/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 7 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) AND (21) QDP (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] (23) YES (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] (26) YES (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy _ _ [] = []; deleteBy eq x (y : ys) = if x `eq` y then ys else y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if eq x y then ys else y : deleteBy eq x ys" is transformed to "deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy _ _ [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy xw xx [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy xw xx [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(List.\\)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="xy3 (List.\\)",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="xy3 (List.\\) xy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", 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55[label="List.deleteBy (==) [] xy31",fontsize=16,color="magenta"];55 -> 80[label="",style="dashed", color="magenta", weight=3]; 55 -> 81[label="",style="dashed", color="magenta", weight=3]; 345[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];1005[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];345 -> 1005[label="",style="solid", color="burlywood", weight=9]; 1005 -> 363[label="",style="solid", color="burlywood", weight=3]; 1006[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];345 -> 1006[label="",style="solid", color="burlywood", weight=9]; 1006 -> 364[label="",style="solid", color="burlywood", weight=3]; 346[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];346 -> 365[label="",style="solid", color="black", weight=3]; 347[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];347 -> 366[label="",style="solid", color="black", weight=3]; 348[label="xy400 == 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1020[label="xy301/[]",fontsize=10,color="white",style="solid",shape="box"];359 -> 1020[label="",style="solid", color="burlywood", weight=9]; 1020 -> 384[label="",style="solid", color="burlywood", weight=3]; 360[label="[] == xy301",fontsize=16,color="burlywood",shape="box"];1021[label="xy301/xy3010 : xy3011",fontsize=10,color="white",style="solid",shape="box"];360 -> 1021[label="",style="solid", color="burlywood", weight=9]; 1021 -> 385[label="",style="solid", color="burlywood", weight=3]; 1022[label="xy301/[]",fontsize=10,color="white",style="solid",shape="box"];360 -> 1022[label="",style="solid", color="burlywood", weight=9]; 1022 -> 386[label="",style="solid", color="burlywood", weight=3]; 361[label="False && xy31",fontsize=16,color="black",shape="box"];361 -> 387[label="",style="solid", color="black", weight=3]; 362[label="True && xy31",fontsize=16,color="black",shape="box"];362 -> 388[label="",style="solid", color="black", weight=3]; 150[label="(xy13 : xy14) : List.deleteBy (==) (xy15 : xy16) xy12",fontsize=16,color="green",shape="box"];150 -> 174[label="",style="dashed", color="green", weight=3]; 151[label="xy12",fontsize=16,color="green",shape="box"];78[label="xy400 : xy401",fontsize=16,color="green",shape="box"];79[label="xy31",fontsize=16,color="green",shape="box"];80[label="[]",fontsize=16,color="green",shape="box"];81[label="xy31",fontsize=16,color="green",shape="box"];363[label="Left xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];1023[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];363 -> 1023[label="",style="solid", color="burlywood", weight=9]; 1023 -> 389[label="",style="solid", color="burlywood", weight=3]; 1024[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];363 -> 1024[label="",style="solid", color="burlywood", weight=9]; 1024 -> 390[label="",style="solid", color="burlywood", weight=3]; 364[label="Right xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];1025[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];364 -> 1025[label="",style="solid", color="burlywood", weight=9]; 1025 -> 391[label="",style="solid", color="burlywood", weight=3]; 1026[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];364 -> 1026[label="",style="solid", color="burlywood", weight=9]; 1026 -> 392[label="",style="solid", color="burlywood", weight=3]; 365[label="primEqChar xy400 xy300",fontsize=16,color="burlywood",shape="box"];1027[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];365 -> 1027[label="",style="solid", color="burlywood", weight=9]; 1027 -> 393[label="",style="solid", color="burlywood", weight=3]; 366[label="primEqFloat xy400 xy300",fontsize=16,color="burlywood",shape="box"];1028[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];366 -> 1028[label="",style="solid", color="burlywood", weight=9]; 1028 -> 394[label="",style="solid", color="burlywood", weight=3]; 367[label="primEqDouble xy400 xy300",fontsize=16,color="burlywood",shape="box"];1029[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];367 -> 1029[label="",style="solid", color="burlywood", weight=9]; 1029 -> 395[label="",style="solid", color="burlywood", weight=3]; 368[label="Integer xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];1030[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];368 -> 1030[label="",style="solid", color="burlywood", weight=9]; 1030 -> 396[label="",style="solid", color="burlywood", weight=3]; 369[label="(xy4000,xy4001,xy4002) == xy300",fontsize=16,color="burlywood",shape="box"];1031[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];369 -> 1031[label="",style="solid", color="burlywood", weight=9]; 1031 -> 397[label="",style="solid", color="burlywood", weight=3]; 370[label="() == xy300",fontsize=16,color="burlywood",shape="box"];1032[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];370 -> 1032[label="",style="solid", color="burlywood", weight=9]; 1032 -> 398[label="",style="solid", color="burlywood", weight=3]; 371[label="False == xy300",fontsize=16,color="burlywood",shape="box"];1033[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];371 -> 1033[label="",style="solid", color="burlywood", weight=9]; 1033 -> 399[label="",style="solid", color="burlywood", weight=3]; 1034[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];371 -> 1034[label="",style="solid", color="burlywood", weight=9]; 1034 -> 400[label="",style="solid", color="burlywood", weight=3]; 372[label="True == xy300",fontsize=16,color="burlywood",shape="box"];1035[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];372 -> 1035[label="",style="solid", color="burlywood", weight=9]; 1035 -> 401[label="",style="solid", color="burlywood", weight=3]; 1036[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];372 -> 1036[label="",style="solid", color="burlywood", weight=9]; 1036 -> 402[label="",style="solid", color="burlywood", weight=3]; 373[label="LT == xy300",fontsize=16,color="burlywood",shape="box"];1037[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];373 -> 1037[label="",style="solid", color="burlywood", weight=9]; 1037 -> 403[label="",style="solid", color="burlywood", weight=3]; 1038[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];373 -> 1038[label="",style="solid", color="burlywood", weight=9]; 1038 -> 404[label="",style="solid", color="burlywood", weight=3]; 1039[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];373 -> 1039[label="",style="solid", color="burlywood", weight=9]; 1039 -> 405[label="",style="solid", color="burlywood", weight=3]; 374[label="EQ == xy300",fontsize=16,color="burlywood",shape="box"];1040[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];374 -> 1040[label="",style="solid", color="burlywood", weight=9]; 1040 -> 406[label="",style="solid", color="burlywood", weight=3]; 1041[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];374 -> 1041[label="",style="solid", color="burlywood", weight=9]; 1041 -> 407[label="",style="solid", color="burlywood", weight=3]; 1042[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];374 -> 1042[label="",style="solid", color="burlywood", weight=9]; 1042 -> 408[label="",style="solid", color="burlywood", weight=3]; 375[label="GT == xy300",fontsize=16,color="burlywood",shape="box"];1043[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];375 -> 1043[label="",style="solid", color="burlywood", weight=9]; 1043 -> 409[label="",style="solid", color="burlywood", weight=3]; 1044[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];375 -> 1044[label="",style="solid", color="burlywood", weight=9]; 1044 -> 410[label="",style="solid", color="burlywood", weight=3]; 1045[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];375 -> 1045[label="",style="solid", color="burlywood", weight=9]; 1045 -> 411[label="",style="solid", color="burlywood", weight=3]; 376[label="(xy4000,xy4001) == xy300",fontsize=16,color="burlywood",shape="box"];1046[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];376 -> 1046[label="",style="solid", color="burlywood", weight=9]; 1046 -> 412[label="",style="solid", color="burlywood", weight=3]; 377[label="Nothing == xy300",fontsize=16,color="burlywood",shape="box"];1047[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];377 -> 1047[label="",style="solid", color="burlywood", weight=9]; 1047 -> 413[label="",style="solid", color="burlywood", weight=3]; 1048[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];377 -> 1048[label="",style="solid", color="burlywood", weight=9]; 1048 -> 414[label="",style="solid", color="burlywood", weight=3]; 378[label="Just xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];1049[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];378 -> 1049[label="",style="solid", color="burlywood", weight=9]; 1049 -> 415[label="",style="solid", color="burlywood", weight=3]; 1050[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];378 -> 1050[label="",style="solid", color="burlywood", weight=9]; 1050 -> 416[label="",style="solid", color="burlywood", weight=3]; 379[label="xy4000 :% xy4001 == xy300",fontsize=16,color="burlywood",shape="box"];1051[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];379 -> 1051[label="",style="solid", color="burlywood", weight=9]; 1051 -> 417[label="",style="solid", color="burlywood", weight=3]; 380[label="xy300",fontsize=16,color="green",shape="box"];381[label="xy400",fontsize=16,color="green",shape="box"];382[label="primEqInt xy400 xy300",fontsize=16,color="burlywood",shape="triangle"];1052[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];382 -> 1052[label="",style="solid", color="burlywood", weight=9]; 1052 -> 418[label="",style="solid", color="burlywood", weight=3]; 1053[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];382 -> 1053[label="",style="solid", color="burlywood", weight=9]; 1053 -> 419[label="",style="solid", color="burlywood", weight=3]; 383[label="xy4010 : xy4011 == xy3010 : xy3011",fontsize=16,color="black",shape="box"];383 -> 420[label="",style="solid", color="black", weight=3]; 384[label="xy4010 : xy4011 == []",fontsize=16,color="black",shape="box"];384 -> 421[label="",style="solid", color="black", weight=3]; 385[label="[] == xy3010 : xy3011",fontsize=16,color="black",shape="box"];385 -> 422[label="",style="solid", color="black", weight=3]; 386[label="[] == []",fontsize=16,color="black",shape="box"];386 -> 423[label="",style="solid", color="black", weight=3]; 387[label="False",fontsize=16,color="green",shape="box"];388[label="xy31",fontsize=16,color="green",shape="box"];174 -> 13[label="",style="dashed", color="red", weight=0]; 174[label="List.deleteBy (==) (xy15 : xy16) xy12",fontsize=16,color="magenta"];174 -> 224[label="",style="dashed", color="magenta", weight=3]; 174 -> 225[label="",style="dashed", color="magenta", weight=3]; 389[label="Left xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];389 -> 424[label="",style="solid", color="black", weight=3]; 390[label="Left xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];390 -> 425[label="",style="solid", color="black", weight=3]; 391[label="Right xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];391 -> 426[label="",style="solid", color="black", weight=3]; 392[label="Right xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];392 -> 427[label="",style="solid", color="black", weight=3]; 393[label="primEqChar (Char xy4000) xy300",fontsize=16,color="burlywood",shape="box"];1054[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];393 -> 1054[label="",style="solid", color="burlywood", weight=9]; 1054 -> 428[label="",style="solid", color="burlywood", weight=3]; 394[label="primEqFloat (Float xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];1055[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];394 -> 1055[label="",style="solid", color="burlywood", weight=9]; 1055 -> 429[label="",style="solid", color="burlywood", weight=3]; 395[label="primEqDouble (Double xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];1056[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];395 -> 1056[label="",style="solid", color="burlywood", weight=9]; 1056 -> 430[label="",style="solid", color="burlywood", weight=3]; 396[label="Integer xy4000 == Integer xy3000",fontsize=16,color="black",shape="box"];396 -> 431[label="",style="solid", color="black", weight=3]; 397[label="(xy4000,xy4001,xy4002) == (xy3000,xy3001,xy3002)",fontsize=16,color="black",shape="box"];397 -> 432[label="",style="solid", color="black", weight=3]; 398[label="() == ()",fontsize=16,color="black",shape="box"];398 -> 433[label="",style="solid", color="black", weight=3]; 399[label="False == False",fontsize=16,color="black",shape="box"];399 -> 434[label="",style="solid", color="black", weight=3]; 400[label="False == True",fontsize=16,color="black",shape="box"];400 -> 435[label="",style="solid", color="black", weight=3]; 401[label="True == False",fontsize=16,color="black",shape="box"];401 -> 436[label="",style="solid", color="black", weight=3]; 402[label="True == True",fontsize=16,color="black",shape="box"];402 -> 437[label="",style="solid", color="black", weight=3]; 403[label="LT == LT",fontsize=16,color="black",shape="box"];403 -> 438[label="",style="solid", color="black", weight=3]; 404[label="LT == EQ",fontsize=16,color="black",shape="box"];404 -> 439[label="",style="solid", color="black", weight=3]; 405[label="LT == GT",fontsize=16,color="black",shape="box"];405 -> 440[label="",style="solid", color="black", weight=3]; 406[label="EQ == LT",fontsize=16,color="black",shape="box"];406 -> 441[label="",style="solid", color="black", weight=3]; 407[label="EQ == EQ",fontsize=16,color="black",shape="box"];407 -> 442[label="",style="solid", color="black", weight=3]; 408[label="EQ == GT",fontsize=16,color="black",shape="box"];408 -> 443[label="",style="solid", color="black", weight=3]; 409[label="GT == LT",fontsize=16,color="black",shape="box"];409 -> 444[label="",style="solid", color="black", weight=3]; 410[label="GT == EQ",fontsize=16,color="black",shape="box"];410 -> 445[label="",style="solid", color="black", weight=3]; 411[label="GT == GT",fontsize=16,color="black",shape="box"];411 -> 446[label="",style="solid", color="black", weight=3]; 412[label="(xy4000,xy4001) == (xy3000,xy3001)",fontsize=16,color="black",shape="box"];412 -> 447[label="",style="solid", color="black", weight=3]; 413[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];413 -> 448[label="",style="solid", color="black", weight=3]; 414[label="Nothing == Just xy3000",fontsize=16,color="black",shape="box"];414 -> 449[label="",style="solid", color="black", weight=3]; 415[label="Just xy4000 == Nothing",fontsize=16,color="black",shape="box"];415 -> 450[label="",style="solid", color="black", weight=3]; 416[label="Just xy4000 == Just xy3000",fontsize=16,color="black",shape="box"];416 -> 451[label="",style="solid", color="black", weight=3]; 417[label="xy4000 :% xy4001 == xy3000 :% xy3001",fontsize=16,color="black",shape="box"];417 -> 452[label="",style="solid", color="black", weight=3]; 418[label="primEqInt (Pos xy4000) xy300",fontsize=16,color="burlywood",shape="box"];1057[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];418 -> 1057[label="",style="solid", color="burlywood", weight=9]; 1057 -> 453[label="",style="solid", color="burlywood", weight=3]; 1058[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];418 -> 1058[label="",style="solid", color="burlywood", weight=9]; 1058 -> 454[label="",style="solid", color="burlywood", weight=3]; 419[label="primEqInt (Neg xy4000) xy300",fontsize=16,color="burlywood",shape="box"];1059[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];419 -> 1059[label="",style="solid", color="burlywood", weight=9]; 1059 -> 455[label="",style="solid", color="burlywood", weight=3]; 1060[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];419 -> 1060[label="",style="solid", color="burlywood", weight=9]; 1060 -> 456[label="",style="solid", color="burlywood", weight=3]; 420 -> 340[label="",style="dashed", color="red", weight=0]; 420[label="xy4010 == xy3010 && xy4011 == xy3011",fontsize=16,color="magenta"];420 -> 457[label="",style="dashed", color="magenta", weight=3]; 420 -> 458[label="",style="dashed", color="magenta", weight=3]; 421[label="False",fontsize=16,color="green",shape="box"];422[label="False",fontsize=16,color="green",shape="box"];423[label="True",fontsize=16,color="green",shape="box"];224[label="xy15 : xy16",fontsize=16,color="green",shape="box"];225[label="xy12",fontsize=16,color="green",shape="box"];424[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1061[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1061[label="",style="solid", color="blue", weight=9]; 1061 -> 459[label="",style="solid", color="blue", weight=3]; 1062[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1062[label="",style="solid", color="blue", weight=9]; 1062 -> 460[label="",style="solid", color="blue", weight=3]; 1063[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1063[label="",style="solid", color="blue", weight=9]; 1063 -> 461[label="",style="solid", color="blue", weight=3]; 1064[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1064[label="",style="solid", color="blue", weight=9]; 1064 -> 462[label="",style="solid", color="blue", weight=3]; 1065[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1065[label="",style="solid", color="blue", weight=9]; 1065 -> 463[label="",style="solid", color="blue", weight=3]; 1066[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1066[label="",style="solid", color="blue", weight=9]; 1066 -> 464[label="",style="solid", color="blue", weight=3]; 1067[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1067[label="",style="solid", color="blue", weight=9]; 1067 -> 465[label="",style="solid", color="blue", weight=3]; 1068[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1068[label="",style="solid", color="blue", weight=9]; 1068 -> 466[label="",style="solid", color="blue", weight=3]; 1069[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1069[label="",style="solid", color="blue", weight=9]; 1069 -> 467[label="",style="solid", color="blue", weight=3]; 1070[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1070[label="",style="solid", color="blue", weight=9]; 1070 -> 468[label="",style="solid", color="blue", weight=3]; 1071[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1071[label="",style="solid", color="blue", weight=9]; 1071 -> 469[label="",style="solid", color="blue", weight=3]; 1072[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1072[label="",style="solid", color="blue", weight=9]; 1072 -> 470[label="",style="solid", color="blue", weight=3]; 1073[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1073[label="",style="solid", color="blue", weight=9]; 1073 -> 471[label="",style="solid", color="blue", weight=3]; 1074[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1074[label="",style="solid", color="blue", weight=9]; 1074 -> 472[label="",style="solid", color="blue", weight=3]; 425[label="False",fontsize=16,color="green",shape="box"];426[label="False",fontsize=16,color="green",shape="box"];427[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1075[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1075[label="",style="solid", color="blue", weight=9]; 1075 -> 473[label="",style="solid", color="blue", weight=3]; 1076[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1076[label="",style="solid", color="blue", weight=9]; 1076 -> 474[label="",style="solid", color="blue", weight=3]; 1077[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1077[label="",style="solid", color="blue", weight=9]; 1077 -> 475[label="",style="solid", color="blue", weight=3]; 1078[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1078[label="",style="solid", color="blue", weight=9]; 1078 -> 476[label="",style="solid", color="blue", weight=3]; 1079[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1079[label="",style="solid", color="blue", weight=9]; 1079 -> 477[label="",style="solid", color="blue", weight=3]; 1080[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1080[label="",style="solid", color="blue", weight=9]; 1080 -> 478[label="",style="solid", color="blue", weight=3]; 1081[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1081[label="",style="solid", color="blue", weight=9]; 1081 -> 479[label="",style="solid", color="blue", weight=3]; 1082[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1082[label="",style="solid", color="blue", weight=9]; 1082 -> 480[label="",style="solid", color="blue", weight=3]; 1083[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1083[label="",style="solid", color="blue", weight=9]; 1083 -> 481[label="",style="solid", color="blue", weight=3]; 1084[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1084[label="",style="solid", color="blue", weight=9]; 1084 -> 482[label="",style="solid", color="blue", weight=3]; 1085[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1085[label="",style="solid", color="blue", weight=9]; 1085 -> 483[label="",style="solid", color="blue", weight=3]; 1086[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1086[label="",style="solid", color="blue", weight=9]; 1086 -> 484[label="",style="solid", color="blue", weight=3]; 1087[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1087[label="",style="solid", color="blue", weight=9]; 1087 -> 485[label="",style="solid", color="blue", weight=3]; 1088[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];427 -> 1088[label="",style="solid", color="blue", weight=9]; 1088 -> 486[label="",style="solid", color="blue", weight=3]; 428[label="primEqChar (Char xy4000) (Char xy3000)",fontsize=16,color="black",shape="box"];428 -> 487[label="",style="solid", color="black", weight=3]; 429[label="primEqFloat (Float xy4000 xy4001) (Float xy3000 xy3001)",fontsize=16,color="black",shape="box"];429 -> 488[label="",style="solid", color="black", weight=3]; 430[label="primEqDouble (Double xy4000 xy4001) (Double xy3000 xy3001)",fontsize=16,color="black",shape="box"];430 -> 489[label="",style="solid", color="black", weight=3]; 431 -> 382[label="",style="dashed", color="red", weight=0]; 431[label="primEqInt xy4000 xy3000",fontsize=16,color="magenta"];431 -> 490[label="",style="dashed", color="magenta", weight=3]; 431 -> 491[label="",style="dashed", color="magenta", weight=3]; 432 -> 340[label="",style="dashed", color="red", weight=0]; 432[label="xy4000 == xy3000 && xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];432 -> 492[label="",style="dashed", color="magenta", weight=3]; 432 -> 493[label="",style="dashed", color="magenta", weight=3]; 433[label="True",fontsize=16,color="green",shape="box"];434[label="True",fontsize=16,color="green",shape="box"];435[label="False",fontsize=16,color="green",shape="box"];436[label="False",fontsize=16,color="green",shape="box"];437[label="True",fontsize=16,color="green",shape="box"];438[label="True",fontsize=16,color="green",shape="box"];439[label="False",fontsize=16,color="green",shape="box"];440[label="False",fontsize=16,color="green",shape="box"];441[label="False",fontsize=16,color="green",shape="box"];442[label="True",fontsize=16,color="green",shape="box"];443[label="False",fontsize=16,color="green",shape="box"];444[label="False",fontsize=16,color="green",shape="box"];445[label="False",fontsize=16,color="green",shape="box"];446[label="True",fontsize=16,color="green",shape="box"];447 -> 340[label="",style="dashed", color="red", weight=0]; 447[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];447 -> 494[label="",style="dashed", color="magenta", weight=3]; 447 -> 495[label="",style="dashed", color="magenta", weight=3]; 448[label="True",fontsize=16,color="green",shape="box"];449[label="False",fontsize=16,color="green",shape="box"];450[label="False",fontsize=16,color="green",shape="box"];451[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1089[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1089[label="",style="solid", color="blue", weight=9]; 1089 -> 496[label="",style="solid", color="blue", weight=3]; 1090[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1090[label="",style="solid", color="blue", weight=9]; 1090 -> 497[label="",style="solid", color="blue", weight=3]; 1091[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1091[label="",style="solid", color="blue", weight=9]; 1091 -> 498[label="",style="solid", color="blue", weight=3]; 1092[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1092[label="",style="solid", color="blue", weight=9]; 1092 -> 499[label="",style="solid", color="blue", weight=3]; 1093[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1093[label="",style="solid", color="blue", weight=9]; 1093 -> 500[label="",style="solid", color="blue", weight=3]; 1094[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1094[label="",style="solid", color="blue", weight=9]; 1094 -> 501[label="",style="solid", color="blue", weight=3]; 1095[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1095[label="",style="solid", color="blue", weight=9]; 1095 -> 502[label="",style="solid", color="blue", weight=3]; 1096[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1096[label="",style="solid", color="blue", weight=9]; 1096 -> 503[label="",style="solid", color="blue", weight=3]; 1097[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1097[label="",style="solid", color="blue", weight=9]; 1097 -> 504[label="",style="solid", color="blue", weight=3]; 1098[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1098[label="",style="solid", color="blue", weight=9]; 1098 -> 505[label="",style="solid", color="blue", weight=3]; 1099[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1099[label="",style="solid", color="blue", weight=9]; 1099 -> 506[label="",style="solid", color="blue", weight=3]; 1100[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1100[label="",style="solid", color="blue", weight=9]; 1100 -> 507[label="",style="solid", color="blue", weight=3]; 1101[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1101[label="",style="solid", color="blue", weight=9]; 1101 -> 508[label="",style="solid", color="blue", weight=3]; 1102[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];451 -> 1102[label="",style="solid", color="blue", weight=9]; 1102 -> 509[label="",style="solid", color="blue", weight=3]; 452 -> 340[label="",style="dashed", color="red", weight=0]; 452[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];452 -> 510[label="",style="dashed", color="magenta", weight=3]; 452 -> 511[label="",style="dashed", color="magenta", weight=3]; 453[label="primEqInt (Pos (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];1103[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];453 -> 1103[label="",style="solid", color="burlywood", weight=9]; 1103 -> 512[label="",style="solid", color="burlywood", weight=3]; 1104[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];453 -> 1104[label="",style="solid", color="burlywood", weight=9]; 1104 -> 513[label="",style="solid", color="burlywood", weight=3]; 454[label="primEqInt (Pos Zero) xy300",fontsize=16,color="burlywood",shape="box"];1105[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];454 -> 1105[label="",style="solid", color="burlywood", weight=9]; 1105 -> 514[label="",style="solid", color="burlywood", weight=3]; 1106[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];454 -> 1106[label="",style="solid", color="burlywood", weight=9]; 1106 -> 515[label="",style="solid", color="burlywood", weight=3]; 455[label="primEqInt (Neg (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];1107[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];455 -> 1107[label="",style="solid", color="burlywood", weight=9]; 1107 -> 516[label="",style="solid", color="burlywood", weight=3]; 1108[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];455 -> 1108[label="",style="solid", color="burlywood", weight=9]; 1108 -> 517[label="",style="solid", color="burlywood", weight=3]; 456[label="primEqInt (Neg Zero) xy300",fontsize=16,color="burlywood",shape="box"];1109[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];456 -> 1109[label="",style="solid", color="burlywood", weight=9]; 1109 -> 518[label="",style="solid", color="burlywood", weight=3]; 1110[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];456 -> 1110[label="",style="solid", color="burlywood", weight=9]; 1110 -> 519[label="",style="solid", color="burlywood", weight=3]; 457[label="xy4010 == xy3010",fontsize=16,color="blue",shape="box"];1111[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1111[label="",style="solid", color="blue", weight=9]; 1111 -> 520[label="",style="solid", color="blue", weight=3]; 1112[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1112[label="",style="solid", color="blue", weight=9]; 1112 -> 521[label="",style="solid", color="blue", weight=3]; 1113[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1113[label="",style="solid", color="blue", weight=9]; 1113 -> 522[label="",style="solid", color="blue", weight=3]; 1114[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1114[label="",style="solid", color="blue", weight=9]; 1114 -> 523[label="",style="solid", color="blue", weight=3]; 1115[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1115[label="",style="solid", color="blue", weight=9]; 1115 -> 524[label="",style="solid", color="blue", weight=3]; 1116[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1116[label="",style="solid", color="blue", weight=9]; 1116 -> 525[label="",style="solid", color="blue", weight=3]; 1117[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1117[label="",style="solid", color="blue", weight=9]; 1117 -> 526[label="",style="solid", color="blue", weight=3]; 1118[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1118[label="",style="solid", color="blue", weight=9]; 1118 -> 527[label="",style="solid", color="blue", weight=3]; 1119[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1119[label="",style="solid", color="blue", weight=9]; 1119 -> 528[label="",style="solid", color="blue", weight=3]; 1120[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1120[label="",style="solid", color="blue", weight=9]; 1120 -> 529[label="",style="solid", color="blue", weight=3]; 1121[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1121[label="",style="solid", color="blue", weight=9]; 1121 -> 530[label="",style="solid", color="blue", weight=3]; 1122[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1122[label="",style="solid", color="blue", weight=9]; 1122 -> 531[label="",style="solid", color="blue", weight=3]; 1123[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1123[label="",style="solid", color="blue", weight=9]; 1123 -> 532[label="",style="solid", color="blue", weight=3]; 1124[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];457 -> 1124[label="",style="solid", color="blue", weight=9]; 1124 -> 533[label="",style="solid", color="blue", weight=3]; 458 -> 342[label="",style="dashed", color="red", weight=0]; 458[label="xy4011 == xy3011",fontsize=16,color="magenta"];458 -> 534[label="",style="dashed", color="magenta", weight=3]; 458 -> 535[label="",style="dashed", color="magenta", weight=3]; 459 -> 345[label="",style="dashed", color="red", weight=0]; 459[label="xy4000 == xy3000",fontsize=16,color="magenta"];459 -> 536[label="",style="dashed", color="magenta", weight=3]; 459 -> 537[label="",style="dashed", color="magenta", weight=3]; 460 -> 346[label="",style="dashed", color="red", weight=0]; 460[label="xy4000 == xy3000",fontsize=16,color="magenta"];460 -> 538[label="",style="dashed", color="magenta", weight=3]; 460 -> 539[label="",style="dashed", color="magenta", weight=3]; 461 -> 347[label="",style="dashed", color="red", weight=0]; 461[label="xy4000 == xy3000",fontsize=16,color="magenta"];461 -> 540[label="",style="dashed", color="magenta", weight=3]; 461 -> 541[label="",style="dashed", color="magenta", weight=3]; 462 -> 348[label="",style="dashed", color="red", weight=0]; 462[label="xy4000 == xy3000",fontsize=16,color="magenta"];462 -> 542[label="",style="dashed", color="magenta", weight=3]; 462 -> 543[label="",style="dashed", color="magenta", weight=3]; 463 -> 349[label="",style="dashed", color="red", weight=0]; 463[label="xy4000 == xy3000",fontsize=16,color="magenta"];463 -> 544[label="",style="dashed", color="magenta", weight=3]; 463 -> 545[label="",style="dashed", color="magenta", weight=3]; 464 -> 350[label="",style="dashed", color="red", weight=0]; 464[label="xy4000 == xy3000",fontsize=16,color="magenta"];464 -> 546[label="",style="dashed", color="magenta", weight=3]; 464 -> 547[label="",style="dashed", color="magenta", weight=3]; 465 -> 351[label="",style="dashed", color="red", weight=0]; 465[label="xy4000 == xy3000",fontsize=16,color="magenta"];465 -> 548[label="",style="dashed", color="magenta", weight=3]; 465 -> 549[label="",style="dashed", color="magenta", weight=3]; 466 -> 352[label="",style="dashed", color="red", weight=0]; 466[label="xy4000 == xy3000",fontsize=16,color="magenta"];466 -> 550[label="",style="dashed", color="magenta", weight=3]; 466 -> 551[label="",style="dashed", color="magenta", weight=3]; 467 -> 353[label="",style="dashed", color="red", weight=0]; 467[label="xy4000 == xy3000",fontsize=16,color="magenta"];467 -> 552[label="",style="dashed", color="magenta", weight=3]; 467 -> 553[label="",style="dashed", color="magenta", weight=3]; 468 -> 354[label="",style="dashed", color="red", weight=0]; 468[label="xy4000 == xy3000",fontsize=16,color="magenta"];468 -> 554[label="",style="dashed", color="magenta", weight=3]; 468 -> 555[label="",style="dashed", color="magenta", weight=3]; 469 -> 355[label="",style="dashed", color="red", weight=0]; 469[label="xy4000 == xy3000",fontsize=16,color="magenta"];469 -> 556[label="",style="dashed", color="magenta", weight=3]; 469 -> 557[label="",style="dashed", color="magenta", weight=3]; 470 -> 356[label="",style="dashed", color="red", weight=0]; 470[label="xy4000 == xy3000",fontsize=16,color="magenta"];470 -> 558[label="",style="dashed", color="magenta", weight=3]; 470 -> 559[label="",style="dashed", color="magenta", weight=3]; 471 -> 342[label="",style="dashed", color="red", weight=0]; 471[label="xy4000 == xy3000",fontsize=16,color="magenta"];471 -> 560[label="",style="dashed", color="magenta", weight=3]; 471 -> 561[label="",style="dashed", color="magenta", weight=3]; 472 -> 358[label="",style="dashed", color="red", weight=0]; 472[label="xy4000 == xy3000",fontsize=16,color="magenta"];472 -> 562[label="",style="dashed", color="magenta", weight=3]; 472 -> 563[label="",style="dashed", color="magenta", weight=3]; 473 -> 345[label="",style="dashed", color="red", weight=0]; 473[label="xy4000 == xy3000",fontsize=16,color="magenta"];473 -> 564[label="",style="dashed", color="magenta", weight=3]; 473 -> 565[label="",style="dashed", color="magenta", weight=3]; 474 -> 346[label="",style="dashed", color="red", weight=0]; 474[label="xy4000 == xy3000",fontsize=16,color="magenta"];474 -> 566[label="",style="dashed", color="magenta", weight=3]; 474 -> 567[label="",style="dashed", color="magenta", weight=3]; 475 -> 347[label="",style="dashed", color="red", weight=0]; 475[label="xy4000 == xy3000",fontsize=16,color="magenta"];475 -> 568[label="",style="dashed", color="magenta", weight=3]; 475 -> 569[label="",style="dashed", color="magenta", weight=3]; 476 -> 348[label="",style="dashed", color="red", weight=0]; 476[label="xy4000 == xy3000",fontsize=16,color="magenta"];476 -> 570[label="",style="dashed", color="magenta", weight=3]; 476 -> 571[label="",style="dashed", color="magenta", weight=3]; 477 -> 349[label="",style="dashed", color="red", weight=0]; 477[label="xy4000 == xy3000",fontsize=16,color="magenta"];477 -> 572[label="",style="dashed", color="magenta", weight=3]; 477 -> 573[label="",style="dashed", color="magenta", weight=3]; 478 -> 350[label="",style="dashed", color="red", weight=0]; 478[label="xy4000 == xy3000",fontsize=16,color="magenta"];478 -> 574[label="",style="dashed", color="magenta", weight=3]; 478 -> 575[label="",style="dashed", color="magenta", weight=3]; 479 -> 351[label="",style="dashed", color="red", weight=0]; 479[label="xy4000 == xy3000",fontsize=16,color="magenta"];479 -> 576[label="",style="dashed", color="magenta", weight=3]; 479 -> 577[label="",style="dashed", color="magenta", weight=3]; 480 -> 352[label="",style="dashed", color="red", weight=0]; 480[label="xy4000 == xy3000",fontsize=16,color="magenta"];480 -> 578[label="",style="dashed", color="magenta", weight=3]; 480 -> 579[label="",style="dashed", color="magenta", weight=3]; 481 -> 353[label="",style="dashed", color="red", weight=0]; 481[label="xy4000 == xy3000",fontsize=16,color="magenta"];481 -> 580[label="",style="dashed", color="magenta", weight=3]; 481 -> 581[label="",style="dashed", color="magenta", weight=3]; 482 -> 354[label="",style="dashed", color="red", weight=0]; 482[label="xy4000 == xy3000",fontsize=16,color="magenta"];482 -> 582[label="",style="dashed", color="magenta", weight=3]; 482 -> 583[label="",style="dashed", color="magenta", weight=3]; 483 -> 355[label="",style="dashed", color="red", weight=0]; 483[label="xy4000 == xy3000",fontsize=16,color="magenta"];483 -> 584[label="",style="dashed", color="magenta", weight=3]; 483 -> 585[label="",style="dashed", color="magenta", weight=3]; 484 -> 356[label="",style="dashed", color="red", weight=0]; 484[label="xy4000 == xy3000",fontsize=16,color="magenta"];484 -> 586[label="",style="dashed", color="magenta", weight=3]; 484 -> 587[label="",style="dashed", color="magenta", weight=3]; 485 -> 342[label="",style="dashed", color="red", weight=0]; 485[label="xy4000 == xy3000",fontsize=16,color="magenta"];485 -> 588[label="",style="dashed", color="magenta", weight=3]; 485 -> 589[label="",style="dashed", color="magenta", weight=3]; 486 -> 358[label="",style="dashed", color="red", weight=0]; 486[label="xy4000 == xy3000",fontsize=16,color="magenta"];486 -> 590[label="",style="dashed", color="magenta", weight=3]; 486 -> 591[label="",style="dashed", color="magenta", weight=3]; 487[label="primEqNat xy4000 xy3000",fontsize=16,color="burlywood",shape="triangle"];1125[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];487 -> 1125[label="",style="solid", color="burlywood", weight=9]; 1125 -> 592[label="",style="solid", color="burlywood", weight=3]; 1126[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];487 -> 1126[label="",style="solid", color="burlywood", weight=9]; 1126 -> 593[label="",style="solid", color="burlywood", weight=3]; 488 -> 358[label="",style="dashed", color="red", weight=0]; 488[label="xy4000 * xy3001 == xy4001 * xy3000",fontsize=16,color="magenta"];488 -> 594[label="",style="dashed", color="magenta", weight=3]; 488 -> 595[label="",style="dashed", color="magenta", weight=3]; 489 -> 358[label="",style="dashed", color="red", weight=0]; 489[label="xy4000 * xy3001 == xy4001 * xy3000",fontsize=16,color="magenta"];489 -> 596[label="",style="dashed", color="magenta", weight=3]; 489 -> 597[label="",style="dashed", color="magenta", weight=3]; 490[label="xy3000",fontsize=16,color="green",shape="box"];491[label="xy4000",fontsize=16,color="green",shape="box"];492[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1127[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1127[label="",style="solid", color="blue", weight=9]; 1127 -> 598[label="",style="solid", color="blue", weight=3]; 1128[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1128[label="",style="solid", color="blue", weight=9]; 1128 -> 599[label="",style="solid", color="blue", weight=3]; 1129[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1129[label="",style="solid", color="blue", weight=9]; 1129 -> 600[label="",style="solid", color="blue", weight=3]; 1130[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1130[label="",style="solid", color="blue", weight=9]; 1130 -> 601[label="",style="solid", color="blue", weight=3]; 1131[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1131[label="",style="solid", color="blue", weight=9]; 1131 -> 602[label="",style="solid", color="blue", weight=3]; 1132[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1132[label="",style="solid", color="blue", weight=9]; 1132 -> 603[label="",style="solid", color="blue", weight=3]; 1133[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1133[label="",style="solid", color="blue", weight=9]; 1133 -> 604[label="",style="solid", color="blue", weight=3]; 1134[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1134[label="",style="solid", color="blue", weight=9]; 1134 -> 605[label="",style="solid", color="blue", weight=3]; 1135[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1135[label="",style="solid", color="blue", weight=9]; 1135 -> 606[label="",style="solid", color="blue", weight=3]; 1136[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1136[label="",style="solid", color="blue", weight=9]; 1136 -> 607[label="",style="solid", color="blue", weight=3]; 1137[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1137[label="",style="solid", color="blue", weight=9]; 1137 -> 608[label="",style="solid", color="blue", weight=3]; 1138[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1138[label="",style="solid", color="blue", weight=9]; 1138 -> 609[label="",style="solid", color="blue", weight=3]; 1139[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1139[label="",style="solid", color="blue", weight=9]; 1139 -> 610[label="",style="solid", color="blue", weight=3]; 1140[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];492 -> 1140[label="",style="solid", color="blue", weight=9]; 1140 -> 611[label="",style="solid", color="blue", weight=3]; 493 -> 340[label="",style="dashed", color="red", weight=0]; 493[label="xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];493 -> 612[label="",style="dashed", color="magenta", weight=3]; 493 -> 613[label="",style="dashed", color="magenta", weight=3]; 494[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1141[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1141[label="",style="solid", color="blue", weight=9]; 1141 -> 614[label="",style="solid", color="blue", weight=3]; 1142[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1142[label="",style="solid", color="blue", weight=9]; 1142 -> 615[label="",style="solid", color="blue", weight=3]; 1143[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1143[label="",style="solid", color="blue", weight=9]; 1143 -> 616[label="",style="solid", color="blue", weight=3]; 1144[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1144[label="",style="solid", color="blue", weight=9]; 1144 -> 617[label="",style="solid", color="blue", weight=3]; 1145[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1145[label="",style="solid", color="blue", weight=9]; 1145 -> 618[label="",style="solid", color="blue", weight=3]; 1146[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1146[label="",style="solid", color="blue", weight=9]; 1146 -> 619[label="",style="solid", color="blue", weight=3]; 1147[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1147[label="",style="solid", color="blue", weight=9]; 1147 -> 620[label="",style="solid", color="blue", weight=3]; 1148[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1148[label="",style="solid", color="blue", weight=9]; 1148 -> 621[label="",style="solid", color="blue", weight=3]; 1149[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1149[label="",style="solid", color="blue", weight=9]; 1149 -> 622[label="",style="solid", color="blue", weight=3]; 1150[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1150[label="",style="solid", color="blue", weight=9]; 1150 -> 623[label="",style="solid", color="blue", weight=3]; 1151[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1151[label="",style="solid", color="blue", weight=9]; 1151 -> 624[label="",style="solid", color="blue", weight=3]; 1152[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1152[label="",style="solid", color="blue", weight=9]; 1152 -> 625[label="",style="solid", color="blue", weight=3]; 1153[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1153[label="",style="solid", color="blue", weight=9]; 1153 -> 626[label="",style="solid", color="blue", weight=3]; 1154[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1154[label="",style="solid", color="blue", weight=9]; 1154 -> 627[label="",style="solid", color="blue", weight=3]; 495[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];1155[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1155[label="",style="solid", color="blue", weight=9]; 1155 -> 628[label="",style="solid", color="blue", weight=3]; 1156[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1156[label="",style="solid", color="blue", weight=9]; 1156 -> 629[label="",style="solid", color="blue", weight=3]; 1157[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1157[label="",style="solid", color="blue", weight=9]; 1157 -> 630[label="",style="solid", color="blue", weight=3]; 1158[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1158[label="",style="solid", color="blue", weight=9]; 1158 -> 631[label="",style="solid", color="blue", weight=3]; 1159[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1159[label="",style="solid", color="blue", weight=9]; 1159 -> 632[label="",style="solid", color="blue", weight=3]; 1160[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1160[label="",style="solid", color="blue", weight=9]; 1160 -> 633[label="",style="solid", color="blue", weight=3]; 1161[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1161[label="",style="solid", color="blue", weight=9]; 1161 -> 634[label="",style="solid", color="blue", weight=3]; 1162[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1162[label="",style="solid", color="blue", weight=9]; 1162 -> 635[label="",style="solid", color="blue", weight=3]; 1163[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1163[label="",style="solid", color="blue", weight=9]; 1163 -> 636[label="",style="solid", color="blue", weight=3]; 1164[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1164[label="",style="solid", color="blue", weight=9]; 1164 -> 637[label="",style="solid", color="blue", weight=3]; 1165[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1165[label="",style="solid", color="blue", weight=9]; 1165 -> 638[label="",style="solid", color="blue", weight=3]; 1166[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1166[label="",style="solid", color="blue", weight=9]; 1166 -> 639[label="",style="solid", color="blue", weight=3]; 1167[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1167[label="",style="solid", color="blue", weight=9]; 1167 -> 640[label="",style="solid", color="blue", weight=3]; 1168[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];495 -> 1168[label="",style="solid", color="blue", weight=9]; 1168 -> 641[label="",style="solid", color="blue", weight=3]; 496 -> 345[label="",style="dashed", color="red", weight=0]; 496[label="xy4000 == xy3000",fontsize=16,color="magenta"];496 -> 642[label="",style="dashed", color="magenta", weight=3]; 496 -> 643[label="",style="dashed", color="magenta", weight=3]; 497 -> 346[label="",style="dashed", color="red", weight=0]; 497[label="xy4000 == xy3000",fontsize=16,color="magenta"];497 -> 644[label="",style="dashed", color="magenta", weight=3]; 497 -> 645[label="",style="dashed", color="magenta", weight=3]; 498 -> 347[label="",style="dashed", color="red", weight=0]; 498[label="xy4000 == xy3000",fontsize=16,color="magenta"];498 -> 646[label="",style="dashed", color="magenta", weight=3]; 498 -> 647[label="",style="dashed", color="magenta", weight=3]; 499 -> 348[label="",style="dashed", color="red", weight=0]; 499[label="xy4000 == xy3000",fontsize=16,color="magenta"];499 -> 648[label="",style="dashed", color="magenta", weight=3]; 499 -> 649[label="",style="dashed", color="magenta", weight=3]; 500 -> 349[label="",style="dashed", color="red", weight=0]; 500[label="xy4000 == xy3000",fontsize=16,color="magenta"];500 -> 650[label="",style="dashed", color="magenta", weight=3]; 500 -> 651[label="",style="dashed", color="magenta", weight=3]; 501 -> 350[label="",style="dashed", color="red", weight=0]; 501[label="xy4000 == xy3000",fontsize=16,color="magenta"];501 -> 652[label="",style="dashed", color="magenta", weight=3]; 501 -> 653[label="",style="dashed", color="magenta", weight=3]; 502 -> 351[label="",style="dashed", color="red", weight=0]; 502[label="xy4000 == xy3000",fontsize=16,color="magenta"];502 -> 654[label="",style="dashed", color="magenta", weight=3]; 502 -> 655[label="",style="dashed", color="magenta", weight=3]; 503 -> 352[label="",style="dashed", color="red", weight=0]; 503[label="xy4000 == xy3000",fontsize=16,color="magenta"];503 -> 656[label="",style="dashed", color="magenta", weight=3]; 503 -> 657[label="",style="dashed", color="magenta", weight=3]; 504 -> 353[label="",style="dashed", color="red", weight=0]; 504[label="xy4000 == xy3000",fontsize=16,color="magenta"];504 -> 658[label="",style="dashed", color="magenta", weight=3]; 504 -> 659[label="",style="dashed", color="magenta", weight=3]; 505 -> 354[label="",style="dashed", color="red", weight=0]; 505[label="xy4000 == xy3000",fontsize=16,color="magenta"];505 -> 660[label="",style="dashed", color="magenta", weight=3]; 505 -> 661[label="",style="dashed", color="magenta", weight=3]; 506 -> 355[label="",style="dashed", color="red", weight=0]; 506[label="xy4000 == xy3000",fontsize=16,color="magenta"];506 -> 662[label="",style="dashed", color="magenta", weight=3]; 506 -> 663[label="",style="dashed", color="magenta", weight=3]; 507 -> 356[label="",style="dashed", color="red", weight=0]; 507[label="xy4000 == xy3000",fontsize=16,color="magenta"];507 -> 664[label="",style="dashed", color="magenta", weight=3]; 507 -> 665[label="",style="dashed", color="magenta", weight=3]; 508 -> 342[label="",style="dashed", color="red", weight=0]; 508[label="xy4000 == xy3000",fontsize=16,color="magenta"];508 -> 666[label="",style="dashed", color="magenta", weight=3]; 508 -> 667[label="",style="dashed", color="magenta", weight=3]; 509 -> 358[label="",style="dashed", color="red", weight=0]; 509[label="xy4000 == xy3000",fontsize=16,color="magenta"];509 -> 668[label="",style="dashed", color="magenta", weight=3]; 509 -> 669[label="",style="dashed", color="magenta", weight=3]; 510[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];1169[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];510 -> 1169[label="",style="solid", color="blue", weight=9]; 1169 -> 670[label="",style="solid", color="blue", weight=3]; 1170[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];510 -> 1170[label="",style="solid", color="blue", weight=9]; 1170 -> 671[label="",style="solid", color="blue", weight=3]; 511[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];1171[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];511 -> 1171[label="",style="solid", color="blue", weight=9]; 1171 -> 672[label="",style="solid", color="blue", weight=3]; 1172[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];511 -> 1172[label="",style="solid", color="blue", weight=9]; 1172 -> 673[label="",style="solid", color="blue", weight=3]; 512[label="primEqInt (Pos (Succ xy40000)) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];1173[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];512 -> 1173[label="",style="solid", color="burlywood", weight=9]; 1173 -> 674[label="",style="solid", color="burlywood", weight=3]; 1174[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];512 -> 1174[label="",style="solid", color="burlywood", weight=9]; 1174 -> 675[label="",style="solid", color="burlywood", weight=3]; 513[label="primEqInt (Pos (Succ xy40000)) (Neg xy3000)",fontsize=16,color="black",shape="box"];513 -> 676[label="",style="solid", color="black", weight=3]; 514[label="primEqInt (Pos Zero) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];1175[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];514 -> 1175[label="",style="solid", color="burlywood", weight=9]; 1175 -> 677[label="",style="solid", color="burlywood", weight=3]; 1176[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];514 -> 1176[label="",style="solid", color="burlywood", weight=9]; 1176 -> 678[label="",style="solid", color="burlywood", weight=3]; 515[label="primEqInt (Pos Zero) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];1177[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];515 -> 1177[label="",style="solid", color="burlywood", weight=9]; 1177 -> 679[label="",style="solid", color="burlywood", weight=3]; 1178[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];515 -> 1178[label="",style="solid", color="burlywood", weight=9]; 1178 -> 680[label="",style="solid", color="burlywood", weight=3]; 516[label="primEqInt (Neg (Succ xy40000)) (Pos xy3000)",fontsize=16,color="black",shape="box"];516 -> 681[label="",style="solid", color="black", weight=3]; 517[label="primEqInt (Neg (Succ xy40000)) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];1179[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];517 -> 1179[label="",style="solid", color="burlywood", weight=9]; 1179 -> 682[label="",style="solid", color="burlywood", weight=3]; 1180[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];517 -> 1180[label="",style="solid", color="burlywood", weight=9]; 1180 -> 683[label="",style="solid", color="burlywood", weight=3]; 518[label="primEqInt (Neg Zero) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];1181[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];518 -> 1181[label="",style="solid", color="burlywood", weight=9]; 1181 -> 684[label="",style="solid", color="burlywood", weight=3]; 1182[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];518 -> 1182[label="",style="solid", color="burlywood", weight=9]; 1182 -> 685[label="",style="solid", color="burlywood", weight=3]; 519[label="primEqInt (Neg Zero) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];1183[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];519 -> 1183[label="",style="solid", color="burlywood", weight=9]; 1183 -> 686[label="",style="solid", color="burlywood", weight=3]; 1184[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];519 -> 1184[label="",style="solid", color="burlywood", weight=9]; 1184 -> 687[label="",style="solid", color="burlywood", weight=3]; 520 -> 345[label="",style="dashed", color="red", weight=0]; 520[label="xy4010 == xy3010",fontsize=16,color="magenta"];520 -> 688[label="",style="dashed", color="magenta", weight=3]; 520 -> 689[label="",style="dashed", color="magenta", weight=3]; 521 -> 346[label="",style="dashed", color="red", weight=0]; 521[label="xy4010 == xy3010",fontsize=16,color="magenta"];521 -> 690[label="",style="dashed", color="magenta", weight=3]; 521 -> 691[label="",style="dashed", color="magenta", weight=3]; 522 -> 347[label="",style="dashed", color="red", weight=0]; 522[label="xy4010 == xy3010",fontsize=16,color="magenta"];522 -> 692[label="",style="dashed", color="magenta", weight=3]; 522 -> 693[label="",style="dashed", color="magenta", weight=3]; 523 -> 348[label="",style="dashed", color="red", weight=0]; 523[label="xy4010 == xy3010",fontsize=16,color="magenta"];523 -> 694[label="",style="dashed", color="magenta", weight=3]; 523 -> 695[label="",style="dashed", color="magenta", weight=3]; 524 -> 349[label="",style="dashed", color="red", weight=0]; 524[label="xy4010 == xy3010",fontsize=16,color="magenta"];524 -> 696[label="",style="dashed", color="magenta", weight=3]; 524 -> 697[label="",style="dashed", color="magenta", weight=3]; 525 -> 350[label="",style="dashed", color="red", weight=0]; 525[label="xy4010 == xy3010",fontsize=16,color="magenta"];525 -> 698[label="",style="dashed", color="magenta", weight=3]; 525 -> 699[label="",style="dashed", color="magenta", weight=3]; 526 -> 351[label="",style="dashed", color="red", weight=0]; 526[label="xy4010 == xy3010",fontsize=16,color="magenta"];526 -> 700[label="",style="dashed", color="magenta", weight=3]; 526 -> 701[label="",style="dashed", color="magenta", weight=3]; 527 -> 352[label="",style="dashed", color="red", weight=0]; 527[label="xy4010 == xy3010",fontsize=16,color="magenta"];527 -> 702[label="",style="dashed", color="magenta", weight=3]; 527 -> 703[label="",style="dashed", color="magenta", weight=3]; 528 -> 353[label="",style="dashed", color="red", weight=0]; 528[label="xy4010 == xy3010",fontsize=16,color="magenta"];528 -> 704[label="",style="dashed", color="magenta", weight=3]; 528 -> 705[label="",style="dashed", color="magenta", weight=3]; 529 -> 354[label="",style="dashed", color="red", weight=0]; 529[label="xy4010 == xy3010",fontsize=16,color="magenta"];529 -> 706[label="",style="dashed", color="magenta", weight=3]; 529 -> 707[label="",style="dashed", color="magenta", weight=3]; 530 -> 355[label="",style="dashed", color="red", weight=0]; 530[label="xy4010 == xy3010",fontsize=16,color="magenta"];530 -> 708[label="",style="dashed", color="magenta", weight=3]; 530 -> 709[label="",style="dashed", color="magenta", weight=3]; 531 -> 356[label="",style="dashed", color="red", weight=0]; 531[label="xy4010 == xy3010",fontsize=16,color="magenta"];531 -> 710[label="",style="dashed", color="magenta", weight=3]; 531 -> 711[label="",style="dashed", color="magenta", weight=3]; 532 -> 342[label="",style="dashed", color="red", weight=0]; 532[label="xy4010 == xy3010",fontsize=16,color="magenta"];532 -> 712[label="",style="dashed", color="magenta", weight=3]; 532 -> 713[label="",style="dashed", color="magenta", weight=3]; 533 -> 358[label="",style="dashed", color="red", weight=0]; 533[label="xy4010 == xy3010",fontsize=16,color="magenta"];533 -> 714[label="",style="dashed", color="magenta", weight=3]; 533 -> 715[label="",style="dashed", color="magenta", weight=3]; 534[label="xy3011",fontsize=16,color="green",shape="box"];535[label="xy4011",fontsize=16,color="green",shape="box"];536[label="xy3000",fontsize=16,color="green",shape="box"];537[label="xy4000",fontsize=16,color="green",shape="box"];538[label="xy3000",fontsize=16,color="green",shape="box"];539[label="xy4000",fontsize=16,color="green",shape="box"];540[label="xy3000",fontsize=16,color="green",shape="box"];541[label="xy4000",fontsize=16,color="green",shape="box"];542[label="xy3000",fontsize=16,color="green",shape="box"];543[label="xy4000",fontsize=16,color="green",shape="box"];544[label="xy3000",fontsize=16,color="green",shape="box"];545[label="xy4000",fontsize=16,color="green",shape="box"];546[label="xy3000",fontsize=16,color="green",shape="box"];547[label="xy4000",fontsize=16,color="green",shape="box"];548[label="xy3000",fontsize=16,color="green",shape="box"];549[label="xy4000",fontsize=16,color="green",shape="box"];550[label="xy3000",fontsize=16,color="green",shape="box"];551[label="xy4000",fontsize=16,color="green",shape="box"];552[label="xy3000",fontsize=16,color="green",shape="box"];553[label="xy4000",fontsize=16,color="green",shape="box"];554[label="xy3000",fontsize=16,color="green",shape="box"];555[label="xy4000",fontsize=16,color="green",shape="box"];556[label="xy3000",fontsize=16,color="green",shape="box"];557[label="xy4000",fontsize=16,color="green",shape="box"];558[label="xy3000",fontsize=16,color="green",shape="box"];559[label="xy4000",fontsize=16,color="green",shape="box"];560[label="xy3000",fontsize=16,color="green",shape="box"];561[label="xy4000",fontsize=16,color="green",shape="box"];562[label="xy3000",fontsize=16,color="green",shape="box"];563[label="xy4000",fontsize=16,color="green",shape="box"];564[label="xy3000",fontsize=16,color="green",shape="box"];565[label="xy4000",fontsize=16,color="green",shape="box"];566[label="xy3000",fontsize=16,color="green",shape="box"];567[label="xy4000",fontsize=16,color="green",shape="box"];568[label="xy3000",fontsize=16,color="green",shape="box"];569[label="xy4000",fontsize=16,color="green",shape="box"];570[label="xy3000",fontsize=16,color="green",shape="box"];571[label="xy4000",fontsize=16,color="green",shape="box"];572[label="xy3000",fontsize=16,color="green",shape="box"];573[label="xy4000",fontsize=16,color="green",shape="box"];574[label="xy3000",fontsize=16,color="green",shape="box"];575[label="xy4000",fontsize=16,color="green",shape="box"];576[label="xy3000",fontsize=16,color="green",shape="box"];577[label="xy4000",fontsize=16,color="green",shape="box"];578[label="xy3000",fontsize=16,color="green",shape="box"];579[label="xy4000",fontsize=16,color="green",shape="box"];580[label="xy3000",fontsize=16,color="green",shape="box"];581[label="xy4000",fontsize=16,color="green",shape="box"];582[label="xy3000",fontsize=16,color="green",shape="box"];583[label="xy4000",fontsize=16,color="green",shape="box"];584[label="xy3000",fontsize=16,color="green",shape="box"];585[label="xy4000",fontsize=16,color="green",shape="box"];586[label="xy3000",fontsize=16,color="green",shape="box"];587[label="xy4000",fontsize=16,color="green",shape="box"];588[label="xy3000",fontsize=16,color="green",shape="box"];589[label="xy4000",fontsize=16,color="green",shape="box"];590[label="xy3000",fontsize=16,color="green",shape="box"];591[label="xy4000",fontsize=16,color="green",shape="box"];592[label="primEqNat 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594[label="xy4001 * xy3000",fontsize=16,color="black",shape="triangle"];594 -> 720[label="",style="solid", color="black", weight=3]; 595 -> 594[label="",style="dashed", color="red", weight=0]; 595[label="xy4000 * xy3001",fontsize=16,color="magenta"];595 -> 721[label="",style="dashed", color="magenta", weight=3]; 595 -> 722[label="",style="dashed", color="magenta", weight=3]; 596 -> 594[label="",style="dashed", color="red", weight=0]; 596[label="xy4001 * xy3000",fontsize=16,color="magenta"];596 -> 723[label="",style="dashed", color="magenta", weight=3]; 596 -> 724[label="",style="dashed", color="magenta", weight=3]; 597 -> 594[label="",style="dashed", color="red", weight=0]; 597[label="xy4000 * xy3001",fontsize=16,color="magenta"];597 -> 725[label="",style="dashed", color="magenta", weight=3]; 597 -> 726[label="",style="dashed", color="magenta", weight=3]; 598 -> 345[label="",style="dashed", color="red", weight=0]; 598[label="xy4000 == xy3000",fontsize=16,color="magenta"];598 -> 727[label="",style="dashed", color="magenta", weight=3]; 598 -> 728[label="",style="dashed", color="magenta", weight=3]; 599 -> 346[label="",style="dashed", color="red", weight=0]; 599[label="xy4000 == xy3000",fontsize=16,color="magenta"];599 -> 729[label="",style="dashed", color="magenta", weight=3]; 599 -> 730[label="",style="dashed", color="magenta", weight=3]; 600 -> 347[label="",style="dashed", color="red", weight=0]; 600[label="xy4000 == xy3000",fontsize=16,color="magenta"];600 -> 731[label="",style="dashed", color="magenta", weight=3]; 600 -> 732[label="",style="dashed", color="magenta", weight=3]; 601 -> 348[label="",style="dashed", color="red", weight=0]; 601[label="xy4000 == xy3000",fontsize=16,color="magenta"];601 -> 733[label="",style="dashed", color="magenta", weight=3]; 601 -> 734[label="",style="dashed", color="magenta", weight=3]; 602 -> 349[label="",style="dashed", color="red", weight=0]; 602[label="xy4000 == xy3000",fontsize=16,color="magenta"];602 -> 735[label="",style="dashed", color="magenta", weight=3]; 602 -> 736[label="",style="dashed", color="magenta", weight=3]; 603 -> 350[label="",style="dashed", color="red", weight=0]; 603[label="xy4000 == xy3000",fontsize=16,color="magenta"];603 -> 737[label="",style="dashed", color="magenta", weight=3]; 603 -> 738[label="",style="dashed", color="magenta", weight=3]; 604 -> 351[label="",style="dashed", color="red", weight=0]; 604[label="xy4000 == xy3000",fontsize=16,color="magenta"];604 -> 739[label="",style="dashed", color="magenta", weight=3]; 604 -> 740[label="",style="dashed", color="magenta", weight=3]; 605 -> 352[label="",style="dashed", color="red", weight=0]; 605[label="xy4000 == xy3000",fontsize=16,color="magenta"];605 -> 741[label="",style="dashed", color="magenta", weight=3]; 605 -> 742[label="",style="dashed", color="magenta", weight=3]; 606 -> 353[label="",style="dashed", color="red", weight=0]; 606[label="xy4000 == xy3000",fontsize=16,color="magenta"];606 -> 743[label="",style="dashed", color="magenta", weight=3]; 606 -> 744[label="",style="dashed", color="magenta", weight=3]; 607 -> 354[label="",style="dashed", color="red", weight=0]; 607[label="xy4000 == xy3000",fontsize=16,color="magenta"];607 -> 745[label="",style="dashed", color="magenta", weight=3]; 607 -> 746[label="",style="dashed", color="magenta", weight=3]; 608 -> 355[label="",style="dashed", color="red", weight=0]; 608[label="xy4000 == xy3000",fontsize=16,color="magenta"];608 -> 747[label="",style="dashed", color="magenta", weight=3]; 608 -> 748[label="",style="dashed", color="magenta", weight=3]; 609 -> 356[label="",style="dashed", color="red", weight=0]; 609[label="xy4000 == xy3000",fontsize=16,color="magenta"];609 -> 749[label="",style="dashed", color="magenta", weight=3]; 609 -> 750[label="",style="dashed", color="magenta", weight=3]; 610 -> 342[label="",style="dashed", color="red", weight=0]; 610[label="xy4000 == xy3000",fontsize=16,color="magenta"];610 -> 751[label="",style="dashed", color="magenta", weight=3]; 610 -> 752[label="",style="dashed", color="magenta", weight=3]; 611 -> 358[label="",style="dashed", color="red", weight=0]; 611[label="xy4000 == xy3000",fontsize=16,color="magenta"];611 -> 753[label="",style="dashed", color="magenta", weight=3]; 611 -> 754[label="",style="dashed", color="magenta", weight=3]; 612[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];1189[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1189[label="",style="solid", color="blue", weight=9]; 1189 -> 755[label="",style="solid", color="blue", weight=3]; 1190[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1190[label="",style="solid", color="blue", weight=9]; 1190 -> 756[label="",style="solid", color="blue", weight=3]; 1191[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1191[label="",style="solid", color="blue", weight=9]; 1191 -> 757[label="",style="solid", color="blue", weight=3]; 1192[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1192[label="",style="solid", color="blue", weight=9]; 1192 -> 758[label="",style="solid", color="blue", weight=3]; 1193[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1193[label="",style="solid", color="blue", weight=9]; 1193 -> 759[label="",style="solid", color="blue", weight=3]; 1194[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1194[label="",style="solid", color="blue", weight=9]; 1194 -> 760[label="",style="solid", color="blue", weight=3]; 1195[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1195[label="",style="solid", color="blue", weight=9]; 1195 -> 761[label="",style="solid", color="blue", weight=3]; 1196[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1196[label="",style="solid", color="blue", weight=9]; 1196 -> 762[label="",style="solid", color="blue", weight=3]; 1197[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1197[label="",style="solid", color="blue", weight=9]; 1197 -> 763[label="",style="solid", color="blue", weight=3]; 1198[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1198[label="",style="solid", color="blue", weight=9]; 1198 -> 764[label="",style="solid", color="blue", weight=3]; 1199[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1199[label="",style="solid", color="blue", weight=9]; 1199 -> 765[label="",style="solid", color="blue", weight=3]; 1200[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1200[label="",style="solid", color="blue", weight=9]; 1200 -> 766[label="",style="solid", color="blue", weight=3]; 1201[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1201[label="",style="solid", color="blue", weight=9]; 1201 -> 767[label="",style="solid", color="blue", weight=3]; 1202[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];612 -> 1202[label="",style="solid", color="blue", weight=9]; 1202 -> 768[label="",style="solid", color="blue", weight=3]; 613[label="xy4002 == xy3002",fontsize=16,color="blue",shape="box"];1203[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1203[label="",style="solid", color="blue", weight=9]; 1203 -> 769[label="",style="solid", color="blue", weight=3]; 1204[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1204[label="",style="solid", color="blue", weight=9]; 1204 -> 770[label="",style="solid", color="blue", weight=3]; 1205[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1205[label="",style="solid", color="blue", weight=9]; 1205 -> 771[label="",style="solid", color="blue", weight=3]; 1206[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1206[label="",style="solid", color="blue", weight=9]; 1206 -> 772[label="",style="solid", color="blue", weight=3]; 1207[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1207[label="",style="solid", color="blue", weight=9]; 1207 -> 773[label="",style="solid", color="blue", weight=3]; 1208[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1208[label="",style="solid", color="blue", weight=9]; 1208 -> 774[label="",style="solid", color="blue", weight=3]; 1209[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1209[label="",style="solid", color="blue", weight=9]; 1209 -> 775[label="",style="solid", color="blue", weight=3]; 1210[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1210[label="",style="solid", color="blue", weight=9]; 1210 -> 776[label="",style="solid", color="blue", weight=3]; 1211[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1211[label="",style="solid", color="blue", weight=9]; 1211 -> 777[label="",style="solid", color="blue", weight=3]; 1212[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1212[label="",style="solid", color="blue", weight=9]; 1212 -> 778[label="",style="solid", color="blue", weight=3]; 1213[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1213[label="",style="solid", color="blue", weight=9]; 1213 -> 779[label="",style="solid", color="blue", weight=3]; 1214[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1214[label="",style="solid", color="blue", weight=9]; 1214 -> 780[label="",style="solid", color="blue", weight=3]; 1215[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1215[label="",style="solid", color="blue", weight=9]; 1215 -> 781[label="",style="solid", color="blue", weight=3]; 1216[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];613 -> 1216[label="",style="solid", color="blue", weight=9]; 1216 -> 782[label="",style="solid", color="blue", weight=3]; 614 -> 345[label="",style="dashed", color="red", weight=0]; 614[label="xy4000 == xy3000",fontsize=16,color="magenta"];614 -> 783[label="",style="dashed", color="magenta", weight=3]; 614 -> 784[label="",style="dashed", color="magenta", weight=3]; 615 -> 346[label="",style="dashed", color="red", weight=0]; 615[label="xy4000 == xy3000",fontsize=16,color="magenta"];615 -> 785[label="",style="dashed", color="magenta", weight=3]; 615 -> 786[label="",style="dashed", color="magenta", weight=3]; 616 -> 347[label="",style="dashed", color="red", weight=0]; 616[label="xy4000 == xy3000",fontsize=16,color="magenta"];616 -> 787[label="",style="dashed", color="magenta", weight=3]; 616 -> 788[label="",style="dashed", color="magenta", weight=3]; 617 -> 348[label="",style="dashed", color="red", weight=0]; 617[label="xy4000 == xy3000",fontsize=16,color="magenta"];617 -> 789[label="",style="dashed", color="magenta", weight=3]; 617 -> 790[label="",style="dashed", color="magenta", weight=3]; 618 -> 349[label="",style="dashed", color="red", weight=0]; 618[label="xy4000 == xy3000",fontsize=16,color="magenta"];618 -> 791[label="",style="dashed", color="magenta", weight=3]; 618 -> 792[label="",style="dashed", color="magenta", weight=3]; 619 -> 350[label="",style="dashed", color="red", weight=0]; 619[label="xy4000 == xy3000",fontsize=16,color="magenta"];619 -> 793[label="",style="dashed", color="magenta", weight=3]; 619 -> 794[label="",style="dashed", color="magenta", weight=3]; 620 -> 351[label="",style="dashed", color="red", weight=0]; 620[label="xy4000 == xy3000",fontsize=16,color="magenta"];620 -> 795[label="",style="dashed", color="magenta", weight=3]; 620 -> 796[label="",style="dashed", color="magenta", weight=3]; 621 -> 352[label="",style="dashed", color="red", weight=0]; 621[label="xy4000 == xy3000",fontsize=16,color="magenta"];621 -> 797[label="",style="dashed", color="magenta", weight=3]; 621 -> 798[label="",style="dashed", color="magenta", weight=3]; 622 -> 353[label="",style="dashed", color="red", weight=0]; 622[label="xy4000 == xy3000",fontsize=16,color="magenta"];622 -> 799[label="",style="dashed", color="magenta", weight=3]; 622 -> 800[label="",style="dashed", color="magenta", weight=3]; 623 -> 354[label="",style="dashed", color="red", weight=0]; 623[label="xy4000 == xy3000",fontsize=16,color="magenta"];623 -> 801[label="",style="dashed", color="magenta", weight=3]; 623 -> 802[label="",style="dashed", color="magenta", weight=3]; 624 -> 355[label="",style="dashed", color="red", weight=0]; 624[label="xy4000 == xy3000",fontsize=16,color="magenta"];624 -> 803[label="",style="dashed", color="magenta", weight=3]; 624 -> 804[label="",style="dashed", color="magenta", weight=3]; 625 -> 356[label="",style="dashed", color="red", weight=0]; 625[label="xy4000 == xy3000",fontsize=16,color="magenta"];625 -> 805[label="",style="dashed", color="magenta", weight=3]; 625 -> 806[label="",style="dashed", color="magenta", weight=3]; 626 -> 342[label="",style="dashed", color="red", weight=0]; 626[label="xy4000 == xy3000",fontsize=16,color="magenta"];626 -> 807[label="",style="dashed", color="magenta", weight=3]; 626 -> 808[label="",style="dashed", color="magenta", weight=3]; 627 -> 358[label="",style="dashed", color="red", weight=0]; 627[label="xy4000 == xy3000",fontsize=16,color="magenta"];627 -> 809[label="",style="dashed", color="magenta", weight=3]; 627 -> 810[label="",style="dashed", color="magenta", weight=3]; 628 -> 345[label="",style="dashed", color="red", weight=0]; 628[label="xy4001 == xy3001",fontsize=16,color="magenta"];628 -> 811[label="",style="dashed", color="magenta", weight=3]; 628 -> 812[label="",style="dashed", color="magenta", weight=3]; 629 -> 346[label="",style="dashed", color="red", weight=0]; 629[label="xy4001 == xy3001",fontsize=16,color="magenta"];629 -> 813[label="",style="dashed", color="magenta", weight=3]; 629 -> 814[label="",style="dashed", color="magenta", weight=3]; 630 -> 347[label="",style="dashed", color="red", weight=0]; 630[label="xy4001 == xy3001",fontsize=16,color="magenta"];630 -> 815[label="",style="dashed", color="magenta", weight=3]; 630 -> 816[label="",style="dashed", color="magenta", weight=3]; 631 -> 348[label="",style="dashed", color="red", weight=0]; 631[label="xy4001 == xy3001",fontsize=16,color="magenta"];631 -> 817[label="",style="dashed", color="magenta", weight=3]; 631 -> 818[label="",style="dashed", color="magenta", weight=3]; 632 -> 349[label="",style="dashed", color="red", weight=0]; 632[label="xy4001 == xy3001",fontsize=16,color="magenta"];632 -> 819[label="",style="dashed", color="magenta", weight=3]; 632 -> 820[label="",style="dashed", color="magenta", weight=3]; 633 -> 350[label="",style="dashed", color="red", weight=0]; 633[label="xy4001 == xy3001",fontsize=16,color="magenta"];633 -> 821[label="",style="dashed", color="magenta", weight=3]; 633 -> 822[label="",style="dashed", color="magenta", weight=3]; 634 -> 351[label="",style="dashed", color="red", weight=0]; 634[label="xy4001 == xy3001",fontsize=16,color="magenta"];634 -> 823[label="",style="dashed", color="magenta", weight=3]; 634 -> 824[label="",style="dashed", color="magenta", weight=3]; 635 -> 352[label="",style="dashed", color="red", weight=0]; 635[label="xy4001 == xy3001",fontsize=16,color="magenta"];635 -> 825[label="",style="dashed", color="magenta", weight=3]; 635 -> 826[label="",style="dashed", color="magenta", weight=3]; 636 -> 353[label="",style="dashed", color="red", weight=0]; 636[label="xy4001 == xy3001",fontsize=16,color="magenta"];636 -> 827[label="",style="dashed", color="magenta", weight=3]; 636 -> 828[label="",style="dashed", color="magenta", weight=3]; 637 -> 354[label="",style="dashed", color="red", weight=0]; 637[label="xy4001 == xy3001",fontsize=16,color="magenta"];637 -> 829[label="",style="dashed", color="magenta", weight=3]; 637 -> 830[label="",style="dashed", color="magenta", weight=3]; 638 -> 355[label="",style="dashed", color="red", weight=0]; 638[label="xy4001 == xy3001",fontsize=16,color="magenta"];638 -> 831[label="",style="dashed", color="magenta", weight=3]; 638 -> 832[label="",style="dashed", color="magenta", weight=3]; 639 -> 356[label="",style="dashed", color="red", weight=0]; 639[label="xy4001 == xy3001",fontsize=16,color="magenta"];639 -> 833[label="",style="dashed", color="magenta", weight=3]; 639 -> 834[label="",style="dashed", color="magenta", weight=3]; 640 -> 342[label="",style="dashed", color="red", weight=0]; 640[label="xy4001 == xy3001",fontsize=16,color="magenta"];640 -> 835[label="",style="dashed", color="magenta", weight=3]; 640 -> 836[label="",style="dashed", color="magenta", weight=3]; 641 -> 358[label="",style="dashed", color="red", weight=0]; 641[label="xy4001 == xy3001",fontsize=16,color="magenta"];641 -> 837[label="",style="dashed", color="magenta", weight=3]; 641 -> 838[label="",style="dashed", color="magenta", weight=3]; 642[label="xy3000",fontsize=16,color="green",shape="box"];643[label="xy4000",fontsize=16,color="green",shape="box"];644[label="xy3000",fontsize=16,color="green",shape="box"];645[label="xy4000",fontsize=16,color="green",shape="box"];646[label="xy3000",fontsize=16,color="green",shape="box"];647[label="xy4000",fontsize=16,color="green",shape="box"];648[label="xy3000",fontsize=16,color="green",shape="box"];649[label="xy4000",fontsize=16,color="green",shape="box"];650[label="xy3000",fontsize=16,color="green",shape="box"];651[label="xy4000",fontsize=16,color="green",shape="box"];652[label="xy3000",fontsize=16,color="green",shape="box"];653[label="xy4000",fontsize=16,color="green",shape="box"];654[label="xy3000",fontsize=16,color="green",shape="box"];655[label="xy4000",fontsize=16,color="green",shape="box"];656[label="xy3000",fontsize=16,color="green",shape="box"];657[label="xy4000",fontsize=16,color="green",shape="box"];658[label="xy3000",fontsize=16,color="green",shape="box"];659[label="xy4000",fontsize=16,color="green",shape="box"];660[label="xy3000",fontsize=16,color="green",shape="box"];661[label="xy4000",fontsize=16,color="green",shape="box"];662[label="xy3000",fontsize=16,color="green",shape="box"];663[label="xy4000",fontsize=16,color="green",shape="box"];664[label="xy3000",fontsize=16,color="green",shape="box"];665[label="xy4000",fontsize=16,color="green",shape="box"];666[label="xy3000",fontsize=16,color="green",shape="box"];667[label="xy4000",fontsize=16,color="green",shape="box"];668[label="xy3000",fontsize=16,color="green",shape="box"];669[label="xy4000",fontsize=16,color="green",shape="box"];670 -> 349[label="",style="dashed", color="red", weight=0]; 670[label="xy4000 == xy3000",fontsize=16,color="magenta"];670 -> 839[label="",style="dashed", color="magenta", weight=3]; 670 -> 840[label="",style="dashed", color="magenta", weight=3]; 671 -> 358[label="",style="dashed", color="red", weight=0]; 671[label="xy4000 == xy3000",fontsize=16,color="magenta"];671 -> 841[label="",style="dashed", color="magenta", weight=3]; 671 -> 842[label="",style="dashed", color="magenta", weight=3]; 672 -> 349[label="",style="dashed", color="red", weight=0]; 672[label="xy4001 == xy3001",fontsize=16,color="magenta"];672 -> 843[label="",style="dashed", color="magenta", weight=3]; 672 -> 844[label="",style="dashed", color="magenta", weight=3]; 673 -> 358[label="",style="dashed", color="red", weight=0]; 673[label="xy4001 == xy3001",fontsize=16,color="magenta"];673 -> 845[label="",style="dashed", color="magenta", weight=3]; 673 -> 846[label="",style="dashed", color="magenta", weight=3]; 674[label="primEqInt (Pos (Succ xy40000)) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];674 -> 847[label="",style="solid", color="black", weight=3]; 675[label="primEqInt (Pos (Succ xy40000)) (Pos Zero)",fontsize=16,color="black",shape="box"];675 -> 848[label="",style="solid", color="black", weight=3]; 676[label="False",fontsize=16,color="green",shape="box"];677[label="primEqInt (Pos Zero) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];677 -> 849[label="",style="solid", color="black", weight=3]; 678[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];678 -> 850[label="",style="solid", color="black", weight=3]; 679[label="primEqInt (Pos Zero) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];679 -> 851[label="",style="solid", color="black", weight=3]; 680[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];680 -> 852[label="",style="solid", color="black", weight=3]; 681[label="False",fontsize=16,color="green",shape="box"];682[label="primEqInt (Neg (Succ xy40000)) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];682 -> 853[label="",style="solid", color="black", weight=3]; 683[label="primEqInt (Neg (Succ xy40000)) (Neg Zero)",fontsize=16,color="black",shape="box"];683 -> 854[label="",style="solid", color="black", weight=3]; 684[label="primEqInt (Neg Zero) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];684 -> 855[label="",style="solid", color="black", weight=3]; 685[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];685 -> 856[label="",style="solid", color="black", weight=3]; 686[label="primEqInt (Neg Zero) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];686 -> 857[label="",style="solid", color="black", weight=3]; 687[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];687 -> 858[label="",style="solid", color="black", weight=3]; 688[label="xy3010",fontsize=16,color="green",shape="box"];689[label="xy4010",fontsize=16,color="green",shape="box"];690[label="xy3010",fontsize=16,color="green",shape="box"];691[label="xy4010",fontsize=16,color="green",shape="box"];692[label="xy3010",fontsize=16,color="green",shape="box"];693[label="xy4010",fontsize=16,color="green",shape="box"];694[label="xy3010",fontsize=16,color="green",shape="box"];695[label="xy4010",fontsize=16,color="green",shape="box"];696[label="xy3010",fontsize=16,color="green",shape="box"];697[label="xy4010",fontsize=16,color="green",shape="box"];698[label="xy3010",fontsize=16,color="green",shape="box"];699[label="xy4010",fontsize=16,color="green",shape="box"];700[label="xy3010",fontsize=16,color="green",shape="box"];701[label="xy4010",fontsize=16,color="green",shape="box"];702[label="xy3010",fontsize=16,color="green",shape="box"];703[label="xy4010",fontsize=16,color="green",shape="box"];704[label="xy3010",fontsize=16,color="green",shape="box"];705[label="xy4010",fontsize=16,color="green",shape="box"];706[label="xy3010",fontsize=16,color="green",shape="box"];707[label="xy4010",fontsize=16,color="green",shape="box"];708[label="xy3010",fontsize=16,color="green",shape="box"];709[label="xy4010",fontsize=16,color="green",shape="box"];710[label="xy3010",fontsize=16,color="green",shape="box"];711[label="xy4010",fontsize=16,color="green",shape="box"];712[label="xy3010",fontsize=16,color="green",shape="box"];713[label="xy4010",fontsize=16,color="green",shape="box"];714[label="xy3010",fontsize=16,color="green",shape="box"];715[label="xy4010",fontsize=16,color="green",shape="box"];716[label="primEqNat (Succ xy40000) (Succ xy30000)",fontsize=16,color="black",shape="box"];716 -> 859[label="",style="solid", color="black", weight=3]; 717[label="primEqNat (Succ xy40000) Zero",fontsize=16,color="black",shape="box"];717 -> 860[label="",style="solid", color="black", weight=3]; 718[label="primEqNat Zero (Succ xy30000)",fontsize=16,color="black",shape="box"];718 -> 861[label="",style="solid", color="black", weight=3]; 719[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];719 -> 862[label="",style="solid", color="black", weight=3]; 720[label="primMulInt xy4001 xy3000",fontsize=16,color="burlywood",shape="box"];1217[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];720 -> 1217[label="",style="solid", color="burlywood", weight=9]; 1217 -> 863[label="",style="solid", color="burlywood", weight=3]; 1218[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];720 -> 1218[label="",style="solid", color="burlywood", weight=9]; 1218 -> 864[label="",style="solid", color="burlywood", weight=3]; 721[label="xy4000",fontsize=16,color="green",shape="box"];722[label="xy3001",fontsize=16,color="green",shape="box"];723[label="xy4001",fontsize=16,color="green",shape="box"];724[label="xy3000",fontsize=16,color="green",shape="box"];725[label="xy4000",fontsize=16,color="green",shape="box"];726[label="xy3001",fontsize=16,color="green",shape="box"];727[label="xy3000",fontsize=16,color="green",shape="box"];728[label="xy4000",fontsize=16,color="green",shape="box"];729[label="xy3000",fontsize=16,color="green",shape="box"];730[label="xy4000",fontsize=16,color="green",shape="box"];731[label="xy3000",fontsize=16,color="green",shape="box"];732[label="xy4000",fontsize=16,color="green",shape="box"];733[label="xy3000",fontsize=16,color="green",shape="box"];734[label="xy4000",fontsize=16,color="green",shape="box"];735[label="xy3000",fontsize=16,color="green",shape="box"];736[label="xy4000",fontsize=16,color="green",shape="box"];737[label="xy3000",fontsize=16,color="green",shape="box"];738[label="xy4000",fontsize=16,color="green",shape="box"];739[label="xy3000",fontsize=16,color="green",shape="box"];740[label="xy4000",fontsize=16,color="green",shape="box"];741[label="xy3000",fontsize=16,color="green",shape="box"];742[label="xy4000",fontsize=16,color="green",shape="box"];743[label="xy3000",fontsize=16,color="green",shape="box"];744[label="xy4000",fontsize=16,color="green",shape="box"];745[label="xy3000",fontsize=16,color="green",shape="box"];746[label="xy4000",fontsize=16,color="green",shape="box"];747[label="xy3000",fontsize=16,color="green",shape="box"];748[label="xy4000",fontsize=16,color="green",shape="box"];749[label="xy3000",fontsize=16,color="green",shape="box"];750[label="xy4000",fontsize=16,color="green",shape="box"];751[label="xy3000",fontsize=16,color="green",shape="box"];752[label="xy4000",fontsize=16,color="green",shape="box"];753[label="xy3000",fontsize=16,color="green",shape="box"];754[label="xy4000",fontsize=16,color="green",shape="box"];755 -> 345[label="",style="dashed", color="red", weight=0]; 755[label="xy4001 == xy3001",fontsize=16,color="magenta"];755 -> 865[label="",style="dashed", color="magenta", weight=3]; 755 -> 866[label="",style="dashed", color="magenta", weight=3]; 756 -> 346[label="",style="dashed", color="red", weight=0]; 756[label="xy4001 == xy3001",fontsize=16,color="magenta"];756 -> 867[label="",style="dashed", color="magenta", weight=3]; 756 -> 868[label="",style="dashed", color="magenta", weight=3]; 757 -> 347[label="",style="dashed", color="red", weight=0]; 757[label="xy4001 == xy3001",fontsize=16,color="magenta"];757 -> 869[label="",style="dashed", color="magenta", weight=3]; 757 -> 870[label="",style="dashed", color="magenta", weight=3]; 758 -> 348[label="",style="dashed", color="red", weight=0]; 758[label="xy4001 == xy3001",fontsize=16,color="magenta"];758 -> 871[label="",style="dashed", color="magenta", weight=3]; 758 -> 872[label="",style="dashed", color="magenta", weight=3]; 759 -> 349[label="",style="dashed", color="red", weight=0]; 759[label="xy4001 == xy3001",fontsize=16,color="magenta"];759 -> 873[label="",style="dashed", color="magenta", weight=3]; 759 -> 874[label="",style="dashed", color="magenta", weight=3]; 760 -> 350[label="",style="dashed", color="red", weight=0]; 760[label="xy4001 == xy3001",fontsize=16,color="magenta"];760 -> 875[label="",style="dashed", color="magenta", weight=3]; 760 -> 876[label="",style="dashed", color="magenta", weight=3]; 761 -> 351[label="",style="dashed", color="red", weight=0]; 761[label="xy4001 == xy3001",fontsize=16,color="magenta"];761 -> 877[label="",style="dashed", color="magenta", weight=3]; 761 -> 878[label="",style="dashed", color="magenta", weight=3]; 762 -> 352[label="",style="dashed", color="red", weight=0]; 762[label="xy4001 == xy3001",fontsize=16,color="magenta"];762 -> 879[label="",style="dashed", color="magenta", weight=3]; 762 -> 880[label="",style="dashed", color="magenta", weight=3]; 763 -> 353[label="",style="dashed", color="red", weight=0]; 763[label="xy4001 == xy3001",fontsize=16,color="magenta"];763 -> 881[label="",style="dashed", color="magenta", weight=3]; 763 -> 882[label="",style="dashed", color="magenta", weight=3]; 764 -> 354[label="",style="dashed", color="red", weight=0]; 764[label="xy4001 == xy3001",fontsize=16,color="magenta"];764 -> 883[label="",style="dashed", color="magenta", weight=3]; 764 -> 884[label="",style="dashed", color="magenta", weight=3]; 765 -> 355[label="",style="dashed", color="red", weight=0]; 765[label="xy4001 == xy3001",fontsize=16,color="magenta"];765 -> 885[label="",style="dashed", color="magenta", weight=3]; 765 -> 886[label="",style="dashed", color="magenta", weight=3]; 766 -> 356[label="",style="dashed", color="red", weight=0]; 766[label="xy4001 == xy3001",fontsize=16,color="magenta"];766 -> 887[label="",style="dashed", color="magenta", weight=3]; 766 -> 888[label="",style="dashed", color="magenta", weight=3]; 767 -> 342[label="",style="dashed", color="red", weight=0]; 767[label="xy4001 == xy3001",fontsize=16,color="magenta"];767 -> 889[label="",style="dashed", color="magenta", weight=3]; 767 -> 890[label="",style="dashed", color="magenta", weight=3]; 768 -> 358[label="",style="dashed", color="red", weight=0]; 768[label="xy4001 == xy3001",fontsize=16,color="magenta"];768 -> 891[label="",style="dashed", color="magenta", weight=3]; 768 -> 892[label="",style="dashed", color="magenta", weight=3]; 769 -> 345[label="",style="dashed", color="red", weight=0]; 769[label="xy4002 == xy3002",fontsize=16,color="magenta"];769 -> 893[label="",style="dashed", color="magenta", weight=3]; 769 -> 894[label="",style="dashed", color="magenta", weight=3]; 770 -> 346[label="",style="dashed", color="red", weight=0]; 770[label="xy4002 == xy3002",fontsize=16,color="magenta"];770 -> 895[label="",style="dashed", color="magenta", weight=3]; 770 -> 896[label="",style="dashed", color="magenta", weight=3]; 771 -> 347[label="",style="dashed", color="red", weight=0]; 771[label="xy4002 == xy3002",fontsize=16,color="magenta"];771 -> 897[label="",style="dashed", color="magenta", weight=3]; 771 -> 898[label="",style="dashed", color="magenta", weight=3]; 772 -> 348[label="",style="dashed", color="red", weight=0]; 772[label="xy4002 == xy3002",fontsize=16,color="magenta"];772 -> 899[label="",style="dashed", color="magenta", weight=3]; 772 -> 900[label="",style="dashed", color="magenta", weight=3]; 773 -> 349[label="",style="dashed", color="red", weight=0]; 773[label="xy4002 == xy3002",fontsize=16,color="magenta"];773 -> 901[label="",style="dashed", color="magenta", weight=3]; 773 -> 902[label="",style="dashed", color="magenta", weight=3]; 774 -> 350[label="",style="dashed", color="red", weight=0]; 774[label="xy4002 == xy3002",fontsize=16,color="magenta"];774 -> 903[label="",style="dashed", color="magenta", weight=3]; 774 -> 904[label="",style="dashed", color="magenta", weight=3]; 775 -> 351[label="",style="dashed", color="red", weight=0]; 775[label="xy4002 == xy3002",fontsize=16,color="magenta"];775 -> 905[label="",style="dashed", color="magenta", weight=3]; 775 -> 906[label="",style="dashed", color="magenta", weight=3]; 776 -> 352[label="",style="dashed", color="red", weight=0]; 776[label="xy4002 == xy3002",fontsize=16,color="magenta"];776 -> 907[label="",style="dashed", color="magenta", weight=3]; 776 -> 908[label="",style="dashed", color="magenta", weight=3]; 777 -> 353[label="",style="dashed", color="red", weight=0]; 777[label="xy4002 == xy3002",fontsize=16,color="magenta"];777 -> 909[label="",style="dashed", color="magenta", weight=3]; 777 -> 910[label="",style="dashed", color="magenta", weight=3]; 778 -> 354[label="",style="dashed", color="red", weight=0]; 778[label="xy4002 == xy3002",fontsize=16,color="magenta"];778 -> 911[label="",style="dashed", color="magenta", weight=3]; 778 -> 912[label="",style="dashed", color="magenta", weight=3]; 779 -> 355[label="",style="dashed", color="red", weight=0]; 779[label="xy4002 == xy3002",fontsize=16,color="magenta"];779 -> 913[label="",style="dashed", color="magenta", weight=3]; 779 -> 914[label="",style="dashed", color="magenta", weight=3]; 780 -> 356[label="",style="dashed", color="red", weight=0]; 780[label="xy4002 == xy3002",fontsize=16,color="magenta"];780 -> 915[label="",style="dashed", color="magenta", weight=3]; 780 -> 916[label="",style="dashed", color="magenta", weight=3]; 781 -> 342[label="",style="dashed", color="red", weight=0]; 781[label="xy4002 == xy3002",fontsize=16,color="magenta"];781 -> 917[label="",style="dashed", color="magenta", weight=3]; 781 -> 918[label="",style="dashed", color="magenta", weight=3]; 782 -> 358[label="",style="dashed", color="red", weight=0]; 782[label="xy4002 == xy3002",fontsize=16,color="magenta"];782 -> 919[label="",style="dashed", color="magenta", weight=3]; 782 -> 920[label="",style="dashed", color="magenta", weight=3]; 783[label="xy3000",fontsize=16,color="green",shape="box"];784[label="xy4000",fontsize=16,color="green",shape="box"];785[label="xy3000",fontsize=16,color="green",shape="box"];786[label="xy4000",fontsize=16,color="green",shape="box"];787[label="xy3000",fontsize=16,color="green",shape="box"];788[label="xy4000",fontsize=16,color="green",shape="box"];789[label="xy3000",fontsize=16,color="green",shape="box"];790[label="xy4000",fontsize=16,color="green",shape="box"];791[label="xy3000",fontsize=16,color="green",shape="box"];792[label="xy4000",fontsize=16,color="green",shape="box"];793[label="xy3000",fontsize=16,color="green",shape="box"];794[label="xy4000",fontsize=16,color="green",shape="box"];795[label="xy3000",fontsize=16,color="green",shape="box"];796[label="xy4000",fontsize=16,color="green",shape="box"];797[label="xy3000",fontsize=16,color="green",shape="box"];798[label="xy4000",fontsize=16,color="green",shape="box"];799[label="xy3000",fontsize=16,color="green",shape="box"];800[label="xy4000",fontsize=16,color="green",shape="box"];801[label="xy3000",fontsize=16,color="green",shape="box"];802[label="xy4000",fontsize=16,color="green",shape="box"];803[label="xy3000",fontsize=16,color="green",shape="box"];804[label="xy4000",fontsize=16,color="green",shape="box"];805[label="xy3000",fontsize=16,color="green",shape="box"];806[label="xy4000",fontsize=16,color="green",shape="box"];807[label="xy3000",fontsize=16,color="green",shape="box"];808[label="xy4000",fontsize=16,color="green",shape="box"];809[label="xy3000",fontsize=16,color="green",shape="box"];810[label="xy4000",fontsize=16,color="green",shape="box"];811[label="xy3001",fontsize=16,color="green",shape="box"];812[label="xy4001",fontsize=16,color="green",shape="box"];813[label="xy3001",fontsize=16,color="green",shape="box"];814[label="xy4001",fontsize=16,color="green",shape="box"];815[label="xy3001",fontsize=16,color="green",shape="box"];816[label="xy4001",fontsize=16,color="green",shape="box"];817[label="xy3001",fontsize=16,color="green",shape="box"];818[label="xy4001",fontsize=16,color="green",shape="box"];819[label="xy3001",fontsize=16,color="green",shape="box"];820[label="xy4001",fontsize=16,color="green",shape="box"];821[label="xy3001",fontsize=16,color="green",shape="box"];822[label="xy4001",fontsize=16,color="green",shape="box"];823[label="xy3001",fontsize=16,color="green",shape="box"];824[label="xy4001",fontsize=16,color="green",shape="box"];825[label="xy3001",fontsize=16,color="green",shape="box"];826[label="xy4001",fontsize=16,color="green",shape="box"];827[label="xy3001",fontsize=16,color="green",shape="box"];828[label="xy4001",fontsize=16,color="green",shape="box"];829[label="xy3001",fontsize=16,color="green",shape="box"];830[label="xy4001",fontsize=16,color="green",shape="box"];831[label="xy3001",fontsize=16,color="green",shape="box"];832[label="xy4001",fontsize=16,color="green",shape="box"];833[label="xy3001",fontsize=16,color="green",shape="box"];834[label="xy4001",fontsize=16,color="green",shape="box"];835[label="xy3001",fontsize=16,color="green",shape="box"];836[label="xy4001",fontsize=16,color="green",shape="box"];837[label="xy3001",fontsize=16,color="green",shape="box"];838[label="xy4001",fontsize=16,color="green",shape="box"];839[label="xy3000",fontsize=16,color="green",shape="box"];840[label="xy4000",fontsize=16,color="green",shape="box"];841[label="xy3000",fontsize=16,color="green",shape="box"];842[label="xy4000",fontsize=16,color="green",shape="box"];843[label="xy3001",fontsize=16,color="green",shape="box"];844[label="xy4001",fontsize=16,color="green",shape="box"];845[label="xy3001",fontsize=16,color="green",shape="box"];846[label="xy4001",fontsize=16,color="green",shape="box"];847 -> 487[label="",style="dashed", color="red", weight=0]; 847[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];847 -> 921[label="",style="dashed", color="magenta", weight=3]; 847 -> 922[label="",style="dashed", color="magenta", weight=3]; 848[label="False",fontsize=16,color="green",shape="box"];849[label="False",fontsize=16,color="green",shape="box"];850[label="True",fontsize=16,color="green",shape="box"];851[label="False",fontsize=16,color="green",shape="box"];852[label="True",fontsize=16,color="green",shape="box"];853 -> 487[label="",style="dashed", color="red", weight=0]; 853[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];853 -> 923[label="",style="dashed", color="magenta", weight=3]; 853 -> 924[label="",style="dashed", color="magenta", weight=3]; 854[label="False",fontsize=16,color="green",shape="box"];855[label="False",fontsize=16,color="green",shape="box"];856[label="True",fontsize=16,color="green",shape="box"];857[label="False",fontsize=16,color="green",shape="box"];858[label="True",fontsize=16,color="green",shape="box"];859 -> 487[label="",style="dashed", color="red", weight=0]; 859[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];859 -> 925[label="",style="dashed", color="magenta", weight=3]; 859 -> 926[label="",style="dashed", color="magenta", weight=3]; 860[label="False",fontsize=16,color="green",shape="box"];861[label="False",fontsize=16,color="green",shape="box"];862[label="True",fontsize=16,color="green",shape="box"];863[label="primMulInt (Pos xy40010) xy3000",fontsize=16,color="burlywood",shape="box"];1219[label="xy3000/Pos xy30000",fontsize=10,color="white",style="solid",shape="box"];863 -> 1219[label="",style="solid", color="burlywood", weight=9]; 1219 -> 927[label="",style="solid", color="burlywood", weight=3]; 1220[label="xy3000/Neg xy30000",fontsize=10,color="white",style="solid",shape="box"];863 -> 1220[label="",style="solid", color="burlywood", weight=9]; 1220 -> 928[label="",style="solid", color="burlywood", weight=3]; 864[label="primMulInt (Neg xy40010) xy3000",fontsize=16,color="burlywood",shape="box"];1221[label="xy3000/Pos xy30000",fontsize=10,color="white",style="solid",shape="box"];864 -> 1221[label="",style="solid", color="burlywood", weight=9]; 1221 -> 929[label="",style="solid", color="burlywood", weight=3]; 1222[label="xy3000/Neg xy30000",fontsize=10,color="white",style="solid",shape="box"];864 -> 1222[label="",style="solid", color="burlywood", weight=9]; 1222 -> 930[label="",style="solid", color="burlywood", weight=3]; 865[label="xy3001",fontsize=16,color="green",shape="box"];866[label="xy4001",fontsize=16,color="green",shape="box"];867[label="xy3001",fontsize=16,color="green",shape="box"];868[label="xy4001",fontsize=16,color="green",shape="box"];869[label="xy3001",fontsize=16,color="green",shape="box"];870[label="xy4001",fontsize=16,color="green",shape="box"];871[label="xy3001",fontsize=16,color="green",shape="box"];872[label="xy4001",fontsize=16,color="green",shape="box"];873[label="xy3001",fontsize=16,color="green",shape="box"];874[label="xy4001",fontsize=16,color="green",shape="box"];875[label="xy3001",fontsize=16,color="green",shape="box"];876[label="xy4001",fontsize=16,color="green",shape="box"];877[label="xy3001",fontsize=16,color="green",shape="box"];878[label="xy4001",fontsize=16,color="green",shape="box"];879[label="xy3001",fontsize=16,color="green",shape="box"];880[label="xy4001",fontsize=16,color="green",shape="box"];881[label="xy3001",fontsize=16,color="green",shape="box"];882[label="xy4001",fontsize=16,color="green",shape="box"];883[label="xy3001",fontsize=16,color="green",shape="box"];884[label="xy4001",fontsize=16,color="green",shape="box"];885[label="xy3001",fontsize=16,color="green",shape="box"];886[label="xy4001",fontsize=16,color="green",shape="box"];887[label="xy3001",fontsize=16,color="green",shape="box"];888[label="xy4001",fontsize=16,color="green",shape="box"];889[label="xy3001",fontsize=16,color="green",shape="box"];890[label="xy4001",fontsize=16,color="green",shape="box"];891[label="xy3001",fontsize=16,color="green",shape="box"];892[label="xy4001",fontsize=16,color="green",shape="box"];893[label="xy3002",fontsize=16,color="green",shape="box"];894[label="xy4002",fontsize=16,color="green",shape="box"];895[label="xy3002",fontsize=16,color="green",shape="box"];896[label="xy4002",fontsize=16,color="green",shape="box"];897[label="xy3002",fontsize=16,color="green",shape="box"];898[label="xy4002",fontsize=16,color="green",shape="box"];899[label="xy3002",fontsize=16,color="green",shape="box"];900[label="xy4002",fontsize=16,color="green",shape="box"];901[label="xy3002",fontsize=16,color="green",shape="box"];902[label="xy4002",fontsize=16,color="green",shape="box"];903[label="xy3002",fontsize=16,color="green",shape="box"];904[label="xy4002",fontsize=16,color="green",shape="box"];905[label="xy3002",fontsize=16,color="green",shape="box"];906[label="xy4002",fontsize=16,color="green",shape="box"];907[label="xy3002",fontsize=16,color="green",shape="box"];908[label="xy4002",fontsize=16,color="green",shape="box"];909[label="xy3002",fontsize=16,color="green",shape="box"];910[label="xy4002",fontsize=16,color="green",shape="box"];911[label="xy3002",fontsize=16,color="green",shape="box"];912[label="xy4002",fontsize=16,color="green",shape="box"];913[label="xy3002",fontsize=16,color="green",shape="box"];914[label="xy4002",fontsize=16,color="green",shape="box"];915[label="xy3002",fontsize=16,color="green",shape="box"];916[label="xy4002",fontsize=16,color="green",shape="box"];917[label="xy3002",fontsize=16,color="green",shape="box"];918[label="xy4002",fontsize=16,color="green",shape="box"];919[label="xy3002",fontsize=16,color="green",shape="box"];920[label="xy4002",fontsize=16,color="green",shape="box"];921[label="xy30000",fontsize=16,color="green",shape="box"];922[label="xy40000",fontsize=16,color="green",shape="box"];923[label="xy30000",fontsize=16,color="green",shape="box"];924[label="xy40000",fontsize=16,color="green",shape="box"];925[label="xy30000",fontsize=16,color="green",shape="box"];926[label="xy40000",fontsize=16,color="green",shape="box"];927[label="primMulInt (Pos xy40010) (Pos xy30000)",fontsize=16,color="black",shape="box"];927 -> 931[label="",style="solid", color="black", weight=3]; 928[label="primMulInt (Pos xy40010) (Neg xy30000)",fontsize=16,color="black",shape="box"];928 -> 932[label="",style="solid", color="black", weight=3]; 929[label="primMulInt (Neg xy40010) (Pos xy30000)",fontsize=16,color="black",shape="box"];929 -> 933[label="",style="solid", color="black", weight=3]; 930[label="primMulInt (Neg xy40010) (Neg xy30000)",fontsize=16,color="black",shape="box"];930 -> 934[label="",style="solid", color="black", weight=3]; 931[label="Pos (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];931 -> 935[label="",style="dashed", color="green", weight=3]; 932[label="Neg (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];932 -> 936[label="",style="dashed", color="green", weight=3]; 933[label="Neg (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];933 -> 937[label="",style="dashed", color="green", weight=3]; 934[label="Pos (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];934 -> 938[label="",style="dashed", color="green", weight=3]; 935[label="primMulNat xy40010 xy30000",fontsize=16,color="burlywood",shape="triangle"];1223[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];935 -> 1223[label="",style="solid", color="burlywood", weight=9]; 1223 -> 939[label="",style="solid", color="burlywood", weight=3]; 1224[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];935 -> 1224[label="",style="solid", color="burlywood", weight=9]; 1224 -> 940[label="",style="solid", color="burlywood", weight=3]; 936 -> 935[label="",style="dashed", color="red", weight=0]; 936[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];936 -> 941[label="",style="dashed", color="magenta", weight=3]; 937 -> 935[label="",style="dashed", color="red", weight=0]; 937[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];937 -> 942[label="",style="dashed", color="magenta", weight=3]; 938 -> 935[label="",style="dashed", color="red", weight=0]; 938[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];938 -> 943[label="",style="dashed", color="magenta", weight=3]; 938 -> 944[label="",style="dashed", color="magenta", weight=3]; 939[label="primMulNat (Succ xy400100) xy30000",fontsize=16,color="burlywood",shape="box"];1225[label="xy30000/Succ xy300000",fontsize=10,color="white",style="solid",shape="box"];939 -> 1225[label="",style="solid", color="burlywood", weight=9]; 1225 -> 945[label="",style="solid", color="burlywood", weight=3]; 1226[label="xy30000/Zero",fontsize=10,color="white",style="solid",shape="box"];939 -> 1226[label="",style="solid", color="burlywood", weight=9]; 1226 -> 946[label="",style="solid", color="burlywood", weight=3]; 940[label="primMulNat Zero xy30000",fontsize=16,color="burlywood",shape="box"];1227[label="xy30000/Succ xy300000",fontsize=10,color="white",style="solid",shape="box"];940 -> 1227[label="",style="solid", color="burlywood", weight=9]; 1227 -> 947[label="",style="solid", color="burlywood", weight=3]; 1228[label="xy30000/Zero",fontsize=10,color="white",style="solid",shape="box"];940 -> 1228[label="",style="solid", color="burlywood", weight=9]; 1228 -> 948[label="",style="solid", color="burlywood", weight=3]; 941[label="xy30000",fontsize=16,color="green",shape="box"];942[label="xy40010",fontsize=16,color="green",shape="box"];943[label="xy30000",fontsize=16,color="green",shape="box"];944[label="xy40010",fontsize=16,color="green",shape="box"];945[label="primMulNat (Succ xy400100) (Succ xy300000)",fontsize=16,color="black",shape="box"];945 -> 949[label="",style="solid", color="black", weight=3]; 946[label="primMulNat (Succ xy400100) Zero",fontsize=16,color="black",shape="box"];946 -> 950[label="",style="solid", color="black", weight=3]; 947[label="primMulNat Zero (Succ xy300000)",fontsize=16,color="black",shape="box"];947 -> 951[label="",style="solid", color="black", weight=3]; 948[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];948 -> 952[label="",style="solid", color="black", weight=3]; 949 -> 953[label="",style="dashed", color="red", weight=0]; 949[label="primPlusNat (primMulNat xy400100 (Succ xy300000)) (Succ xy300000)",fontsize=16,color="magenta"];949 -> 954[label="",style="dashed", color="magenta", weight=3]; 950[label="Zero",fontsize=16,color="green",shape="box"];951[label="Zero",fontsize=16,color="green",shape="box"];952[label="Zero",fontsize=16,color="green",shape="box"];954 -> 935[label="",style="dashed", color="red", weight=0]; 954[label="primMulNat xy400100 (Succ xy300000)",fontsize=16,color="magenta"];954 -> 955[label="",style="dashed", color="magenta", weight=3]; 954 -> 956[label="",style="dashed", color="magenta", weight=3]; 953[label="primPlusNat xy32 (Succ xy300000)",fontsize=16,color="burlywood",shape="triangle"];1229[label="xy32/Succ xy320",fontsize=10,color="white",style="solid",shape="box"];953 -> 1229[label="",style="solid", color="burlywood", weight=9]; 1229 -> 957[label="",style="solid", color="burlywood", weight=3]; 1230[label="xy32/Zero",fontsize=10,color="white",style="solid",shape="box"];953 -> 1230[label="",style="solid", color="burlywood", weight=9]; 1230 -> 958[label="",style="solid", color="burlywood", weight=3]; 955[label="Succ xy300000",fontsize=16,color="green",shape="box"];956[label="xy400100",fontsize=16,color="green",shape="box"];957[label="primPlusNat (Succ xy320) (Succ xy300000)",fontsize=16,color="black",shape="box"];957 -> 959[label="",style="solid", color="black", weight=3]; 958[label="primPlusNat Zero (Succ xy300000)",fontsize=16,color="black",shape="box"];958 -> 960[label="",style="solid", color="black", weight=3]; 959[label="Succ (Succ (primPlusNat xy320 xy300000))",fontsize=16,color="green",shape="box"];959 -> 961[label="",style="dashed", color="green", weight=3]; 960[label="Succ xy300000",fontsize=16,color="green",shape="box"];961[label="primPlusNat xy320 xy300000",fontsize=16,color="burlywood",shape="triangle"];1231[label="xy320/Succ xy3200",fontsize=10,color="white",style="solid",shape="box"];961 -> 1231[label="",style="solid", color="burlywood", weight=9]; 1231 -> 962[label="",style="solid", color="burlywood", weight=3]; 1232[label="xy320/Zero",fontsize=10,color="white",style="solid",shape="box"];961 -> 1232[label="",style="solid", color="burlywood", weight=9]; 1232 -> 963[label="",style="solid", color="burlywood", weight=3]; 962[label="primPlusNat (Succ xy3200) xy300000",fontsize=16,color="burlywood",shape="box"];1233[label="xy300000/Succ xy3000000",fontsize=10,color="white",style="solid",shape="box"];962 -> 1233[label="",style="solid", color="burlywood", weight=9]; 1233 -> 964[label="",style="solid", color="burlywood", weight=3]; 1234[label="xy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];962 -> 1234[label="",style="solid", color="burlywood", weight=9]; 1234 -> 965[label="",style="solid", color="burlywood", weight=3]; 963[label="primPlusNat Zero xy300000",fontsize=16,color="burlywood",shape="box"];1235[label="xy300000/Succ xy3000000",fontsize=10,color="white",style="solid",shape="box"];963 -> 1235[label="",style="solid", color="burlywood", weight=9]; 1235 -> 966[label="",style="solid", color="burlywood", weight=3]; 1236[label="xy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];963 -> 1236[label="",style="solid", color="burlywood", weight=9]; 1236 -> 967[label="",style="solid", color="burlywood", weight=3]; 964[label="primPlusNat (Succ xy3200) (Succ xy3000000)",fontsize=16,color="black",shape="box"];964 -> 968[label="",style="solid", color="black", weight=3]; 965[label="primPlusNat (Succ xy3200) Zero",fontsize=16,color="black",shape="box"];965 -> 969[label="",style="solid", color="black", weight=3]; 966[label="primPlusNat Zero (Succ xy3000000)",fontsize=16,color="black",shape="box"];966 -> 970[label="",style="solid", color="black", weight=3]; 967[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];967 -> 971[label="",style="solid", color="black", weight=3]; 968[label="Succ (Succ (primPlusNat xy3200 xy3000000))",fontsize=16,color="green",shape="box"];968 -> 972[label="",style="dashed", color="green", weight=3]; 969[label="Succ xy3200",fontsize=16,color="green",shape="box"];970[label="Succ xy3000000",fontsize=16,color="green",shape="box"];971[label="Zero",fontsize=16,color="green",shape="box"];972 -> 961[label="",style="dashed", color="red", weight=0]; 972[label="primPlusNat xy3200 xy3000000",fontsize=16,color="magenta"];972 -> 973[label="",style="dashed", color="magenta", weight=3]; 972 -> 974[label="",style="dashed", color="magenta", weight=3]; 973[label="xy3000000",fontsize=16,color="green",shape="box"];974[label="xy3200",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldl(xy3, :(xy40, xy41), ba) -> new_foldl(new_deleteBy1(xy40, xy3, ba), xy41, ba) The TRS R consists of the following rules: new_esEs21(xy4010, xy3010, app(app(ty_Either, eb), ec)) -> new_esEs6(xy4010, xy3010, eb, ec) new_esEs16(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs14(GT, GT) -> True new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(app(ty_@2, bad), bae)) -> new_esEs15(xy4002, xy3002, bad, bae) new_esEs22(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs19(xy4000, xy3000, app(ty_Ratio, ce)) -> new_esEs17(xy4000, xy3000, ce) new_esEs6(Right(xy4000), Right(xy3000), eb, app(app(ty_Either, bcc), bcd)) -> new_esEs6(xy4000, xy3000, bcc, bcd) new_esEs21(xy4010, xy3010, ty_Float) -> new_esEs8(xy4010, xy3010) new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), ed, ee, ef) -> new_asAs(new_esEs22(xy4000, xy3000, ed), new_asAs(new_esEs23(xy4001, xy3001, ee), new_esEs24(xy4002, xy3002, ef))) new_esEs17(:%(xy4000, xy4001), :%(xy3000, xy3001), eh) -> new_asAs(new_esEs25(xy4000, xy3000, eh), new_esEs26(xy4001, xy3001, eh)) new_esEs19(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs13(False, False) -> True new_esEs20(xy4001, xy3001, app(ty_Maybe, dg)) -> new_esEs16(xy4001, xy3001, dg) new_esEs14(EQ, EQ) -> True new_esEs5([], [], ba) -> True new_esEs14(EQ, GT) -> False new_esEs14(GT, EQ) -> False new_esEs20(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs16(xy4000, xy3000, gb) new_esEs20(xy4001, xy3001, app(ty_[], ea)) -> new_esEs5(xy4001, xy3001, ea) new_esEs18(xy400, xy300) -> new_primEqInt(xy400, xy300) new_asAs(True, xy31) -> xy31 new_esEs23(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_esEs10(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs24(xy4002, xy3002, ty_Char) -> new_esEs7(xy4002, xy3002) new_esEs21(xy4010, xy3010, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs11(xy4010, xy3010, ed, ee, ef) new_esEs19(xy4000, xy3000, app(ty_Maybe, cd)) -> new_esEs16(xy4000, xy3000, cd) new_esEs4(xy400, xy300, app(ty_Ratio, eh)) -> new_esEs17(xy400, xy300, eh) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs6(Left(xy4000), Right(xy3000), eb, ec) -> False new_esEs6(Right(xy4000), Left(xy3000), eb, ec) -> False new_esEs4(xy400, xy300, app(ty_[], fa)) -> new_esEs5(xy400, xy300, fa) new_esEs19(xy4000, xy3000, app(ty_[], cf)) -> new_esEs5(xy4000, xy3000, cf) new_esEs6(Left(xy4000), Left(xy3000), ty_Double, ec) -> new_esEs9(xy4000, xy3000) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_@2, beb), bec)) -> new_esEs15(xy4000, xy3000, beb, bec) new_esEs24(xy4002, xy3002, ty_Bool) -> new_esEs13(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Double) -> new_esEs9(xy400, xy300) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs6(Right(xy4000), Right(xy3000), eb, app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs11(xy4000, xy3000, bce, bcf, bcg) new_esEs20(xy4001, xy3001, app(ty_Ratio, dh)) -> new_esEs17(xy4001, xy3001, dh) new_esEs22(xy4000, xy3000, app(ty_[], gd)) -> new_esEs5(xy4000, xy3000, gd) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_@0) -> new_esEs12(xy4000, xy3000) new_deleteBy1(xy40, [], ba) -> [] new_deleteBy00(xy12, xy13, xy14, xy15, xy16, False, bb) -> :(:(xy13, xy14), new_deleteBy1(:(xy15, xy16), xy12, bb)) new_esEs22(xy4000, xy3000, app(ty_Ratio, gc)) -> new_esEs17(xy4000, xy3000, gc) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs11(xy4001, xy3001, gg, gh, ha) new_esEs23(xy4001, xy3001, app(ty_[], hf)) -> new_esEs5(xy4001, xy3001, hf) new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs21(xy4010, xy3010, ty_Integer) -> new_esEs10(xy4010, xy3010) new_esEs24(xy4002, xy3002, ty_Int) -> new_esEs18(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Int) -> new_esEs18(xy400, xy300) new_esEs23(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs21(xy4010, xy3010, app(ty_Ratio, eh)) -> new_esEs17(xy4010, xy3010, eh) new_esEs16(Nothing, Just(xy3000), eg) -> False new_esEs16(Just(xy4000), Nothing, eg) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs14(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_deleteBy1([], :(:(xy300, xy301), xy31), ba) -> :(:(xy300, xy301), new_deleteBy1([], xy31, ba)) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs20(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs4(xy400, xy300, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs11(xy400, xy300, ed, ee, ef) new_esEs24(xy4002, xy3002, app(ty_[], bah)) -> new_esEs5(xy4002, xy3002, bah) new_esEs23(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Char) -> new_esEs7(xy4010, xy3010) new_esEs6(Left(xy4000), Left(xy3000), ty_@0, ec) -> new_esEs12(xy4000, xy3000) new_esEs9(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs19(xy4000, xy3000, app(app(ty_Either, be), bf)) -> new_esEs6(xy4000, xy3000, be, bf) new_esEs24(xy4002, xy3002, ty_Ordering) -> new_esEs14(xy4002, xy3002) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Ratio, bee)) -> new_esEs17(xy4000, xy3000, bee) new_esEs6(Left(xy4000), Left(xy3000), ty_Float, ec) -> new_esEs8(xy4000, xy3000) new_deleteBy1([], :([], xy31), ba) -> xy31 new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs21(xy4010, xy3010, app(ty_Maybe, eg)) -> new_esEs16(xy4010, xy3010, eg) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_Either, bde), bdf)) -> new_esEs6(xy4000, xy3000, bde, bdf) new_esEs23(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Double) -> new_esEs9(xy4002, xy3002) new_esEs20(xy4001, xy3001, app(app(ty_Either, cg), da)) -> new_esEs6(xy4001, xy3001, cg, da) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_primPlusNat1(Succ(xy3200), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3200, xy3000000))) new_esEs16(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(app(ty_@2, fh), ga)) -> new_esEs15(xy4000, xy3000, fh, ga) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs22(xy4000, xy3000, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs11(xy4000, xy3000, fd, ff, fg) new_esEs16(Nothing, Nothing, eg) -> True new_esEs24(xy4002, xy3002, ty_@0) -> new_esEs12(xy4002, xy3002) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Maybe, bed)) -> new_esEs16(xy4000, xy3000, bed) new_esEs5(:(xy4010, xy4011), :(xy3010, xy3011), ba) -> new_asAs(new_esEs21(xy4010, xy3010, ba), new_esEs5(xy4011, xy3011, ba)) new_esEs4(xy400, xy300, app(app(ty_@2, bc), bd)) -> new_esEs15(xy400, xy300, bc, bd) new_esEs19(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(app(ty_@2, hb), hc)) -> new_esEs15(xy4001, xy3001, hb, hc) new_esEs20(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs22(xy4000, xy3000, app(app(ty_Either, fb), fc)) -> new_esEs6(xy4000, xy3000, fb, fc) new_esEs6(Right(xy4000), Right(xy3000), eb, app(ty_Maybe, bdb)) -> new_esEs16(xy4000, xy3000, bdb) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs13(xy400, xy300) new_esEs20(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs6(Right(xy4000), Right(xy3000), eb, app(ty_[], bdd)) -> new_esEs5(xy4000, xy3000, bdd) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Ratio, bca), ec) -> new_esEs17(xy4000, xy3000, bca) new_esEs21(xy4010, xy3010, ty_Bool) -> new_esEs13(xy4010, xy3010) new_esEs19(xy4000, xy3000, app(app(app(ty_@3, bg), bh), ca)) -> new_esEs11(xy4000, xy3000, bg, bh, ca) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs20(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Bool, ec) -> new_esEs13(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Integer, ec) -> new_esEs10(xy4000, xy3000) new_esEs7(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs22(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs10(xy400, xy300) new_esEs6(Left(xy4000), Left(xy3000), ty_Char, ec) -> new_esEs7(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(app(ty_@2, bc), bd)) -> new_esEs15(xy4010, xy3010, bc, bd) new_esEs19(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(app(ty_@3, db), dc), dd)) -> new_esEs11(xy4001, xy3001, db, dc, dd) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs7(xy400, xy300) new_primPlusNat0(Succ(xy320), xy300000) -> Succ(Succ(new_primPlusNat1(xy320, xy300000))) new_esEs22(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4002, xy3002, app(app(ty_Either, hg), hh)) -> new_esEs6(xy4002, xy3002, hg, hh) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_Either, bba), bbb), ec) -> new_esEs6(xy4000, xy3000, bba, bbb) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), ec) -> new_esEs16(xy4000, xy3000, bbh) new_esEs19(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs14(LT, GT) -> False new_esEs14(GT, LT) -> False new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primPlusNat1(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs20(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs6(Left(xy4000), Left(xy3000), app(ty_[], bcb), ec) -> new_esEs5(xy4000, xy3000, bcb) new_esEs16(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs11(xy4000, xy3000, bdg, bdh, bea) new_esEs6(Left(xy4000), Left(xy3000), ty_Int, ec) -> new_esEs18(xy4000, xy3000) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs14(LT, LT) -> True new_esEs24(xy4002, xy3002, ty_Float) -> new_esEs8(xy4002, xy3002) new_deleteBy00(xy12, xy13, xy14, xy15, xy16, True, bb) -> xy12 new_esEs22(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs14(LT, EQ) -> False new_esEs14(EQ, LT) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs12(xy4000, xy3000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs16(Just(xy4000), Just(xy3000), app(ty_[], bef)) -> new_esEs5(xy4000, xy3000, bef) new_esEs22(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs22(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Maybe, eg)) -> new_esEs16(xy400, xy300, eg) new_esEs6(Left(xy4000), Left(xy3000), ty_Ordering, ec) -> new_esEs14(xy4000, xy3000) new_esEs12(@0, @0) -> True new_esEs24(xy4002, xy3002, app(app(app(ty_@3, baa), bab), bac)) -> new_esEs11(xy4002, xy3002, baa, bab, bac) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_primPlusNat1(Succ(xy3200), Zero) -> Succ(xy3200) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4001, xy3001, app(ty_Ratio, he)) -> new_esEs17(xy4001, xy3001, he) new_esEs8(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs21(xy4010, xy3010, ty_@0) -> new_esEs12(xy4010, xy3010) new_esEs19(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_@0) -> new_esEs12(xy400, xy300) new_esEs20(xy4001, xy3001, app(app(ty_@2, de), df)) -> new_esEs15(xy4001, xy3001, de, df) new_esEs13(True, True) -> True new_esEs6(Right(xy4000), Right(xy3000), eb, app(app(ty_@2, bch), bda)) -> new_esEs15(xy4000, xy3000, bch, bda) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Int) -> new_esEs18(xy4000, xy3000) new_deleteBy1(:(xy400, xy401), :(:(xy300, xy301), xy31), ba) -> new_deleteBy00(xy31, xy300, xy301, xy400, xy401, new_asAs(new_esEs4(xy400, xy300, ba), new_esEs5(xy401, xy301, ba)), ba) new_esEs4(xy400, xy300, app(app(ty_Either, eb), ec)) -> new_esEs6(xy400, xy300, eb, ec) new_esEs24(xy4002, xy3002, app(ty_Maybe, baf)) -> new_esEs16(xy4002, xy3002, baf) new_deleteBy1(:(xy400, xy401), :([], xy31), ba) -> :([], new_deleteBy1(:(xy400, xy401), xy31, ba)) new_esEs24(xy4002, xy3002, app(ty_Ratio, bag)) -> new_esEs17(xy4002, xy3002, bag) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Integer) -> new_esEs10(xy4002, xy3002) new_esEs5(:(xy4010, xy4011), [], ba) -> False new_esEs5([], :(xy3010, xy3011), ba) -> False new_primEqNat0(Zero, Zero) -> True new_esEs21(xy4010, xy3010, ty_Int) -> new_esEs18(xy4010, xy3010) new_esEs20(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs19(xy4000, xy3000, app(app(ty_@2, cb), cc)) -> new_esEs15(xy4000, xy3000, cb, cc) new_esEs16(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(ty_[], fa)) -> new_esEs5(xy4010, xy3010, fa) new_esEs6(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bbc), bbd), bbe), ec) -> new_esEs11(xy4000, xy3000, bbc, bbd, bbe) new_asAs(False, xy31) -> False new_esEs15(@2(xy4000, xy4001), @2(xy3000, xy3001), bc, bd) -> new_asAs(new_esEs19(xy4000, xy3000, bc), new_esEs20(xy4001, xy3001, bd)) new_esEs4(xy400, xy300, ty_Float) -> new_esEs8(xy400, xy300) new_esEs21(xy4010, xy3010, ty_Ordering) -> new_esEs14(xy4010, xy3010) new_esEs6(Right(xy4000), Right(xy3000), eb, app(ty_Ratio, bdc)) -> new_esEs17(xy4000, xy3000, bdc) new_esEs23(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(ty_Maybe, hd)) -> new_esEs16(xy4001, xy3001, hd) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_@2, bbf), bbg), ec) -> new_esEs15(xy4000, xy3000, bbf, bbg) new_esEs16(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Double) -> new_esEs9(xy4010, xy3010) new_esEs16(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4001, xy3001, app(app(ty_Either, ge), gf)) -> new_esEs6(xy4001, xy3001, ge, gf) new_esEs6(Right(xy4000), Right(xy3000), eb, ty_Bool) -> new_esEs13(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(x0, x1, ty_Char) new_esEs14(EQ, EQ) new_esEs4(x0, x1, app(ty_[], x2)) new_deleteBy1([], :([], x0), x1) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs6(Right(x0), Right(x1), x2, ty_Char) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(:(x0, x1), :(x2, x3), x4) new_esEs25(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Bool) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_@0) new_esEs4(x0, x1, ty_Bool) new_esEs6(Left(x0), Left(x1), ty_Integer, x2) new_primPlusNat1(Zero, Zero) new_esEs20(x0, x1, ty_Bool) new_esEs15(@2(x0, x1), @2(x2, x3), x4, x5) new_primPlusNat0(Zero, x0) new_esEs20(x0, x1, ty_@0) new_esEs6(Left(x0), Left(x1), ty_Bool, x2) new_esEs22(x0, x1, ty_Int) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Zero) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_@0) new_esEs16(Just(x0), Nothing, x1) new_esEs26(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Integer) new_esEs6(Left(x0), Left(x1), ty_@0, x2) new_esEs16(Just(x0), Just(x1), ty_Float) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, ty_@0) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs19(x0, x1, ty_Double) new_deleteBy1([], :(:(x0, x1), x2), x3) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs21(x0, x1, ty_Bool) new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3)) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Float) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs22(x0, x1, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Int) new_esEs17(:%(x0, x1), :%(x2, x3), x4) new_esEs6(Right(x0), Right(x1), x2, ty_Float) new_esEs16(Nothing, Nothing, x0) new_deleteBy1(:(x0, x1), :(:(x2, x3), x4), x5) new_primPlusNat0(Succ(x0), x1) new_esEs19(x0, x1, ty_Float) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs6(Right(x0), Right(x1), x2, ty_Double) new_esEs6(Right(x0), Right(x1), x2, ty_@0) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Integer) new_esEs19(x0, x1, ty_@0) new_asAs(True, x0) new_asAs(False, x0) new_esEs23(x0, x1, ty_Ordering) new_esEs14(EQ, GT) new_esEs14(GT, EQ) new_esEs21(x0, x1, ty_Char) new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs13(True, True) new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, ty_Int) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Bool) new_esEs5([], :(x0, x1), x2) new_esEs6(Right(x0), Right(x1), x2, ty_Int) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs21(x0, x1, ty_@0) new_sr(Neg(x0), Neg(x1)) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(x0, x1, ty_Float) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs16(Just(x0), Just(x1), ty_Char) new_esEs22(x0, x1, ty_Bool) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs16(Just(x0), Just(x1), ty_Double) new_deleteBy00(x0, x1, x2, x3, x4, False, x5) new_esEs24(x0, x1, ty_Double) new_esEs10(Integer(x0), Integer(x1)) new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs24(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_deleteBy00(x0, x1, x2, x3, x4, True, x5) new_esEs21(x0, x1, ty_Ordering) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Ordering) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(Just(x0), Just(x1), app(ty_[], x2)) new_primMulNat0(Zero, Succ(x0)) new_esEs6(Left(x0), Left(x1), ty_Ordering, x2) new_esEs21(x0, x1, ty_Int) new_esEs21(x0, x1, ty_Double) new_esEs12(@0, @0) new_esEs24(x0, x1, ty_Ordering) new_esEs6(Left(x0), Left(x1), ty_Float, x2) new_esEs20(x0, x1, ty_Ordering) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, ty_Float) new_esEs16(Just(x0), Just(x1), ty_@0) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, ty_Integer) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs6(Left(x0), Left(x1), ty_Char, x2) new_esEs6(Left(x0), Left(x1), ty_Double, x2) new_esEs23(x0, x1, ty_Float) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, ty_Char) new_esEs14(LT, EQ) new_esEs14(EQ, LT) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Int) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs14(GT, GT) new_esEs19(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Int) new_esEs9(Double(x0, x1), Double(x2, x3)) new_deleteBy1(:(x0, x1), :([], x2), x3) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs6(Left(x0), Left(x1), ty_Int, x2) new_esEs14(LT, GT) new_esEs14(GT, LT) new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs6(Left(x0), Right(x1), x2, x3) new_esEs6(Right(x0), Left(x1), x2, x3) new_esEs6(Right(x0), Right(x1), x2, ty_Bool) new_primPlusNat1(Zero, Succ(x0)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs19(x0, x1, ty_Bool) new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs5([], [], x0) new_esEs13(False, True) new_esEs13(True, False) new_esEs19(x0, x1, ty_Ordering) new_esEs8(Float(x0, x1), Float(x2, x3)) new_esEs6(Right(x0), Right(x1), x2, ty_Ordering) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs16(Just(x0), Just(x1), ty_Integer) new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), Zero) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs14(LT, LT) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Ordering) new_esEs23(x0, x1, ty_Int) new_deleteBy1(x0, [], x1) new_esEs23(x0, x1, ty_Double) new_sr(Pos(x0), Pos(x1)) new_esEs16(Nothing, Just(x0), x1) new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Integer) new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs18(x0, x1) new_esEs21(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(:(x0, x1), [], x2) new_esEs23(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Char) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs7(Char(x0), Char(x1)) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs6(Right(x0), Right(x1), x2, ty_Integer) new_esEs20(x0, x1, ty_Double) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_foldl(xy3, :(xy40, xy41), ba) -> new_foldl(new_deleteBy1(xy40, xy3, ba), xy41, ba) The graph contains the following edges 2 > 2, 3 >= 3 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bd), be), bf), bc) -> new_esEs0(xy4000, xy3000, bd, be, bf) new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_@2, bcf), bcg)) -> new_esEs1(xy4000, xy3000, bcf, bcg) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(ty_Maybe, gb), ea) -> new_esEs2(xy4001, xy3001, gb) new_esEs(Right(xy4000), Right(xy3000), cc, app(app(app(ty_@3, cf), cg), da)) -> new_esEs0(xy4000, xy3000, cf, cg, da) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, eg), dh, ea) -> new_esEs2(xy4000, xy3000, eg) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(ty_Either, cc), bc)) -> new_esEs(xy4010, xy3010, cc, bc) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(ty_@2, ha), hb)) -> new_esEs1(xy4002, xy3002, ha, hb) new_esEs(Right(xy4000), Right(xy3000), cc, app(app(ty_@2, db), dc)) -> new_esEs1(xy4000, xy3000, db, dc) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_Either, df), dg), dh, ea) -> new_esEs(xy4000, xy3000, df, dg) new_esEs(Left(xy4000), Left(xy3000), app(ty_Maybe, ca), bc) -> new_esEs2(xy4000, xy3000, ca) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(app(ty_@3, fd), ff), fg), ea) -> new_esEs0(xy4001, xy3001, fd, ff, fg) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(ty_@2, fh), ga), ea) -> new_esEs1(xy4001, xy3001, fh, ga) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(ty_Maybe, bdb)) -> new_esEs2(xy4010, xy3010, bdb) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(ty_[], bdc)) -> new_esEs3(xy4010, xy3010, bdc) new_esEs2(Just(xy4000), Just(xy3000), app(ty_Maybe, bch)) -> new_esEs2(xy4000, xy3000, bch) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(ty_Either, gd), ge)) -> new_esEs(xy4002, xy3002, gd, ge) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(ty_Either, bah), bba)) -> new_esEs(xy4001, xy3001, bah, bba) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, hh), baa), bab), hg) -> new_esEs0(xy4000, xy3000, hh, baa, bab) new_esEs(Left(xy4000), Left(xy3000), app(app(ty_@2, bg), bh), bc) -> new_esEs1(xy4000, xy3000, bg, bh) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(ty_[], hd)) -> new_esEs3(xy4002, xy3002, hd) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], baf), hg) -> new_esEs3(xy4000, xy3000, baf) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(ty_Maybe, bbg)) -> new_esEs2(xy4001, xy3001, bbg) new_esEs2(Just(xy4000), Just(xy3000), app(ty_[], bda)) -> new_esEs3(xy4000, xy3000, bda) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(app(ty_@3, gf), gg), gh)) -> new_esEs0(xy4002, xy3002, gf, gg, gh) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(ty_@2, bag), hg)) -> new_esEs1(xy4010, xy3010, bag, hg) new_esEs(Right(xy4000), Right(xy3000), cc, app(app(ty_Either, cd), ce)) -> new_esEs(xy4000, xy3000, cd, ce) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(ty_Maybe, hc)) -> new_esEs2(xy4002, xy3002, hc) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(ty_[], bbh)) -> new_esEs3(xy4001, xy3001, bbh) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, bae), hg) -> new_esEs2(xy4000, xy3000, bae) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(app(ty_@3, bbb), bbc), bbd)) -> new_esEs0(xy4001, xy3001, bbb, bbc, bbd) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(ty_Either, fb), fc), ea) -> new_esEs(xy4001, xy3001, fb, fc) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), bdd) -> new_esEs3(xy4011, xy3011, bdd) new_esEs(Right(xy4000), Right(xy3000), cc, app(ty_[], de)) -> new_esEs3(xy4000, xy3000, de) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(ty_[], gc), ea) -> new_esEs3(xy4001, xy3001, gc) new_esEs(Left(xy4000), Left(xy3000), app(app(ty_Either, ba), bb), bc) -> new_esEs(xy4000, xy3000, ba, bb) new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(app(ty_@3, fa), dh), ea)) -> new_esEs0(xy4010, xy3010, fa, dh, ea) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], eh), dh, ea) -> new_esEs3(xy4000, xy3000, eh) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, bac), bad), hg) -> new_esEs1(xy4000, xy3000, bac, bad) new_esEs(Right(xy4000), Right(xy3000), cc, app(ty_Maybe, dd)) -> new_esEs2(xy4000, xy3000, dd) new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_Either, bca), bcb)) -> new_esEs(xy4000, xy3000, bca, bcb) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, he), hf), hg) -> new_esEs(xy4000, xy3000, he, hf) new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(ty_@2, bbe), bbf)) -> new_esEs1(xy4001, xy3001, bbe, bbf) new_esEs2(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(xy4000, xy3000, bcc, bcd, bce) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(app(ty_@3, eb), ec), ed), dh, ea) -> new_esEs0(xy4000, xy3000, eb, ec, ed) new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_@2, ee), ef), dh, ea) -> new_esEs1(xy4000, xy3000, ee, ef) new_esEs(Left(xy4000), Left(xy3000), app(ty_[], cb), bc) -> new_esEs3(xy4000, xy3000, cb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (13) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_esEs2(Just(xy4000), Just(xy3000), app(app(ty_Either, bca), bcb)) -> new_esEs(xy4000, xy3000, bca, bcb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Just(xy4000), Just(xy3000), app(ty_Maybe, bch)) -> new_esEs2(xy4000, xy3000, bch) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(xy4000, xy3000, bcc, bcd, bce) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(ty_Either, cc), bc)) -> new_esEs(xy4010, xy3010, cc, bc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(ty_Maybe, bdb)) -> new_esEs2(xy4010, xy3010, bdb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Just(xy4000), Just(xy3000), app(ty_[], bda)) -> new_esEs3(xy4000, xy3000, bda) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_@2, bcf), bcg)) -> new_esEs1(xy4000, xy3000, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(app(ty_@3, fa), dh), ea)) -> new_esEs0(xy4010, xy3010, fa, dh, ea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(app(ty_@2, bag), hg)) -> new_esEs1(xy4010, xy3010, bag, hg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_Either, df), dg), dh, ea) -> new_esEs(xy4000, xy3000, df, dg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(ty_Either, gd), ge)) -> new_esEs(xy4002, xy3002, gd, ge) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(ty_Either, fb), fc), ea) -> new_esEs(xy4001, xy3001, fb, fc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(ty_Maybe, gb), ea) -> new_esEs2(xy4001, xy3001, gb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, eg), dh, ea) -> new_esEs2(xy4000, xy3000, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(ty_Maybe, hc)) -> new_esEs2(xy4002, xy3002, hc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(app(ty_@3, fd), ff), fg), ea) -> new_esEs0(xy4001, xy3001, fd, ff, fg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(app(ty_@3, gf), gg), gh)) -> new_esEs0(xy4002, xy3002, gf, gg, gh) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(app(ty_@3, eb), ec), ed), dh, ea) -> new_esEs0(xy4000, xy3000, eb, ec, ed) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(ty_[], hd)) -> new_esEs3(xy4002, xy3002, hd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(ty_[], gc), ea) -> new_esEs3(xy4001, xy3001, gc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], eh), dh, ea) -> new_esEs3(xy4000, xy3000, eh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, dh, app(app(ty_@2, ha), hb)) -> new_esEs1(xy4002, xy3002, ha, hb) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), fa, app(app(ty_@2, fh), ga), ea) -> new_esEs1(xy4001, xy3001, fh, ga) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_@2, ee), ef), dh, ea) -> new_esEs1(xy4000, xy3000, ee, ef) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(ty_Either, bah), bba)) -> new_esEs(xy4001, xy3001, bah, bba) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, he), hf), hg) -> new_esEs(xy4000, xy3000, he, hf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(Right(xy4000), Right(xy3000), cc, app(app(ty_Either, cd), ce)) -> new_esEs(xy4000, xy3000, cd, ce) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(Left(xy4000), Left(xy3000), app(app(ty_Either, ba), bb), bc) -> new_esEs(xy4000, xy3000, ba, bb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(ty_Maybe, bbg)) -> new_esEs2(xy4001, xy3001, bbg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, bae), hg) -> new_esEs2(xy4000, xy3000, bae) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, hh), baa), bab), hg) -> new_esEs0(xy4000, xy3000, hh, baa, bab) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(app(ty_@3, bbb), bbc), bbd)) -> new_esEs0(xy4001, xy3001, bbb, bbc, bbd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], baf), hg) -> new_esEs3(xy4000, xy3000, baf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(ty_[], bbh)) -> new_esEs3(xy4001, xy3001, bbh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, bac), bad), hg) -> new_esEs1(xy4000, xy3000, bac, bad) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@2(xy4000, xy4001), @2(xy3000, xy3001), bag, app(app(ty_@2, bbe), bbf)) -> new_esEs1(xy4001, xy3001, bbe, bbf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(Left(xy4000), Left(xy3000), app(ty_Maybe, ca), bc) -> new_esEs2(xy4000, xy3000, ca) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(Right(xy4000), Right(xy3000), cc, app(ty_Maybe, dd)) -> new_esEs2(xy4000, xy3000, dd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bd), be), bf), bc) -> new_esEs0(xy4000, xy3000, bd, be, bf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(Right(xy4000), Right(xy3000), cc, app(app(app(ty_@3, cf), cg), da)) -> new_esEs0(xy4000, xy3000, cf, cg, da) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs(Right(xy4000), Right(xy3000), cc, app(ty_[], de)) -> new_esEs3(xy4000, xy3000, de) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(Left(xy4000), Left(xy3000), app(ty_[], cb), bc) -> new_esEs3(xy4000, xy3000, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(Right(xy4000), Right(xy3000), cc, app(app(ty_@2, db), dc)) -> new_esEs1(xy4000, xy3000, db, dc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(Left(xy4000), Left(xy3000), app(app(ty_@2, bg), bh), bc) -> new_esEs1(xy4000, xy3000, bg, bh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), app(ty_[], bdc)) -> new_esEs3(xy4010, xy3010, bdc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(:(xy4010, xy4011), :(xy3010, xy3011), bdd) -> new_esEs3(xy4011, xy3011, bdd) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (14) YES ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(xy400100), Succ(xy300000)) -> new_primMulNat(xy400100, Succ(xy300000)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_primMulNat(Succ(xy400100), Succ(xy300000)) -> new_primMulNat(xy400100, Succ(xy300000)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) -> new_deleteBy(:(xy15, xy16), xy12, ba) new_deleteBy(:(xy400, xy401), :(:(xy300, xy301), xy31), bb) -> new_deleteBy0(xy31, xy300, xy301, xy400, xy401, new_asAs(new_esEs4(xy400, xy300, bb), new_esEs5(xy401, xy301, bb)), bb) new_deleteBy(:(xy400, xy401), :([], xy31), bb) -> new_deleteBy(:(xy400, xy401), xy31, bb) new_deleteBy([], :(:(xy300, xy301), xy31), bb) -> new_deleteBy([], xy31, bb) The TRS R consists of the following rules: new_esEs21(xy4010, xy3010, app(app(ty_Either, bc), bd)) -> new_esEs6(xy4010, xy3010, bc, bd) new_esEs16(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs14(GT, GT) -> True new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(app(ty_@2, bad), bae)) -> new_esEs15(xy4002, xy3002, bad, bae) new_esEs22(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs19(xy4000, xy3000, app(ty_Ratio, df)) -> new_esEs17(xy4000, xy3000, df) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_Either, bcc), bcd)) -> new_esEs6(xy4000, xy3000, bcc, bcd) new_esEs21(xy4010, xy3010, ty_Float) -> new_esEs8(xy4010, xy3010) new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), be, bf, bg) -> new_asAs(new_esEs22(xy4000, xy3000, be), new_asAs(new_esEs23(xy4001, xy3001, bf), new_esEs24(xy4002, xy3002, bg))) new_esEs17(:%(xy4000, xy4001), :%(xy3000, xy3001), cc) -> new_asAs(new_esEs25(xy4000, xy3000, cc), new_esEs26(xy4001, xy3001, cc)) new_esEs19(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs13(False, False) -> True new_esEs20(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs16(xy4001, xy3001, eg) new_esEs14(EQ, EQ) -> True new_esEs5([], [], bb) -> True new_esEs14(EQ, GT) -> False new_esEs14(GT, EQ) -> False new_esEs20(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs16(xy4000, xy3000, gb) new_esEs20(xy4001, xy3001, app(ty_[], fa)) -> new_esEs5(xy4001, xy3001, fa) new_esEs18(xy400, xy300) -> new_primEqInt(xy400, xy300) new_asAs(True, xy31) -> xy31 new_esEs23(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_esEs10(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs24(xy4002, xy3002, ty_Char) -> new_esEs7(xy4002, xy3002) new_esEs21(xy4010, xy3010, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy4010, xy3010, be, bf, bg) new_esEs4(xy400, xy300, app(ty_Ratio, cc)) -> new_esEs17(xy400, xy300, cc) new_esEs19(xy4000, xy3000, app(ty_Maybe, de)) -> new_esEs16(xy4000, xy3000, de) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs6(Left(xy4000), Right(xy3000), bc, bd) -> False new_esEs6(Right(xy4000), Left(xy3000), bc, bd) -> False new_esEs4(xy400, xy300, app(ty_[], cd)) -> new_esEs5(xy400, xy300, cd) new_esEs19(xy4000, xy3000, app(ty_[], dg)) -> new_esEs5(xy4000, xy3000, dg) new_esEs6(Left(xy4000), Left(xy3000), ty_Double, bd) -> new_esEs9(xy4000, xy3000) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_@2, beb), bec)) -> new_esEs15(xy4000, xy3000, beb, bec) new_esEs24(xy4002, xy3002, ty_Bool) -> new_esEs13(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Double) -> new_esEs9(xy400, xy300) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs11(xy4000, xy3000, bce, bcf, bcg) new_esEs20(xy4001, xy3001, app(ty_Ratio, eh)) -> new_esEs17(xy4001, xy3001, eh) new_esEs22(xy4000, xy3000, app(ty_[], gd)) -> new_esEs5(xy4000, xy3000, gd) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(ty_Ratio, gc)) -> new_esEs17(xy4000, xy3000, gc) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs11(xy4001, xy3001, gg, gh, ha) new_esEs23(xy4001, xy3001, app(ty_[], hf)) -> new_esEs5(xy4001, xy3001, hf) new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs18(xy400, xy300) new_esEs21(xy4010, xy3010, ty_Integer) -> new_esEs10(xy4010, xy3010) new_esEs24(xy4002, xy3002, ty_Int) -> new_esEs18(xy4002, xy3002) new_esEs23(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs21(xy4010, xy3010, app(ty_Ratio, cc)) -> new_esEs17(xy4010, xy3010, cc) new_esEs16(Nothing, Just(xy3000), cb) -> False new_esEs16(Just(xy4000), Nothing, cb) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs14(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy400, xy300, be, bf, bg) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs20(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(ty_[], bah)) -> new_esEs5(xy4002, xy3002, bah) new_esEs23(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Char) -> new_esEs7(xy4010, xy3010) new_esEs6(Left(xy4000), Left(xy3000), ty_@0, bd) -> new_esEs12(xy4000, xy3000) new_esEs9(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs19(xy4000, xy3000, app(app(ty_Either, ce), cf)) -> new_esEs6(xy4000, xy3000, ce, cf) new_esEs24(xy4002, xy3002, ty_Ordering) -> new_esEs14(xy4002, xy3002) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Ratio, bee)) -> new_esEs17(xy4000, xy3000, bee) new_esEs6(Left(xy4000), Left(xy3000), ty_Float, bd) -> new_esEs8(xy4000, xy3000) new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs21(xy4010, xy3010, app(ty_Maybe, cb)) -> new_esEs16(xy4010, xy3010, cb) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_Either, bde), bdf)) -> new_esEs6(xy4000, xy3000, bde, bdf) new_esEs23(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Double) -> new_esEs9(xy4002, xy3002) new_esEs20(xy4001, xy3001, app(app(ty_Either, dh), ea)) -> new_esEs6(xy4001, xy3001, dh, ea) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_primPlusNat1(Succ(xy3200), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3200, xy3000000))) new_esEs16(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(app(ty_@2, fh), ga)) -> new_esEs15(xy4000, xy3000, fh, ga) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs22(xy4000, xy3000, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs11(xy4000, xy3000, fd, ff, fg) new_esEs16(Nothing, Nothing, cb) -> True new_esEs24(xy4002, xy3002, ty_@0) -> new_esEs12(xy4002, xy3002) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Maybe, bed)) -> new_esEs16(xy4000, xy3000, bed) new_esEs4(xy400, xy300, app(app(ty_@2, bh), ca)) -> new_esEs15(xy400, xy300, bh, ca) new_esEs5(:(xy4010, xy4011), :(xy3010, xy3011), bb) -> new_asAs(new_esEs21(xy4010, xy3010, bb), new_esEs5(xy4011, xy3011, bb)) new_esEs19(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(app(ty_@2, hb), hc)) -> new_esEs15(xy4001, xy3001, hb, hc) new_esEs20(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs22(xy4000, xy3000, app(app(ty_Either, fb), fc)) -> new_esEs6(xy4000, xy3000, fb, fc) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Maybe, bdb)) -> new_esEs16(xy4000, xy3000, bdb) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs13(xy400, xy300) new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_[], bdd)) -> new_esEs5(xy4000, xy3000, bdd) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Ratio, bca), bd) -> new_esEs17(xy4000, xy3000, bca) new_esEs21(xy4010, xy3010, ty_Bool) -> new_esEs13(xy4010, xy3010) new_esEs19(xy4000, xy3000, app(app(app(ty_@3, cg), da), db)) -> new_esEs11(xy4000, xy3000, cg, da, db) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs20(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Bool, bd) -> new_esEs13(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Integer, bd) -> new_esEs10(xy4000, xy3000) new_esEs7(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs22(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs10(xy400, xy300) new_esEs6(Left(xy4000), Left(xy3000), ty_Char, bd) -> new_esEs7(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(app(ty_@2, bh), ca)) -> new_esEs15(xy4010, xy3010, bh, ca) new_esEs19(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs11(xy4001, xy3001, eb, ec, ed) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs7(xy400, xy300) new_primPlusNat0(Succ(xy320), xy300000) -> Succ(Succ(new_primPlusNat1(xy320, xy300000))) new_esEs22(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4002, xy3002, app(app(ty_Either, hg), hh)) -> new_esEs6(xy4002, xy3002, hg, hh) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_Either, bba), bbb), bd) -> new_esEs6(xy4000, xy3000, bba, bbb) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), bd) -> new_esEs16(xy4000, xy3000, bbh) new_esEs19(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs14(LT, GT) -> False new_esEs14(GT, LT) -> False new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primPlusNat1(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs20(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs6(Left(xy4000), Left(xy3000), app(ty_[], bcb), bd) -> new_esEs5(xy4000, xy3000, bcb) new_esEs16(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs11(xy4000, xy3000, bdg, bdh, bea) new_esEs6(Left(xy4000), Left(xy3000), ty_Int, bd) -> new_esEs18(xy4000, xy3000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs14(LT, LT) -> True new_esEs24(xy4002, xy3002, ty_Float) -> new_esEs8(xy4002, xy3002) new_esEs22(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs14(LT, EQ) -> False new_esEs14(EQ, LT) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs12(xy4000, xy3000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs16(Just(xy4000), Just(xy3000), app(ty_[], bef)) -> new_esEs5(xy4000, xy3000, bef) new_esEs22(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Maybe, cb)) -> new_esEs16(xy400, xy300, cb) new_esEs22(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Ordering, bd) -> new_esEs14(xy4000, xy3000) new_esEs12(@0, @0) -> True new_esEs24(xy4002, xy3002, app(app(app(ty_@3, baa), bab), bac)) -> new_esEs11(xy4002, xy3002, baa, bab, bac) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_primPlusNat1(Succ(xy3200), Zero) -> Succ(xy3200) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4001, xy3001, app(ty_Ratio, he)) -> new_esEs17(xy4001, xy3001, he) new_esEs8(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs21(xy4010, xy3010, ty_@0) -> new_esEs12(xy4010, xy3010) new_esEs4(xy400, xy300, ty_@0) -> new_esEs12(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(ty_@2, ee), ef)) -> new_esEs15(xy4001, xy3001, ee, ef) new_esEs13(True, True) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_@2, bch), bda)) -> new_esEs15(xy4000, xy3000, bch, bda) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bc), bd)) -> new_esEs6(xy400, xy300, bc, bd) new_esEs24(xy4002, xy3002, app(ty_Maybe, baf)) -> new_esEs16(xy4002, xy3002, baf) new_esEs24(xy4002, xy3002, app(ty_Ratio, bag)) -> new_esEs17(xy4002, xy3002, bag) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Integer) -> new_esEs10(xy4002, xy3002) new_esEs5(:(xy4010, xy4011), [], bb) -> False new_esEs5([], :(xy3010, xy3011), bb) -> False new_primEqNat0(Zero, Zero) -> True new_esEs21(xy4010, xy3010, ty_Int) -> new_esEs18(xy4010, xy3010) new_esEs20(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs19(xy4000, xy3000, app(app(ty_@2, dc), dd)) -> new_esEs15(xy4000, xy3000, dc, dd) new_esEs16(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(ty_[], cd)) -> new_esEs5(xy4010, xy3010, cd) new_esEs6(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bbc), bbd), bbe), bd) -> new_esEs11(xy4000, xy3000, bbc, bbd, bbe) new_asAs(False, xy31) -> False new_esEs4(xy400, xy300, ty_Float) -> new_esEs8(xy400, xy300) new_esEs15(@2(xy4000, xy4001), @2(xy3000, xy3001), bh, ca) -> new_asAs(new_esEs19(xy4000, xy3000, bh), new_esEs20(xy4001, xy3001, ca)) new_esEs21(xy4010, xy3010, ty_Ordering) -> new_esEs14(xy4010, xy3010) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Ratio, bdc)) -> new_esEs17(xy4000, xy3000, bdc) new_esEs23(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(ty_Maybe, hd)) -> new_esEs16(xy4001, xy3001, hd) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_@2, bbf), bbg), bd) -> new_esEs15(xy4000, xy3000, bbf, bbg) new_esEs16(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Double) -> new_esEs9(xy4010, xy3010) new_esEs16(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4001, xy3001, app(app(ty_Either, ge), gf)) -> new_esEs6(xy4001, xy3001, ge, gf) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Bool) -> new_esEs13(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(x0, x1, ty_Char) new_esEs14(EQ, EQ) new_esEs17(:%(x0, x1), :%(x2, x3), x4) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs16(Nothing, Nothing, x0) new_esEs25(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Bool) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_@0) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs20(x0, x1, ty_Bool) new_primPlusNat0(Zero, x0) new_esEs20(x0, x1, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Zero) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs6(Right(x0), Right(x1), x2, ty_Char) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs23(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Integer) new_esEs6(Right(x0), Right(x1), x2, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, ty_@0) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5([], [], x0) new_esEs19(x0, x1, ty_Double) new_esEs16(Just(x0), Nothing, x1) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Integer, x2) new_esEs21(x0, x1, ty_Bool) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Float) new_esEs6(Left(x0), Left(x1), ty_@0, x2) new_esEs22(x0, x1, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Int) new_primPlusNat0(Succ(x0), x1) new_esEs19(x0, x1, ty_Float) new_esEs6(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Double, x2) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Integer) new_esEs19(x0, x1, ty_@0) new_asAs(True, x0) new_asAs(False, x0) new_esEs23(x0, x1, ty_Ordering) new_esEs14(EQ, GT) new_esEs14(GT, EQ) new_esEs21(x0, x1, ty_Char) new_esEs13(True, True) new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Bool) new_esEs6(Right(x0), Right(x1), x2, ty_Float) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs21(x0, x1, ty_@0) new_sr(Neg(x0), Neg(x1)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(x0, x1, ty_Float) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs6(Left(x0), Left(x1), ty_Bool, x2) new_esEs16(Just(x0), Just(x1), ty_Char) new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(x0, x1, ty_Bool) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs16(Just(x0), Just(x1), ty_Double) new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs24(x0, x1, ty_Double) new_esEs10(Integer(x0), Integer(x1)) new_esEs6(Left(x0), Right(x1), x2, x3) new_esEs6(Right(x0), Left(x1), x2, x3) new_esEs5(:(x0, x1), [], x2) new_esEs6(Left(x0), Left(x1), ty_Char, x2) new_esEs24(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Ordering) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Ordering) new_esEs16(Just(x0), Just(x1), app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_primMulNat0(Zero, Succ(x0)) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Int) new_esEs21(x0, x1, ty_Double) new_esEs12(@0, @0) new_esEs6(Left(x0), Left(x1), ty_Int, x2) new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs24(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Float) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(Just(x0), Just(x1), ty_@0) new_esEs5(:(x0, x1), :(x2, x3), x4) new_esEs26(x0, x1, ty_Integer) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Float) new_esEs4(x0, x1, ty_Char) new_esEs14(LT, EQ) new_esEs14(EQ, LT) new_esEs6(Right(x0), Right(x1), x2, ty_Double) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs15(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs4(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Int) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Ordering, x2) new_esEs6(Right(x0), Right(x1), x2, ty_Ordering) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs14(GT, GT) new_esEs19(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Int) new_esEs9(Double(x0, x1), Double(x2, x3)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs14(LT, GT) new_esEs14(GT, LT) new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs6(Left(x0), Left(x1), ty_Float, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat1(Zero, Succ(x0)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs19(x0, x1, ty_Bool) new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs13(False, True) new_esEs13(True, False) new_esEs19(x0, x1, ty_Ordering) new_esEs8(Float(x0, x1), Float(x2, x3)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs16(Just(x0), Just(x1), ty_Integer) new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Ordering) new_esEs6(Right(x0), Right(x1), x2, ty_Integer) new_esEs20(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs6(Right(x0), Right(x1), x2, ty_Bool) new_esEs14(LT, LT) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Ordering) new_esEs23(x0, x1, ty_Int) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs23(x0, x1, ty_Double) new_sr(Pos(x0), Pos(x1)) new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Integer) new_esEs18(x0, x1) new_esEs21(x0, x1, ty_Integer) new_esEs23(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Char) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs16(Nothing, Just(x0), x1) new_esEs7(Char(x0), Char(x1)) new_esEs5([], :(x0, x1), x2) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (20) Complex Obligation (AND) ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy([], :(:(xy300, xy301), xy31), bb) -> new_deleteBy([], xy31, bb) The TRS R consists of the following rules: new_esEs21(xy4010, xy3010, app(app(ty_Either, bc), bd)) -> new_esEs6(xy4010, xy3010, bc, bd) new_esEs16(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs14(GT, GT) -> True new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(app(ty_@2, bad), bae)) -> new_esEs15(xy4002, xy3002, bad, bae) new_esEs22(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs19(xy4000, xy3000, app(ty_Ratio, df)) -> new_esEs17(xy4000, xy3000, df) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_Either, bcc), bcd)) -> new_esEs6(xy4000, xy3000, bcc, bcd) new_esEs21(xy4010, xy3010, ty_Float) -> new_esEs8(xy4010, xy3010) new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), be, bf, bg) -> new_asAs(new_esEs22(xy4000, xy3000, be), new_asAs(new_esEs23(xy4001, xy3001, bf), new_esEs24(xy4002, xy3002, bg))) new_esEs17(:%(xy4000, xy4001), :%(xy3000, xy3001), cc) -> new_asAs(new_esEs25(xy4000, xy3000, cc), new_esEs26(xy4001, xy3001, cc)) new_esEs19(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs13(False, False) -> True new_esEs20(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs16(xy4001, xy3001, eg) new_esEs14(EQ, EQ) -> True new_esEs5([], [], bb) -> True new_esEs14(EQ, GT) -> False new_esEs14(GT, EQ) -> False new_esEs20(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs16(xy4000, xy3000, gb) new_esEs20(xy4001, xy3001, app(ty_[], fa)) -> new_esEs5(xy4001, xy3001, fa) new_esEs18(xy400, xy300) -> new_primEqInt(xy400, xy300) new_asAs(True, xy31) -> xy31 new_esEs23(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_esEs10(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs24(xy4002, xy3002, ty_Char) -> new_esEs7(xy4002, xy3002) new_esEs21(xy4010, xy3010, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy4010, xy3010, be, bf, bg) new_esEs4(xy400, xy300, app(ty_Ratio, cc)) -> new_esEs17(xy400, xy300, cc) new_esEs19(xy4000, xy3000, app(ty_Maybe, de)) -> new_esEs16(xy4000, xy3000, de) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs6(Left(xy4000), Right(xy3000), bc, bd) -> False new_esEs6(Right(xy4000), Left(xy3000), bc, bd) -> False new_esEs4(xy400, xy300, app(ty_[], cd)) -> new_esEs5(xy400, xy300, cd) new_esEs19(xy4000, xy3000, app(ty_[], dg)) -> new_esEs5(xy4000, xy3000, dg) new_esEs6(Left(xy4000), Left(xy3000), ty_Double, bd) -> new_esEs9(xy4000, xy3000) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_@2, beb), bec)) -> new_esEs15(xy4000, xy3000, beb, bec) new_esEs24(xy4002, xy3002, ty_Bool) -> new_esEs13(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Double) -> new_esEs9(xy400, xy300) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs11(xy4000, xy3000, bce, bcf, bcg) new_esEs20(xy4001, xy3001, app(ty_Ratio, eh)) -> new_esEs17(xy4001, xy3001, eh) new_esEs22(xy4000, xy3000, app(ty_[], gd)) -> new_esEs5(xy4000, xy3000, gd) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(ty_Ratio, gc)) -> new_esEs17(xy4000, xy3000, gc) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs11(xy4001, xy3001, gg, gh, ha) new_esEs23(xy4001, xy3001, app(ty_[], hf)) -> new_esEs5(xy4001, xy3001, hf) new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs18(xy400, xy300) new_esEs21(xy4010, xy3010, ty_Integer) -> new_esEs10(xy4010, xy3010) new_esEs24(xy4002, xy3002, ty_Int) -> new_esEs18(xy4002, xy3002) new_esEs23(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs21(xy4010, xy3010, app(ty_Ratio, cc)) -> new_esEs17(xy4010, xy3010, cc) new_esEs16(Nothing, Just(xy3000), cb) -> False new_esEs16(Just(xy4000), Nothing, cb) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs14(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy400, xy300, be, bf, bg) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs20(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(ty_[], bah)) -> new_esEs5(xy4002, xy3002, bah) new_esEs23(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Char) -> new_esEs7(xy4010, xy3010) new_esEs6(Left(xy4000), Left(xy3000), ty_@0, bd) -> new_esEs12(xy4000, xy3000) new_esEs9(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs19(xy4000, xy3000, app(app(ty_Either, ce), cf)) -> new_esEs6(xy4000, xy3000, ce, cf) new_esEs24(xy4002, xy3002, ty_Ordering) -> new_esEs14(xy4002, xy3002) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Ratio, bee)) -> new_esEs17(xy4000, xy3000, bee) new_esEs6(Left(xy4000), Left(xy3000), ty_Float, bd) -> new_esEs8(xy4000, xy3000) new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs21(xy4010, xy3010, app(ty_Maybe, cb)) -> new_esEs16(xy4010, xy3010, cb) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_Either, bde), bdf)) -> new_esEs6(xy4000, xy3000, bde, bdf) new_esEs23(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Double) -> new_esEs9(xy4002, xy3002) new_esEs20(xy4001, xy3001, app(app(ty_Either, dh), ea)) -> new_esEs6(xy4001, xy3001, dh, ea) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_primPlusNat1(Succ(xy3200), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3200, xy3000000))) new_esEs16(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(app(ty_@2, fh), ga)) -> new_esEs15(xy4000, xy3000, fh, ga) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs22(xy4000, xy3000, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs11(xy4000, xy3000, fd, ff, fg) new_esEs16(Nothing, Nothing, cb) -> True new_esEs24(xy4002, xy3002, ty_@0) -> new_esEs12(xy4002, xy3002) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Maybe, bed)) -> new_esEs16(xy4000, xy3000, bed) new_esEs4(xy400, xy300, app(app(ty_@2, bh), ca)) -> new_esEs15(xy400, xy300, bh, ca) new_esEs5(:(xy4010, xy4011), :(xy3010, xy3011), bb) -> new_asAs(new_esEs21(xy4010, xy3010, bb), new_esEs5(xy4011, xy3011, bb)) new_esEs19(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(app(ty_@2, hb), hc)) -> new_esEs15(xy4001, xy3001, hb, hc) new_esEs20(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs22(xy4000, xy3000, app(app(ty_Either, fb), fc)) -> new_esEs6(xy4000, xy3000, fb, fc) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Maybe, bdb)) -> new_esEs16(xy4000, xy3000, bdb) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs13(xy400, xy300) new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_[], bdd)) -> new_esEs5(xy4000, xy3000, bdd) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Ratio, bca), bd) -> new_esEs17(xy4000, xy3000, bca) new_esEs21(xy4010, xy3010, ty_Bool) -> new_esEs13(xy4010, xy3010) new_esEs19(xy4000, xy3000, app(app(app(ty_@3, cg), da), db)) -> new_esEs11(xy4000, xy3000, cg, da, db) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs20(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Bool, bd) -> new_esEs13(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Integer, bd) -> new_esEs10(xy4000, xy3000) new_esEs7(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs22(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs10(xy400, xy300) new_esEs6(Left(xy4000), Left(xy3000), ty_Char, bd) -> new_esEs7(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(app(ty_@2, bh), ca)) -> new_esEs15(xy4010, xy3010, bh, ca) new_esEs19(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs11(xy4001, xy3001, eb, ec, ed) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs7(xy400, xy300) new_primPlusNat0(Succ(xy320), xy300000) -> Succ(Succ(new_primPlusNat1(xy320, xy300000))) new_esEs22(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4002, xy3002, app(app(ty_Either, hg), hh)) -> new_esEs6(xy4002, xy3002, hg, hh) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_Either, bba), bbb), bd) -> new_esEs6(xy4000, xy3000, bba, bbb) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), bd) -> new_esEs16(xy4000, xy3000, bbh) new_esEs19(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs14(LT, GT) -> False new_esEs14(GT, LT) -> False new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primPlusNat1(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs20(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs6(Left(xy4000), Left(xy3000), app(ty_[], bcb), bd) -> new_esEs5(xy4000, xy3000, bcb) new_esEs16(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs11(xy4000, xy3000, bdg, bdh, bea) new_esEs6(Left(xy4000), Left(xy3000), ty_Int, bd) -> new_esEs18(xy4000, xy3000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs14(LT, LT) -> True new_esEs24(xy4002, xy3002, ty_Float) -> new_esEs8(xy4002, xy3002) new_esEs22(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs14(LT, EQ) -> False new_esEs14(EQ, LT) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs12(xy4000, xy3000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs16(Just(xy4000), Just(xy3000), app(ty_[], bef)) -> new_esEs5(xy4000, xy3000, bef) new_esEs22(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Maybe, cb)) -> new_esEs16(xy400, xy300, cb) new_esEs22(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Ordering, bd) -> new_esEs14(xy4000, xy3000) new_esEs12(@0, @0) -> True new_esEs24(xy4002, xy3002, app(app(app(ty_@3, baa), bab), bac)) -> new_esEs11(xy4002, xy3002, baa, bab, bac) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_primPlusNat1(Succ(xy3200), Zero) -> Succ(xy3200) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4001, xy3001, app(ty_Ratio, he)) -> new_esEs17(xy4001, xy3001, he) new_esEs8(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs21(xy4010, xy3010, ty_@0) -> new_esEs12(xy4010, xy3010) new_esEs4(xy400, xy300, ty_@0) -> new_esEs12(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(ty_@2, ee), ef)) -> new_esEs15(xy4001, xy3001, ee, ef) new_esEs13(True, True) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_@2, bch), bda)) -> new_esEs15(xy4000, xy3000, bch, bda) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bc), bd)) -> new_esEs6(xy400, xy300, bc, bd) new_esEs24(xy4002, xy3002, app(ty_Maybe, baf)) -> new_esEs16(xy4002, xy3002, baf) new_esEs24(xy4002, xy3002, app(ty_Ratio, bag)) -> new_esEs17(xy4002, xy3002, bag) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Integer) -> new_esEs10(xy4002, xy3002) new_esEs5(:(xy4010, xy4011), [], bb) -> False new_esEs5([], :(xy3010, xy3011), bb) -> False new_primEqNat0(Zero, Zero) -> True new_esEs21(xy4010, xy3010, ty_Int) -> new_esEs18(xy4010, xy3010) new_esEs20(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs19(xy4000, xy3000, app(app(ty_@2, dc), dd)) -> new_esEs15(xy4000, xy3000, dc, dd) new_esEs16(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(ty_[], cd)) -> new_esEs5(xy4010, xy3010, cd) new_esEs6(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bbc), bbd), bbe), bd) -> new_esEs11(xy4000, xy3000, bbc, bbd, bbe) new_asAs(False, xy31) -> False new_esEs4(xy400, xy300, ty_Float) -> new_esEs8(xy400, xy300) new_esEs15(@2(xy4000, xy4001), @2(xy3000, xy3001), bh, ca) -> new_asAs(new_esEs19(xy4000, xy3000, bh), new_esEs20(xy4001, xy3001, ca)) new_esEs21(xy4010, xy3010, ty_Ordering) -> new_esEs14(xy4010, xy3010) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Ratio, bdc)) -> new_esEs17(xy4000, xy3000, bdc) new_esEs23(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(ty_Maybe, hd)) -> new_esEs16(xy4001, xy3001, hd) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_@2, bbf), bbg), bd) -> new_esEs15(xy4000, xy3000, bbf, bbg) new_esEs16(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Double) -> new_esEs9(xy4010, xy3010) new_esEs16(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4001, xy3001, app(app(ty_Either, ge), gf)) -> new_esEs6(xy4001, xy3001, ge, gf) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Bool) -> new_esEs13(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(x0, x1, ty_Char) new_esEs14(EQ, EQ) new_esEs17(:%(x0, x1), :%(x2, x3), x4) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs16(Nothing, Nothing, x0) new_esEs25(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Bool) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_@0) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs20(x0, x1, ty_Bool) new_primPlusNat0(Zero, x0) new_esEs20(x0, x1, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Zero) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs6(Right(x0), Right(x1), x2, ty_Char) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs23(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Integer) new_esEs6(Right(x0), Right(x1), x2, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, ty_@0) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5([], [], x0) new_esEs19(x0, x1, ty_Double) new_esEs16(Just(x0), Nothing, x1) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Integer, x2) new_esEs21(x0, x1, ty_Bool) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Float) new_esEs6(Left(x0), Left(x1), ty_@0, x2) new_esEs22(x0, x1, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Int) new_primPlusNat0(Succ(x0), x1) new_esEs19(x0, x1, ty_Float) new_esEs6(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Double, x2) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Integer) new_esEs19(x0, x1, ty_@0) new_asAs(True, x0) new_asAs(False, x0) new_esEs23(x0, x1, ty_Ordering) new_esEs14(EQ, GT) new_esEs14(GT, EQ) new_esEs21(x0, x1, ty_Char) new_esEs13(True, True) new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Bool) new_esEs6(Right(x0), Right(x1), x2, ty_Float) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs21(x0, x1, ty_@0) new_sr(Neg(x0), Neg(x1)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(x0, x1, ty_Float) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs6(Left(x0), Left(x1), ty_Bool, x2) new_esEs16(Just(x0), Just(x1), ty_Char) new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(x0, x1, ty_Bool) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs16(Just(x0), Just(x1), ty_Double) new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs24(x0, x1, ty_Double) new_esEs10(Integer(x0), Integer(x1)) new_esEs6(Left(x0), Right(x1), x2, x3) new_esEs6(Right(x0), Left(x1), x2, x3) new_esEs5(:(x0, x1), [], x2) new_esEs6(Left(x0), Left(x1), ty_Char, x2) new_esEs24(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Ordering) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Ordering) new_esEs16(Just(x0), Just(x1), app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_primMulNat0(Zero, Succ(x0)) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Int) new_esEs21(x0, x1, ty_Double) new_esEs12(@0, @0) new_esEs6(Left(x0), Left(x1), ty_Int, x2) new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs24(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Float) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(Just(x0), Just(x1), ty_@0) new_esEs5(:(x0, x1), :(x2, x3), x4) new_esEs26(x0, x1, ty_Integer) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Float) new_esEs4(x0, x1, ty_Char) new_esEs14(LT, EQ) new_esEs14(EQ, LT) new_esEs6(Right(x0), Right(x1), x2, ty_Double) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs15(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs4(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Int) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Ordering, x2) new_esEs6(Right(x0), Right(x1), x2, ty_Ordering) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs14(GT, GT) new_esEs19(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Int) new_esEs9(Double(x0, x1), Double(x2, x3)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs14(LT, GT) new_esEs14(GT, LT) new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs6(Left(x0), Left(x1), ty_Float, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat1(Zero, Succ(x0)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs19(x0, x1, ty_Bool) new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs13(False, True) new_esEs13(True, False) new_esEs19(x0, x1, ty_Ordering) new_esEs8(Float(x0, x1), Float(x2, x3)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs16(Just(x0), Just(x1), ty_Integer) new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Ordering) new_esEs6(Right(x0), Right(x1), x2, ty_Integer) new_esEs20(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs6(Right(x0), Right(x1), x2, ty_Bool) new_esEs14(LT, LT) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Ordering) new_esEs23(x0, x1, ty_Int) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs23(x0, x1, ty_Double) new_sr(Pos(x0), Pos(x1)) new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Integer) new_esEs18(x0, x1) new_esEs21(x0, x1, ty_Integer) new_esEs23(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Char) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs16(Nothing, Just(x0), x1) new_esEs7(Char(x0), Char(x1)) new_esEs5([], :(x0, x1), x2) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (22) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_deleteBy([], :(:(xy300, xy301), xy31), bb) -> new_deleteBy([], xy31, bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 ---------------------------------------- (23) YES ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy(:(xy400, xy401), :(:(xy300, xy301), xy31), bb) -> new_deleteBy0(xy31, xy300, xy301, xy400, xy401, new_asAs(new_esEs4(xy400, xy300, bb), new_esEs5(xy401, xy301, bb)), bb) new_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) -> new_deleteBy(:(xy15, xy16), xy12, ba) new_deleteBy(:(xy400, xy401), :([], xy31), bb) -> new_deleteBy(:(xy400, xy401), xy31, bb) The TRS R consists of the following rules: new_esEs21(xy4010, xy3010, app(app(ty_Either, bc), bd)) -> new_esEs6(xy4010, xy3010, bc, bd) new_esEs16(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs14(GT, GT) -> True new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(app(ty_@2, bad), bae)) -> new_esEs15(xy4002, xy3002, bad, bae) new_esEs22(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs19(xy4000, xy3000, app(ty_Ratio, df)) -> new_esEs17(xy4000, xy3000, df) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_Either, bcc), bcd)) -> new_esEs6(xy4000, xy3000, bcc, bcd) new_esEs21(xy4010, xy3010, ty_Float) -> new_esEs8(xy4010, xy3010) new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), be, bf, bg) -> new_asAs(new_esEs22(xy4000, xy3000, be), new_asAs(new_esEs23(xy4001, xy3001, bf), new_esEs24(xy4002, xy3002, bg))) new_esEs17(:%(xy4000, xy4001), :%(xy3000, xy3001), cc) -> new_asAs(new_esEs25(xy4000, xy3000, cc), new_esEs26(xy4001, xy3001, cc)) new_esEs19(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs13(False, False) -> True new_esEs20(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs16(xy4001, xy3001, eg) new_esEs14(EQ, EQ) -> True new_esEs5([], [], bb) -> True new_esEs14(EQ, GT) -> False new_esEs14(GT, EQ) -> False new_esEs20(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs16(xy4000, xy3000, gb) new_esEs20(xy4001, xy3001, app(ty_[], fa)) -> new_esEs5(xy4001, xy3001, fa) new_esEs18(xy400, xy300) -> new_primEqInt(xy400, xy300) new_asAs(True, xy31) -> xy31 new_esEs23(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_esEs10(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs24(xy4002, xy3002, ty_Char) -> new_esEs7(xy4002, xy3002) new_esEs21(xy4010, xy3010, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy4010, xy3010, be, bf, bg) new_esEs4(xy400, xy300, app(ty_Ratio, cc)) -> new_esEs17(xy400, xy300, cc) new_esEs19(xy4000, xy3000, app(ty_Maybe, de)) -> new_esEs16(xy4000, xy3000, de) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs6(Left(xy4000), Right(xy3000), bc, bd) -> False new_esEs6(Right(xy4000), Left(xy3000), bc, bd) -> False new_esEs4(xy400, xy300, app(ty_[], cd)) -> new_esEs5(xy400, xy300, cd) new_esEs19(xy4000, xy3000, app(ty_[], dg)) -> new_esEs5(xy4000, xy3000, dg) new_esEs6(Left(xy4000), Left(xy3000), ty_Double, bd) -> new_esEs9(xy4000, xy3000) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_@2, beb), bec)) -> new_esEs15(xy4000, xy3000, beb, bec) new_esEs24(xy4002, xy3002, ty_Bool) -> new_esEs13(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Double) -> new_esEs9(xy400, xy300) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs11(xy4000, xy3000, bce, bcf, bcg) new_esEs20(xy4001, xy3001, app(ty_Ratio, eh)) -> new_esEs17(xy4001, xy3001, eh) new_esEs22(xy4000, xy3000, app(ty_[], gd)) -> new_esEs5(xy4000, xy3000, gd) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_@0) -> new_esEs12(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(ty_Ratio, gc)) -> new_esEs17(xy4000, xy3000, gc) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs11(xy4001, xy3001, gg, gh, ha) new_esEs23(xy4001, xy3001, app(ty_[], hf)) -> new_esEs5(xy4001, xy3001, hf) new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs18(xy400, xy300) new_esEs21(xy4010, xy3010, ty_Integer) -> new_esEs10(xy4010, xy3010) new_esEs24(xy4002, xy3002, ty_Int) -> new_esEs18(xy4002, xy3002) new_esEs23(xy4001, xy3001, ty_@0) -> new_esEs12(xy4001, xy3001) new_esEs21(xy4010, xy3010, app(ty_Ratio, cc)) -> new_esEs17(xy4010, xy3010, cc) new_esEs16(Nothing, Just(xy3000), cb) -> False new_esEs16(Just(xy4000), Nothing, cb) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs14(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, be), bf), bg)) -> new_esEs11(xy400, xy300, be, bf, bg) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs20(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs24(xy4002, xy3002, app(ty_[], bah)) -> new_esEs5(xy4002, xy3002, bah) new_esEs23(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Char) -> new_esEs7(xy4010, xy3010) new_esEs6(Left(xy4000), Left(xy3000), ty_@0, bd) -> new_esEs12(xy4000, xy3000) new_esEs9(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs19(xy4000, xy3000, app(app(ty_Either, ce), cf)) -> new_esEs6(xy4000, xy3000, ce, cf) new_esEs24(xy4002, xy3002, ty_Ordering) -> new_esEs14(xy4002, xy3002) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Ratio, bee)) -> new_esEs17(xy4000, xy3000, bee) new_esEs6(Left(xy4000), Left(xy3000), ty_Float, bd) -> new_esEs8(xy4000, xy3000) new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs21(xy4010, xy3010, app(ty_Maybe, cb)) -> new_esEs16(xy4010, xy3010, cb) new_esEs16(Just(xy4000), Just(xy3000), app(app(ty_Either, bde), bdf)) -> new_esEs6(xy4000, xy3000, bde, bdf) new_esEs23(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Double) -> new_esEs9(xy4002, xy3002) new_esEs20(xy4001, xy3001, app(app(ty_Either, dh), ea)) -> new_esEs6(xy4001, xy3001, dh, ea) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_primPlusNat1(Succ(xy3200), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3200, xy3000000))) new_esEs16(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs22(xy4000, xy3000, app(app(ty_@2, fh), ga)) -> new_esEs15(xy4000, xy3000, fh, ga) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs22(xy4000, xy3000, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs11(xy4000, xy3000, fd, ff, fg) new_esEs16(Nothing, Nothing, cb) -> True new_esEs24(xy4002, xy3002, ty_@0) -> new_esEs12(xy4002, xy3002) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), app(ty_Maybe, bed)) -> new_esEs16(xy4000, xy3000, bed) new_esEs4(xy400, xy300, app(app(ty_@2, bh), ca)) -> new_esEs15(xy400, xy300, bh, ca) new_esEs5(:(xy4010, xy4011), :(xy3010, xy3011), bb) -> new_asAs(new_esEs21(xy4010, xy3010, bb), new_esEs5(xy4011, xy3011, bb)) new_esEs19(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(app(ty_@2, hb), hc)) -> new_esEs15(xy4001, xy3001, hb, hc) new_esEs20(xy4001, xy3001, ty_Double) -> new_esEs9(xy4001, xy3001) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs22(xy4000, xy3000, app(app(ty_Either, fb), fc)) -> new_esEs6(xy4000, xy3000, fb, fc) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Maybe, bdb)) -> new_esEs16(xy4000, xy3000, bdb) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs13(xy400, xy300) new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs20(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_[], bdd)) -> new_esEs5(xy4000, xy3000, bdd) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Ratio, bca), bd) -> new_esEs17(xy4000, xy3000, bca) new_esEs21(xy4010, xy3010, ty_Bool) -> new_esEs13(xy4010, xy3010) new_esEs19(xy4000, xy3000, app(app(app(ty_@3, cg), da), db)) -> new_esEs11(xy4000, xy3000, cg, da, db) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs20(xy4001, xy3001, ty_Ordering) -> new_esEs14(xy4001, xy3001) new_esEs16(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Bool, bd) -> new_esEs13(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Integer, bd) -> new_esEs10(xy4000, xy3000) new_esEs7(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs22(xy4000, xy3000, ty_Float) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs10(xy400, xy300) new_esEs6(Left(xy4000), Left(xy3000), ty_Char, bd) -> new_esEs7(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(app(ty_@2, bh), ca)) -> new_esEs15(xy4010, xy3010, bh, ca) new_esEs19(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs11(xy4001, xy3001, eb, ec, ed) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs7(xy400, xy300) new_primPlusNat0(Succ(xy320), xy300000) -> Succ(Succ(new_primPlusNat1(xy320, xy300000))) new_esEs22(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs19(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4002, xy3002, app(app(ty_Either, hg), hh)) -> new_esEs6(xy4002, xy3002, hg, hh) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_Either, bba), bbb), bd) -> new_esEs6(xy4000, xy3000, bba, bbb) new_esEs6(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), bd) -> new_esEs16(xy4000, xy3000, bbh) new_esEs19(xy4000, xy3000, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs14(LT, GT) -> False new_esEs14(GT, LT) -> False new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primPlusNat1(Zero, Zero) -> Zero new_esEs23(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs18(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs20(xy4001, xy3001, ty_Integer) -> new_esEs10(xy4001, xy3001) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs6(Left(xy4000), Left(xy3000), app(ty_[], bcb), bd) -> new_esEs5(xy4000, xy3000, bcb) new_esEs16(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs11(xy4000, xy3000, bdg, bdh, bea) new_esEs6(Left(xy4000), Left(xy3000), ty_Int, bd) -> new_esEs18(xy4000, xy3000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Integer) -> new_esEs10(xy4000, xy3000) new_esEs14(LT, LT) -> True new_esEs24(xy4002, xy3002, ty_Float) -> new_esEs8(xy4002, xy3002) new_esEs22(xy4000, xy3000, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs14(LT, EQ) -> False new_esEs14(EQ, LT) -> False new_esEs16(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs12(xy4000, xy3000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs16(Just(xy4000), Just(xy3000), app(ty_[], bef)) -> new_esEs5(xy4000, xy3000, bef) new_esEs22(xy4000, xy3000, ty_@0) -> new_esEs12(xy4000, xy3000) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Maybe, cb)) -> new_esEs16(xy400, xy300, cb) new_esEs22(xy4000, xy3000, ty_Char) -> new_esEs7(xy4000, xy3000) new_esEs6(Left(xy4000), Left(xy3000), ty_Ordering, bd) -> new_esEs14(xy4000, xy3000) new_esEs12(@0, @0) -> True new_esEs24(xy4002, xy3002, app(app(app(ty_@3, baa), bab), bac)) -> new_esEs11(xy4002, xy3002, baa, bab, bac) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Ordering) -> new_esEs14(xy4000, xy3000) new_primPlusNat1(Succ(xy3200), Zero) -> Succ(xy3200) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4001, xy3001, app(ty_Ratio, he)) -> new_esEs17(xy4001, xy3001, he) new_esEs8(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs18(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs21(xy4010, xy3010, ty_@0) -> new_esEs12(xy4010, xy3010) new_esEs4(xy400, xy300, ty_@0) -> new_esEs12(xy400, xy300) new_esEs19(xy4000, xy3000, ty_Bool) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4001, xy3001, app(app(ty_@2, ee), ef)) -> new_esEs15(xy4001, xy3001, ee, ef) new_esEs13(True, True) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, app(app(ty_@2, bch), bda)) -> new_esEs15(xy4000, xy3000, bch, bda) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bc), bd)) -> new_esEs6(xy400, xy300, bc, bd) new_esEs24(xy4002, xy3002, app(ty_Maybe, baf)) -> new_esEs16(xy4002, xy3002, baf) new_esEs24(xy4002, xy3002, app(ty_Ratio, bag)) -> new_esEs17(xy4002, xy3002, bag) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs18(xy4001, xy3001) new_esEs24(xy4002, xy3002, ty_Integer) -> new_esEs10(xy4002, xy3002) new_esEs5(:(xy4010, xy4011), [], bb) -> False new_esEs5([], :(xy3010, xy3011), bb) -> False new_primEqNat0(Zero, Zero) -> True new_esEs21(xy4010, xy3010, ty_Int) -> new_esEs18(xy4010, xy3010) new_esEs20(xy4001, xy3001, ty_Bool) -> new_esEs13(xy4001, xy3001) new_esEs19(xy4000, xy3000, app(app(ty_@2, dc), dd)) -> new_esEs15(xy4000, xy3000, dc, dd) new_esEs16(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs9(xy4000, xy3000) new_esEs21(xy4010, xy3010, app(ty_[], cd)) -> new_esEs5(xy4010, xy3010, cd) new_esEs6(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bbc), bbd), bbe), bd) -> new_esEs11(xy4000, xy3000, bbc, bbd, bbe) new_asAs(False, xy31) -> False new_esEs4(xy400, xy300, ty_Float) -> new_esEs8(xy400, xy300) new_esEs15(@2(xy4000, xy4001), @2(xy3000, xy3001), bh, ca) -> new_asAs(new_esEs19(xy4000, xy3000, bh), new_esEs20(xy4001, xy3001, ca)) new_esEs21(xy4010, xy3010, ty_Ordering) -> new_esEs14(xy4010, xy3010) new_esEs6(Right(xy4000), Right(xy3000), bc, app(ty_Ratio, bdc)) -> new_esEs17(xy4000, xy3000, bdc) new_esEs23(xy4001, xy3001, ty_Float) -> new_esEs8(xy4001, xy3001) new_esEs23(xy4001, xy3001, app(ty_Maybe, hd)) -> new_esEs16(xy4001, xy3001, hd) new_esEs6(Left(xy4000), Left(xy3000), app(app(ty_@2, bbf), bbg), bd) -> new_esEs15(xy4000, xy3000, bbf, bbg) new_esEs16(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs18(xy4000, xy3000) new_esEs23(xy4001, xy3001, ty_Char) -> new_esEs7(xy4001, xy3001) new_esEs21(xy4010, xy3010, ty_Double) -> new_esEs9(xy4010, xy3010) new_esEs16(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4001, xy3001, app(app(ty_Either, ge), gf)) -> new_esEs6(xy4001, xy3001, ge, gf) new_esEs6(Right(xy4000), Right(xy3000), bc, ty_Bool) -> new_esEs13(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(x0, x1, ty_Char) new_esEs14(EQ, EQ) new_esEs17(:%(x0, x1), :%(x2, x3), x4) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs16(Nothing, Nothing, x0) new_esEs25(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Bool) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primMulNat0(Zero, Zero) new_esEs24(x0, x1, ty_@0) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs20(x0, x1, ty_Bool) new_primPlusNat0(Zero, x0) new_esEs20(x0, x1, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_Integer) new_primMulNat0(Succ(x0), Zero) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs6(Right(x0), Right(x1), x2, ty_Char) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs23(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs24(x0, x1, ty_Integer) new_esEs6(Right(x0), Right(x1), x2, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, ty_@0) new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5([], [], x0) new_esEs19(x0, x1, ty_Double) new_esEs16(Just(x0), Nothing, x1) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Integer, x2) new_esEs21(x0, x1, ty_Bool) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Float) new_esEs6(Left(x0), Left(x1), ty_@0, x2) new_esEs22(x0, x1, ty_@0) new_esEs16(Just(x0), Just(x1), ty_Int) new_primPlusNat0(Succ(x0), x1) new_esEs19(x0, x1, ty_Float) new_esEs6(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Double, x2) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Integer) new_esEs19(x0, x1, ty_@0) new_asAs(True, x0) new_asAs(False, x0) new_esEs23(x0, x1, ty_Ordering) new_esEs14(EQ, GT) new_esEs14(GT, EQ) new_esEs21(x0, x1, ty_Char) new_esEs13(True, True) new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Bool) new_esEs6(Right(x0), Right(x1), x2, ty_Float) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs21(x0, x1, ty_@0) new_sr(Neg(x0), Neg(x1)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(x0, x1, ty_Float) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs6(Left(x0), Left(x1), ty_Bool, x2) new_esEs16(Just(x0), Just(x1), ty_Char) new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(x0, x1, ty_Bool) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs16(Just(x0), Just(x1), ty_Double) new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs24(x0, x1, ty_Double) new_esEs10(Integer(x0), Integer(x1)) new_esEs6(Left(x0), Right(x1), x2, x3) new_esEs6(Right(x0), Left(x1), x2, x3) new_esEs5(:(x0, x1), [], x2) new_esEs6(Left(x0), Left(x1), ty_Char, x2) new_esEs24(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Ordering) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Ordering) new_esEs16(Just(x0), Just(x1), app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_primMulNat0(Zero, Succ(x0)) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_Int) new_esEs21(x0, x1, ty_Double) new_esEs12(@0, @0) new_esEs6(Left(x0), Left(x1), ty_Int, x2) new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs24(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Float) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(Just(x0), Just(x1), ty_@0) new_esEs5(:(x0, x1), :(x2, x3), x4) new_esEs26(x0, x1, ty_Integer) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Float) new_esEs4(x0, x1, ty_Char) new_esEs14(LT, EQ) new_esEs14(EQ, LT) new_esEs6(Right(x0), Right(x1), x2, ty_Double) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs15(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs4(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Int) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs6(Left(x0), Left(x1), ty_Ordering, x2) new_esEs6(Right(x0), Right(x1), x2, ty_Ordering) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs14(GT, GT) new_esEs19(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Int) new_esEs9(Double(x0, x1), Double(x2, x3)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs14(LT, GT) new_esEs14(GT, LT) new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs6(Left(x0), Left(x1), ty_Float, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat1(Zero, Succ(x0)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs19(x0, x1, ty_Bool) new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs13(False, True) new_esEs13(True, False) new_esEs19(x0, x1, ty_Ordering) new_esEs8(Float(x0, x1), Float(x2, x3)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs16(Just(x0), Just(x1), ty_Integer) new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Ordering) new_esEs6(Right(x0), Right(x1), x2, ty_Integer) new_esEs20(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs6(Right(x0), Right(x1), x2, ty_Bool) new_esEs14(LT, LT) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs16(Just(x0), Just(x1), ty_Ordering) new_esEs23(x0, x1, ty_Int) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs23(x0, x1, ty_Double) new_sr(Pos(x0), Pos(x1)) new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Integer) new_esEs18(x0, x1) new_esEs21(x0, x1, ty_Integer) new_esEs23(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Char) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs16(Nothing, Just(x0), x1) new_esEs7(Char(x0), Char(x1)) new_esEs5([], :(x0, x1), x2) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (25) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) -> new_deleteBy(:(xy15, xy16), xy12, ba) The graph contains the following edges 1 >= 2, 7 >= 3 *new_deleteBy(:(xy400, xy401), :([], xy31), bb) -> new_deleteBy(:(xy400, xy401), xy31, bb) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 *new_deleteBy(:(xy400, xy401), :(:(xy300, xy301), xy31), bb) -> new_deleteBy0(xy31, xy300, xy301, xy400, xy401, new_asAs(new_esEs4(xy400, xy300, bb), new_esEs5(xy401, xy301, bb)), bb) The graph contains the following edges 2 > 1, 2 > 2, 2 > 3, 1 > 4, 1 > 5, 3 >= 7 ---------------------------------------- (26) YES ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(xy3200), Succ(xy3000000)) -> new_primPlusNat(xy3200, xy3000000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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(xy3200), Succ(xy3000000)) -> new_primPlusNat(xy3200, xy3000000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (29) YES ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(xy40000), Succ(xy30000)) -> new_primEqNat(xy40000, xy30000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_primEqNat(Succ(xy40000), Succ(xy30000)) -> new_primEqNat(xy40000, xy30000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (32) YES