="box"];200 -> 893[label="",style="solid", color="burlywood", weight=9];
893 -> 228[label="",style="solid", color="burlywood", weight=3];
894[label="xv3/Neg xv30",fontsize=10,color="white",style="solid",shape="box"];200 -> 894[label="",style="solid", color="burlywood", weight=9];
894 -> 229[label="",style="solid", color="burlywood", weight=3];
201[label="Left xv30 == xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];895[label="xv4/Left xv40",fontsize=10,color="white",style="solid",shape="box"];201 -> 895[label="",style="solid", color="burlywood", weight=9];
895 -> 230[label="",style="solid", color="burlywood", weight=3];
896[label="xv4/Right xv40",fontsize=10,color="white",style="solid",shape="box"];201 -> 896[label="",style="solid", color="burlywood", weight=9];
896 -> 231[label="",style="solid", color="burlywood", weight=3];
202[label="Right xv30 == xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];897[label="xv4/Left xv40",fontsize=10,color="white",style="solid",shape="box"];202 -> 897[label="",style="solid", color="burlywood", weight=9];
897 -> 232[label="",style="solid", color="burlywood", weight=3];
898[label="xv4/Right xv40",fontsize=10,color="white",style="solid",shape="box"];202 -> 898[label="",style="solid", color="burlywood", weight=9];
898 -> 233[label="",style="solid", color="burlywood", weight=3];
203[label="Nothing == xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];899[label="xv4/Nothing",fontsize=10,color="white",style="solid",shape="box"];203 -> 899[label="",style="solid", color="burlywood", weight=9];
899 -> 234[label="",style="solid", color="burlywood", weight=3];
900[label="xv4/Just xv40",fontsize=10,color="white",style="solid",shape="box"];203 -> 900[label="",style="solid", color="burlywood", weight=9];
900 -> 235[label="",style="solid", color="burlywood", weight=3];
204[label="Just xv30 == xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];901[label="xv4/Nothing",fontsize=10,color="white",style="solid",shape="box"];204 -> 901[label="",style="solid", color="burlywood", weight=9];
901 -> 236[label="",style="solid", color="burlywood", weight=3];
902[label="xv4/Just xv40",fontsize=10,color="white",style="solid",shape="box"];204 -> 902[label="",style="solid", color="burlywood", weight=9];
902 -> 237[label="",style="solid", color="burlywood", weight=3];
205[label="xv30 : xv31 == xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];903[label="xv4/xv40 : xv41",fontsize=10,color="white",style="solid",shape="box"];205 -> 903[label="",style="solid", color="burlywood", weight=9];
903 -> 238[label="",style="solid", color="burlywood", weight=3];
904[label="xv4/[]",fontsize=10,color="white",style="solid",shape="box"];205 -> 904[label="",style="solid", color="burlywood", weight=9];
904 -> 239[label="",style="solid", color="burlywood", weight=3];
206[label="[] == xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];905[label="xv4/xv40 : xv41",fontsize=10,color="white",style="solid",shape="box"];206 -> 905[label="",style="solid", color="burlywood", weight=9];
905 -> 240[label="",style="solid", color="burlywood", weight=3];
906[label="xv4/[]",fontsize=10,color="white",style="solid",shape="box"];206 -> 906[label="",style="solid", color="burlywood", weight=9];
906 -> 241[label="",style="solid", color="burlywood", weight=3];
207[label="() == xv4",fontsize=16,color="burlywood",shape="box"];907[label="xv4/()",fontsize=10,color="white",style="solid",shape="box"];207 -> 907[label="",style="solid", color="burlywood", weight=9];
907 -> 242[label="",style="solid", color="burlywood", weight=3];
208[label="primEqFloat xv3 xv4",fontsize=16,color="burlywood",shape="box"];908[label="xv3/Float xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];208 -> 908[label="",style="solid", color="burlywood", weight=9];
908 -> 243[label="",style="solid", color="burlywood", weight=3];
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909 -> 244[label="",style="solid", color="burlywood", weight=3];
210[label="(xv30,xv31) == xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];910[label="xv4/(xv40,xv41)",fontsize=10,color="white",style="solid",shape="box"];210 -> 910[label="",style="solid", color="burlywood", weight=9];
910 -> 245[label="",style="solid", color="burlywood", weight=3];
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911 -> 246[label="",style="solid", color="burlywood", weight=3];
212[label="False == xv4",fontsize=16,color="burlywood",shape="box"];912[label="xv4/False",fontsize=10,color="white",style="solid",shape="box"];212 -> 912[label="",style="solid", color="burlywood", weight=9];
912 -> 247[label="",style="solid", color="burlywood", weight=3];
913[label="xv4/True",fontsize=10,color="white",style="solid",shape="box"];212 -> 913[label="",style="solid", color="burlywood", weight=9];
913 -> 248[label="",style="solid", color="burlywood", weight=3];
213[label="True == xv4",fontsize=16,color="burlywood",shape="box"];914[label="xv4/False",fontsize=10,color="white",style="solid",shape="box"];213 -> 914[label="",style="solid", color="burlywood", weight=9];
914 -> 249[label="",style="solid", color="burlywood", weight=3];
915[label="xv4/True",fontsize=10,color="white",style="solid",shape="box"];213 -> 915[label="",style="solid", color="burlywood", weight=9];
915 -> 250[label="",style="solid", color="burlywood", weight=3];
214[label="primEqDouble xv3 xv4",fontsize=16,color="burlywood",shape="box"];916[label="xv3/Double xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];214 -> 916[label="",style="solid", color="burlywood", weight=9];
916 -> 251[label="",style="solid", color="burlywood", weight=3];
215[label="(xv30,xv31,xv32) == (xv40,xv41,xv42)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];215 -> 252[label="",style="solid", color="black", weight=3];
216[label="True",fontsize=16,color="green",shape="box"];217[label="False",fontsize=16,color="green",shape="box"];218[label="LT == LT",fontsize=16,color="black",shape="box"];218 -> 253[label="",style="solid", color="black", weight=3];
219[label="LT == EQ",fontsize=16,color="black",shape="box"];219 -> 254[label="",style="solid", color="black", weight=3];
220[label="LT == GT",fontsize=16,color="black",shape="box"];220 -> 255[label="",style="solid", color="black", weight=3];
221[label="EQ == LT",fontsize=16,color="black",shape="box"];221 -> 256[label="",style="solid", color="black", weight=3];
222[label="EQ == EQ",fontsize=16,color="black",shape="box"];222 -> 257[label="",style="solid", color="black", weight=3];
223[label="EQ == GT",fontsize=16,color="black",shape="box"];223 -> 258[label="",style="solid", color="black", weight=3];
224[label="GT == LT",fontsize=16,color="black",shape="box"];224 -> 259[label="",style="solid", color="black", weight=3];
225[label="GT == EQ",fontsize=16,color="black",shape="box"];225 -> 260[label="",style="solid", color="black", weight=3];
226[label="GT == GT",fontsize=16,color="black",shape="box"];226 -> 261[label="",style="solid", color="black", weight=3];
227[label="primEqChar (Char xv30) xv4",fontsize=16,color="burlywood",shape="box"];917[label="xv4/Char xv40",fontsize=10,color="white",style="solid",shape="box"];227 -> 917[label="",style="solid", color="burlywood", weight=9];
917 -> 262[label="",style="solid", color="burlywood", weight=3];
228[label="primEqInt (Pos xv30) xv4",fontsize=16,color="burlywood",shape="box"];918[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];228 -> 918[label="",style="solid", color="burlywood", weight=9];
918 -> 263[label="",style="solid", color="burlywood", weight=3];
919[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];228 -> 919[label="",style="solid", color="burlywood", weight=9];
919 -> 264[label="",style="solid", color="burlywood", weight=3];
229[label="primEqInt (Neg xv30) xv4",fontsize=16,color="burlywood",shape="box"];920[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];229 -> 920[label="",style="solid", color="burlywood", weight=9];
920 -> 265[label="",style="solid", color="burlywood", weight=3];
921[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];229 -> 921[label="",style="solid", color="burlywood", weight=9];
921 -> 266[label="",style="solid", color="burlywood", weight=3];
230[label="Left xv30 == Left xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];230 -> 267[label="",style="solid", color="black", weight=3];
231[label="Left xv30 == Right xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];231 -> 268[label="",style="solid", color="black", weight=3];
232[label="Right xv30 == Left xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];232 -> 269[label="",style="solid", color="black", weight=3];
233[label="Right xv30 == Right xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];233 -> 270[label="",style="solid", color="black", weight=3];
234[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];234 -> 271[label="",style="solid", color="black", weight=3];
235[label="Nothing == Just xv40\n  Eq a",fontsize=16,color="black",shape="box"];235 -> 272[label="",style="solid", color="black", weight=3];
236[label="Just xv30 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];236 -> 273[label="",style="solid", color="black", weight=3];
237[label="Just xv30 == Just xv40\n  Eq a",fontsize=16,color="black",shape="box"];237 -> 274[label="",style="solid", color="black", weight=3];
238[label="xv30 : xv31 == xv40 : xv41\n  Eq a",fontsize=16,color="black",shape="box"];238 -> 275[label="",style="solid", color="black", weight=3];
239[label="xv30 : xv31 == []\n  Eq a",fontsize=16,color="black",shape="box"];239 -> 276[label="",style="solid", color="black", weight=3];
240[label="[] == xv40 : xv41\n  Eq a",fontsize=16,color="black",shape="box"];240 -> 277[label="",style="solid", color="black", weight=3];
241[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];241 -> 278[label="",style="solid", color="black", weight=3];
242[label="() == ()",fontsize=16,color="black",shape="box"];242 -> 279[label="",style="solid", color="black", weight=3];
243[label="primEqFloat (Float xv30 xv31) xv4",fontsize=16,color="burlywood",shape="box"];922[label="xv4/Float xv40 xv41",fontsize=10,color="white",style="solid",shape="box"];243 -> 922[label="",style="solid", color="burlywood", weight=9];
922 -> 280[label="",style="solid", color="burlywood", weight=3];
244[label="Integer xv30 == Integer xv40",fontsize=16,color="black",shape="box"];244 -> 281[label="",style="solid", color="black", weight=3];
245[label="(xv30,xv31) == (xv40,xv41)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];245 -> 282[label="",style="solid", color="black", weight=3];
246[label="xv30 :% xv31 == xv40 :% xv41\n  Integral a",fontsize=16,color="black",shape="box"];246 -> 283[label="",style="solid", color="black", weight=3];
247[label="False == False",fontsize=16,color="black",shape="box"];247 -> 284[label="",style="solid", color="black", weight=3];
248[label="False == True",fontsize=16,color="black",shape="box"];248 -> 285[label="",style="solid", color="black", weight=3];
249[label="True == False",fontsize=16,color="black",shape="box"];249 -> 286[label="",style="solid", color="black", weight=3];
250[label="True == True",fontsize=16,color="black",shape="box"];250 -> 287[label="",style="solid", color="black", weight=3];
251[label="primEqDouble (Double xv30 xv31) xv4",fontsize=16,color="burlywood",shape="box"];923[label="xv4/Double xv40 xv41",fontsize=10,color="white",style="solid",shape="box"];251 -> 923[label="",style="solid", color="burlywood", weight=9];
923 -> 288[label="",style="solid", color="burlywood", weight=3];
252 -> 364[label="",style="dashed", color="red", weight=0];
252[label="xv30 == xv40 && xv31 == xv41 && xv32 == xv42\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];252 -> 365[label="",style="dashed", color="magenta", weight=3];
252 -> 366[label="",style="dashed", color="magenta", weight=3];
253[label="True",fontsize=16,color="green",shape="box"];254[label="False",fontsize=16,color="green",shape="box"];255[label="False",fontsize=16,color="green",shape="box"];256[label="False",fontsize=16,color="green",shape="box"];257[label="True",fontsize=16,color="green",shape="box"];258[label="False",fontsize=16,color="green",shape="box"];259[label="False",fontsize=16,color="green",shape="box"];260[label="False",fontsize=16,color="green",shape="box"];261[label="True",fontsize=16,color="green",shape="box"];262[label="primEqChar (Char xv30) (Char xv40)",fontsize=16,color="black",shape="box"];262 -> 295[label="",style="solid", color="black", weight=3];
263[label="primEqInt (Pos (Succ xv300)) xv4",fontsize=16,color="burlywood",shape="box"];925[label="xv4/Pos xv40",fontsize=10,color="white",style="solid",shape="box"];263 -> 925[label="",style="solid", color="burlywood", weight=9];
925 -> 296[label="",style="solid", color="burlywood", weight=3];
926[label="xv4/Neg xv40",fontsize=10,color="white",style="solid",shape="box"];263 -> 926[label="",style="solid", color="burlywood", weight=9];
926 -> 297[label="",style="solid", color="burlywood", weight=3];
264[label="primEqInt (Pos Zero) xv4",fontsize=16,color="burlywood",shape="box"];927[label="xv4/Pos xv40",fontsize=10,color="white",style="solid",shape="box"];264 -> 927[label="",style="solid", color="burlywood", weight=9];
927 -> 298[label="",style="solid", color="burlywood", weight=3];
928[label="xv4/Neg xv40",fontsize=10,color="white",style="solid",shape="box"];264 -> 928[label="",style="solid", color="burlywood", weight=9];
928 -> 299[label="",style="solid", color="burlywood", weight=3];
265[label="primEqInt (Neg (Succ xv300)) xv4",fontsize=16,color="burlywood",shape="box"];929[label="xv4/Pos xv40",fontsize=10,color="white",style="solid",shape="box"];265 -> 929[label="",style="solid", color="burlywood", weight=9];
929 -> 300[label="",style="solid", color="burlywood", weight=3];
930[label="xv4/Neg xv40",fontsize=10,color="white",style="solid",shape="box"];265 -> 930[label="",style="solid", color="burlywood", weight=9];
930 -> 301[label="",style="solid", color="burlywood", weight=3];
266[label="primEqInt (Neg Zero) xv4",fontsize=16,color="burlywood",shape="box"];931[label="xv4/Pos xv40",fontsize=10,color="white",style="solid",shape="box"];266 -> 931[label="",style="solid", color="burlywood", weight=9];
931 -> 302[label="",style="solid", color="burlywood", weight=3];
932[label="xv4/Neg xv40",fontsize=10,color="white",style="solid",shape="box"];266 -> 932[label="",style="solid", color="burlywood", weight=9];
932 -> 303[label="",style="solid", color="burlywood", weight=3];
267[label="xv30 == xv40\n  Eq a",fontsize=16,color="blue",shape="box"];933[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 933[label="",style="solid", color="blue", weight=9];
933 -> 304[label="",style="solid", color="blue", weight=3];
934[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 934[label="",style="solid", color="blue", weight=9];
934 -> 305[label="",style="solid", color="blue", weight=3];
935[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 935[label="",style="solid", color="blue", weight=9];
935 -> 306[label="",style="solid", color="blue", weight=3];
936[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 936[label="",style="solid", color="blue", weight=9];
936 -> 307[label="",style="solid", color="blue", weight=3];
937[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 937[label="",style="solid", color="blue", weight=9];
937 -> 308[label="",style="solid", color="blue", weight=3];
938[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 938[label="",style="solid", color="blue", weight=9];
938 -> 309[label="",style="solid", color="blue", weight=3];
939[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 939[label="",style="solid", color="blue", weight=9];
939 -> 310[label="",style="solid", color="blue", weight=3];
940[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 940[label="",style="solid", color="blue", weight=9];
940 -> 311[label="",style="solid", color="blue", weight=3];
941[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 941[label="",style="solid", color="blue", weight=9];
941 -> 312[label="",style="solid", color="blue", weight=3];
942[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 942[label="",style="solid", color="blue", weight=9];
942 -> 313[label="",style="solid", color="blue", weight=3];
943[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 943[label="",style="solid", color="blue", weight=9];
943 -> 314[label="",style="solid", color="blue", weight=3];
944[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 944[label="",style="solid", color="blue", weight=9];
944 -> 315[label="",style="solid", color="blue", weight=3];
945[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 945[label="",style="solid", color="blue", weight=9];
945 -> 316[label="",style="solid", color="blue", weight=3];
946[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];267 -> 946[label="",style="solid", color="blue", weight=9];
946 -> 317[label="",style="solid", color="blue", weight=3];
268[label="False",fontsize=16,color="green",shape="box"];269[label="False",fontsize=16,color="green",shape="box"];270[label="xv30 == xv40\n  Eq a",fontsize=16,color="blue",shape="box"];947[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 947[label="",style="solid", color="blue", weight=9];
947 -> 318[label="",style="solid", color="blue", weight=3];
948[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 948[label="",style="solid", color="blue", weight=9];
948 -> 319[label="",style="solid", color="blue", weight=3];
949[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 949[label="",style="solid", color="blue", weight=9];
949 -> 320[label="",style="solid", color="blue", weight=3];
950[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 950[label="",style="solid", color="blue", weight=9];
950 -> 321[label="",style="solid", color="blue", weight=3];
951[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 951[label="",style="solid", color="blue", weight=9];
951 -> 322[label="",style="solid", color="blue", weight=3];
952[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 952[label="",style="solid", color="blue", weight=9];
952 -> 323[label="",style="solid", color="blue", weight=3];
953[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 953[label="",style="solid", color="blue", weight=9];
953 -> 324[label="",style="solid", color="blue", weight=3];
954[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 954[label="",style="solid", color="blue", weight=9];
954 -> 325[label="",style="solid", color="blue", weight=3];
955[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 955[label="",style="solid", color="blue", weight=9];
955 -> 326[label="",style="solid", color="blue", weight=3];
956[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 956[label="",style="solid", color="blue", weight=9];
956 -> 327[label="",style="solid", color="blue", weight=3];
957[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 957[label="",style="solid", color="blue", weight=9];
957 -> 328[label="",style="solid", color="blue", weight=3];
958[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 958[label="",style="solid", color="blue", weight=9];
958 -> 329[label="",style="solid", color="blue", weight=3];
959[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 959[label="",style="solid", color="blue", weight=9];
959 -> 330[label="",style="solid", color="blue", weight=3];
960[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 960[label="",style="solid", color="blue", weight=9];
960 -> 331[label="",style="solid", color="blue", weight=3];
271[label="True",fontsize=16,color="green",shape="box"];272[label="False",fontsize=16,color="green",shape="box"];273[label="False",fontsize=16,color="green",shape="box"];274[label="xv30 == xv40\n  Eq a",fontsize=16,color="blue",shape="box"];961[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 961[label="",style="solid", color="blue", weight=9];
961 -> 332[label="",style="solid", color="blue", weight=3];
962[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 962[label="",style="solid", color="blue", weight=9];
962 -> 333[label="",style="solid", color="blue", weight=3];
963[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 963[label="",style="solid", color="blue", weight=9];
963 -> 334[label="",style="solid", color="blue", weight=3];
964[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 964[label="",style="solid", color="blue", weight=9];
964 -> 335[label="",style="solid", color="blue", weight=3];
965[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 965[label="",style="solid", color="blue", weight=9];
965 -> 336[label="",style="solid", color="blue", weight=3];
966[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 966[label="",style="solid", color="blue", weight=9];
966 -> 337[label="",style="solid", color="blue", weight=3];
967[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 967[label="",style="solid", color="blue", weight=9];
967 -> 338[label="",style="solid", color="blue", weight=3];
968[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 968[label="",style="solid", color="blue", weight=9];
968 -> 339[label="",style="solid", color="blue", weight=3];
969[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 969[label="",style="solid", color="blue", weight=9];
969 -> 340[label="",style="solid", color="blue", weight=3];
970[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 970[label="",style="solid", color="blue", weight=9];
970 -> 341[label="",style="solid", color="blue", weight=3];
971[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 971[label="",style="solid", color="blue", weight=9];
971 -> 342[label="",style="solid", color="blue", weight=3];
972[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 972[label="",style="solid", color="blue", weight=9];
972 -> 343[label="",style="solid", color="blue", weight=3];
973[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 973[label="",style="solid", color="blue", weight=9];
973 -> 344[label="",style="solid", color="blue", weight=3];
974[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 974[label="",style="solid", color="blue", weight=9];
974 -> 345[label="",style="solid", color="blue", weight=3];
275 -> 364[label="",style="dashed", color="red", weight=0];
275[label="xv30 == xv40 && xv31 == xv41\n  Eq a",fontsize=16,color="magenta"];275 -> 367[label="",style="dashed", color="magenta", weight=3];
275 -> 368[label="",style="dashed", color="magenta", weight=3];
276[label="False",fontsize=16,color="green",shape="box"];277[label="False",fontsize=16,color="green",shape="box"];278[label="True",fontsize=16,color="green",shape="box"];279[label="True",fontsize=16,color="green",shape="box"];280[label="primEqFloat (Float xv30 xv31) (Float xv40 xv41)",fontsize=16,color="black",shape="box"];280 -> 357[label="",style="solid", color="black", weight=3];
281 -> 200[label="",style="dashed", color="red", weight=0];
281[label="primEqInt xv30 xv40",fontsize=16,color="magenta"];281 -> 358[label="",style="dashed", color="magenta", weight=3];
281 -> 359[label="",style="dashed", color="magenta", weight=3];
282 -> 364[label="",style="dashed", color="red", weight=0];
282[label="xv30 == xv40 && xv31 == xv41\n  Eq a  Eq b",fontsize=16,color="magenta"];282 -> 369[label="",style="dashed", color="magenta", weight=3];
282 -> 370[label="",style="dashed", color="magenta", weight=3];
283 -> 364[label="",style="dashed", color="red", weight=0];
283[label="xv30 == xv40 && xv31 == xv41\n  Integral a",fontsize=16,color="magenta"];283 -> 371[label="",style="dashed", color="magenta", weight=3];
283 -> 372[label="",style="dashed", color="magenta", weight=3];
284[label="True",fontsize=16,color="green",shape="box"];285[label="False",fontsize=16,color="green",shape="box"];286[label="False",fontsize=16,color="green",shape="box"];287[label="True",fontsize=16,color="green",shape="box"];288[label="primEqDouble (Double xv30 xv31) (Double xv40 xv41)",fontsize=16,color="black",shape="box"];288 -> 360[label="",style="solid", color="black", weight=3];
365 -> 364[label="",style="dashed", color="red", weight=0];
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800[label="primMulNat (Succ xv3100) xv410",fontsize=16,color="burlywood",shape="box"];1238[label="xv410/Succ xv4100",fontsize=10,color="white",style="solid",shape="box"];800 -> 1238[label="",style="solid", color="burlywood", weight=9];
1238 -> 806[label="",style="solid", color="burlywood", weight=3];
1239[label="xv410/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 1239[label="",style="solid", color="burlywood", weight=9];
1239 -> 807[label="",style="solid", color="burlywood", weight=3];
801[label="primMulNat Zero xv410",fontsize=16,color="burlywood",shape="box"];1240[label="xv410/Succ xv4100",fontsize=10,color="white",style="solid",shape="box"];801 -> 1240[label="",style="solid", color="burlywood", weight=9];
1240 -> 808[label="",style="solid", color="burlywood", weight=3];
1241[label="xv410/Zero",fontsize=10,color="white",style="solid",shape="box"];801 -> 1241[label="",style="solid", color="burlywood", weight=9];
1241 -> 809[label="",style="solid", color="burlywood", weight=3];
802[label="xv410",fontsize=16,color="green",shape="box"];803[label="xv310",fontsize=16,color="green",shape="box"];804[label="xv410",fontsize=16,color="green",shape="box"];805[label="xv310",fontsize=16,color="green",shape="box"];806[label="primMulNat (Succ xv3100) (Succ xv4100)",fontsize=16,color="black",shape="box"];806 -> 810[label="",style="solid", color="black", weight=3];
807[label="primMulNat (Succ xv3100) Zero",fontsize=16,color="black",shape="box"];807 -> 811[label="",style="solid", color="black", weight=3];
808[label="primMulNat Zero (Succ xv4100)",fontsize=16,color="black",shape="box"];808 -> 812[label="",style="solid", color="black", weight=3];
809[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];809 -> 813[label="",style="solid", color="black", weight=3];
810 -> 814[label="",style="dashed", color="red", weight=0];
810[label="primPlusNat (primMulNat xv3100 (Succ xv4100)) (Succ xv4100)",fontsize=16,color="magenta"];810 -> 815[label="",style="dashed", color="magenta", weight=3];
811[label="Zero",fontsize=16,color="green",shape="box"];812[label="Zero",fontsize=16,color="green",shape="box"];813[label="Zero",fontsize=16,color="green",shape="box"];815 -> 796[label="",style="dashed", color="red", weight=0];
815[label="primMulNat xv3100 (Succ xv4100)",fontsize=16,color="magenta"];815 -> 816[label="",style="dashed", color="magenta", weight=3];
815 -> 817[label="",style="dashed", color="magenta", weight=3];
814[label="primPlusNat xv36 (Succ xv4100)",fontsize=16,color="burlywood",shape="triangle"];1244[label="xv36/Succ xv360",fontsize=10,color="white",style="solid",shape="box"];814 -> 1244[label="",style="solid", color="burlywood", weight=9];
1244 -> 818[label="",style="solid", color="burlywood", weight=3];
1245[label="xv36/Zero",fontsize=10,color="white",style="solid",shape="box"];814 -> 1245[label="",style="solid", color="burlywood", weight=9];
1245 -> 819[label="",style="solid", color="burlywood", weight=3];
816[label="Succ xv4100",fontsize=16,color="green",shape="box"];817[label="xv3100",fontsize=16,color="green",shape="box"];818[label="primPlusNat (Succ xv360) (Succ xv4100)",fontsize=16,color="black",shape="box"];818 -> 820[label="",style="solid", color="black", weight=3];
819[label="primPlusNat Zero (Succ xv4100)",fontsize=16,color="black",shape="box"];819 -> 821[label="",style="solid", color="black", weight=3];
820[label="Succ (Succ (primPlusNat xv360 xv4100))",fontsize=16,color="green",shape="box"];820 -> 822[label="",style="dashed", color="green", weight=3];
821[label="Succ xv4100",fontsize=16,color="green",shape="box"];822[label="primPlusNat xv360 xv4100",fontsize=16,color="burlywood",shape="triangle"];1246[label="xv360/Succ xv3600",fontsize=10,color="white",style="solid",shape="box"];822 -> 1246[label="",style="solid", color="burlywood", weight=9];
1246 -> 823[label="",style="solid", color="burlywood", weight=3];
1247[label="xv360/Zero",fontsize=10,color="white",style="solid",shape="box"];822 -> 1247[label="",style="solid", color="burlywood", weight=9];
1247 -> 824[label="",style="solid", color="burlywood", weight=3];
823[label="primPlusNat (Succ xv3600) xv4100",fontsize=16,color="burlywood",shape="box"];1248[label="xv4100/Succ xv41000",fontsize=10,color="white",style="solid",shape="box"];823 -> 1248[label="",style="solid", color="burlywood", weight=9];
1248 -> 825[label="",style="solid", color="burlywood", weight=3];
1249[label="xv4100/Zero",fontsize=10,color="white",style="solid",shape="box"];823 -> 1249[label="",style="solid", color="burlywood", weight=9];
1249 -> 826[label="",style="solid", color="burlywood", weight=3];
824[label="primPlusNat Zero xv4100",fontsize=16,color="burlywood",shape="box"];1250[label="xv4100/Succ xv41000",fontsize=10,color="white",style="solid",shape="box"];824 -> 1250[label="",style="solid", color="burlywood", weight=9];
1250 -> 827[label="",style="solid", color="burlywood", weight=3];
1251[label="xv4100/Zero",fontsize=10,color="white",style="solid",shape="box"];824 -> 1251[label="",style="solid", color="burlywood", weight=9];
1251 -> 828[label="",style="solid", color="burlywood", weight=3];
825[label="primPlusNat (Succ xv3600) (Succ xv41000)",fontsize=16,color="black",shape="box"];825 -> 829[label="",style="solid", color="black", weight=3];
826[label="primPlusNat (Succ xv3600) Zero",fontsize=16,color="black",shape="box"];826 -> 830[label="",style="solid", color="black", weight=3];
827[label="primPlusNat Zero (Succ xv41000)",fontsize=16,color="black",shape="box"];827 -> 831[label="",style="solid", color="black", weight=3];
828[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];828 -> 832[label="",style="solid", color="black", weight=3];
829[label="Succ (Succ (primPlusNat xv3600 xv41000))",fontsize=16,color="green",shape="box"];829 -> 833[label="",style="dashed", color="green", weight=3];
830[label="Succ xv3600",fontsize=16,color="green",shape="box"];831[label="Succ xv41000",fontsize=16,color="green",shape="box"];832[label="Zero",fontsize=16,color="green",shape="box"];833 -> 822[label="",style="dashed", color="red", weight=0];
833[label="primPlusNat xv3600 xv41000",fontsize=16,color="magenta"];833 -> 834[label="",style="dashed", color="magenta", weight=3];
833 -> 835[label="",style="dashed", color="magenta", weight=3];
834[label="xv41000",fontsize=16,color="green",shape="box"];835[label="xv3600",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xv3600), Succ(xv41000)) → new_primPlusNat(xv3600, xv41000)

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(xv3600), Succ(xv41000)) → new_primPlusNat(xv3600, xv41000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xv3100), Succ(xv4100)) → new_primMulNat(xv3100, Succ(xv4100))

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

new_primMulNat(Succ(xv3100), Succ(xv4100)) → new_primMulNat(xv3100, Succ(xv4100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_primEqNat(Succ(xv300), Succ(xv400)) → new_primEqNat(xv300, xv400)

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

new_primEqNat(Succ(xv300), Succ(xv400)) → new_primEqNat(xv300, xv400)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_Either, eb), ec), bb, cg) → new_esEs0(xv30, xv40, eb, ec)
new_esEs1(Just(xv30), Just(xv40), app(app(app(ty_@3, he), hf), hg)) → new_esEs(xv30, xv40, he, hf, hg)
new_esEs0(Left(xv30), Left(xv40), app(ty_Maybe, fg), fc) → new_esEs1(xv30, xv40, fg)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(ty_Either, bf), bg)) → new_esEs0(xv32, xv42, bf, bg)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(ty_[], bcg)) → new_esEs2(xv31, xv41, bcg)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(ty_Maybe, bh)) → new_esEs1(xv32, xv42, bh)
new_esEs0(Right(xv30), Right(xv40), gc, app(app(app(ty_@3, gd), ge), gf)) → new_esEs(xv30, xv40, gd, ge, gf)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_Maybe, bbd)) → new_esEs1(xv30, xv40, bbd)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(app(ty_@3, bdb), bdc), bdd), bde) → new_esEs(xv30, xv40, bdb, bdc, bdd)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xv30, xv40, dg, dh, ea)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(ty_[], bea), bde) → new_esEs2(xv30, xv40, bea)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(ty_Maybe, bdh), bde) → new_esEs1(xv30, xv40, bdh)
new_esEs0(Left(xv30), Left(xv40), app(app(ty_Either, fd), ff), fc) → new_esEs0(xv30, xv40, fd, ff)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(ty_@2, cb), cc)) → new_esEs3(xv32, xv42, cb, cc)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(ty_Either, bcd), bce)) → new_esEs0(xv31, xv41, bcd, bce)
new_esEs0(Right(xv30), Right(xv40), gc, app(ty_[], hb)) → new_esEs2(xv30, xv40, hb)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_Maybe, ed), bb, cg) → new_esEs1(xv30, xv40, ed)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs(xv31, xv41, bca, bcb, bcc)
new_esEs0(Right(xv30), Right(xv40), gc, app(app(ty_Either, gg), gh)) → new_esEs0(xv30, xv40, gg, gh)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(ty_@2, bch), bda)) → new_esEs3(xv31, xv41, bch, bda)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(ty_Maybe, dc), cg) → new_esEs1(xv31, xv41, dc)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(ty_Maybe, bcf)) → new_esEs1(xv31, xv41, bcf)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(ty_Either, da), db), cg) → new_esEs0(xv31, xv41, da, db)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_Either, bbb), bbc)) → new_esEs0(xv30, xv40, bbb, bbc)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(app(ty_@3, bag), bah), bba)) → new_esEs(xv30, xv40, bag, bah, bba)
new_esEs1(Just(xv30), Just(xv40), app(app(ty_@2, bad), bae)) → new_esEs3(xv30, xv40, bad, bae)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_@2, ef), eg), bb, cg) → new_esEs3(xv30, xv40, ef, eg)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xv31, xv41, cd, ce, cf)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_@2, bbf), bbg)) → new_esEs3(xv30, xv40, bbf, bbg)
new_esEs2(:(xv30, xv31), :(xv40, xv41), baf) → new_esEs2(xv31, xv41, baf)
new_esEs1(Just(xv30), Just(xv40), app(ty_[], bac)) → new_esEs2(xv30, xv40, bac)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_@2, beb), bec), bde) → new_esEs3(xv30, xv40, beb, bec)
new_esEs0(Right(xv30), Right(xv40), gc, app(app(ty_@2, hc), hd)) → new_esEs3(xv30, xv40, hc, hd)
new_esEs1(Just(xv30), Just(xv40), app(ty_Maybe, bab)) → new_esEs1(xv30, xv40, bab)
new_esEs0(Left(xv30), Left(xv40), app(ty_[], fh), fc) → new_esEs2(xv30, xv40, fh)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_[], bbe)) → new_esEs2(xv30, xv40, bbe)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_[], ee), bb, cg) → new_esEs2(xv30, xv40, ee)
new_esEs0(Right(xv30), Right(xv40), gc, app(ty_Maybe, ha)) → new_esEs1(xv30, xv40, ha)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(ty_[], dd), cg) → new_esEs2(xv31, xv41, dd)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(ty_[], ca)) → new_esEs2(xv32, xv42, ca)
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_Either, bdf), bdg), bde) → new_esEs0(xv30, xv40, bdf, bdg)
new_esEs0(Left(xv30), Left(xv40), app(app(app(ty_@3, eh), fa), fb), fc) → new_esEs(xv30, xv40, eh, fa, fb)
new_esEs0(Left(xv30), Left(xv40), app(app(ty_@2, ga), gb), fc) → new_esEs3(xv30, xv40, ga, gb)
new_esEs1(Just(xv30), Just(xv40), app(app(ty_Either, hh), baa)) → new_esEs0(xv30, xv40, hh, baa)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xv32, xv42, bc, bd, be)
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(ty_@2, de), df), cg) → new_esEs3(xv31, xv41, de, df)

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

new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_Maybe, bbd)) → new_esEs1(xv30, xv40, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(app(ty_@3, bag), bah), bba)) → new_esEs(xv30, xv40, bag, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_@2, bbf), bbg)) → new_esEs3(xv30, xv40, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xv30), Just(xv40), app(ty_Maybe, bab)) → new_esEs1(xv30, xv40, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Just(xv30), Just(xv40), app(app(app(ty_@3, he), hf), hg)) → new_esEs(xv30, xv40, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_Either, bbb), bbc)) → new_esEs0(xv30, xv40, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xv30), Just(xv40), app(app(ty_@2, bad), bae)) → new_esEs3(xv30, xv40, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xv30), Just(xv40), app(app(ty_Either, hh), baa)) → new_esEs0(xv30, xv40, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xv30), Just(xv40), app(ty_[], bac)) → new_esEs2(xv30, xv40, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(ty_Maybe, bh)) → new_esEs1(xv32, xv42, bh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_Maybe, ed), bb, cg) → new_esEs1(xv30, xv40, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(ty_Maybe, dc), cg) → new_esEs1(xv31, xv41, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xv30, xv40, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xv31, xv41, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xv32, xv42, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(ty_@2, cb), cc)) → new_esEs3(xv32, xv42, cb, cc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_@2, ef), eg), bb, cg) → new_esEs3(xv30, xv40, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(ty_@2, de), df), cg) → new_esEs3(xv31, xv41, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_Either, eb), ec), bb, cg) → new_esEs0(xv30, xv40, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(app(ty_Either, bf), bg)) → new_esEs0(xv32, xv42, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(app(ty_Either, da), db), cg) → new_esEs0(xv31, xv41, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_[], ee), bb, cg) → new_esEs2(xv30, xv40, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, app(ty_[], dd), cg) → new_esEs2(xv31, xv41, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), ba, bb, app(ty_[], ca)) → new_esEs2(xv32, xv42, ca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(Left(xv30), Left(xv40), app(ty_Maybe, fg), fc) → new_esEs1(xv30, xv40, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xv30), Right(xv40), gc, app(ty_Maybe, ha)) → new_esEs1(xv30, xv40, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(ty_Maybe, bdh), bde) → new_esEs1(xv30, xv40, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(ty_Maybe, bcf)) → new_esEs1(xv31, xv41, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Right(xv30), Right(xv40), gc, app(app(app(ty_@3, gd), ge), gf)) → new_esEs(xv30, xv40, gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(Left(xv30), Left(xv40), app(app(app(ty_@3, eh), fa), fb), fc) → new_esEs(xv30, xv40, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Right(xv30), Right(xv40), gc, app(app(ty_@2, hc), hd)) → new_esEs3(xv30, xv40, hc, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Left(xv30), Left(xv40), app(app(ty_@2, ga), gb), fc) → new_esEs3(xv30, xv40, ga, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Left(xv30), Left(xv40), app(app(ty_Either, fd), ff), fc) → new_esEs0(xv30, xv40, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(xv30), Right(xv40), gc, app(app(ty_Either, gg), gh)) → new_esEs0(xv30, xv40, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Right(xv30), Right(xv40), gc, app(ty_[], hb)) → new_esEs2(xv30, xv40, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Left(xv30), Left(xv40), app(ty_[], fh), fc) → new_esEs2(xv30, xv40, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(app(ty_@3, bdb), bdc), bdd), bde) → new_esEs(xv30, xv40, bdb, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs(xv31, xv41, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(:(xv30, xv31), :(xv40, xv41), baf) → new_esEs2(xv31, xv41, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_[], bbe)) → new_esEs2(xv30, xv40, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(ty_@2, bch), bda)) → new_esEs3(xv31, xv41, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_@2, beb), bec), bde) → new_esEs3(xv30, xv40, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(app(ty_Either, bcd), bce)) → new_esEs0(xv31, xv41, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_Either, bdf), bdg), bde) → new_esEs0(xv30, xv40, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), bbh, app(ty_[], bcg)) → new_esEs2(xv31, xv41, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@2(xv30, xv31), @2(xv40, xv41), app(ty_[], bea), bde) → new_esEs2(xv30, xv40, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3