/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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, 12 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) DependencyGraphProof [EQUIVALENT, 0 ms] (11) AND (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] (23) YES (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 14 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", weight=3]; 5[label="foldl (flip List.delete) xy3 xy4",fontsize=16,color="burlywood",shape="triangle"];717[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 717[label="",style="solid", color="burlywood", weight=9]; 717 -> 6[label="",style="solid", color="burlywood", weight=3]; 718[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 718[label="",style="solid", color="burlywood", weight=9]; 718 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="foldl (flip List.delete) xy3 (xy40 : xy41)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="foldl (flip List.delete) xy3 []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8 -> 5[label="",style="dashed", color="red", weight=0]; 8[label="foldl (flip List.delete) (flip List.delete xy3 xy40) xy41",fontsize=16,color="magenta"];8 -> 10[label="",style="dashed", color="magenta", weight=3]; 8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="xy3",fontsize=16,color="green",shape="box"];10[label="xy41",fontsize=16,color="green",shape="box"];11[label="flip List.delete xy3 xy40",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 12[label="List.delete xy40 xy3",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 13[label="List.deleteBy (==) xy40 xy3",fontsize=16,color="burlywood",shape="triangle"];719[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];13 -> 719[label="",style="solid", color="burlywood", weight=9]; 719 -> 14[label="",style="solid", color="burlywood", weight=3]; 720[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 720[label="",style="solid", color="burlywood", weight=9]; 720 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="List.deleteBy (==) xy40 (xy30 : 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32[label="xy300",fontsize=16,color="green",shape="box"];33[label="xy400 == xy300",fontsize=16,color="blue",shape="box"];727[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 727[label="",style="solid", color="blue", weight=9]; 727 -> 38[label="",style="solid", color="blue", weight=3]; 728[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 728[label="",style="solid", color="blue", weight=9]; 728 -> 39[label="",style="solid", color="blue", weight=3]; 729[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 729[label="",style="solid", color="blue", weight=9]; 729 -> 40[label="",style="solid", color="blue", weight=3]; 730[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 730[label="",style="solid", color="blue", weight=9]; 730 -> 41[label="",style="solid", color="blue", weight=3]; 731[label="== :: (Either a 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Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 740[label="",style="solid", color="blue", weight=9]; 740 -> 51[label="",style="solid", color="blue", weight=3]; 34[label="xy31",fontsize=16,color="green",shape="box"];35[label="xy400",fontsize=16,color="green",shape="box"];31[label="List.deleteBy0 xy10 (Just xy11) (==) (Just xy12) xy13",fontsize=16,color="burlywood",shape="triangle"];741[label="xy13/False",fontsize=10,color="white",style="solid",shape="box"];31 -> 741[label="",style="solid", color="burlywood", weight=9]; 741 -> 52[label="",style="solid", color="burlywood", weight=3]; 742[label="xy13/True",fontsize=10,color="white",style="solid",shape="box"];31 -> 742[label="",style="solid", color="burlywood", weight=9]; 742 -> 53[label="",style="solid", color="burlywood", weight=3]; 36 -> 13[label="",style="dashed", color="red", weight=0]; 36[label="List.deleteBy (==) Nothing xy31",fontsize=16,color="magenta"];36 -> 54[label="",style="dashed", color="magenta", weight=3]; 36 -> 55[label="",style="dashed", color="magenta", weight=3]; 37 -> 13[label="",style="dashed", color="red", weight=0]; 37[label="List.deleteBy (==) (Just xy400) xy31",fontsize=16,color="magenta"];37 -> 56[label="",style="dashed", color="magenta", weight=3]; 37 -> 57[label="",style="dashed", color="magenta", weight=3]; 38[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];743[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];38 -> 743[label="",style="solid", color="burlywood", weight=9]; 743 -> 58[label="",style="solid", color="burlywood", weight=3]; 744[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];38 -> 744[label="",style="solid", color="burlywood", weight=9]; 744 -> 59[label="",style="solid", color="burlywood", weight=3]; 39[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];745[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];39 -> 745[label="",style="solid", color="burlywood", weight=9]; 745 -> 60[label="",style="solid", color="burlywood", weight=3]; 40[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];746[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];40 -> 746[label="",style="solid", color="burlywood", weight=9]; 746 -> 61[label="",style="solid", color="burlywood", weight=3]; 41[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];747[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];41 -> 747[label="",style="solid", color="burlywood", weight=9]; 747 -> 62[label="",style="solid", color="burlywood", weight=3]; 42[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];748[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];42 -> 748[label="",style="solid", color="burlywood", weight=9]; 748 -> 63[label="",style="solid", color="burlywood", weight=3]; 749[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];42 -> 749[label="",style="solid", color="burlywood", weight=9]; 749 -> 64[label="",style="solid", color="burlywood", weight=3]; 43[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];750[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];43 -> 750[label="",style="solid", color="burlywood", weight=9]; 750 -> 65[label="",style="solid", color="burlywood", weight=3]; 44[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];751[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];44 -> 751[label="",style="solid", color="burlywood", weight=9]; 751 -> 66[label="",style="solid", color="burlywood", weight=3]; 752[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];44 -> 752[label="",style="solid", color="burlywood", weight=9]; 752 -> 67[label="",style="solid", color="burlywood", weight=3]; 45[label="xy400 == 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color="burlywood", weight=9]; 758 -> 77[label="",style="solid", color="burlywood", weight=3]; 52[label="List.deleteBy0 xy10 (Just xy11) (==) (Just xy12) False",fontsize=16,color="black",shape="box"];52 -> 78[label="",style="solid", color="black", weight=3]; 53[label="List.deleteBy0 xy10 (Just xy11) (==) (Just xy12) True",fontsize=16,color="black",shape="box"];53 -> 79[label="",style="solid", color="black", weight=3]; 54[label="Nothing",fontsize=16,color="green",shape="box"];55[label="xy31",fontsize=16,color="green",shape="box"];56[label="Just xy400",fontsize=16,color="green",shape="box"];57[label="xy31",fontsize=16,color="green",shape="box"];58[label="False == xy300",fontsize=16,color="burlywood",shape="box"];759[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];58 -> 759[label="",style="solid", color="burlywood", weight=9]; 759 -> 80[label="",style="solid", color="burlywood", weight=3]; 760[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];58 -> 760[label="",style="solid", color="burlywood", weight=9]; 760 -> 81[label="",style="solid", color="burlywood", weight=3]; 59[label="True == xy300",fontsize=16,color="burlywood",shape="box"];761[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];59 -> 761[label="",style="solid", color="burlywood", weight=9]; 761 -> 82[label="",style="solid", color="burlywood", weight=3]; 762[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];59 -> 762[label="",style="solid", color="burlywood", weight=9]; 762 -> 83[label="",style="solid", color="burlywood", weight=3]; 60[label="Integer xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];763[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];60 -> 763[label="",style="solid", color="burlywood", weight=9]; 763 -> 84[label="",style="solid", color="burlywood", weight=3]; 61[label="() == xy300",fontsize=16,color="burlywood",shape="box"];764[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];61 -> 764[label="",style="solid", color="burlywood", weight=9]; 764 -> 85[label="",style="solid", color="burlywood", weight=3]; 62[label="(xy4000,xy4001) == xy300",fontsize=16,color="burlywood",shape="box"];765[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];62 -> 765[label="",style="solid", color="burlywood", weight=9]; 765 -> 86[label="",style="solid", color="burlywood", weight=3]; 63[label="Left xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];766[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];63 -> 766[label="",style="solid", color="burlywood", weight=9]; 766 -> 87[label="",style="solid", color="burlywood", weight=3]; 767[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];63 -> 767[label="",style="solid", color="burlywood", weight=9]; 767 -> 88[label="",style="solid", color="burlywood", weight=3]; 64[label="Right xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];768[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];64 -> 768[label="",style="solid", color="burlywood", weight=9]; 768 -> 89[label="",style="solid", color="burlywood", weight=3]; 769[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];64 -> 769[label="",style="solid", color="burlywood", weight=9]; 769 -> 90[label="",style="solid", color="burlywood", weight=3]; 65[label="(xy4000,xy4001,xy4002) == xy300",fontsize=16,color="burlywood",shape="box"];770[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];65 -> 770[label="",style="solid", color="burlywood", weight=9]; 770 -> 91[label="",style="solid", color="burlywood", weight=3]; 66[label="Nothing == xy300",fontsize=16,color="burlywood",shape="box"];771[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];66 -> 771[label="",style="solid", color="burlywood", weight=9]; 771 -> 92[label="",style="solid", color="burlywood", weight=3]; 772[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];66 -> 772[label="",style="solid", color="burlywood", weight=9]; 772 -> 93[label="",style="solid", color="burlywood", weight=3]; 67[label="Just xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];773[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];67 -> 773[label="",style="solid", color="burlywood", weight=9]; 773 -> 94[label="",style="solid", color="burlywood", weight=3]; 774[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];67 -> 774[label="",style="solid", color="burlywood", weight=9]; 774 -> 95[label="",style="solid", color="burlywood", weight=3]; 68[label="primEqChar xy400 xy300",fontsize=16,color="burlywood",shape="box"];775[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];68 -> 775[label="",style="solid", color="burlywood", weight=9]; 775 -> 96[label="",style="solid", color="burlywood", weight=3]; 69[label="primEqInt xy400 xy300",fontsize=16,color="burlywood",shape="triangle"];776[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];69 -> 776[label="",style="solid", color="burlywood", weight=9]; 776 -> 97[label="",style="solid", color="burlywood", weight=3]; 777[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];69 -> 777[label="",style="solid", color="burlywood", weight=9]; 777 -> 98[label="",style="solid", color="burlywood", weight=3]; 70[label="primEqDouble xy400 xy300",fontsize=16,color="burlywood",shape="box"];778[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];70 -> 778[label="",style="solid", color="burlywood", weight=9]; 778 -> 99[label="",style="solid", color="burlywood", weight=3]; 71[label="xy4000 : xy4001 == xy300",fontsize=16,color="burlywood",shape="box"];779[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];71 -> 779[label="",style="solid", color="burlywood", weight=9]; 779 -> 100[label="",style="solid", color="burlywood", weight=3]; 780[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];71 -> 780[label="",style="solid", color="burlywood", weight=9]; 780 -> 101[label="",style="solid", color="burlywood", weight=3]; 72[label="[] == xy300",fontsize=16,color="burlywood",shape="box"];781[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];72 -> 781[label="",style="solid", color="burlywood", weight=9]; 781 -> 102[label="",style="solid", color="burlywood", weight=3]; 782[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];72 -> 782[label="",style="solid", color="burlywood", weight=9]; 782 -> 103[label="",style="solid", color="burlywood", weight=3]; 73[label="LT == xy300",fontsize=16,color="burlywood",shape="box"];783[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];73 -> 783[label="",style="solid", color="burlywood", weight=9]; 783 -> 104[label="",style="solid", color="burlywood", weight=3]; 784[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];73 -> 784[label="",style="solid", color="burlywood", weight=9]; 784 -> 105[label="",style="solid", color="burlywood", weight=3]; 785[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];73 -> 785[label="",style="solid", color="burlywood", weight=9]; 785 -> 106[label="",style="solid", color="burlywood", weight=3]; 74[label="EQ == xy300",fontsize=16,color="burlywood",shape="box"];786[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];74 -> 786[label="",style="solid", color="burlywood", weight=9]; 786 -> 107[label="",style="solid", color="burlywood", weight=3]; 787[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];74 -> 787[label="",style="solid", color="burlywood", weight=9]; 787 -> 108[label="",style="solid", color="burlywood", weight=3]; 788[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];74 -> 788[label="",style="solid", color="burlywood", weight=9]; 788 -> 109[label="",style="solid", color="burlywood", weight=3]; 75[label="GT == xy300",fontsize=16,color="burlywood",shape="box"];789[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];75 -> 789[label="",style="solid", color="burlywood", weight=9]; 789 -> 110[label="",style="solid", color="burlywood", weight=3]; 790[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];75 -> 790[label="",style="solid", color="burlywood", weight=9]; 790 -> 111[label="",style="solid", color="burlywood", weight=3]; 791[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];75 -> 791[label="",style="solid", color="burlywood", weight=9]; 791 -> 112[label="",style="solid", color="burlywood", weight=3]; 76[label="primEqFloat xy400 xy300",fontsize=16,color="burlywood",shape="box"];792[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];76 -> 792[label="",style="solid", color="burlywood", weight=9]; 792 -> 113[label="",style="solid", color="burlywood", weight=3]; 77[label="xy4000 :% xy4001 == xy300",fontsize=16,color="burlywood",shape="box"];793[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];77 -> 793[label="",style="solid", color="burlywood", weight=9]; 793 -> 114[label="",style="solid", color="burlywood", weight=3]; 78[label="Just xy11 : List.deleteBy (==) (Just xy12) xy10",fontsize=16,color="green",shape="box"];78 -> 115[label="",style="dashed", color="green", weight=3]; 79[label="xy10",fontsize=16,color="green",shape="box"];80[label="False == False",fontsize=16,color="black",shape="box"];80 -> 116[label="",style="solid", color="black", weight=3]; 81[label="False == True",fontsize=16,color="black",shape="box"];81 -> 117[label="",style="solid", color="black", weight=3]; 82[label="True == False",fontsize=16,color="black",shape="box"];82 -> 118[label="",style="solid", color="black", weight=3]; 83[label="True == True",fontsize=16,color="black",shape="box"];83 -> 119[label="",style="solid", color="black", weight=3]; 84[label="Integer xy4000 == Integer xy3000",fontsize=16,color="black",shape="box"];84 -> 120[label="",style="solid", color="black", weight=3]; 85[label="() == ()",fontsize=16,color="black",shape="box"];85 -> 121[label="",style="solid", color="black", weight=3]; 86[label="(xy4000,xy4001) == (xy3000,xy3001)",fontsize=16,color="black",shape="box"];86 -> 122[label="",style="solid", color="black", weight=3]; 87[label="Left xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];87 -> 123[label="",style="solid", color="black", weight=3]; 88[label="Left xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];88 -> 124[label="",style="solid", color="black", weight=3]; 89[label="Right xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];89 -> 125[label="",style="solid", color="black", weight=3]; 90[label="Right xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];90 -> 126[label="",style="solid", color="black", weight=3]; 91[label="(xy4000,xy4001,xy4002) == (xy3000,xy3001,xy3002)",fontsize=16,color="black",shape="box"];91 -> 127[label="",style="solid", color="black", weight=3]; 92[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];92 -> 128[label="",style="solid", color="black", weight=3]; 93[label="Nothing == Just xy3000",fontsize=16,color="black",shape="box"];93 -> 129[label="",style="solid", color="black", weight=3]; 94[label="Just xy4000 == Nothing",fontsize=16,color="black",shape="box"];94 -> 130[label="",style="solid", color="black", weight=3]; 95[label="Just xy4000 == Just xy3000",fontsize=16,color="black",shape="box"];95 -> 131[label="",style="solid", color="black", weight=3]; 96[label="primEqChar (Char xy4000) xy300",fontsize=16,color="burlywood",shape="box"];794[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];96 -> 794[label="",style="solid", color="burlywood", weight=9]; 794 -> 132[label="",style="solid", color="burlywood", weight=3]; 97[label="primEqInt (Pos xy4000) xy300",fontsize=16,color="burlywood",shape="box"];795[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];97 -> 795[label="",style="solid", color="burlywood", weight=9]; 795 -> 133[label="",style="solid", color="burlywood", weight=3]; 796[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];97 -> 796[label="",style="solid", color="burlywood", weight=9]; 796 -> 134[label="",style="solid", color="burlywood", weight=3]; 98[label="primEqInt (Neg xy4000) xy300",fontsize=16,color="burlywood",shape="box"];797[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];98 -> 797[label="",style="solid", color="burlywood", weight=9]; 797 -> 135[label="",style="solid", color="burlywood", weight=3]; 798[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];98 -> 798[label="",style="solid", color="burlywood", weight=9]; 798 -> 136[label="",style="solid", color="burlywood", weight=3]; 99[label="primEqDouble (Double xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];799[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];99 -> 799[label="",style="solid", color="burlywood", weight=9]; 799 -> 137[label="",style="solid", color="burlywood", weight=3]; 100[label="xy4000 : xy4001 == xy3000 : xy3001",fontsize=16,color="black",shape="box"];100 -> 138[label="",style="solid", color="black", weight=3]; 101[label="xy4000 : xy4001 == []",fontsize=16,color="black",shape="box"];101 -> 139[label="",style="solid", color="black", weight=3]; 102[label="[] == xy3000 : xy3001",fontsize=16,color="black",shape="box"];102 -> 140[label="",style="solid", color="black", weight=3]; 103[label="[] == []",fontsize=16,color="black",shape="box"];103 -> 141[label="",style="solid", color="black", weight=3]; 104[label="LT == LT",fontsize=16,color="black",shape="box"];104 -> 142[label="",style="solid", color="black", weight=3]; 105[label="LT == EQ",fontsize=16,color="black",shape="box"];105 -> 143[label="",style="solid", color="black", weight=3]; 106[label="LT == GT",fontsize=16,color="black",shape="box"];106 -> 144[label="",style="solid", color="black", weight=3]; 107[label="EQ == LT",fontsize=16,color="black",shape="box"];107 -> 145[label="",style="solid", color="black", weight=3]; 108[label="EQ == EQ",fontsize=16,color="black",shape="box"];108 -> 146[label="",style="solid", color="black", weight=3]; 109[label="EQ == GT",fontsize=16,color="black",shape="box"];109 -> 147[label="",style="solid", color="black", weight=3]; 110[label="GT == LT",fontsize=16,color="black",shape="box"];110 -> 148[label="",style="solid", color="black", weight=3]; 111[label="GT == EQ",fontsize=16,color="black",shape="box"];111 -> 149[label="",style="solid", color="black", weight=3]; 112[label="GT == GT",fontsize=16,color="black",shape="box"];112 -> 150[label="",style="solid", color="black", weight=3]; 113[label="primEqFloat (Float xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];800[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];113 -> 800[label="",style="solid", color="burlywood", weight=9]; 800 -> 151[label="",style="solid", color="burlywood", weight=3]; 114[label="xy4000 :% xy4001 == xy3000 :% xy3001",fontsize=16,color="black",shape="box"];114 -> 152[label="",style="solid", color="black", weight=3]; 115 -> 13[label="",style="dashed", color="red", weight=0]; 115[label="List.deleteBy (==) (Just xy12) xy10",fontsize=16,color="magenta"];115 -> 153[label="",style="dashed", color="magenta", weight=3]; 115 -> 154[label="",style="dashed", color="magenta", weight=3]; 116[label="True",fontsize=16,color="green",shape="box"];117[label="False",fontsize=16,color="green",shape="box"];118[label="False",fontsize=16,color="green",shape="box"];119[label="True",fontsize=16,color="green",shape="box"];120 -> 69[label="",style="dashed", color="red", weight=0]; 120[label="primEqInt xy4000 xy3000",fontsize=16,color="magenta"];120 -> 155[label="",style="dashed", color="magenta", weight=3]; 120 -> 156[label="",style="dashed", color="magenta", weight=3]; 121[label="True",fontsize=16,color="green",shape="box"];122 -> 245[label="",style="dashed", color="red", weight=0]; 122[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];122 -> 246[label="",style="dashed", color="magenta", weight=3]; 122 -> 247[label="",style="dashed", color="magenta", weight=3]; 123[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];801[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 801[label="",style="solid", color="blue", weight=9]; 801 -> 167[label="",style="solid", color="blue", weight=3]; 802[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 802[label="",style="solid", color="blue", weight=9]; 802 -> 168[label="",style="solid", color="blue", weight=3]; 803[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 803[label="",style="solid", color="blue", weight=9]; 803 -> 169[label="",style="solid", color="blue", weight=3]; 804[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 804[label="",style="solid", color="blue", weight=9]; 804 -> 170[label="",style="solid", color="blue", weight=3]; 805[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 805[label="",style="solid", color="blue", weight=9]; 805 -> 171[label="",style="solid", color="blue", weight=3]; 806[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 806[label="",style="solid", color="blue", weight=9]; 806 -> 172[label="",style="solid", color="blue", weight=3]; 807[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 807[label="",style="solid", color="blue", weight=9]; 807 -> 173[label="",style="solid", color="blue", weight=3]; 808[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 808[label="",style="solid", color="blue", weight=9]; 808 -> 174[label="",style="solid", color="blue", weight=3]; 809[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 809[label="",style="solid", color="blue", weight=9]; 809 -> 175[label="",style="solid", color="blue", weight=3]; 810[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 810[label="",style="solid", color="blue", weight=9]; 810 -> 176[label="",style="solid", color="blue", weight=3]; 811[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 811[label="",style="solid", color="blue", weight=9]; 811 -> 177[label="",style="solid", color="blue", weight=3]; 812[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 812[label="",style="solid", color="blue", weight=9]; 812 -> 178[label="",style="solid", color="blue", weight=3]; 813[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 813[label="",style="solid", color="blue", weight=9]; 813 -> 179[label="",style="solid", color="blue", weight=3]; 814[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];123 -> 814[label="",style="solid", color="blue", weight=9]; 814 -> 180[label="",style="solid", color="blue", weight=3]; 124[label="False",fontsize=16,color="green",shape="box"];125[label="False",fontsize=16,color="green",shape="box"];126[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];815[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 815[label="",style="solid", color="blue", weight=9]; 815 -> 181[label="",style="solid", color="blue", weight=3]; 816[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 816[label="",style="solid", color="blue", weight=9]; 816 -> 182[label="",style="solid", color="blue", weight=3]; 817[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 817[label="",style="solid", color="blue", weight=9]; 817 -> 183[label="",style="solid", color="blue", weight=3]; 818[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 818[label="",style="solid", color="blue", weight=9]; 818 -> 184[label="",style="solid", color="blue", weight=3]; 819[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 819[label="",style="solid", color="blue", weight=9]; 819 -> 185[label="",style="solid", color="blue", weight=3]; 820[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 820[label="",style="solid", color="blue", weight=9]; 820 -> 186[label="",style="solid", color="blue", weight=3]; 821[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 821[label="",style="solid", color="blue", weight=9]; 821 -> 187[label="",style="solid", color="blue", weight=3]; 822[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 822[label="",style="solid", color="blue", weight=9]; 822 -> 188[label="",style="solid", color="blue", weight=3]; 823[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 823[label="",style="solid", color="blue", weight=9]; 823 -> 189[label="",style="solid", color="blue", weight=3]; 824[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 824[label="",style="solid", color="blue", weight=9]; 824 -> 190[label="",style="solid", color="blue", weight=3]; 825[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 825[label="",style="solid", color="blue", weight=9]; 825 -> 191[label="",style="solid", color="blue", weight=3]; 826[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 826[label="",style="solid", color="blue", weight=9]; 826 -> 192[label="",style="solid", color="blue", weight=3]; 827[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 827[label="",style="solid", color="blue", weight=9]; 827 -> 193[label="",style="solid", color="blue", weight=3]; 828[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];126 -> 828[label="",style="solid", color="blue", weight=9]; 828 -> 194[label="",style="solid", color="blue", weight=3]; 127 -> 245[label="",style="dashed", color="red", weight=0]; 127[label="xy4000 == xy3000 && xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];127 -> 248[label="",style="dashed", color="magenta", weight=3]; 127 -> 249[label="",style="dashed", color="magenta", weight=3]; 128[label="True",fontsize=16,color="green",shape="box"];129[label="False",fontsize=16,color="green",shape="box"];130[label="False",fontsize=16,color="green",shape="box"];131[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];829[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 829[label="",style="solid", color="blue", weight=9]; 829 -> 206[label="",style="solid", color="blue", weight=3]; 830[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 830[label="",style="solid", color="blue", weight=9]; 830 -> 207[label="",style="solid", color="blue", weight=3]; 831[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 831[label="",style="solid", color="blue", weight=9]; 831 -> 208[label="",style="solid", color="blue", weight=3]; 832[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 832[label="",style="solid", color="blue", weight=9]; 832 -> 209[label="",style="solid", color="blue", weight=3]; 833[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 833[label="",style="solid", color="blue", weight=9]; 833 -> 210[label="",style="solid", color="blue", weight=3]; 834[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 834[label="",style="solid", color="blue", weight=9]; 834 -> 211[label="",style="solid", color="blue", weight=3]; 835[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 835[label="",style="solid", color="blue", weight=9]; 835 -> 212[label="",style="solid", color="blue", weight=3]; 836[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 836[label="",style="solid", color="blue", weight=9]; 836 -> 213[label="",style="solid", color="blue", weight=3]; 837[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 837[label="",style="solid", color="blue", weight=9]; 837 -> 214[label="",style="solid", color="blue", weight=3]; 838[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 838[label="",style="solid", color="blue", weight=9]; 838 -> 215[label="",style="solid", color="blue", weight=3]; 839[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 839[label="",style="solid", color="blue", weight=9]; 839 -> 216[label="",style="solid", color="blue", weight=3]; 840[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 840[label="",style="solid", color="blue", weight=9]; 840 -> 217[label="",style="solid", color="blue", weight=3]; 841[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 841[label="",style="solid", color="blue", weight=9]; 841 -> 218[label="",style="solid", color="blue", weight=3]; 842[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 842[label="",style="solid", color="blue", weight=9]; 842 -> 219[label="",style="solid", color="blue", weight=3]; 132[label="primEqChar (Char xy4000) (Char xy3000)",fontsize=16,color="black",shape="box"];132 -> 220[label="",style="solid", color="black", weight=3]; 133[label="primEqInt (Pos (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];843[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];133 -> 843[label="",style="solid", color="burlywood", weight=9]; 843 -> 221[label="",style="solid", color="burlywood", weight=3]; 844[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];133 -> 844[label="",style="solid", color="burlywood", weight=9]; 844 -> 222[label="",style="solid", color="burlywood", weight=3]; 134[label="primEqInt (Pos Zero) xy300",fontsize=16,color="burlywood",shape="box"];845[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];134 -> 845[label="",style="solid", color="burlywood", weight=9]; 845 -> 223[label="",style="solid", color="burlywood", weight=3]; 846[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];134 -> 846[label="",style="solid", color="burlywood", weight=9]; 846 -> 224[label="",style="solid", color="burlywood", weight=3]; 135[label="primEqInt (Neg (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];847[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];135 -> 847[label="",style="solid", color="burlywood", weight=9]; 847 -> 225[label="",style="solid", color="burlywood", weight=3]; 848[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];135 -> 848[label="",style="solid", color="burlywood", weight=9]; 848 -> 226[label="",style="solid", color="burlywood", weight=3]; 136[label="primEqInt (Neg Zero) xy300",fontsize=16,color="burlywood",shape="box"];849[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];136 -> 849[label="",style="solid", color="burlywood", weight=9]; 849 -> 227[label="",style="solid", color="burlywood", weight=3]; 850[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];136 -> 850[label="",style="solid", color="burlywood", weight=9]; 850 -> 228[label="",style="solid", color="burlywood", weight=3]; 137[label="primEqDouble (Double xy4000 xy4001) (Double xy3000 xy3001)",fontsize=16,color="black",shape="box"];137 -> 229[label="",style="solid", color="black", weight=3]; 138 -> 245[label="",style="dashed", color="red", weight=0]; 138[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];138 -> 250[label="",style="dashed", color="magenta", weight=3]; 138 -> 251[label="",style="dashed", color="magenta", weight=3]; 139[label="False",fontsize=16,color="green",shape="box"];140[label="False",fontsize=16,color="green",shape="box"];141[label="True",fontsize=16,color="green",shape="box"];142[label="True",fontsize=16,color="green",shape="box"];143[label="False",fontsize=16,color="green",shape="box"];144[label="False",fontsize=16,color="green",shape="box"];145[label="False",fontsize=16,color="green",shape="box"];146[label="True",fontsize=16,color="green",shape="box"];147[label="False",fontsize=16,color="green",shape="box"];148[label="False",fontsize=16,color="green",shape="box"];149[label="False",fontsize=16,color="green",shape="box"];150[label="True",fontsize=16,color="green",shape="box"];151[label="primEqFloat (Float xy4000 xy4001) (Float xy3000 xy3001)",fontsize=16,color="black",shape="box"];151 -> 230[label="",style="solid", color="black", weight=3]; 152 -> 245[label="",style="dashed", color="red", weight=0]; 152[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];152 -> 252[label="",style="dashed", color="magenta", weight=3]; 152 -> 253[label="",style="dashed", color="magenta", weight=3]; 153[label="Just xy12",fontsize=16,color="green",shape="box"];154[label="xy10",fontsize=16,color="green",shape="box"];155[label="xy4000",fontsize=16,color="green",shape="box"];156[label="xy3000",fontsize=16,color="green",shape="box"];246[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];851[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 851[label="",style="solid", color="blue", weight=9]; 851 -> 258[label="",style="solid", color="blue", weight=3]; 852[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 852[label="",style="solid", color="blue", weight=9]; 852 -> 259[label="",style="solid", color="blue", weight=3]; 853[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 853[label="",style="solid", color="blue", weight=9]; 853 -> 260[label="",style="solid", color="blue", weight=3]; 854[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 854[label="",style="solid", color="blue", weight=9]; 854 -> 261[label="",style="solid", color="blue", weight=3]; 855[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 855[label="",style="solid", color="blue", weight=9]; 855 -> 262[label="",style="solid", color="blue", weight=3]; 856[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 856[label="",style="solid", color="blue", weight=9]; 856 -> 263[label="",style="solid", color="blue", weight=3]; 857[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 857[label="",style="solid", color="blue", weight=9]; 857 -> 264[label="",style="solid", color="blue", weight=3]; 858[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 858[label="",style="solid", color="blue", weight=9]; 858 -> 265[label="",style="solid", color="blue", weight=3]; 859[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 859[label="",style="solid", color="blue", weight=9]; 859 -> 266[label="",style="solid", color="blue", weight=3]; 860[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 860[label="",style="solid", color="blue", weight=9]; 860 -> 267[label="",style="solid", color="blue", weight=3]; 861[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 861[label="",style="solid", color="blue", weight=9]; 861 -> 268[label="",style="solid", color="blue", weight=3]; 862[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 862[label="",style="solid", color="blue", weight=9]; 862 -> 269[label="",style="solid", color="blue", weight=3]; 863[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 863[label="",style="solid", color="blue", weight=9]; 863 -> 270[label="",style="solid", color="blue", weight=3]; 864[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];246 -> 864[label="",style="solid", color="blue", weight=9]; 864 -> 271[label="",style="solid", color="blue", weight=3]; 247[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];865[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 865[label="",style="solid", color="blue", weight=9]; 865 -> 272[label="",style="solid", color="blue", weight=3]; 866[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 866[label="",style="solid", color="blue", weight=9]; 866 -> 273[label="",style="solid", color="blue", weight=3]; 867[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 867[label="",style="solid", color="blue", weight=9]; 867 -> 274[label="",style="solid", color="blue", weight=3]; 868[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 868[label="",style="solid", color="blue", weight=9]; 868 -> 275[label="",style="solid", color="blue", weight=3]; 869[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 869[label="",style="solid", color="blue", weight=9]; 869 -> 276[label="",style="solid", color="blue", weight=3]; 870[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 870[label="",style="solid", color="blue", weight=9]; 870 -> 277[label="",style="solid", color="blue", weight=3]; 871[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 871[label="",style="solid", color="blue", weight=9]; 871 -> 278[label="",style="solid", color="blue", weight=3]; 872[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 872[label="",style="solid", color="blue", weight=9]; 872 -> 279[label="",style="solid", color="blue", weight=3]; 873[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 873[label="",style="solid", color="blue", weight=9]; 873 -> 280[label="",style="solid", color="blue", weight=3]; 874[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 874[label="",style="solid", color="blue", weight=9]; 874 -> 281[label="",style="solid", color="blue", weight=3]; 875[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 875[label="",style="solid", color="blue", weight=9]; 875 -> 282[label="",style="solid", color="blue", weight=3]; 876[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 876[label="",style="solid", color="blue", weight=9]; 876 -> 283[label="",style="solid", color="blue", weight=3]; 877[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 877[label="",style="solid", color="blue", weight=9]; 877 -> 284[label="",style="solid", color="blue", weight=3]; 878[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 878[label="",style="solid", color="blue", weight=9]; 878 -> 285[label="",style="solid", color="blue", weight=3]; 245[label="xy25 && xy26",fontsize=16,color="burlywood",shape="triangle"];879[label="xy25/False",fontsize=10,color="white",style="solid",shape="box"];245 -> 879[label="",style="solid", color="burlywood", weight=9]; 879 -> 286[label="",style="solid", color="burlywood", weight=3]; 880[label="xy25/True",fontsize=10,color="white",style="solid",shape="box"];245 -> 880[label="",style="solid", color="burlywood", weight=9]; 880 -> 287[label="",style="solid", color="burlywood", weight=3]; 167 -> 38[label="",style="dashed", color="red", weight=0]; 167[label="xy4000 == xy3000",fontsize=16,color="magenta"];167 -> 288[label="",style="dashed", color="magenta", weight=3]; 167 -> 289[label="",style="dashed", color="magenta", weight=3]; 168 -> 39[label="",style="dashed", color="red", weight=0]; 168[label="xy4000 == xy3000",fontsize=16,color="magenta"];168 -> 290[label="",style="dashed", color="magenta", weight=3]; 168 -> 291[label="",style="dashed", color="magenta", weight=3]; 169 -> 40[label="",style="dashed", color="red", weight=0]; 169[label="xy4000 == xy3000",fontsize=16,color="magenta"];169 -> 292[label="",style="dashed", color="magenta", weight=3]; 169 -> 293[label="",style="dashed", color="magenta", weight=3]; 170 -> 41[label="",style="dashed", color="red", weight=0]; 170[label="xy4000 == xy3000",fontsize=16,color="magenta"];170 -> 294[label="",style="dashed", color="magenta", weight=3]; 170 -> 295[label="",style="dashed", color="magenta", weight=3]; 171 -> 42[label="",style="dashed", color="red", weight=0]; 171[label="xy4000 == xy3000",fontsize=16,color="magenta"];171 -> 296[label="",style="dashed", color="magenta", weight=3]; 171 -> 297[label="",style="dashed", color="magenta", weight=3]; 172 -> 43[label="",style="dashed", color="red", weight=0]; 172[label="xy4000 == xy3000",fontsize=16,color="magenta"];172 -> 298[label="",style="dashed", color="magenta", weight=3]; 172 -> 299[label="",style="dashed", color="magenta", weight=3]; 173 -> 44[label="",style="dashed", color="red", weight=0]; 173[label="xy4000 == xy3000",fontsize=16,color="magenta"];173 -> 300[label="",style="dashed", color="magenta", weight=3]; 173 -> 301[label="",style="dashed", color="magenta", weight=3]; 174 -> 45[label="",style="dashed", color="red", weight=0]; 174[label="xy4000 == xy3000",fontsize=16,color="magenta"];174 -> 302[label="",style="dashed", color="magenta", weight=3]; 174 -> 303[label="",style="dashed", color="magenta", weight=3]; 175 -> 46[label="",style="dashed", color="red", weight=0]; 175[label="xy4000 == xy3000",fontsize=16,color="magenta"];175 -> 304[label="",style="dashed", color="magenta", weight=3]; 175 -> 305[label="",style="dashed", color="magenta", weight=3]; 176 -> 47[label="",style="dashed", color="red", weight=0]; 176[label="xy4000 == xy3000",fontsize=16,color="magenta"];176 -> 306[label="",style="dashed", color="magenta", weight=3]; 176 -> 307[label="",style="dashed", color="magenta", weight=3]; 177 -> 48[label="",style="dashed", color="red", weight=0]; 177[label="xy4000 == xy3000",fontsize=16,color="magenta"];177 -> 308[label="",style="dashed", color="magenta", weight=3]; 177 -> 309[label="",style="dashed", color="magenta", weight=3]; 178 -> 49[label="",style="dashed", color="red", weight=0]; 178[label="xy4000 == xy3000",fontsize=16,color="magenta"];178 -> 310[label="",style="dashed", color="magenta", weight=3]; 178 -> 311[label="",style="dashed", color="magenta", weight=3]; 179 -> 50[label="",style="dashed", color="red", weight=0]; 179[label="xy4000 == xy3000",fontsize=16,color="magenta"];179 -> 312[label="",style="dashed", color="magenta", weight=3]; 179 -> 313[label="",style="dashed", color="magenta", weight=3]; 180 -> 51[label="",style="dashed", color="red", weight=0]; 180[label="xy4000 == xy3000",fontsize=16,color="magenta"];180 -> 314[label="",style="dashed", color="magenta", weight=3]; 180 -> 315[label="",style="dashed", color="magenta", weight=3]; 181 -> 38[label="",style="dashed", color="red", weight=0]; 181[label="xy4000 == xy3000",fontsize=16,color="magenta"];181 -> 316[label="",style="dashed", color="magenta", weight=3]; 181 -> 317[label="",style="dashed", color="magenta", weight=3]; 182 -> 39[label="",style="dashed", color="red", weight=0]; 182[label="xy4000 == xy3000",fontsize=16,color="magenta"];182 -> 318[label="",style="dashed", color="magenta", weight=3]; 182 -> 319[label="",style="dashed", color="magenta", weight=3]; 183 -> 40[label="",style="dashed", color="red", weight=0]; 183[label="xy4000 == xy3000",fontsize=16,color="magenta"];183 -> 320[label="",style="dashed", color="magenta", weight=3]; 183 -> 321[label="",style="dashed", color="magenta", weight=3]; 184 -> 41[label="",style="dashed", color="red", weight=0]; 184[label="xy4000 == xy3000",fontsize=16,color="magenta"];184 -> 322[label="",style="dashed", color="magenta", weight=3]; 184 -> 323[label="",style="dashed", color="magenta", weight=3]; 185 -> 42[label="",style="dashed", color="red", weight=0]; 185[label="xy4000 == xy3000",fontsize=16,color="magenta"];185 -> 324[label="",style="dashed", color="magenta", weight=3]; 185 -> 325[label="",style="dashed", color="magenta", weight=3]; 186 -> 43[label="",style="dashed", color="red", weight=0]; 186[label="xy4000 == xy3000",fontsize=16,color="magenta"];186 -> 326[label="",style="dashed", color="magenta", weight=3]; 186 -> 327[label="",style="dashed", color="magenta", weight=3]; 187 -> 44[label="",style="dashed", color="red", weight=0]; 187[label="xy4000 == xy3000",fontsize=16,color="magenta"];187 -> 328[label="",style="dashed", color="magenta", weight=3]; 187 -> 329[label="",style="dashed", color="magenta", weight=3]; 188 -> 45[label="",style="dashed", color="red", weight=0]; 188[label="xy4000 == xy3000",fontsize=16,color="magenta"];188 -> 330[label="",style="dashed", color="magenta", weight=3]; 188 -> 331[label="",style="dashed", color="magenta", weight=3]; 189 -> 46[label="",style="dashed", color="red", weight=0]; 189[label="xy4000 == xy3000",fontsize=16,color="magenta"];189 -> 332[label="",style="dashed", color="magenta", weight=3]; 189 -> 333[label="",style="dashed", color="magenta", weight=3]; 190 -> 47[label="",style="dashed", color="red", weight=0]; 190[label="xy4000 == xy3000",fontsize=16,color="magenta"];190 -> 334[label="",style="dashed", color="magenta", weight=3]; 190 -> 335[label="",style="dashed", color="magenta", weight=3]; 191 -> 48[label="",style="dashed", color="red", weight=0]; 191[label="xy4000 == xy3000",fontsize=16,color="magenta"];191 -> 336[label="",style="dashed", color="magenta", weight=3]; 191 -> 337[label="",style="dashed", color="magenta", weight=3]; 192 -> 49[label="",style="dashed", color="red", weight=0]; 192[label="xy4000 == xy3000",fontsize=16,color="magenta"];192 -> 338[label="",style="dashed", color="magenta", weight=3]; 192 -> 339[label="",style="dashed", color="magenta", weight=3]; 193 -> 50[label="",style="dashed", color="red", weight=0]; 193[label="xy4000 == xy3000",fontsize=16,color="magenta"];193 -> 340[label="",style="dashed", color="magenta", weight=3]; 193 -> 341[label="",style="dashed", color="magenta", weight=3]; 194 -> 51[label="",style="dashed", color="red", weight=0]; 194[label="xy4000 == xy3000",fontsize=16,color="magenta"];194 -> 342[label="",style="dashed", color="magenta", weight=3]; 194 -> 343[label="",style="dashed", color="magenta", weight=3]; 248 -> 245[label="",style="dashed", color="red", weight=0]; 248[label="xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];248 -> 344[label="",style="dashed", color="magenta", weight=3]; 248 -> 345[label="",style="dashed", color="magenta", weight=3]; 249[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];881[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 881[label="",style="solid", color="blue", weight=9]; 881 -> 346[label="",style="solid", color="blue", weight=3]; 882[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 882[label="",style="solid", color="blue", weight=9]; 882 -> 347[label="",style="solid", color="blue", weight=3]; 883[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 883[label="",style="solid", color="blue", weight=9]; 883 -> 348[label="",style="solid", color="blue", weight=3]; 884[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 884[label="",style="solid", color="blue", weight=9]; 884 -> 349[label="",style="solid", color="blue", weight=3]; 885[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 885[label="",style="solid", color="blue", weight=9]; 885 -> 350[label="",style="solid", color="blue", weight=3]; 886[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 886[label="",style="solid", color="blue", weight=9]; 886 -> 351[label="",style="solid", color="blue", weight=3]; 887[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 887[label="",style="solid", color="blue", weight=9]; 887 -> 352[label="",style="solid", color="blue", weight=3]; 888[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 888[label="",style="solid", color="blue", weight=9]; 888 -> 353[label="",style="solid", color="blue", weight=3]; 889[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 889[label="",style="solid", color="blue", weight=9]; 889 -> 354[label="",style="solid", color="blue", weight=3]; 890[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 890[label="",style="solid", color="blue", weight=9]; 890 -> 355[label="",style="solid", color="blue", weight=3]; 891[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 891[label="",style="solid", color="blue", weight=9]; 891 -> 356[label="",style="solid", color="blue", weight=3]; 892[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];249 -> 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911[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 911[label="",style="solid", color="blue", weight=9]; 911 -> 410[label="",style="solid", color="blue", weight=3]; 912[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 912[label="",style="solid", color="blue", weight=9]; 912 -> 411[label="",style="solid", color="blue", weight=3]; 913[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 913[label="",style="solid", color="blue", weight=9]; 913 -> 412[label="",style="solid", color="blue", weight=3]; 914[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 914[label="",style="solid", color="blue", weight=9]; 914 -> 413[label="",style="solid", color="blue", weight=3]; 915[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 915[label="",style="solid", color="blue", weight=9]; 915 -> 414[label="",style="solid", color="blue", weight=3]; 916[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 916[label="",style="solid", color="blue", weight=9]; 916 -> 415[label="",style="solid", color="blue", weight=3]; 917[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 917[label="",style="solid", color="blue", weight=9]; 917 -> 416[label="",style="solid", color="blue", weight=3]; 918[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 918[label="",style="solid", color="blue", weight=9]; 918 -> 417[label="",style="solid", color="blue", weight=3]; 919[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];251 -> 919[label="",style="solid", color="blue", weight=9]; 919 -> 418[label="",style="solid", color="blue", weight=3]; 920[label="== :: Ordering -> 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288[label="xy4000",fontsize=16,color="green",shape="box"];289[label="xy3000",fontsize=16,color="green",shape="box"];290[label="xy4000",fontsize=16,color="green",shape="box"];291[label="xy3000",fontsize=16,color="green",shape="box"];292[label="xy4000",fontsize=16,color="green",shape="box"];293[label="xy3000",fontsize=16,color="green",shape="box"];294[label="xy4000",fontsize=16,color="green",shape="box"];295[label="xy3000",fontsize=16,color="green",shape="box"];296[label="xy4000",fontsize=16,color="green",shape="box"];297[label="xy3000",fontsize=16,color="green",shape="box"];298[label="xy4000",fontsize=16,color="green",shape="box"];299[label="xy3000",fontsize=16,color="green",shape="box"];300[label="xy4000",fontsize=16,color="green",shape="box"];301[label="xy3000",fontsize=16,color="green",shape="box"];302[label="xy4000",fontsize=16,color="green",shape="box"];303[label="xy3000",fontsize=16,color="green",shape="box"];304[label="xy4000",fontsize=16,color="green",shape="box"];305[label="xy3000",fontsize=16,color="green",shape="box"];306[label="xy4000",fontsize=16,color="green",shape="box"];307[label="xy3000",fontsize=16,color="green",shape="box"];308[label="xy4000",fontsize=16,color="green",shape="box"];309[label="xy3000",fontsize=16,color="green",shape="box"];310[label="xy4000",fontsize=16,color="green",shape="box"];311[label="xy3000",fontsize=16,color="green",shape="box"];312[label="xy4000",fontsize=16,color="green",shape="box"];313[label="xy3000",fontsize=16,color="green",shape="box"];314[label="xy4000",fontsize=16,color="green",shape="box"];315[label="xy3000",fontsize=16,color="green",shape="box"];316[label="xy4000",fontsize=16,color="green",shape="box"];317[label="xy3000",fontsize=16,color="green",shape="box"];318[label="xy4000",fontsize=16,color="green",shape="box"];319[label="xy3000",fontsize=16,color="green",shape="box"];320[label="xy4000",fontsize=16,color="green",shape="box"];321[label="xy3000",fontsize=16,color="green",shape="box"];322[label="xy4000",fontsize=16,color="green",shape="box"];323[label="xy3000",fontsize=16,color="green",shape="box"];324[label="xy4000",fontsize=16,color="green",shape="box"];325[label="xy3000",fontsize=16,color="green",shape="box"];326[label="xy4000",fontsize=16,color="green",shape="box"];327[label="xy3000",fontsize=16,color="green",shape="box"];328[label="xy4000",fontsize=16,color="green",shape="box"];329[label="xy3000",fontsize=16,color="green",shape="box"];330[label="xy4000",fontsize=16,color="green",shape="box"];331[label="xy3000",fontsize=16,color="green",shape="box"];332[label="xy4000",fontsize=16,color="green",shape="box"];333[label="xy3000",fontsize=16,color="green",shape="box"];334[label="xy4000",fontsize=16,color="green",shape="box"];335[label="xy3000",fontsize=16,color="green",shape="box"];336[label="xy4000",fontsize=16,color="green",shape="box"];337[label="xy3000",fontsize=16,color="green",shape="box"];338[label="xy4000",fontsize=16,color="green",shape="box"];339[label="xy3000",fontsize=16,color="green",shape="box"];340[label="xy4000",fontsize=16,color="green",shape="box"];341[label="xy3000",fontsize=16,color="green",shape="box"];342[label="xy4000",fontsize=16,color="green",shape="box"];343[label="xy3000",fontsize=16,color="green",shape="box"];344[label="xy4002 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Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 931[label="",style="solid", color="blue", weight=9]; 931 -> 490[label="",style="solid", color="blue", weight=3]; 932[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 932[label="",style="solid", color="blue", weight=9]; 932 -> 491[label="",style="solid", color="blue", weight=3]; 933[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 933[label="",style="solid", color="blue", weight=9]; 933 -> 492[label="",style="solid", color="blue", weight=3]; 934[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 934[label="",style="solid", color="blue", weight=9]; 934 -> 493[label="",style="solid", color="blue", weight=3]; 935[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 935[label="",style="solid", color="blue", weight=9]; 935 -> 494[label="",style="solid", color="blue", weight=3]; 936[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 936[label="",style="solid", color="blue", weight=9]; 936 -> 495[label="",style="solid", color="blue", weight=3]; 937[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 937[label="",style="solid", color="blue", weight=9]; 937 -> 496[label="",style="solid", color="blue", weight=3]; 938[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 938[label="",style="solid", color="blue", weight=9]; 938 -> 497[label="",style="solid", color="blue", weight=3]; 939[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 939[label="",style="solid", color="blue", weight=9]; 939 -> 498[label="",style="solid", color="blue", weight=3]; 940[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];344 -> 940[label="",style="solid", color="blue", weight=9]; 940 -> 499[label="",style="solid", color="blue", weight=3]; 345[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];941[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 941[label="",style="solid", color="blue", weight=9]; 941 -> 500[label="",style="solid", color="blue", weight=3]; 942[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 942[label="",style="solid", color="blue", weight=9]; 942 -> 501[label="",style="solid", color="blue", weight=3]; 943[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 943[label="",style="solid", color="blue", weight=9]; 943 -> 502[label="",style="solid", color="blue", weight=3]; 944[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 944[label="",style="solid", color="blue", weight=9]; 944 -> 503[label="",style="solid", color="blue", weight=3]; 945[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 945[label="",style="solid", color="blue", weight=9]; 945 -> 504[label="",style="solid", color="blue", weight=3]; 946[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 946[label="",style="solid", color="blue", weight=9]; 946 -> 505[label="",style="solid", color="blue", weight=3]; 947[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 947[label="",style="solid", color="blue", weight=9]; 947 -> 506[label="",style="solid", color="blue", weight=3]; 948[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 948[label="",style="solid", color="blue", weight=9]; 948 -> 507[label="",style="solid", color="blue", weight=3]; 949[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 949[label="",style="solid", color="blue", weight=9]; 949 -> 508[label="",style="solid", color="blue", weight=3]; 950[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 950[label="",style="solid", color="blue", weight=9]; 950 -> 509[label="",style="solid", color="blue", weight=3]; 951[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 951[label="",style="solid", color="blue", weight=9]; 951 -> 510[label="",style="solid", color="blue", weight=3]; 952[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 952[label="",style="solid", color="blue", weight=9]; 952 -> 511[label="",style="solid", color="blue", weight=3]; 953[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 953[label="",style="solid", color="blue", weight=9]; 953 -> 512[label="",style="solid", color="blue", weight=3]; 954[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 954[label="",style="solid", color="blue", weight=9]; 954 -> 513[label="",style="solid", color="blue", weight=3]; 346 -> 38[label="",style="dashed", color="red", weight=0]; 346[label="xy4000 == xy3000",fontsize=16,color="magenta"];346 -> 514[label="",style="dashed", color="magenta", weight=3]; 346 -> 515[label="",style="dashed", color="magenta", weight=3]; 347 -> 39[label="",style="dashed", color="red", weight=0]; 347[label="xy4000 == xy3000",fontsize=16,color="magenta"];347 -> 516[label="",style="dashed", color="magenta", weight=3]; 347 -> 517[label="",style="dashed", color="magenta", weight=3]; 348 -> 40[label="",style="dashed", color="red", weight=0]; 348[label="xy4000 == xy3000",fontsize=16,color="magenta"];348 -> 518[label="",style="dashed", color="magenta", weight=3]; 348 -> 519[label="",style="dashed", color="magenta", weight=3]; 349 -> 41[label="",style="dashed", color="red", weight=0]; 349[label="xy4000 == xy3000",fontsize=16,color="magenta"];349 -> 520[label="",style="dashed", color="magenta", weight=3]; 349 -> 521[label="",style="dashed", color="magenta", weight=3]; 350 -> 42[label="",style="dashed", color="red", weight=0]; 350[label="xy4000 == xy3000",fontsize=16,color="magenta"];350 -> 522[label="",style="dashed", color="magenta", weight=3]; 350 -> 523[label="",style="dashed", color="magenta", weight=3]; 351 -> 43[label="",style="dashed", color="red", weight=0]; 351[label="xy4000 == xy3000",fontsize=16,color="magenta"];351 -> 524[label="",style="dashed", color="magenta", weight=3]; 351 -> 525[label="",style="dashed", color="magenta", weight=3]; 352 -> 44[label="",style="dashed", color="red", weight=0]; 352[label="xy4000 == xy3000",fontsize=16,color="magenta"];352 -> 526[label="",style="dashed", color="magenta", weight=3]; 352 -> 527[label="",style="dashed", color="magenta", weight=3]; 353 -> 45[label="",style="dashed", color="red", weight=0]; 353[label="xy4000 == xy3000",fontsize=16,color="magenta"];353 -> 528[label="",style="dashed", color="magenta", weight=3]; 353 -> 529[label="",style="dashed", color="magenta", weight=3]; 354 -> 46[label="",style="dashed", color="red", weight=0]; 354[label="xy4000 == xy3000",fontsize=16,color="magenta"];354 -> 530[label="",style="dashed", color="magenta", weight=3]; 354 -> 531[label="",style="dashed", color="magenta", weight=3]; 355 -> 47[label="",style="dashed", color="red", weight=0]; 355[label="xy4000 == xy3000",fontsize=16,color="magenta"];355 -> 532[label="",style="dashed", color="magenta", weight=3]; 355 -> 533[label="",style="dashed", color="magenta", weight=3]; 356 -> 48[label="",style="dashed", color="red", weight=0]; 356[label="xy4000 == xy3000",fontsize=16,color="magenta"];356 -> 534[label="",style="dashed", color="magenta", weight=3]; 356 -> 535[label="",style="dashed", color="magenta", weight=3]; 357 -> 49[label="",style="dashed", color="red", weight=0]; 357[label="xy4000 == xy3000",fontsize=16,color="magenta"];357 -> 536[label="",style="dashed", color="magenta", weight=3]; 357 -> 537[label="",style="dashed", color="magenta", weight=3]; 358 -> 50[label="",style="dashed", color="red", weight=0]; 358[label="xy4000 == xy3000",fontsize=16,color="magenta"];358 -> 538[label="",style="dashed", color="magenta", weight=3]; 358 -> 539[label="",style="dashed", color="magenta", weight=3]; 359 -> 51[label="",style="dashed", color="red", weight=0]; 359[label="xy4000 == xy3000",fontsize=16,color="magenta"];359 -> 540[label="",style="dashed", color="magenta", weight=3]; 359 -> 541[label="",style="dashed", color="magenta", weight=3]; 360[label="xy4000",fontsize=16,color="green",shape="box"];361[label="xy3000",fontsize=16,color="green",shape="box"];362[label="xy4000",fontsize=16,color="green",shape="box"];363[label="xy3000",fontsize=16,color="green",shape="box"];364[label="xy4000",fontsize=16,color="green",shape="box"];365[label="xy3000",fontsize=16,color="green",shape="box"];366[label="xy4000",fontsize=16,color="green",shape="box"];367[label="xy3000",fontsize=16,color="green",shape="box"];368[label="xy4000",fontsize=16,color="green",shape="box"];369[label="xy3000",fontsize=16,color="green",shape="box"];370[label="xy4000",fontsize=16,color="green",shape="box"];371[label="xy3000",fontsize=16,color="green",shape="box"];372[label="xy4000",fontsize=16,color="green",shape="box"];373[label="xy3000",fontsize=16,color="green",shape="box"];374[label="xy4000",fontsize=16,color="green",shape="box"];375[label="xy3000",fontsize=16,color="green",shape="box"];376[label="xy4000",fontsize=16,color="green",shape="box"];377[label="xy3000",fontsize=16,color="green",shape="box"];378[label="xy4000",fontsize=16,color="green",shape="box"];379[label="xy3000",fontsize=16,color="green",shape="box"];380[label="xy4000",fontsize=16,color="green",shape="box"];381[label="xy3000",fontsize=16,color="green",shape="box"];382[label="xy4000",fontsize=16,color="green",shape="box"];383[label="xy3000",fontsize=16,color="green",shape="box"];384[label="xy4000",fontsize=16,color="green",shape="box"];385[label="xy3000",fontsize=16,color="green",shape="box"];386[label="xy4000",fontsize=16,color="green",shape="box"];387[label="xy3000",fontsize=16,color="green",shape="box"];388[label="primEqNat 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390[label="primEqInt (Pos (Succ xy40000)) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];390 -> 546[label="",style="solid", color="black", weight=3]; 391[label="primEqInt (Pos (Succ xy40000)) (Pos Zero)",fontsize=16,color="black",shape="box"];391 -> 547[label="",style="solid", color="black", weight=3]; 392[label="False",fontsize=16,color="green",shape="box"];393[label="primEqInt (Pos Zero) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];393 -> 548[label="",style="solid", color="black", weight=3]; 394[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];394 -> 549[label="",style="solid", color="black", weight=3]; 395[label="primEqInt (Pos Zero) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];395 -> 550[label="",style="solid", color="black", weight=3]; 396[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];396 -> 551[label="",style="solid", color="black", weight=3]; 397[label="False",fontsize=16,color="green",shape="box"];398[label="primEqInt (Neg (Succ xy40000)) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];398 -> 552[label="",style="solid", color="black", weight=3]; 399[label="primEqInt (Neg (Succ xy40000)) (Neg Zero)",fontsize=16,color="black",shape="box"];399 -> 553[label="",style="solid", color="black", weight=3]; 400[label="primEqInt (Neg Zero) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];400 -> 554[label="",style="solid", color="black", weight=3]; 401[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];401 -> 555[label="",style="solid", color="black", weight=3]; 402[label="primEqInt (Neg Zero) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];402 -> 556[label="",style="solid", color="black", weight=3]; 403[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];403 -> 557[label="",style="solid", color="black", weight=3]; 404[label="xy4000 * xy3001",fontsize=16,color="black",shape="triangle"];404 -> 558[label="",style="solid", color="black", weight=3]; 405 -> 404[label="",style="dashed", color="red", weight=0]; 405[label="xy4001 * xy3000",fontsize=16,color="magenta"];405 -> 559[label="",style="dashed", color="magenta", weight=3]; 405 -> 560[label="",style="dashed", color="magenta", weight=3]; 406[label="xy4001",fontsize=16,color="green",shape="box"];407[label="xy3001",fontsize=16,color="green",shape="box"];408 -> 38[label="",style="dashed", color="red", weight=0]; 408[label="xy4000 == xy3000",fontsize=16,color="magenta"];408 -> 561[label="",style="dashed", color="magenta", weight=3]; 408 -> 562[label="",style="dashed", color="magenta", weight=3]; 409 -> 39[label="",style="dashed", color="red", weight=0]; 409[label="xy4000 == xy3000",fontsize=16,color="magenta"];409 -> 563[label="",style="dashed", color="magenta", weight=3]; 409 -> 564[label="",style="dashed", color="magenta", weight=3]; 410 -> 40[label="",style="dashed", color="red", weight=0]; 410[label="xy4000 == xy3000",fontsize=16,color="magenta"];410 -> 565[label="",style="dashed", color="magenta", weight=3]; 410 -> 566[label="",style="dashed", color="magenta", weight=3]; 411 -> 41[label="",style="dashed", color="red", weight=0]; 411[label="xy4000 == xy3000",fontsize=16,color="magenta"];411 -> 567[label="",style="dashed", color="magenta", weight=3]; 411 -> 568[label="",style="dashed", color="magenta", weight=3]; 412 -> 42[label="",style="dashed", color="red", weight=0]; 412[label="xy4000 == xy3000",fontsize=16,color="magenta"];412 -> 569[label="",style="dashed", color="magenta", weight=3]; 412 -> 570[label="",style="dashed", color="magenta", weight=3]; 413 -> 43[label="",style="dashed", color="red", weight=0]; 413[label="xy4000 == xy3000",fontsize=16,color="magenta"];413 -> 571[label="",style="dashed", color="magenta", weight=3]; 413 -> 572[label="",style="dashed", color="magenta", weight=3]; 414 -> 44[label="",style="dashed", color="red", weight=0]; 414[label="xy4000 == xy3000",fontsize=16,color="magenta"];414 -> 573[label="",style="dashed", color="magenta", weight=3]; 414 -> 574[label="",style="dashed", color="magenta", weight=3]; 415 -> 45[label="",style="dashed", color="red", weight=0]; 415[label="xy4000 == xy3000",fontsize=16,color="magenta"];415 -> 575[label="",style="dashed", color="magenta", weight=3]; 415 -> 576[label="",style="dashed", color="magenta", weight=3]; 416 -> 46[label="",style="dashed", color="red", weight=0]; 416[label="xy4000 == xy3000",fontsize=16,color="magenta"];416 -> 577[label="",style="dashed", color="magenta", weight=3]; 416 -> 578[label="",style="dashed", color="magenta", weight=3]; 417 -> 47[label="",style="dashed", color="red", weight=0]; 417[label="xy4000 == xy3000",fontsize=16,color="magenta"];417 -> 579[label="",style="dashed", color="magenta", weight=3]; 417 -> 580[label="",style="dashed", color="magenta", weight=3]; 418 -> 48[label="",style="dashed", color="red", weight=0]; 418[label="xy4000 == xy3000",fontsize=16,color="magenta"];418 -> 581[label="",style="dashed", color="magenta", weight=3]; 418 -> 582[label="",style="dashed", color="magenta", weight=3]; 419 -> 49[label="",style="dashed", color="red", weight=0]; 419[label="xy4000 == xy3000",fontsize=16,color="magenta"];419 -> 583[label="",style="dashed", color="magenta", weight=3]; 419 -> 584[label="",style="dashed", color="magenta", weight=3]; 420 -> 50[label="",style="dashed", color="red", weight=0]; 420[label="xy4000 == xy3000",fontsize=16,color="magenta"];420 -> 585[label="",style="dashed", color="magenta", weight=3]; 420 -> 586[label="",style="dashed", color="magenta", weight=3]; 421 -> 51[label="",style="dashed", color="red", weight=0]; 421[label="xy4000 == xy3000",fontsize=16,color="magenta"];421 -> 587[label="",style="dashed", color="magenta", weight=3]; 421 -> 588[label="",style="dashed", color="magenta", weight=3]; 422 -> 404[label="",style="dashed", color="red", weight=0]; 422[label="xy4000 * xy3001",fontsize=16,color="magenta"];422 -> 589[label="",style="dashed", color="magenta", weight=3]; 422 -> 590[label="",style="dashed", color="magenta", weight=3]; 423 -> 404[label="",style="dashed", color="red", weight=0]; 423[label="xy4001 * xy3000",fontsize=16,color="magenta"];423 -> 591[label="",style="dashed", color="magenta", weight=3]; 423 -> 592[label="",style="dashed", color="magenta", weight=3]; 424 -> 39[label="",style="dashed", color="red", weight=0]; 424[label="xy4001 == xy3001",fontsize=16,color="magenta"];424 -> 593[label="",style="dashed", color="magenta", weight=3]; 424 -> 594[label="",style="dashed", color="magenta", weight=3]; 425 -> 46[label="",style="dashed", color="red", weight=0]; 425[label="xy4001 == xy3001",fontsize=16,color="magenta"];425 -> 595[label="",style="dashed", color="magenta", weight=3]; 425 -> 596[label="",style="dashed", color="magenta", weight=3]; 426 -> 39[label="",style="dashed", color="red", weight=0]; 426[label="xy4000 == xy3000",fontsize=16,color="magenta"];426 -> 597[label="",style="dashed", color="magenta", weight=3]; 426 -> 598[label="",style="dashed", color="magenta", weight=3]; 427 -> 46[label="",style="dashed", color="red", weight=0]; 427[label="xy4000 == xy3000",fontsize=16,color="magenta"];427 -> 599[label="",style="dashed", color="magenta", weight=3]; 427 -> 600[label="",style="dashed", color="magenta", weight=3]; 428[label="xy4001",fontsize=16,color="green",shape="box"];429[label="xy3001",fontsize=16,color="green",shape="box"];430[label="xy4001",fontsize=16,color="green",shape="box"];431[label="xy3001",fontsize=16,color="green",shape="box"];432[label="xy4001",fontsize=16,color="green",shape="box"];433[label="xy3001",fontsize=16,color="green",shape="box"];434[label="xy4001",fontsize=16,color="green",shape="box"];435[label="xy3001",fontsize=16,color="green",shape="box"];436[label="xy4001",fontsize=16,color="green",shape="box"];437[label="xy3001",fontsize=16,color="green",shape="box"];438[label="xy4001",fontsize=16,color="green",shape="box"];439[label="xy3001",fontsize=16,color="green",shape="box"];440[label="xy4001",fontsize=16,color="green",shape="box"];441[label="xy3001",fontsize=16,color="green",shape="box"];442[label="xy4001",fontsize=16,color="green",shape="box"];443[label="xy3001",fontsize=16,color="green",shape="box"];444[label="xy4001",fontsize=16,color="green",shape="box"];445[label="xy3001",fontsize=16,color="green",shape="box"];446[label="xy4001",fontsize=16,color="green",shape="box"];447[label="xy3001",fontsize=16,color="green",shape="box"];448[label="xy4001",fontsize=16,color="green",shape="box"];449[label="xy3001",fontsize=16,color="green",shape="box"];450[label="xy4001",fontsize=16,color="green",shape="box"];451[label="xy3001",fontsize=16,color="green",shape="box"];452[label="xy4001",fontsize=16,color="green",shape="box"];453[label="xy3001",fontsize=16,color="green",shape="box"];454[label="xy4001",fontsize=16,color="green",shape="box"];455[label="xy3001",fontsize=16,color="green",shape="box"];456[label="xy4000",fontsize=16,color="green",shape="box"];457[label="xy3000",fontsize=16,color="green",shape="box"];458[label="xy4000",fontsize=16,color="green",shape="box"];459[label="xy3000",fontsize=16,color="green",shape="box"];460[label="xy4000",fontsize=16,color="green",shape="box"];461[label="xy3000",fontsize=16,color="green",shape="box"];462[label="xy4000",fontsize=16,color="green",shape="box"];463[label="xy3000",fontsize=16,color="green",shape="box"];464[label="xy4000",fontsize=16,color="green",shape="box"];465[label="xy3000",fontsize=16,color="green",shape="box"];466[label="xy4000",fontsize=16,color="green",shape="box"];467[label="xy3000",fontsize=16,color="green",shape="box"];468[label="xy4000",fontsize=16,color="green",shape="box"];469[label="xy3000",fontsize=16,color="green",shape="box"];470[label="xy4000",fontsize=16,color="green",shape="box"];471[label="xy3000",fontsize=16,color="green",shape="box"];472[label="xy4000",fontsize=16,color="green",shape="box"];473[label="xy3000",fontsize=16,color="green",shape="box"];474[label="xy4000",fontsize=16,color="green",shape="box"];475[label="xy3000",fontsize=16,color="green",shape="box"];476[label="xy4000",fontsize=16,color="green",shape="box"];477[label="xy3000",fontsize=16,color="green",shape="box"];478[label="xy4000",fontsize=16,color="green",shape="box"];479[label="xy3000",fontsize=16,color="green",shape="box"];480[label="xy4000",fontsize=16,color="green",shape="box"];481[label="xy3000",fontsize=16,color="green",shape="box"];482[label="xy4000",fontsize=16,color="green",shape="box"];483[label="xy3000",fontsize=16,color="green",shape="box"];484[label="False",fontsize=16,color="green",shape="box"];485[label="xy26",fontsize=16,color="green",shape="box"];486 -> 38[label="",style="dashed", color="red", weight=0]; 486[label="xy4002 == xy3002",fontsize=16,color="magenta"];486 -> 601[label="",style="dashed", color="magenta", weight=3]; 486 -> 602[label="",style="dashed", color="magenta", weight=3]; 487 -> 39[label="",style="dashed", color="red", weight=0]; 487[label="xy4002 == xy3002",fontsize=16,color="magenta"];487 -> 603[label="",style="dashed", color="magenta", weight=3]; 487 -> 604[label="",style="dashed", color="magenta", weight=3]; 488 -> 40[label="",style="dashed", color="red", weight=0]; 488[label="xy4002 == xy3002",fontsize=16,color="magenta"];488 -> 605[label="",style="dashed", color="magenta", weight=3]; 488 -> 606[label="",style="dashed", color="magenta", weight=3]; 489 -> 41[label="",style="dashed", color="red", weight=0]; 489[label="xy4002 == xy3002",fontsize=16,color="magenta"];489 -> 607[label="",style="dashed", color="magenta", weight=3]; 489 -> 608[label="",style="dashed", color="magenta", weight=3]; 490 -> 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48[label="",style="dashed", color="red", weight=0]; 510[label="xy4001 == xy3001",fontsize=16,color="magenta"];510 -> 649[label="",style="dashed", color="magenta", weight=3]; 510 -> 650[label="",style="dashed", color="magenta", weight=3]; 511 -> 49[label="",style="dashed", color="red", weight=0]; 511[label="xy4001 == xy3001",fontsize=16,color="magenta"];511 -> 651[label="",style="dashed", color="magenta", weight=3]; 511 -> 652[label="",style="dashed", color="magenta", weight=3]; 512 -> 50[label="",style="dashed", color="red", weight=0]; 512[label="xy4001 == xy3001",fontsize=16,color="magenta"];512 -> 653[label="",style="dashed", color="magenta", weight=3]; 512 -> 654[label="",style="dashed", color="magenta", weight=3]; 513 -> 51[label="",style="dashed", color="red", weight=0]; 513[label="xy4001 == xy3001",fontsize=16,color="magenta"];513 -> 655[label="",style="dashed", color="magenta", weight=3]; 513 -> 656[label="",style="dashed", color="magenta", weight=3]; 514[label="xy4000",fontsize=16,color="green",shape="box"];515[label="xy3000",fontsize=16,color="green",shape="box"];516[label="xy4000",fontsize=16,color="green",shape="box"];517[label="xy3000",fontsize=16,color="green",shape="box"];518[label="xy4000",fontsize=16,color="green",shape="box"];519[label="xy3000",fontsize=16,color="green",shape="box"];520[label="xy4000",fontsize=16,color="green",shape="box"];521[label="xy3000",fontsize=16,color="green",shape="box"];522[label="xy4000",fontsize=16,color="green",shape="box"];523[label="xy3000",fontsize=16,color="green",shape="box"];524[label="xy4000",fontsize=16,color="green",shape="box"];525[label="xy3000",fontsize=16,color="green",shape="box"];526[label="xy4000",fontsize=16,color="green",shape="box"];527[label="xy3000",fontsize=16,color="green",shape="box"];528[label="xy4000",fontsize=16,color="green",shape="box"];529[label="xy3000",fontsize=16,color="green",shape="box"];530[label="xy4000",fontsize=16,color="green",shape="box"];531[label="xy3000",fontsize=16,color="green",shape="box"];532[label="xy4000",fontsize=16,color="green",shape="box"];533[label="xy3000",fontsize=16,color="green",shape="box"];534[label="xy4000",fontsize=16,color="green",shape="box"];535[label="xy3000",fontsize=16,color="green",shape="box"];536[label="xy4000",fontsize=16,color="green",shape="box"];537[label="xy3000",fontsize=16,color="green",shape="box"];538[label="xy4000",fontsize=16,color="green",shape="box"];539[label="xy3000",fontsize=16,color="green",shape="box"];540[label="xy4000",fontsize=16,color="green",shape="box"];541[label="xy3000",fontsize=16,color="green",shape="box"];542[label="primEqNat (Succ xy40000) (Succ xy30000)",fontsize=16,color="black",shape="box"];542 -> 657[label="",style="solid", color="black", weight=3]; 543[label="primEqNat (Succ xy40000) Zero",fontsize=16,color="black",shape="box"];543 -> 658[label="",style="solid", color="black", weight=3]; 544[label="primEqNat Zero (Succ xy30000)",fontsize=16,color="black",shape="box"];544 -> 659[label="",style="solid", color="black", weight=3]; 545[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];545 -> 660[label="",style="solid", color="black", weight=3]; 546 -> 220[label="",style="dashed", color="red", weight=0]; 546[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];546 -> 661[label="",style="dashed", color="magenta", weight=3]; 546 -> 662[label="",style="dashed", color="magenta", weight=3]; 547[label="False",fontsize=16,color="green",shape="box"];548[label="False",fontsize=16,color="green",shape="box"];549[label="True",fontsize=16,color="green",shape="box"];550[label="False",fontsize=16,color="green",shape="box"];551[label="True",fontsize=16,color="green",shape="box"];552 -> 220[label="",style="dashed", color="red", weight=0]; 552[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];552 -> 663[label="",style="dashed", color="magenta", weight=3]; 552 -> 664[label="",style="dashed", color="magenta", weight=3]; 553[label="False",fontsize=16,color="green",shape="box"];554[label="False",fontsize=16,color="green",shape="box"];555[label="True",fontsize=16,color="green",shape="box"];556[label="False",fontsize=16,color="green",shape="box"];557[label="True",fontsize=16,color="green",shape="box"];558[label="primMulInt xy4000 xy3001",fontsize=16,color="burlywood",shape="box"];959[label="xy4000/Pos xy40000",fontsize=10,color="white",style="solid",shape="box"];558 -> 959[label="",style="solid", color="burlywood", weight=9]; 959 -> 665[label="",style="solid", color="burlywood", weight=3]; 960[label="xy4000/Neg xy40000",fontsize=10,color="white",style="solid",shape="box"];558 -> 960[label="",style="solid", color="burlywood", weight=9]; 960 -> 666[label="",style="solid", color="burlywood", weight=3]; 559[label="xy4001",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="xy3001",fontsize=16,color="green",shape="box"];591[label="xy4001",fontsize=16,color="green",shape="box"];592[label="xy3000",fontsize=16,color="green",shape="box"];593[label="xy4001",fontsize=16,color="green",shape="box"];594[label="xy3001",fontsize=16,color="green",shape="box"];595[label="xy4001",fontsize=16,color="green",shape="box"];596[label="xy3001",fontsize=16,color="green",shape="box"];597[label="xy4000",fontsize=16,color="green",shape="box"];598[label="xy3000",fontsize=16,color="green",shape="box"];599[label="xy4000",fontsize=16,color="green",shape="box"];600[label="xy3000",fontsize=16,color="green",shape="box"];601[label="xy4002",fontsize=16,color="green",shape="box"];602[label="xy3002",fontsize=16,color="green",shape="box"];603[label="xy4002",fontsize=16,color="green",shape="box"];604[label="xy3002",fontsize=16,color="green",shape="box"];605[label="xy4002",fontsize=16,color="green",shape="box"];606[label="xy3002",fontsize=16,color="green",shape="box"];607[label="xy4002",fontsize=16,color="green",shape="box"];608[label="xy3002",fontsize=16,color="green",shape="box"];609[label="xy4002",fontsize=16,color="green",shape="box"];610[label="xy3002",fontsize=16,color="green",shape="box"];611[label="xy4002",fontsize=16,color="green",shape="box"];612[label="xy3002",fontsize=16,color="green",shape="box"];613[label="xy4002",fontsize=16,color="green",shape="box"];614[label="xy3002",fontsize=16,color="green",shape="box"];615[label="xy4002",fontsize=16,color="green",shape="box"];616[label="xy3002",fontsize=16,color="green",shape="box"];617[label="xy4002",fontsize=16,color="green",shape="box"];618[label="xy3002",fontsize=16,color="green",shape="box"];619[label="xy4002",fontsize=16,color="green",shape="box"];620[label="xy3002",fontsize=16,color="green",shape="box"];621[label="xy4002",fontsize=16,color="green",shape="box"];622[label="xy3002",fontsize=16,color="green",shape="box"];623[label="xy4002",fontsize=16,color="green",shape="box"];624[label="xy3002",fontsize=16,color="green",shape="box"];625[label="xy4002",fontsize=16,color="green",shape="box"];626[label="xy3002",fontsize=16,color="green",shape="box"];627[label="xy4002",fontsize=16,color="green",shape="box"];628[label="xy3002",fontsize=16,color="green",shape="box"];629[label="xy4001",fontsize=16,color="green",shape="box"];630[label="xy3001",fontsize=16,color="green",shape="box"];631[label="xy4001",fontsize=16,color="green",shape="box"];632[label="xy3001",fontsize=16,color="green",shape="box"];633[label="xy4001",fontsize=16,color="green",shape="box"];634[label="xy3001",fontsize=16,color="green",shape="box"];635[label="xy4001",fontsize=16,color="green",shape="box"];636[label="xy3001",fontsize=16,color="green",shape="box"];637[label="xy4001",fontsize=16,color="green",shape="box"];638[label="xy3001",fontsize=16,color="green",shape="box"];639[label="xy4001",fontsize=16,color="green",shape="box"];640[label="xy3001",fontsize=16,color="green",shape="box"];641[label="xy4001",fontsize=16,color="green",shape="box"];642[label="xy3001",fontsize=16,color="green",shape="box"];643[label="xy4001",fontsize=16,color="green",shape="box"];644[label="xy3001",fontsize=16,color="green",shape="box"];645[label="xy4001",fontsize=16,color="green",shape="box"];646[label="xy3001",fontsize=16,color="green",shape="box"];647[label="xy4001",fontsize=16,color="green",shape="box"];648[label="xy3001",fontsize=16,color="green",shape="box"];649[label="xy4001",fontsize=16,color="green",shape="box"];650[label="xy3001",fontsize=16,color="green",shape="box"];651[label="xy4001",fontsize=16,color="green",shape="box"];652[label="xy3001",fontsize=16,color="green",shape="box"];653[label="xy4001",fontsize=16,color="green",shape="box"];654[label="xy3001",fontsize=16,color="green",shape="box"];655[label="xy4001",fontsize=16,color="green",shape="box"];656[label="xy3001",fontsize=16,color="green",shape="box"];657 -> 220[label="",style="dashed", color="red", weight=0]; 657[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];657 -> 667[label="",style="dashed", color="magenta", weight=3]; 657 -> 668[label="",style="dashed", color="magenta", weight=3]; 658[label="False",fontsize=16,color="green",shape="box"];659[label="False",fontsize=16,color="green",shape="box"];660[label="True",fontsize=16,color="green",shape="box"];661[label="xy40000",fontsize=16,color="green",shape="box"];662[label="xy30000",fontsize=16,color="green",shape="box"];663[label="xy40000",fontsize=16,color="green",shape="box"];664[label="xy30000",fontsize=16,color="green",shape="box"];665[label="primMulInt (Pos xy40000) xy3001",fontsize=16,color="burlywood",shape="box"];961[label="xy3001/Pos xy30010",fontsize=10,color="white",style="solid",shape="box"];665 -> 961[label="",style="solid", color="burlywood", weight=9]; 961 -> 669[label="",style="solid", color="burlywood", weight=3]; 962[label="xy3001/Neg xy30010",fontsize=10,color="white",style="solid",shape="box"];665 -> 962[label="",style="solid", color="burlywood", weight=9]; 962 -> 670[label="",style="solid", color="burlywood", weight=3]; 666[label="primMulInt (Neg xy40000) xy3001",fontsize=16,color="burlywood",shape="box"];963[label="xy3001/Pos xy30010",fontsize=10,color="white",style="solid",shape="box"];666 -> 963[label="",style="solid", color="burlywood", weight=9]; 963 -> 671[label="",style="solid", color="burlywood", weight=3]; 964[label="xy3001/Neg xy30010",fontsize=10,color="white",style="solid",shape="box"];666 -> 964[label="",style="solid", color="burlywood", weight=9]; 964 -> 672[label="",style="solid", color="burlywood", weight=3]; 667[label="xy40000",fontsize=16,color="green",shape="box"];668[label="xy30000",fontsize=16,color="green",shape="box"];669[label="primMulInt (Pos xy40000) (Pos xy30010)",fontsize=16,color="black",shape="box"];669 -> 673[label="",style="solid", color="black", weight=3]; 670[label="primMulInt (Pos xy40000) (Neg xy30010)",fontsize=16,color="black",shape="box"];670 -> 674[label="",style="solid", color="black", weight=3]; 671[label="primMulInt (Neg xy40000) (Pos xy30010)",fontsize=16,color="black",shape="box"];671 -> 675[label="",style="solid", color="black", weight=3]; 672[label="primMulInt (Neg xy40000) (Neg xy30010)",fontsize=16,color="black",shape="box"];672 -> 676[label="",style="solid", color="black", weight=3]; 673[label="Pos (primMulNat xy40000 xy30010)",fontsize=16,color="green",shape="box"];673 -> 677[label="",style="dashed", color="green", weight=3]; 674[label="Neg (primMulNat xy40000 xy30010)",fontsize=16,color="green",shape="box"];674 -> 678[label="",style="dashed", color="green", weight=3]; 675[label="Neg (primMulNat xy40000 xy30010)",fontsize=16,color="green",shape="box"];675 -> 679[label="",style="dashed", color="green", weight=3]; 676[label="Pos (primMulNat xy40000 xy30010)",fontsize=16,color="green",shape="box"];676 -> 680[label="",style="dashed", color="green", weight=3]; 677[label="primMulNat xy40000 xy30010",fontsize=16,color="burlywood",shape="triangle"];965[label="xy40000/Succ xy400000",fontsize=10,color="white",style="solid",shape="box"];677 -> 965[label="",style="solid", color="burlywood", weight=9]; 965 -> 681[label="",style="solid", color="burlywood", weight=3]; 966[label="xy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];677 -> 966[label="",style="solid", color="burlywood", weight=9]; 966 -> 682[label="",style="solid", color="burlywood", weight=3]; 678 -> 677[label="",style="dashed", color="red", weight=0]; 678[label="primMulNat xy40000 xy30010",fontsize=16,color="magenta"];678 -> 683[label="",style="dashed", color="magenta", weight=3]; 679 -> 677[label="",style="dashed", color="red", weight=0]; 679[label="primMulNat xy40000 xy30010",fontsize=16,color="magenta"];679 -> 684[label="",style="dashed", color="magenta", weight=3]; 680 -> 677[label="",style="dashed", color="red", weight=0]; 680[label="primMulNat xy40000 xy30010",fontsize=16,color="magenta"];680 -> 685[label="",style="dashed", color="magenta", weight=3]; 680 -> 686[label="",style="dashed", color="magenta", weight=3]; 681[label="primMulNat (Succ xy400000) xy30010",fontsize=16,color="burlywood",shape="box"];967[label="xy30010/Succ xy300100",fontsize=10,color="white",style="solid",shape="box"];681 -> 967[label="",style="solid", color="burlywood", weight=9]; 967 -> 687[label="",style="solid", color="burlywood", weight=3]; 968[label="xy30010/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 968[label="",style="solid", color="burlywood", weight=9]; 968 -> 688[label="",style="solid", color="burlywood", weight=3]; 682[label="primMulNat Zero xy30010",fontsize=16,color="burlywood",shape="box"];969[label="xy30010/Succ xy300100",fontsize=10,color="white",style="solid",shape="box"];682 -> 969[label="",style="solid", color="burlywood", weight=9]; 969 -> 689[label="",style="solid", color="burlywood", weight=3]; 970[label="xy30010/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 970[label="",style="solid", color="burlywood", weight=9]; 970 -> 690[label="",style="solid", color="burlywood", weight=3]; 683[label="xy30010",fontsize=16,color="green",shape="box"];684[label="xy40000",fontsize=16,color="green",shape="box"];685[label="xy30010",fontsize=16,color="green",shape="box"];686[label="xy40000",fontsize=16,color="green",shape="box"];687[label="primMulNat (Succ xy400000) (Succ xy300100)",fontsize=16,color="black",shape="box"];687 -> 691[label="",style="solid", color="black", weight=3]; 688[label="primMulNat (Succ xy400000) Zero",fontsize=16,color="black",shape="box"];688 -> 692[label="",style="solid", color="black", weight=3]; 689[label="primMulNat Zero (Succ xy300100)",fontsize=16,color="black",shape="box"];689 -> 693[label="",style="solid", color="black", weight=3]; 690[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];690 -> 694[label="",style="solid", color="black", weight=3]; 691 -> 695[label="",style="dashed", color="red", weight=0]; 691[label="primPlusNat (primMulNat xy400000 (Succ xy300100)) (Succ xy300100)",fontsize=16,color="magenta"];691 -> 696[label="",style="dashed", color="magenta", weight=3]; 692[label="Zero",fontsize=16,color="green",shape="box"];693[label="Zero",fontsize=16,color="green",shape="box"];694[label="Zero",fontsize=16,color="green",shape="box"];696 -> 677[label="",style="dashed", color="red", weight=0]; 696[label="primMulNat xy400000 (Succ xy300100)",fontsize=16,color="magenta"];696 -> 697[label="",style="dashed", color="magenta", weight=3]; 696 -> 698[label="",style="dashed", color="magenta", weight=3]; 695[label="primPlusNat xy27 (Succ xy300100)",fontsize=16,color="burlywood",shape="triangle"];971[label="xy27/Succ xy270",fontsize=10,color="white",style="solid",shape="box"];695 -> 971[label="",style="solid", color="burlywood", weight=9]; 971 -> 699[label="",style="solid", color="burlywood", weight=3]; 972[label="xy27/Zero",fontsize=10,color="white",style="solid",shape="box"];695 -> 972[label="",style="solid", color="burlywood", weight=9]; 972 -> 700[label="",style="solid", color="burlywood", weight=3]; 697[label="Succ xy300100",fontsize=16,color="green",shape="box"];698[label="xy400000",fontsize=16,color="green",shape="box"];699[label="primPlusNat (Succ xy270) (Succ xy300100)",fontsize=16,color="black",shape="box"];699 -> 701[label="",style="solid", color="black", weight=3]; 700[label="primPlusNat Zero (Succ xy300100)",fontsize=16,color="black",shape="box"];700 -> 702[label="",style="solid", color="black", weight=3]; 701[label="Succ (Succ (primPlusNat xy270 xy300100))",fontsize=16,color="green",shape="box"];701 -> 703[label="",style="dashed", color="green", weight=3]; 702[label="Succ xy300100",fontsize=16,color="green",shape="box"];703[label="primPlusNat xy270 xy300100",fontsize=16,color="burlywood",shape="triangle"];973[label="xy270/Succ xy2700",fontsize=10,color="white",style="solid",shape="box"];703 -> 973[label="",style="solid", color="burlywood", weight=9]; 973 -> 704[label="",style="solid", color="burlywood", weight=3]; 974[label="xy270/Zero",fontsize=10,color="white",style="solid",shape="box"];703 -> 974[label="",style="solid", color="burlywood", weight=9]; 974 -> 705[label="",style="solid", color="burlywood", weight=3]; 704[label="primPlusNat (Succ xy2700) xy300100",fontsize=16,color="burlywood",shape="box"];975[label="xy300100/Succ xy3001000",fontsize=10,color="white",style="solid",shape="box"];704 -> 975[label="",style="solid", color="burlywood", weight=9]; 975 -> 706[label="",style="solid", color="burlywood", weight=3]; 976[label="xy300100/Zero",fontsize=10,color="white",style="solid",shape="box"];704 -> 976[label="",style="solid", color="burlywood", weight=9]; 976 -> 707[label="",style="solid", color="burlywood", weight=3]; 705[label="primPlusNat Zero xy300100",fontsize=16,color="burlywood",shape="box"];977[label="xy300100/Succ xy3001000",fontsize=10,color="white",style="solid",shape="box"];705 -> 977[label="",style="solid", color="burlywood", weight=9]; 977 -> 708[label="",style="solid", color="burlywood", weight=3]; 978[label="xy300100/Zero",fontsize=10,color="white",style="solid",shape="box"];705 -> 978[label="",style="solid", color="burlywood", weight=9]; 978 -> 709[label="",style="solid", color="burlywood", weight=3]; 706[label="primPlusNat (Succ xy2700) (Succ xy3001000)",fontsize=16,color="black",shape="box"];706 -> 710[label="",style="solid", color="black", weight=3]; 707[label="primPlusNat (Succ xy2700) Zero",fontsize=16,color="black",shape="box"];707 -> 711[label="",style="solid", color="black", weight=3]; 708[label="primPlusNat Zero (Succ xy3001000)",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3]; 709[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];709 -> 713[label="",style="solid", color="black", weight=3]; 710[label="Succ (Succ (primPlusNat xy2700 xy3001000))",fontsize=16,color="green",shape="box"];710 -> 714[label="",style="dashed", color="green", weight=3]; 711[label="Succ xy2700",fontsize=16,color="green",shape="box"];712[label="Succ xy3001000",fontsize=16,color="green",shape="box"];713[label="Zero",fontsize=16,color="green",shape="box"];714 -> 703[label="",style="dashed", color="red", weight=0]; 714[label="primPlusNat xy2700 xy3001000",fontsize=16,color="magenta"];714 -> 715[label="",style="dashed", color="magenta", weight=3]; 714 -> 716[label="",style="dashed", color="magenta", weight=3]; 715[label="xy2700",fontsize=16,color="green",shape="box"];716[label="xy3001000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy(Just(xy400), :(Nothing, xy31), ba) -> new_deleteBy(Just(xy400), xy31, ba) new_deleteBy0(xy10, xy11, xy12, False, bb) -> new_deleteBy(Just(xy12), xy10, bb) new_deleteBy(Just(xy400), :(Just(xy300), xy31), ba) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, ba), ba) new_deleteBy(Nothing, :(Just(xy300), xy31), ba) -> new_deleteBy(Nothing, xy31, ba) The TRS R consists of the following rules: new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), dc, dd, de) -> new_asAs(new_esEs25(xy4000, xy3000, dc), new_asAs(new_esEs24(xy4001, xy3001, dd), new_esEs23(xy4002, xy3002, de))) new_esEs10(Left(xy4000), Left(xy3000), ty_Int, db) -> new_esEs13(xy4000, xy3000) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs12(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_[], bdc)) -> new_esEs15(xy4001, xy3001, bdc) new_esEs5(Just(xy4000), Just(xy3000), app(ty_[], cd)) -> new_esEs15(xy4000, xy3000, cd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(app(ty_@3, bac), bad), bae)) -> new_esEs11(xy4000, xy3000, bac, bad, bae) new_esEs6(False, True) -> False new_esEs6(True, False) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs23(xy4002, xy3002, ty_Int) -> new_esEs13(xy4002, xy3002) new_esEs16(GT, GT) -> True new_esEs13(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs25(xy4000, xy3000, app(app(ty_@2, bde), bdf)) -> new_esEs9(xy4000, xy3000, bde, bdf) new_esEs19(xy4001, xy3001, app(app(ty_@2, dh), ea)) -> new_esEs9(xy4001, xy3001, dh, ea) new_esEs19(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs5(xy4001, xy3001, eg) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Ratio, bah)) -> new_esEs18(xy4000, xy3000, bah) new_esEs26(xy4000, xy3000, app(ty_[], bfg)) -> new_esEs15(xy4000, xy3000, bfg) new_asAs(True, xy26) -> xy26 new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_Either, baa), bab)) -> new_esEs10(xy4000, xy3000, baa, bab) new_esEs20(xy4000, xy3000, app(app(ty_@2, fb), fc)) -> new_esEs9(xy4000, xy3000, fb, fc) new_esEs14(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs23(xy4002, xy3002, app(ty_Ratio, bcb)) -> new_esEs18(xy4002, xy3002, bcb) new_esEs26(xy4000, xy3000, app(app(ty_Either, bfa), bfb)) -> new_esEs10(xy4000, xy3000, bfa, bfb) new_esEs20(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs5(xy4000, xy3000, gb) new_esEs23(xy4002, xy3002, app(app(ty_@2, bba), bbb)) -> new_esEs9(xy4002, xy3002, bba, bbb) new_esEs21(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_esEs20(xy4000, xy3000, app(ty_[], gc)) -> new_esEs15(xy4000, xy3000, gc) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs26(xy4000, xy3000, app(app(app(ty_@3, bfc), bfd), bfe)) -> new_esEs11(xy4000, xy3000, bfc, bfd, bfe) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs10(Left(xy4000), Right(xy3000), da, db) -> False new_esEs10(Right(xy4000), Left(xy3000), da, db) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs16(EQ, GT) -> False new_esEs16(GT, EQ) -> False new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_@0, db) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs12(xy400, xy300) new_esEs20(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4002, xy3002, app(app(app(ty_@3, bbe), bbf), bbg)) -> new_esEs11(xy4002, xy3002, bbe, bbf, bbg) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_Char) -> new_esEs12(xy4002, xy3002) new_esEs24(xy4001, xy3001, app(ty_Maybe, bdb)) -> new_esEs5(xy4001, xy3001, bdb) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_Either, bf), bg)) -> new_esEs10(xy4000, xy3000, bf, bg) new_esEs5(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs15(:(xy4000, xy4001), [], df) -> False new_esEs15([], :(xy3000, xy3001), df) -> False new_esEs4(xy400, xy300, ty_@0) -> new_esEs8(xy400, xy300) new_esEs8(@0, @0) -> True new_esEs4(xy400, xy300, app(app(app(ty_@3, dc), dd), de)) -> new_esEs11(xy400, xy300, dc, dd, de) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs19(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Char, db) -> new_esEs12(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs4(xy400, xy300, app(app(ty_Either, da), db)) -> new_esEs10(xy400, xy300, da, db) new_esEs25(xy4000, xy3000, app(ty_Maybe, bed)) -> new_esEs5(xy4000, xy3000, bed) new_esEs26(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(LT, EQ) -> False new_esEs16(EQ, LT) -> False new_esEs10(Left(xy4000), Left(xy3000), app(ty_Ratio, hf), db) -> new_esEs18(xy4000, xy3000, hf) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Ratio, ce)) -> new_esEs18(xy4000, xy3000, ce) new_esEs26(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, dg)) -> new_esEs18(xy400, xy300, dg) new_esEs20(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_@0) -> new_esEs8(xy4002, xy3002) 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_esEs19(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(ty_@2, bcc), bcd)) -> new_esEs9(xy4001, xy3001, bcc, bcd) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bh), ca), cb)) -> new_esEs11(xy4000, xy3000, bh, ca, cb) new_esEs26(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_sr(Pos(xy40000), Neg(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_sr(Neg(xy40000), Pos(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_esEs10(Right(xy4000), Right(xy3000), da, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Succ(xy3001000)) -> Succ(Succ(new_primPlusNat1(xy2700, xy3001000))) new_esEs19(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs20(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(EQ, EQ) -> True new_esEs10(Right(xy4000), Right(xy3000), da, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_Either, gg), gh), db) -> new_esEs10(xy4000, xy3000, gg, gh) new_esEs21(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs7(xy400, xy300) new_esEs4(xy400, xy300, app(ty_[], df)) -> new_esEs15(xy400, xy300, df) new_esEs10(Left(xy4000), Left(xy3000), app(app(app(ty_@3, ha), hb), hc), db) -> new_esEs11(xy4000, xy3000, ha, hb, hc) new_esEs23(xy4002, xy3002, ty_Double) -> new_esEs14(xy4002, xy3002) new_esEs5(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Float) -> new_esEs17(xy400, xy300) new_esEs23(xy4002, xy3002, ty_Float) -> new_esEs17(xy4002, xy3002) new_sr(Neg(xy40000), Neg(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_esEs10(Left(xy4000), Left(xy3000), ty_Integer, db) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(app(ty_@2, beg), beh)) -> new_esEs9(xy4000, xy3000, beg, beh) new_esEs4(xy400, xy300, ty_Double) -> new_esEs14(xy400, xy300) new_esEs25(xy4000, xy3000, app(ty_[], bee)) -> new_esEs15(xy4000, xy3000, bee) new_esEs9(@2(xy4000, xy4001), @2(xy3000, xy3001), cf, cg) -> new_asAs(new_esEs20(xy4000, xy3000, cf), new_esEs19(xy4001, xy3001, cg)) new_esEs18(:%(xy4000, xy4001), :%(xy3000, xy3001), dg) -> new_asAs(new_esEs22(xy4000, xy3000, dg), new_esEs21(xy4001, xy3001, dg)) new_esEs19(xy4001, xy3001, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs11(xy4001, xy3001, ed, ee, ef) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs16(LT, LT) -> True new_esEs23(xy4002, xy3002, ty_Integer) -> new_esEs7(xy4002, xy3002) new_esEs19(xy4001, xy3001, app(app(ty_Either, eb), ec)) -> new_esEs10(xy4001, xy3001, eb, ec) new_esEs20(xy4000, xy3000, app(ty_Ratio, gd)) -> new_esEs18(xy4000, xy3000, gd) new_esEs6(True, True) -> True new_esEs19(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Double, db) -> new_esEs14(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs5(Nothing, Nothing, bc) -> True new_esEs19(xy4001, xy3001, app(ty_[], eh)) -> new_esEs15(xy4001, xy3001, eh) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_Ratio, bdd)) -> new_esEs18(xy4001, xy3001, bdd) new_esEs20(xy4000, xy3000, app(app(app(ty_@3, fg), fh), ga)) -> new_esEs11(xy4000, xy3000, fg, fh, ga) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs23(xy4002, xy3002, ty_Bool) -> new_esEs6(xy4002, xy3002) new_esEs5(Nothing, Just(xy3000), bc) -> False new_esEs5(Just(xy4000), Nothing, bc) -> False new_primPlusNat0(Succ(xy270), xy300100) -> Succ(Succ(new_primPlusNat1(xy270, xy300100))) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(ty_Maybe, bff)) -> new_esEs5(xy4000, xy3000, bff) new_esEs6(False, False) -> True new_esEs26(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs15([], [], df) -> True new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, app(app(ty_Either, fd), ff)) -> new_esEs10(xy4000, xy3000, fd, ff) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400000), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300100)) -> Zero new_sr(Pos(xy40000), Pos(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_primPlusNat0(Zero, xy300100) -> Succ(xy300100) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs23(xy4002, xy3002, app(ty_[], bca)) -> new_esEs15(xy4002, xy3002, bca) new_esEs15(:(xy4000, xy4001), :(xy3000, xy3001), df) -> new_asAs(new_esEs26(xy4000, xy3000, df), new_esEs15(xy4001, xy3001, df)) new_esEs23(xy4002, xy3002, app(ty_Maybe, bbh)) -> new_esEs5(xy4002, xy3002, bbh) new_esEs19(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs18(xy4001, xy3001, fa) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs23(xy4002, xy3002, app(app(ty_Either, bbc), bbd)) -> new_esEs10(xy4002, xy3002, bbc, bbd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_@2, hg), hh)) -> new_esEs9(xy4000, xy3000, hg, hh) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4000, xy3000, app(ty_Ratio, bfh)) -> new_esEs18(xy4000, xy3000, bfh) new_esEs26(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_primMulNat0(Succ(xy400000), Succ(xy300100)) -> new_primPlusNat0(new_primMulNat0(xy400000, Succ(xy300100)), xy300100) new_esEs10(Left(xy4000), Left(xy3000), ty_Bool, db) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_Either, bce), bcf)) -> new_esEs10(xy4001, xy3001, bce, bcf) new_esEs10(Left(xy4000), Left(xy3000), app(ty_[], he), db) -> new_esEs15(xy4000, xy3000, he) new_esEs16(LT, GT) -> False new_esEs16(GT, LT) -> False new_esEs19(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, bcg), bch), bda)) -> new_esEs11(xy4001, xy3001, bcg, bch, bda) new_esEs23(xy4002, xy3002, ty_Ordering) -> new_esEs16(xy4002, xy3002) new_esEs26(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Zero) -> Succ(xy2700) new_primPlusNat1(Zero, Succ(xy3001000)) -> Succ(xy3001000) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_Either, bdg), bdh)) -> new_esEs10(xy4000, xy3000, bdg, bdh) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Double) -> new_esEs14(xy4000, xy3000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bc)) -> new_esEs5(xy400, xy300, bc) new_esEs4(xy400, xy300, app(app(ty_@2, cf), cg)) -> new_esEs9(xy400, xy300, cf, cg) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bea), beb), bec)) -> new_esEs11(xy4000, xy3000, bea, beb, bec) new_primEqNat0(Zero, Zero) -> True new_esEs10(Left(xy4000), Left(xy3000), ty_Float, db) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_@2, bd), be)) -> new_esEs9(xy4000, xy3000, bd, be) new_esEs19(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs6(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_asAs(False, xy26) -> False new_esEs20(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_@2, ge), gf), db) -> new_esEs9(xy4000, xy3000, ge, gf) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Maybe, baf)) -> new_esEs5(xy4000, xy3000, baf) new_esEs25(xy4000, xy3000, app(ty_Ratio, bef)) -> new_esEs18(xy4000, xy3000, bef) new_esEs4(xy400, xy300, ty_Int) -> new_esEs13(xy400, xy300) new_esEs10(Left(xy4000), Left(xy3000), ty_Ordering, db) -> new_esEs16(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_[], bag)) -> new_esEs15(xy4000, xy3000, bag) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Maybe, cc)) -> new_esEs5(xy4000, xy3000, cc) new_esEs10(Left(xy4000), Left(xy3000), app(ty_Maybe, hd), db) -> new_esEs5(xy4000, xy3000, hd) new_esEs17(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs7(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs16(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Float) -> new_esEs17(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_esEs13(x0, x1) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Bool) new_esEs26(x0, x1, ty_Int) new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Just(x1), ty_Double) new_esEs5(Just(x0), Just(x1), ty_Ordering) new_esEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_Int) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_asAs(False, x0) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Double) new_esEs22(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Integer) new_esEs5(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Char) new_esEs10(Right(x0), Right(x1), x2, ty_Integer) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Ordering) new_primPlusNat0(Zero, x0) new_esEs10(Left(x0), Left(x1), ty_Float, x2) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs25(x0, x1, ty_Float) new_esEs10(Right(x0), Right(x1), x2, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Bool) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_@0) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs16(EQ, EQ) new_esEs23(x0, x1, ty_@0) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs10(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(Char(x0), Char(x1)) new_esEs5(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(False, True) new_esEs6(True, False) new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs10(Left(x0), Left(x1), ty_Integer, x2) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs21(x0, x1, ty_Int) new_esEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs5(Just(x0), Just(x1), ty_Char) new_esEs19(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Char) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Double) new_esEs6(False, False) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(Just(x0), Just(x1), ty_Integer) new_esEs24(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs20(x0, x1, ty_Integer) new_esEs24(x0, x1, ty_Float) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs10(Left(x0), Left(x1), ty_Ordering, x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, ty_Ordering) new_esEs26(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs5(Nothing, Nothing, x0) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, ty_Float) new_primMulNat0(Zero, Succ(x0)) new_esEs7(Integer(x0), Integer(x1)) new_esEs24(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_primPlusNat1(Zero, Succ(x0)) new_esEs10(Right(x0), Right(x1), x2, app(ty_[], x3)) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs20(x0, x1, ty_Ordering) new_esEs15([], :(x0, x1), x2) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_primPlusNat0(Succ(x0), x1) new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Bool) new_esEs23(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, ty_Ordering) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs19(x0, x1, ty_@0) new_esEs5(Just(x0), Just(x1), ty_Bool) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, ty_Integer) new_esEs16(LT, GT) new_esEs16(GT, LT) new_esEs4(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Double) new_esEs10(Left(x0), Left(x1), ty_@0, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_Double) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Nothing, x1) new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_esEs23(x0, x1, ty_Float) new_esEs26(x0, x1, ty_Integer) new_asAs(True, x0) new_esEs26(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Float) new_esEs10(Left(x0), Left(x1), ty_Bool, x2) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs5(Just(x0), Just(x1), app(ty_[], x2)) new_esEs15([], [], x0) new_esEs4(x0, x1, ty_Double) new_esEs10(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs5(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_@0) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs19(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs17(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs8(@0, @0) new_esEs23(x0, x1, ty_Int) new_esEs22(x0, x1, ty_Integer) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs6(True, True) new_esEs10(Left(x0), Left(x1), ty_Int, x2) new_esEs20(x0, x1, ty_Bool) new_esEs15(:(x0, x1), :(x2, x3), x4) new_esEs19(x0, x1, ty_Integer) new_primPlusNat1(Succ(x0), Zero) new_esEs16(LT, LT) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs5(Nothing, Just(x0), x1) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_Integer) new_esEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Right(x1), x2, x3) new_esEs10(Right(x0), Left(x1), x2, x3) new_esEs20(x0, x1, ty_Double) new_esEs16(EQ, GT) new_esEs16(GT, EQ) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs20(x0, x1, ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs26(x0, x1, ty_Char) new_esEs15(:(x0, x1), [], x2) new_esEs10(Left(x0), Left(x1), ty_Double, x2) new_esEs26(x0, x1, ty_@0) new_esEs25(x0, x1, app(ty_[], x2)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs26(x0, x1, ty_Double) new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_@0) new_esEs10(Left(x0), Left(x1), ty_Char, x2) new_esEs16(LT, EQ) new_esEs16(EQ, LT) new_esEs19(x0, x1, ty_Ordering) new_esEs14(Double(x0, x1), Double(x2, x3)) new_primEqNat0(Succ(x0), Zero) new_esEs16(GT, GT) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, ty_Ordering) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (11) Complex Obligation (AND) ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy(Nothing, :(Just(xy300), xy31), ba) -> new_deleteBy(Nothing, xy31, ba) The TRS R consists of the following rules: new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), dc, dd, de) -> new_asAs(new_esEs25(xy4000, xy3000, dc), new_asAs(new_esEs24(xy4001, xy3001, dd), new_esEs23(xy4002, xy3002, de))) new_esEs10(Left(xy4000), Left(xy3000), ty_Int, db) -> new_esEs13(xy4000, xy3000) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs12(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_[], bdc)) -> new_esEs15(xy4001, xy3001, bdc) new_esEs5(Just(xy4000), Just(xy3000), app(ty_[], cd)) -> new_esEs15(xy4000, xy3000, cd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(app(ty_@3, bac), bad), bae)) -> new_esEs11(xy4000, xy3000, bac, bad, bae) new_esEs6(False, True) -> False new_esEs6(True, False) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs23(xy4002, xy3002, ty_Int) -> new_esEs13(xy4002, xy3002) new_esEs16(GT, GT) -> True new_esEs13(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs25(xy4000, xy3000, app(app(ty_@2, bde), bdf)) -> new_esEs9(xy4000, xy3000, bde, bdf) new_esEs19(xy4001, xy3001, app(app(ty_@2, dh), ea)) -> new_esEs9(xy4001, xy3001, dh, ea) new_esEs19(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs5(xy4001, xy3001, eg) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Ratio, bah)) -> new_esEs18(xy4000, xy3000, bah) new_esEs26(xy4000, xy3000, app(ty_[], bfg)) -> new_esEs15(xy4000, xy3000, bfg) new_asAs(True, xy26) -> xy26 new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_Either, baa), bab)) -> new_esEs10(xy4000, xy3000, baa, bab) new_esEs20(xy4000, xy3000, app(app(ty_@2, fb), fc)) -> new_esEs9(xy4000, xy3000, fb, fc) new_esEs14(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs23(xy4002, xy3002, app(ty_Ratio, bcb)) -> new_esEs18(xy4002, xy3002, bcb) new_esEs26(xy4000, xy3000, app(app(ty_Either, bfa), bfb)) -> new_esEs10(xy4000, xy3000, bfa, bfb) new_esEs20(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs5(xy4000, xy3000, gb) new_esEs23(xy4002, xy3002, app(app(ty_@2, bba), bbb)) -> new_esEs9(xy4002, xy3002, bba, bbb) new_esEs21(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_esEs20(xy4000, xy3000, app(ty_[], gc)) -> new_esEs15(xy4000, xy3000, gc) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs26(xy4000, xy3000, app(app(app(ty_@3, bfc), bfd), bfe)) -> new_esEs11(xy4000, xy3000, bfc, bfd, bfe) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs10(Left(xy4000), Right(xy3000), da, db) -> False new_esEs10(Right(xy4000), Left(xy3000), da, db) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs16(EQ, GT) -> False new_esEs16(GT, EQ) -> False new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_@0, db) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs12(xy400, xy300) new_esEs20(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4002, xy3002, app(app(app(ty_@3, bbe), bbf), bbg)) -> new_esEs11(xy4002, xy3002, bbe, bbf, bbg) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_Char) -> new_esEs12(xy4002, xy3002) new_esEs24(xy4001, xy3001, app(ty_Maybe, bdb)) -> new_esEs5(xy4001, xy3001, bdb) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_Either, bf), bg)) -> new_esEs10(xy4000, xy3000, bf, bg) new_esEs5(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs15(:(xy4000, xy4001), [], df) -> False new_esEs15([], :(xy3000, xy3001), df) -> False new_esEs4(xy400, xy300, ty_@0) -> new_esEs8(xy400, xy300) new_esEs8(@0, @0) -> True new_esEs4(xy400, xy300, app(app(app(ty_@3, dc), dd), de)) -> new_esEs11(xy400, xy300, dc, dd, de) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs19(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Char, db) -> new_esEs12(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs4(xy400, xy300, app(app(ty_Either, da), db)) -> new_esEs10(xy400, xy300, da, db) new_esEs25(xy4000, xy3000, app(ty_Maybe, bed)) -> new_esEs5(xy4000, xy3000, bed) new_esEs26(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(LT, EQ) -> False new_esEs16(EQ, LT) -> False new_esEs10(Left(xy4000), Left(xy3000), app(ty_Ratio, hf), db) -> new_esEs18(xy4000, xy3000, hf) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Ratio, ce)) -> new_esEs18(xy4000, xy3000, ce) new_esEs26(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, dg)) -> new_esEs18(xy400, xy300, dg) new_esEs20(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_@0) -> new_esEs8(xy4002, xy3002) 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_esEs19(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(ty_@2, bcc), bcd)) -> new_esEs9(xy4001, xy3001, bcc, bcd) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bh), ca), cb)) -> new_esEs11(xy4000, xy3000, bh, ca, cb) new_esEs26(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_sr(Pos(xy40000), Neg(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_sr(Neg(xy40000), Pos(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_esEs10(Right(xy4000), Right(xy3000), da, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Succ(xy3001000)) -> Succ(Succ(new_primPlusNat1(xy2700, xy3001000))) new_esEs19(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs20(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(EQ, EQ) -> True new_esEs10(Right(xy4000), Right(xy3000), da, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_Either, gg), gh), db) -> new_esEs10(xy4000, xy3000, gg, gh) new_esEs21(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs7(xy400, xy300) new_esEs4(xy400, xy300, app(ty_[], df)) -> new_esEs15(xy400, xy300, df) new_esEs10(Left(xy4000), Left(xy3000), app(app(app(ty_@3, ha), hb), hc), db) -> new_esEs11(xy4000, xy3000, ha, hb, hc) new_esEs23(xy4002, xy3002, ty_Double) -> new_esEs14(xy4002, xy3002) new_esEs5(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Float) -> new_esEs17(xy400, xy300) new_esEs23(xy4002, xy3002, ty_Float) -> new_esEs17(xy4002, xy3002) new_sr(Neg(xy40000), Neg(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_esEs10(Left(xy4000), Left(xy3000), ty_Integer, db) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(app(ty_@2, beg), beh)) -> new_esEs9(xy4000, xy3000, beg, beh) new_esEs4(xy400, xy300, ty_Double) -> new_esEs14(xy400, xy300) new_esEs25(xy4000, xy3000, app(ty_[], bee)) -> new_esEs15(xy4000, xy3000, bee) new_esEs9(@2(xy4000, xy4001), @2(xy3000, xy3001), cf, cg) -> new_asAs(new_esEs20(xy4000, xy3000, cf), new_esEs19(xy4001, xy3001, cg)) new_esEs18(:%(xy4000, xy4001), :%(xy3000, xy3001), dg) -> new_asAs(new_esEs22(xy4000, xy3000, dg), new_esEs21(xy4001, xy3001, dg)) new_esEs19(xy4001, xy3001, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs11(xy4001, xy3001, ed, ee, ef) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs16(LT, LT) -> True new_esEs23(xy4002, xy3002, ty_Integer) -> new_esEs7(xy4002, xy3002) new_esEs19(xy4001, xy3001, app(app(ty_Either, eb), ec)) -> new_esEs10(xy4001, xy3001, eb, ec) new_esEs20(xy4000, xy3000, app(ty_Ratio, gd)) -> new_esEs18(xy4000, xy3000, gd) new_esEs6(True, True) -> True new_esEs19(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Double, db) -> new_esEs14(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs5(Nothing, Nothing, bc) -> True new_esEs19(xy4001, xy3001, app(ty_[], eh)) -> new_esEs15(xy4001, xy3001, eh) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_Ratio, bdd)) -> new_esEs18(xy4001, xy3001, bdd) new_esEs20(xy4000, xy3000, app(app(app(ty_@3, fg), fh), ga)) -> new_esEs11(xy4000, xy3000, fg, fh, ga) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs23(xy4002, xy3002, ty_Bool) -> new_esEs6(xy4002, xy3002) new_esEs5(Nothing, Just(xy3000), bc) -> False new_esEs5(Just(xy4000), Nothing, bc) -> False new_primPlusNat0(Succ(xy270), xy300100) -> Succ(Succ(new_primPlusNat1(xy270, xy300100))) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(ty_Maybe, bff)) -> new_esEs5(xy4000, xy3000, bff) new_esEs6(False, False) -> True new_esEs26(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs15([], [], df) -> True new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, app(app(ty_Either, fd), ff)) -> new_esEs10(xy4000, xy3000, fd, ff) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400000), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300100)) -> Zero new_sr(Pos(xy40000), Pos(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_primPlusNat0(Zero, xy300100) -> Succ(xy300100) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs23(xy4002, xy3002, app(ty_[], bca)) -> new_esEs15(xy4002, xy3002, bca) new_esEs15(:(xy4000, xy4001), :(xy3000, xy3001), df) -> new_asAs(new_esEs26(xy4000, xy3000, df), new_esEs15(xy4001, xy3001, df)) new_esEs23(xy4002, xy3002, app(ty_Maybe, bbh)) -> new_esEs5(xy4002, xy3002, bbh) new_esEs19(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs18(xy4001, xy3001, fa) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs23(xy4002, xy3002, app(app(ty_Either, bbc), bbd)) -> new_esEs10(xy4002, xy3002, bbc, bbd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_@2, hg), hh)) -> new_esEs9(xy4000, xy3000, hg, hh) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4000, xy3000, app(ty_Ratio, bfh)) -> new_esEs18(xy4000, xy3000, bfh) new_esEs26(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_primMulNat0(Succ(xy400000), Succ(xy300100)) -> new_primPlusNat0(new_primMulNat0(xy400000, Succ(xy300100)), xy300100) new_esEs10(Left(xy4000), Left(xy3000), ty_Bool, db) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_Either, bce), bcf)) -> new_esEs10(xy4001, xy3001, bce, bcf) new_esEs10(Left(xy4000), Left(xy3000), app(ty_[], he), db) -> new_esEs15(xy4000, xy3000, he) new_esEs16(LT, GT) -> False new_esEs16(GT, LT) -> False new_esEs19(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, bcg), bch), bda)) -> new_esEs11(xy4001, xy3001, bcg, bch, bda) new_esEs23(xy4002, xy3002, ty_Ordering) -> new_esEs16(xy4002, xy3002) new_esEs26(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Zero) -> Succ(xy2700) new_primPlusNat1(Zero, Succ(xy3001000)) -> Succ(xy3001000) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_Either, bdg), bdh)) -> new_esEs10(xy4000, xy3000, bdg, bdh) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Double) -> new_esEs14(xy4000, xy3000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bc)) -> new_esEs5(xy400, xy300, bc) new_esEs4(xy400, xy300, app(app(ty_@2, cf), cg)) -> new_esEs9(xy400, xy300, cf, cg) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bea), beb), bec)) -> new_esEs11(xy4000, xy3000, bea, beb, bec) new_primEqNat0(Zero, Zero) -> True new_esEs10(Left(xy4000), Left(xy3000), ty_Float, db) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_@2, bd), be)) -> new_esEs9(xy4000, xy3000, bd, be) new_esEs19(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs6(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_asAs(False, xy26) -> False new_esEs20(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_@2, ge), gf), db) -> new_esEs9(xy4000, xy3000, ge, gf) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Maybe, baf)) -> new_esEs5(xy4000, xy3000, baf) new_esEs25(xy4000, xy3000, app(ty_Ratio, bef)) -> new_esEs18(xy4000, xy3000, bef) new_esEs4(xy400, xy300, ty_Int) -> new_esEs13(xy400, xy300) new_esEs10(Left(xy4000), Left(xy3000), ty_Ordering, db) -> new_esEs16(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_[], bag)) -> new_esEs15(xy4000, xy3000, bag) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Maybe, cc)) -> new_esEs5(xy4000, xy3000, cc) new_esEs10(Left(xy4000), Left(xy3000), app(ty_Maybe, hd), db) -> new_esEs5(xy4000, xy3000, hd) new_esEs17(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs7(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs16(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Float) -> new_esEs17(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_esEs13(x0, x1) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Bool) new_esEs26(x0, x1, ty_Int) new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Just(x1), ty_Double) new_esEs5(Just(x0), Just(x1), ty_Ordering) new_esEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_Int) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_asAs(False, x0) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Double) new_esEs22(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Integer) new_esEs5(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Char) new_esEs10(Right(x0), Right(x1), x2, ty_Integer) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Ordering) new_primPlusNat0(Zero, x0) new_esEs10(Left(x0), Left(x1), ty_Float, x2) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs25(x0, x1, ty_Float) new_esEs10(Right(x0), Right(x1), x2, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Bool) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_@0) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs16(EQ, EQ) new_esEs23(x0, x1, ty_@0) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs10(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(Char(x0), Char(x1)) new_esEs5(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(False, True) new_esEs6(True, False) new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs10(Left(x0), Left(x1), ty_Integer, x2) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs21(x0, x1, ty_Int) new_esEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs5(Just(x0), Just(x1), ty_Char) new_esEs19(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Char) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Double) new_esEs6(False, False) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(Just(x0), Just(x1), ty_Integer) new_esEs24(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs20(x0, x1, ty_Integer) new_esEs24(x0, x1, ty_Float) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs10(Left(x0), Left(x1), ty_Ordering, x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, ty_Ordering) new_esEs26(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs5(Nothing, Nothing, x0) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, ty_Float) new_primMulNat0(Zero, Succ(x0)) new_esEs7(Integer(x0), Integer(x1)) new_esEs24(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_primPlusNat1(Zero, Succ(x0)) new_esEs10(Right(x0), Right(x1), x2, app(ty_[], x3)) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs20(x0, x1, ty_Ordering) new_esEs15([], :(x0, x1), x2) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_primPlusNat0(Succ(x0), x1) new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Bool) new_esEs23(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, ty_Ordering) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs19(x0, x1, ty_@0) new_esEs5(Just(x0), Just(x1), ty_Bool) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, ty_Integer) new_esEs16(LT, GT) new_esEs16(GT, LT) new_esEs4(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Double) new_esEs10(Left(x0), Left(x1), ty_@0, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_Double) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Nothing, x1) new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_esEs23(x0, x1, ty_Float) new_esEs26(x0, x1, ty_Integer) new_asAs(True, x0) new_esEs26(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Float) new_esEs10(Left(x0), Left(x1), ty_Bool, x2) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs5(Just(x0), Just(x1), app(ty_[], x2)) new_esEs15([], [], x0) new_esEs4(x0, x1, ty_Double) new_esEs10(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs5(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_@0) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs19(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs17(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs8(@0, @0) new_esEs23(x0, x1, ty_Int) new_esEs22(x0, x1, ty_Integer) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs6(True, True) new_esEs10(Left(x0), Left(x1), ty_Int, x2) new_esEs20(x0, x1, ty_Bool) new_esEs15(:(x0, x1), :(x2, x3), x4) new_esEs19(x0, x1, ty_Integer) new_primPlusNat1(Succ(x0), Zero) new_esEs16(LT, LT) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs5(Nothing, Just(x0), x1) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_Integer) new_esEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Right(x1), x2, x3) new_esEs10(Right(x0), Left(x1), x2, x3) new_esEs20(x0, x1, ty_Double) new_esEs16(EQ, GT) new_esEs16(GT, EQ) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs20(x0, x1, ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs26(x0, x1, ty_Char) new_esEs15(:(x0, x1), [], x2) new_esEs10(Left(x0), Left(x1), ty_Double, x2) new_esEs26(x0, x1, ty_@0) new_esEs25(x0, x1, app(ty_[], x2)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs26(x0, x1, ty_Double) new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_@0) new_esEs10(Left(x0), Left(x1), ty_Char, x2) new_esEs16(LT, EQ) new_esEs16(EQ, LT) new_esEs19(x0, x1, ty_Ordering) new_esEs14(Double(x0, x1), Double(x2, x3)) new_primEqNat0(Succ(x0), Zero) new_esEs16(GT, GT) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, ty_Ordering) 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_deleteBy(Nothing, :(Just(xy300), xy31), ba) -> new_deleteBy(Nothing, xy31, ba) 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_deleteBy(Just(xy400), :(Just(xy300), xy31), ba) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, ba), ba) new_deleteBy0(xy10, xy11, xy12, False, bb) -> new_deleteBy(Just(xy12), xy10, bb) new_deleteBy(Just(xy400), :(Nothing, xy31), ba) -> new_deleteBy(Just(xy400), xy31, ba) The TRS R consists of the following rules: new_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), dc, dd, de) -> new_asAs(new_esEs25(xy4000, xy3000, dc), new_asAs(new_esEs24(xy4001, xy3001, dd), new_esEs23(xy4002, xy3002, de))) new_esEs10(Left(xy4000), Left(xy3000), ty_Int, db) -> new_esEs13(xy4000, xy3000) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs12(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_[], bdc)) -> new_esEs15(xy4001, xy3001, bdc) new_esEs5(Just(xy4000), Just(xy3000), app(ty_[], cd)) -> new_esEs15(xy4000, xy3000, cd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(app(ty_@3, bac), bad), bae)) -> new_esEs11(xy4000, xy3000, bac, bad, bae) new_esEs6(False, True) -> False new_esEs6(True, False) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs23(xy4002, xy3002, ty_Int) -> new_esEs13(xy4002, xy3002) new_esEs16(GT, GT) -> True new_esEs13(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs25(xy4000, xy3000, app(app(ty_@2, bde), bdf)) -> new_esEs9(xy4000, xy3000, bde, bdf) new_esEs19(xy4001, xy3001, app(app(ty_@2, dh), ea)) -> new_esEs9(xy4001, xy3001, dh, ea) new_esEs19(xy4001, xy3001, app(ty_Maybe, eg)) -> new_esEs5(xy4001, xy3001, eg) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Ratio, bah)) -> new_esEs18(xy4000, xy3000, bah) new_esEs26(xy4000, xy3000, app(ty_[], bfg)) -> new_esEs15(xy4000, xy3000, bfg) new_asAs(True, xy26) -> xy26 new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_Either, baa), bab)) -> new_esEs10(xy4000, xy3000, baa, bab) new_esEs20(xy4000, xy3000, app(app(ty_@2, fb), fc)) -> new_esEs9(xy4000, xy3000, fb, fc) new_esEs14(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs23(xy4002, xy3002, app(ty_Ratio, bcb)) -> new_esEs18(xy4002, xy3002, bcb) new_esEs26(xy4000, xy3000, app(app(ty_Either, bfa), bfb)) -> new_esEs10(xy4000, xy3000, bfa, bfb) new_esEs20(xy4000, xy3000, app(ty_Maybe, gb)) -> new_esEs5(xy4000, xy3000, gb) new_esEs23(xy4002, xy3002, app(app(ty_@2, bba), bbb)) -> new_esEs9(xy4002, xy3002, bba, bbb) new_esEs21(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_esEs20(xy4000, xy3000, app(ty_[], gc)) -> new_esEs15(xy4000, xy3000, gc) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs26(xy4000, xy3000, app(app(app(ty_@3, bfc), bfd), bfe)) -> new_esEs11(xy4000, xy3000, bfc, bfd, bfe) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs10(Left(xy4000), Right(xy3000), da, db) -> False new_esEs10(Right(xy4000), Left(xy3000), da, db) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs16(EQ, GT) -> False new_esEs16(GT, EQ) -> False new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_@0, db) -> new_esEs8(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Char) -> new_esEs12(xy400, xy300) new_esEs20(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(xy4002, xy3002, app(app(app(ty_@3, bbe), bbf), bbg)) -> new_esEs11(xy4002, xy3002, bbe, bbf, bbg) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_Char) -> new_esEs12(xy4002, xy3002) new_esEs24(xy4001, xy3001, app(ty_Maybe, bdb)) -> new_esEs5(xy4001, xy3001, bdb) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_Either, bf), bg)) -> new_esEs10(xy4000, xy3000, bf, bg) new_esEs5(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs15(:(xy4000, xy4001), [], df) -> False new_esEs15([], :(xy3000, xy3001), df) -> False new_esEs4(xy400, xy300, ty_@0) -> new_esEs8(xy400, xy300) new_esEs8(@0, @0) -> True new_esEs4(xy400, xy300, app(app(app(ty_@3, dc), dd), de)) -> new_esEs11(xy400, xy300, dc, dd, de) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs19(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Char, db) -> new_esEs12(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs4(xy400, xy300, app(app(ty_Either, da), db)) -> new_esEs10(xy400, xy300, da, db) new_esEs25(xy4000, xy3000, app(ty_Maybe, bed)) -> new_esEs5(xy4000, xy3000, bed) new_esEs26(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(LT, EQ) -> False new_esEs16(EQ, LT) -> False new_esEs10(Left(xy4000), Left(xy3000), app(ty_Ratio, hf), db) -> new_esEs18(xy4000, xy3000, hf) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Ratio, ce)) -> new_esEs18(xy4000, xy3000, ce) new_esEs26(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, dg)) -> new_esEs18(xy400, xy300, dg) new_esEs20(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_@0) -> new_esEs8(xy4002, xy3002) 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_esEs19(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(ty_@2, bcc), bcd)) -> new_esEs9(xy4001, xy3001, bcc, bcd) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bh), ca), cb)) -> new_esEs11(xy4000, xy3000, bh, ca, cb) new_esEs26(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_sr(Pos(xy40000), Neg(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_sr(Neg(xy40000), Pos(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_esEs10(Right(xy4000), Right(xy3000), da, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Succ(xy3001000)) -> Succ(Succ(new_primPlusNat1(xy2700, xy3001000))) new_esEs19(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs20(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(EQ, EQ) -> True new_esEs10(Right(xy4000), Right(xy3000), da, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_Either, gg), gh), db) -> new_esEs10(xy4000, xy3000, gg, gh) new_esEs21(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs7(xy400, xy300) new_esEs4(xy400, xy300, app(ty_[], df)) -> new_esEs15(xy400, xy300, df) new_esEs10(Left(xy4000), Left(xy3000), app(app(app(ty_@3, ha), hb), hc), db) -> new_esEs11(xy4000, xy3000, ha, hb, hc) new_esEs23(xy4002, xy3002, ty_Double) -> new_esEs14(xy4002, xy3002) new_esEs5(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Float) -> new_esEs17(xy400, xy300) new_esEs23(xy4002, xy3002, ty_Float) -> new_esEs17(xy4002, xy3002) new_sr(Neg(xy40000), Neg(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_esEs10(Left(xy4000), Left(xy3000), ty_Integer, db) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(app(ty_@2, beg), beh)) -> new_esEs9(xy4000, xy3000, beg, beh) new_esEs4(xy400, xy300, ty_Double) -> new_esEs14(xy400, xy300) new_esEs25(xy4000, xy3000, app(ty_[], bee)) -> new_esEs15(xy4000, xy3000, bee) new_esEs9(@2(xy4000, xy4001), @2(xy3000, xy3001), cf, cg) -> new_asAs(new_esEs20(xy4000, xy3000, cf), new_esEs19(xy4001, xy3001, cg)) new_esEs18(:%(xy4000, xy4001), :%(xy3000, xy3001), dg) -> new_asAs(new_esEs22(xy4000, xy3000, dg), new_esEs21(xy4001, xy3001, dg)) new_esEs19(xy4001, xy3001, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs11(xy4001, xy3001, ed, ee, ef) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs16(LT, LT) -> True new_esEs23(xy4002, xy3002, ty_Integer) -> new_esEs7(xy4002, xy3002) new_esEs19(xy4001, xy3001, app(app(ty_Either, eb), ec)) -> new_esEs10(xy4001, xy3001, eb, ec) new_esEs20(xy4000, xy3000, app(ty_Ratio, gd)) -> new_esEs18(xy4000, xy3000, gd) new_esEs6(True, True) -> True new_esEs19(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Double, db) -> new_esEs14(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs5(Nothing, Nothing, bc) -> True new_esEs19(xy4001, xy3001, app(ty_[], eh)) -> new_esEs15(xy4001, xy3001, eh) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_Ratio, bdd)) -> new_esEs18(xy4001, xy3001, bdd) new_esEs20(xy4000, xy3000, app(app(app(ty_@3, fg), fh), ga)) -> new_esEs11(xy4000, xy3000, fg, fh, ga) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs23(xy4002, xy3002, ty_Bool) -> new_esEs6(xy4002, xy3002) new_esEs5(Nothing, Just(xy3000), bc) -> False new_esEs5(Just(xy4000), Nothing, bc) -> False new_primPlusNat0(Succ(xy270), xy300100) -> Succ(Succ(new_primPlusNat1(xy270, xy300100))) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(ty_Maybe, bff)) -> new_esEs5(xy4000, xy3000, bff) new_esEs6(False, False) -> True new_esEs26(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs15([], [], df) -> True new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, app(app(ty_Either, fd), ff)) -> new_esEs10(xy4000, xy3000, fd, ff) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400000), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300100)) -> Zero new_sr(Pos(xy40000), Pos(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_primPlusNat0(Zero, xy300100) -> Succ(xy300100) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs23(xy4002, xy3002, app(ty_[], bca)) -> new_esEs15(xy4002, xy3002, bca) new_esEs15(:(xy4000, xy4001), :(xy3000, xy3001), df) -> new_asAs(new_esEs26(xy4000, xy3000, df), new_esEs15(xy4001, xy3001, df)) new_esEs23(xy4002, xy3002, app(ty_Maybe, bbh)) -> new_esEs5(xy4002, xy3002, bbh) new_esEs19(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs18(xy4001, xy3001, fa) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs23(xy4002, xy3002, app(app(ty_Either, bbc), bbd)) -> new_esEs10(xy4002, xy3002, bbc, bbd) new_esEs10(Right(xy4000), Right(xy3000), da, app(app(ty_@2, hg), hh)) -> new_esEs9(xy4000, xy3000, hg, hh) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4000, xy3000, app(ty_Ratio, bfh)) -> new_esEs18(xy4000, xy3000, bfh) new_esEs26(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_primMulNat0(Succ(xy400000), Succ(xy300100)) -> new_primPlusNat0(new_primMulNat0(xy400000, Succ(xy300100)), xy300100) new_esEs10(Left(xy4000), Left(xy3000), ty_Bool, db) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_Either, bce), bcf)) -> new_esEs10(xy4001, xy3001, bce, bcf) new_esEs10(Left(xy4000), Left(xy3000), app(ty_[], he), db) -> new_esEs15(xy4000, xy3000, he) new_esEs16(LT, GT) -> False new_esEs16(GT, LT) -> False new_esEs19(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, bcg), bch), bda)) -> new_esEs11(xy4001, xy3001, bcg, bch, bda) new_esEs23(xy4002, xy3002, ty_Ordering) -> new_esEs16(xy4002, xy3002) new_esEs26(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Zero) -> Succ(xy2700) new_primPlusNat1(Zero, Succ(xy3001000)) -> Succ(xy3001000) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_Either, bdg), bdh)) -> new_esEs10(xy4000, xy3000, bdg, bdh) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Double) -> new_esEs14(xy4000, xy3000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bc)) -> new_esEs5(xy400, xy300, bc) new_esEs4(xy400, xy300, app(app(ty_@2, cf), cg)) -> new_esEs9(xy400, xy300, cf, cg) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bea), beb), bec)) -> new_esEs11(xy4000, xy3000, bea, beb, bec) new_primEqNat0(Zero, Zero) -> True new_esEs10(Left(xy4000), Left(xy3000), ty_Float, db) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_@2, bd), be)) -> new_esEs9(xy4000, xy3000, bd, be) new_esEs19(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs6(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_asAs(False, xy26) -> False new_esEs20(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_@2, ge), gf), db) -> new_esEs9(xy4000, xy3000, ge, gf) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_Maybe, baf)) -> new_esEs5(xy4000, xy3000, baf) new_esEs25(xy4000, xy3000, app(ty_Ratio, bef)) -> new_esEs18(xy4000, xy3000, bef) new_esEs4(xy400, xy300, ty_Int) -> new_esEs13(xy400, xy300) new_esEs10(Left(xy4000), Left(xy3000), ty_Ordering, db) -> new_esEs16(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), da, app(ty_[], bag)) -> new_esEs15(xy4000, xy3000, bag) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Maybe, cc)) -> new_esEs5(xy4000, xy3000, cc) new_esEs10(Left(xy4000), Left(xy3000), app(ty_Maybe, hd), db) -> new_esEs5(xy4000, xy3000, hd) new_esEs17(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs7(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs16(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), da, ty_Float) -> new_esEs17(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_esEs13(x0, x1) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Bool) new_esEs26(x0, x1, ty_Int) new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Just(x1), ty_Double) new_esEs5(Just(x0), Just(x1), ty_Ordering) new_esEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_Int) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_asAs(False, x0) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, ty_Double) new_esEs22(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Integer) new_esEs5(Just(x0), Just(x1), ty_Float) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, ty_Char) new_esEs10(Right(x0), Right(x1), x2, ty_Integer) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Ordering) new_primPlusNat0(Zero, x0) new_esEs10(Left(x0), Left(x1), ty_Float, x2) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs25(x0, x1, ty_Float) new_esEs10(Right(x0), Right(x1), x2, ty_@0) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Bool) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_@0) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs16(EQ, EQ) new_esEs23(x0, x1, ty_@0) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs10(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(Char(x0), Char(x1)) new_esEs5(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs6(False, True) new_esEs6(True, False) new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs10(Left(x0), Left(x1), ty_Integer, x2) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs21(x0, x1, ty_Int) new_esEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs5(Just(x0), Just(x1), ty_Char) new_esEs19(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Char) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_Double) new_esEs19(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Double) new_esEs6(False, False) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(Just(x0), Just(x1), ty_Integer) new_esEs24(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs20(x0, x1, ty_Integer) new_esEs24(x0, x1, ty_Float) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs10(Left(x0), Left(x1), ty_Ordering, x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, ty_Ordering) new_esEs26(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs5(Nothing, Nothing, x0) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, ty_Float) new_primMulNat0(Zero, Succ(x0)) new_esEs7(Integer(x0), Integer(x1)) new_esEs24(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_primPlusNat1(Zero, Succ(x0)) new_esEs10(Right(x0), Right(x1), x2, app(ty_[], x3)) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs20(x0, x1, ty_Ordering) new_esEs15([], :(x0, x1), x2) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_primPlusNat0(Succ(x0), x1) new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Bool) new_esEs23(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, ty_Ordering) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs19(x0, x1, ty_@0) new_esEs5(Just(x0), Just(x1), ty_Bool) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, ty_Integer) new_esEs16(LT, GT) new_esEs16(GT, LT) new_esEs4(x0, x1, ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Double) new_esEs10(Left(x0), Left(x1), ty_@0, x2) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_Double) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(Just(x0), Nothing, x1) new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_esEs23(x0, x1, ty_Float) new_esEs26(x0, x1, ty_Integer) new_asAs(True, x0) new_esEs26(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Float) new_esEs10(Left(x0), Left(x1), ty_Bool, x2) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs5(Just(x0), Just(x1), app(ty_[], x2)) new_esEs15([], [], x0) new_esEs4(x0, x1, ty_Double) new_esEs10(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs5(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_@0) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs19(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Int) new_esEs10(Right(x0), Right(x1), x2, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs17(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs8(@0, @0) new_esEs23(x0, x1, ty_Int) new_esEs22(x0, x1, ty_Integer) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs6(True, True) new_esEs10(Left(x0), Left(x1), ty_Int, x2) new_esEs20(x0, x1, ty_Bool) new_esEs15(:(x0, x1), :(x2, x3), x4) new_esEs19(x0, x1, ty_Integer) new_primPlusNat1(Succ(x0), Zero) new_esEs16(LT, LT) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_esEs5(Nothing, Just(x0), x1) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_Integer) new_esEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs10(Left(x0), Right(x1), x2, x3) new_esEs10(Right(x0), Left(x1), x2, x3) new_esEs20(x0, x1, ty_Double) new_esEs16(EQ, GT) new_esEs16(GT, EQ) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs20(x0, x1, ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs26(x0, x1, ty_Char) new_esEs15(:(x0, x1), [], x2) new_esEs10(Left(x0), Left(x1), ty_Double, x2) new_esEs26(x0, x1, ty_@0) new_esEs25(x0, x1, app(ty_[], x2)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs26(x0, x1, ty_Double) new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_@0) new_esEs10(Left(x0), Left(x1), ty_Char, x2) new_esEs16(LT, EQ) new_esEs16(EQ, LT) new_esEs19(x0, x1, ty_Ordering) new_esEs14(Double(x0, x1), Double(x2, x3)) new_primEqNat0(Succ(x0), Zero) new_esEs16(GT, GT) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, ty_Ordering) 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_deleteBy0(xy10, xy11, xy12, False, bb) -> new_deleteBy(Just(xy12), xy10, bb) The graph contains the following edges 1 >= 2, 5 >= 3 *new_deleteBy(Just(xy400), :(Nothing, xy31), ba) -> new_deleteBy(Just(xy400), xy31, ba) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 *new_deleteBy(Just(xy400), :(Just(xy300), xy31), ba) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, ba), ba) The graph contains the following edges 2 > 1, 2 > 2, 1 > 3, 3 >= 5 ---------------------------------------- (17) YES ---------------------------------------- (18) 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_esEs11(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), bad, bae, baf) -> new_asAs(new_esEs25(xy4000, xy3000, bad), new_asAs(new_esEs24(xy4001, xy3001, bae), new_esEs23(xy4002, xy3002, baf))) new_esEs10(Left(xy4000), Left(xy3000), ty_Int, ff) -> new_esEs13(xy4000, xy3000) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs12(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_[], bda)) -> new_esEs15(xy4001, xy3001, bda) new_esEs5(Just(xy4000), Just(xy3000), app(ty_[], cc)) -> new_esEs15(xy4000, xy3000, cc) new_esEs10(Right(xy4000), Right(xy3000), ha, app(app(app(ty_@3, hf), hg), hh)) -> new_esEs11(xy4000, xy3000, hf, hg, hh) new_esEs6(False, True) -> False new_esEs6(True, False) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs23(xy4002, xy3002, ty_Int) -> new_esEs13(xy4002, xy3002) new_esEs16(GT, GT) -> True new_esEs13(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs25(xy4000, xy3000, app(app(ty_@2, bdc), bdd)) -> new_esEs9(xy4000, xy3000, bdc, bdd) new_esEs19(xy4001, xy3001, app(app(ty_@2, cg), da)) -> new_esEs9(xy4001, xy3001, cg, da) new_esEs19(xy4001, xy3001, app(ty_Maybe, dg)) -> new_esEs5(xy4001, xy3001, dg) new_esEs10(Right(xy4000), Right(xy3000), ha, app(ty_Ratio, bac)) -> new_esEs18(xy4000, xy3000, bac) new_esEs26(xy4000, xy3000, app(ty_[], bff)) -> new_esEs15(xy4000, xy3000, bff) new_asAs(True, xy26) -> xy26 new_deleteBy1(Just(xy400), :(Nothing, xy31), ba) -> :(Nothing, new_deleteBy1(Just(xy400), xy31, ba)) new_esEs22(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), ha, app(app(ty_Either, hd), he)) -> new_esEs10(xy4000, xy3000, hd, he) new_esEs20(xy4000, xy3000, app(app(ty_@2, eb), ec)) -> new_esEs9(xy4000, xy3000, eb, ec) new_esEs14(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs23(xy4002, xy3002, app(ty_Ratio, bbh)) -> new_esEs18(xy4002, xy3002, bbh) new_esEs26(xy4000, xy3000, app(app(ty_Either, beh), bfa)) -> new_esEs10(xy4000, xy3000, beh, bfa) new_esEs20(xy4000, xy3000, app(ty_Maybe, fa)) -> new_esEs5(xy4000, xy3000, fa) new_esEs23(xy4002, xy3002, app(app(ty_@2, bag), bah)) -> new_esEs9(xy4002, xy3002, bag, bah) new_esEs21(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_esEs20(xy4000, xy3000, app(ty_[], fb)) -> new_esEs15(xy4000, xy3000, fb) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs26(xy4000, xy3000, app(app(app(ty_@3, bfb), bfc), bfd)) -> new_esEs11(xy4000, xy3000, bfb, bfc, bfd) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs10(Left(xy4000), Right(xy3000), ha, ff) -> False new_esEs10(Right(xy4000), Left(xy3000), ha, ff) -> False new_esEs5(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs14(xy4000, xy3000) new_deleteBy1(xy40, [], ba) -> [] new_esEs16(EQ, GT) -> False new_esEs16(GT, EQ) -> False new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_@0, ff) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_deleteBy1(Just(xy400), :(Just(xy300), xy31), ba) -> new_deleteBy00(xy31, xy300, xy400, new_esEs4(xy400, xy300, ba), ba) new_esEs4(xy400, xy300, ty_Char) -> new_esEs12(xy400, xy300) new_primMulNat0(Zero, Zero) -> Zero new_deleteBy1(Nothing, :(Just(xy300), xy31), ba) -> :(Just(xy300), new_deleteBy1(Nothing, xy31, ba)) new_esEs23(xy4002, xy3002, app(app(app(ty_@3, bbc), bbd), bbe)) -> new_esEs11(xy4002, xy3002, bbc, bbd, bbe) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_Char) -> new_esEs12(xy4002, xy3002) new_esEs24(xy4001, xy3001, app(ty_Maybe, bch)) -> new_esEs5(xy4001, xy3001, bch) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_Either, be), bf)) -> new_esEs10(xy4000, xy3000, be, bf) new_esEs5(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs20(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs15(:(xy4000, xy4001), [], bee) -> False new_esEs15([], :(xy3000, xy3001), bee) -> False new_esEs4(xy400, xy300, ty_@0) -> new_esEs8(xy400, xy300) new_esEs8(@0, @0) -> True new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs4(xy400, xy300, app(app(app(ty_@3, bad), bae), baf)) -> new_esEs11(xy400, xy300, bad, bae, baf) new_esEs19(xy4001, xy3001, ty_Double) -> new_esEs14(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Char, ff) -> new_esEs12(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs5(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Bool) -> new_esEs6(xy4001, xy3001) new_esEs4(xy400, xy300, app(app(ty_Either, ha), ff)) -> new_esEs10(xy400, xy300, ha, ff) new_esEs25(xy4000, xy3000, app(ty_Maybe, beb)) -> new_esEs5(xy4000, xy3000, beb) new_esEs26(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(LT, EQ) -> False new_esEs16(EQ, LT) -> False new_esEs10(Left(xy4000), Left(xy3000), app(ty_Ratio, gh), ff) -> new_esEs18(xy4000, xy3000, gh) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Ratio, cd)) -> new_esEs18(xy4000, xy3000, cd) new_esEs26(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, fd)) -> new_esEs18(xy400, xy300, fd) new_esEs20(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_@0) -> new_esEs8(xy4002, xy3002) 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_esEs19(xy4001, xy3001, ty_Float) -> new_esEs17(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(ty_@2, bca), bcb)) -> new_esEs9(xy4001, xy3001, bca, bcb) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bg), bh), ca)) -> new_esEs11(xy4000, xy3000, bg, bh, ca) new_esEs26(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_sr(Pos(xy40000), Neg(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_sr(Neg(xy40000), Pos(xy30010)) -> Neg(new_primMulNat0(xy40000, xy30010)) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Succ(xy3001000)) -> Succ(Succ(new_primPlusNat1(xy2700, xy3001000))) new_esEs19(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs20(xy4000, xy3000, ty_Float) -> new_esEs17(xy4000, xy3000) new_esEs16(EQ, EQ) -> True new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs19(xy4001, xy3001, ty_Ordering) -> new_esEs16(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_Either, ga), gb), ff) -> new_esEs10(xy4000, xy3000, ga, gb) new_esEs21(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs7(xy400, xy300) new_esEs4(xy400, xy300, app(ty_[], bee)) -> new_esEs15(xy400, xy300, bee) new_esEs10(Left(xy4000), Left(xy3000), app(app(app(ty_@3, gc), gd), ge), ff) -> new_esEs11(xy4000, xy3000, gc, gd, ge) new_esEs23(xy4002, xy3002, ty_Double) -> new_esEs14(xy4002, xy3002) new_esEs5(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs23(xy4002, xy3002, ty_Float) -> new_esEs17(xy4002, xy3002) new_esEs4(xy400, xy300, ty_Float) -> new_esEs17(xy400, xy300) new_sr(Neg(xy40000), Neg(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_esEs10(Left(xy4000), Left(xy3000), ty_Integer, ff) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(app(ty_@2, bef), beg)) -> new_esEs9(xy4000, xy3000, bef, beg) new_esEs4(xy400, xy300, ty_Double) -> new_esEs14(xy400, xy300) new_esEs25(xy4000, xy3000, app(ty_[], bec)) -> new_esEs15(xy4000, xy3000, bec) new_esEs9(@2(xy4000, xy4001), @2(xy3000, xy3001), ce, cf) -> new_asAs(new_esEs20(xy4000, xy3000, ce), new_esEs19(xy4001, xy3001, cf)) new_esEs18(:%(xy4000, xy4001), :%(xy3000, xy3001), fd) -> new_asAs(new_esEs22(xy4000, xy3000, fd), new_esEs21(xy4001, xy3001, fd)) new_esEs19(xy4001, xy3001, app(app(app(ty_@3, dd), de), df)) -> new_esEs11(xy4001, xy3001, dd, de, df) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs13(xy4001, xy3001) new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs16(LT, LT) -> True new_esEs23(xy4002, xy3002, ty_Integer) -> new_esEs7(xy4002, xy3002) new_esEs19(xy4001, xy3001, app(app(ty_Either, db), dc)) -> new_esEs10(xy4001, xy3001, db, dc) new_esEs20(xy4000, xy3000, app(ty_Ratio, fc)) -> new_esEs18(xy4000, xy3000, fc) new_esEs6(True, True) -> True new_esEs19(xy4001, xy3001, ty_Integer) -> new_esEs7(xy4001, xy3001) new_esEs10(Left(xy4000), Left(xy3000), ty_Double, ff) -> new_esEs14(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs5(Nothing, Nothing, bb) -> True new_esEs19(xy4001, xy3001, app(ty_[], dh)) -> new_esEs15(xy4001, xy3001, dh) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs14(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(ty_Ratio, bdb)) -> new_esEs18(xy4001, xy3001, bdb) new_esEs20(xy4000, xy3000, app(app(app(ty_@3, ef), eg), eh)) -> new_esEs11(xy4000, xy3000, ef, eg, eh) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs23(xy4002, xy3002, ty_Bool) -> new_esEs6(xy4002, xy3002) new_esEs5(Nothing, Just(xy3000), bb) -> False new_esEs5(Just(xy4000), Nothing, bb) -> False new_primPlusNat0(Succ(xy270), xy300100) -> Succ(Succ(new_primPlusNat1(xy270, xy300100))) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, app(ty_Maybe, bfe)) -> new_esEs5(xy4000, xy3000, bfe) new_esEs6(False, False) -> True new_deleteBy00(xy10, xy11, xy12, False, bfh) -> :(Just(xy11), new_deleteBy1(Just(xy12), xy10, bfh)) new_esEs26(xy4000, xy3000, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs15([], [], bee) -> True new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs7(xy4000, xy3000) new_esEs26(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs20(xy4000, xy3000, app(app(ty_Either, ed), ee)) -> new_esEs10(xy4000, xy3000, ed, ee) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400000), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300100)) -> Zero new_sr(Pos(xy40000), Pos(xy30010)) -> Pos(new_primMulNat0(xy40000, xy30010)) new_primPlusNat0(Zero, xy300100) -> Succ(xy300100) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs23(xy4002, xy3002, app(ty_[], bbg)) -> new_esEs15(xy4002, xy3002, bbg) new_esEs15(:(xy4000, xy4001), :(xy3000, xy3001), bee) -> new_asAs(new_esEs26(xy4000, xy3000, bee), new_esEs15(xy4001, xy3001, bee)) new_esEs23(xy4002, xy3002, app(ty_Maybe, bbf)) -> new_esEs5(xy4002, xy3002, bbf) new_esEs19(xy4001, xy3001, app(ty_Ratio, ea)) -> new_esEs18(xy4001, xy3001, ea) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs23(xy4002, xy3002, app(app(ty_Either, bba), bbb)) -> new_esEs10(xy4002, xy3002, bba, bbb) new_esEs10(Right(xy4000), Right(xy3000), ha, app(app(ty_@2, hb), hc)) -> new_esEs9(xy4000, xy3000, hb, hc) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4000, xy3000, app(ty_Ratio, bfg)) -> new_esEs18(xy4000, xy3000, bfg) new_esEs26(xy4000, xy3000, ty_Bool) -> new_esEs6(xy4000, xy3000) new_primMulNat0(Succ(xy400000), Succ(xy300100)) -> new_primPlusNat0(new_primMulNat0(xy400000, Succ(xy300100)), xy300100) new_esEs10(Left(xy4000), Left(xy3000), ty_Bool, ff) -> new_esEs6(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_Either, bcc), bcd)) -> new_esEs10(xy4001, xy3001, bcc, bcd) new_esEs10(Left(xy4000), Left(xy3000), app(ty_[], gg), ff) -> new_esEs15(xy4000, xy3000, gg) new_esEs16(LT, GT) -> False new_esEs16(GT, LT) -> False new_esEs19(xy4001, xy3001, ty_@0) -> new_esEs8(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs11(xy4001, xy3001, bce, bcf, bcg) new_esEs23(xy4002, xy3002, ty_Ordering) -> new_esEs16(xy4002, xy3002) new_deleteBy00(xy10, xy11, xy12, True, bfh) -> xy10 new_esEs26(xy4000, xy3000, ty_@0) -> new_esEs8(xy4000, xy3000) new_primPlusNat1(Succ(xy2700), Zero) -> Succ(xy2700) new_primPlusNat1(Zero, Succ(xy3001000)) -> Succ(xy3001000) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_Either, bde), bdf)) -> new_esEs10(xy4000, xy3000, bde, bdf) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Double) -> new_esEs14(xy4000, xy3000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bb)) -> new_esEs5(xy400, xy300, bb) new_esEs4(xy400, xy300, app(app(ty_@2, ce), cf)) -> new_esEs9(xy400, xy300, ce, cf) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Ordering) -> new_esEs16(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs11(xy4000, xy3000, bdg, bdh, bea) new_deleteBy1(Nothing, :(Nothing, xy31), ba) -> xy31 new_primEqNat0(Zero, Zero) -> True new_esEs10(Left(xy4000), Left(xy3000), ty_Float, ff) -> new_esEs17(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), app(app(ty_@2, bc), bd)) -> new_esEs9(xy4000, xy3000, bc, bd) new_esEs19(xy4001, xy3001, ty_Char) -> new_esEs12(xy4001, xy3001) new_esEs22(xy4000, xy3000, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs6(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Int) -> new_esEs13(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_asAs(False, xy26) -> False new_esEs20(xy4000, xy3000, ty_Char) -> new_esEs12(xy4000, xy3000) new_esEs10(Left(xy4000), Left(xy3000), app(app(ty_@2, fg), fh), ff) -> new_esEs9(xy4000, xy3000, fg, fh) new_esEs10(Right(xy4000), Right(xy3000), ha, app(ty_Maybe, baa)) -> new_esEs5(xy4000, xy3000, baa) new_esEs25(xy4000, xy3000, app(ty_Ratio, bed)) -> new_esEs18(xy4000, xy3000, bed) new_esEs4(xy400, xy300, ty_Int) -> new_esEs13(xy400, xy300) new_esEs10(Left(xy4000), Left(xy3000), ty_Ordering, ff) -> new_esEs16(xy4000, xy3000) new_esEs10(Right(xy4000), Right(xy3000), ha, app(ty_[], bab)) -> new_esEs15(xy4000, xy3000, bab) new_esEs5(Just(xy4000), Just(xy3000), app(ty_Maybe, cb)) -> new_esEs5(xy4000, xy3000, cb) new_esEs10(Left(xy4000), Left(xy3000), app(ty_Maybe, gf), ff) -> new_esEs5(xy4000, xy3000, gf) new_esEs17(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs13(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs7(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs5(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs6(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs16(xy400, xy300) new_esEs10(Right(xy4000), Right(xy3000), ha, ty_Float) -> new_esEs17(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_esEs13(x0, x1) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_deleteBy00(x0, x1, x2, True, x3) new_esEs23(x0, x1, ty_Bool) new_esEs26(x0, x1, ty_Int) new_esEs5(Just(x0), Just(x1), ty_Double) new_esEs10(Right(x0), Right(x1), x2, app(ty_[], x3)) new_deleteBy1(Just(x0), :(Nothing, x1), x2) new_esEs5(Nothing, Nothing, x0) new_esEs5(Just(x0), Just(x1), ty_Ordering) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs25(x0, x1, ty_Int) new_esEs15([], :(x0, x1), x2) new_esEs18(:%(x0, x1), :%(x2, x3), x4) new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_esEs10(Right(x0), Right(x1), x2, ty_Int) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs10(Right(x0), Right(x1), x2, ty_Char) new_asAs(False, x0) new_esEs19(x0, x1, ty_Double) new_esEs22(x0, x1, ty_Int) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, ty_Integer) new_esEs5(Just(x0), Just(x1), ty_Float) new_esEs20(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Integer) new_esEs5(Just(x0), Nothing, x1) new_esEs26(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Ordering) new_primPlusNat0(Zero, x0) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Float) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Bool) new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(x0, x1, ty_@0) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs16(EQ, EQ) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, ty_@0) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Left(x0), Left(x1), ty_Bool, x2) new_esEs12(Char(x0), Char(x1)) new_esEs5(Just(x0), Just(x1), ty_Int) new_esEs19(x0, x1, app(ty_Ratio, x2)) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs6(False, True) new_esEs6(True, False) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs21(x0, x1, ty_Int) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(Just(x0), Just(x1), ty_Char) new_esEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs19(x0, x1, ty_Int) new_esEs19(x0, x1, app(app(ty_Either, x2), x3)) new_esEs25(x0, x1, ty_Double) new_esEs10(Left(x0), Left(x1), ty_Char, x2) new_esEs19(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Double) new_esEs6(False, False) new_esEs10(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs5(Just(x0), Just(x1), ty_Integer) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, ty_Integer) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Float) new_esEs5(Nothing, Just(x0), x1) new_esEs10(Right(x0), Right(x1), x2, ty_Ordering) new_sr(Neg(x0), Neg(x1)) new_esEs10(Left(x0), Left(x1), ty_Int, x2) new_esEs26(x0, x1, ty_Ordering) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_deleteBy1(Nothing, :(Nothing, x0), x1) new_esEs10(Left(x0), Left(x1), ty_Float, x2) new_esEs19(x0, x1, ty_Float) new_primMulNat0(Zero, Succ(x0)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs19(x0, x1, app(ty_[], x2)) new_esEs7(Integer(x0), Integer(x1)) new_esEs24(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_primPlusNat1(Zero, Succ(x0)) new_esEs10(Left(x0), Left(x1), ty_@0, x2) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primEqNat0(Zero, Succ(x0)) new_esEs20(x0, x1, ty_Ordering) new_esEs10(Left(x0), Right(x1), x2, x3) new_esEs10(Right(x0), Left(x1), x2, x3) new_esEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_primPlusNat0(Succ(x0), x1) new_esEs23(x0, x1, ty_Ordering) new_deleteBy00(x0, x1, x2, False, x3) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Right(x0), Right(x1), x2, ty_Integer) new_esEs19(x0, x1, ty_@0) new_esEs15(:(x0, x1), [], x2) new_esEs5(Just(x0), Just(x1), ty_Bool) new_esEs10(Left(x0), Left(x1), ty_Ordering, x2) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, ty_Integer) new_esEs16(LT, GT) new_esEs16(GT, LT) new_esEs4(x0, x1, ty_Ordering) new_esEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs10(Left(x0), Left(x1), ty_Double, x2) new_esEs23(x0, x1, ty_Double) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs20(x0, x1, app(ty_[], x2)) new_deleteBy1(Nothing, :(Just(x0), x1), x2) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Float) new_esEs26(x0, x1, ty_Integer) new_asAs(True, x0) new_esEs26(x0, x1, ty_Bool) new_esEs4(x0, x1, ty_Float) new_esEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_primEqNat0(Succ(x0), Succ(x1)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Double) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Char) new_esEs5(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_@0) new_esEs19(x0, x1, ty_Bool) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs15(:(x0, x1), :(x2, x3), x4) new_esEs4(x0, x1, ty_Int) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs17(Float(x0, x1), Float(x2, x3)) new_esEs8(@0, @0) new_esEs23(x0, x1, ty_Int) new_esEs22(x0, x1, ty_Integer) new_esEs10(Right(x0), Right(x1), x2, ty_Bool) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs6(True, True) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs20(x0, x1, ty_Bool) new_esEs19(x0, x1, ty_Integer) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_primPlusNat1(Succ(x0), Zero) new_esEs16(LT, LT) new_esEs10(Right(x0), Right(x1), x2, ty_@0) new_esEs20(x0, x1, ty_Float) new_esEs24(x0, x1, ty_Integer) new_esEs10(Right(x0), Right(x1), x2, ty_Double) new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs20(x0, x1, ty_Double) new_esEs16(EQ, GT) new_esEs16(GT, EQ) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_primPlusNat1(Succ(x0), Succ(x1)) new_deleteBy1(x0, [], x1) new_esEs20(x0, x1, ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs10(Left(x0), Left(x1), ty_Integer, x2) new_esEs26(x0, x1, ty_Char) new_esEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs26(x0, x1, ty_@0) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs19(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, ty_Double) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs10(Right(x0), Right(x1), x2, ty_Float) new_esEs20(x0, x1, ty_@0) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs15([], [], x0) new_deleteBy1(Just(x0), :(Just(x1), x2), x3) new_esEs16(LT, EQ) new_esEs16(EQ, LT) new_esEs19(x0, x1, ty_Ordering) new_esEs14(Double(x0, x1), Double(x2, x3)) new_esEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_primEqNat0(Succ(x0), Zero) new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs16(GT, GT) new_esEs24(x0, x1, ty_Ordering) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs5(Just(x0), Just(x1), app(ty_[], x2)) new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) 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 ---------------------------------------- (20) YES ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(xy400000), Succ(xy300100)) -> new_primMulNat(xy400000, Succ(xy300100)) R is empty. Q is empty. 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_primMulNat(Succ(xy400000), Succ(xy300100)) -> new_primMulNat(xy400000, Succ(xy300100)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (23) YES ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(ty_Either, gg), gh)) -> new_esEs0(xy4002, xy3002, gg, gh) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_Either, baa), bab), hh) -> new_esEs0(xy4001, xy3001, baa, bab) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_Either, bbb), bbc), gd, hh) -> new_esEs0(xy4000, xy3000, bbb, bbc) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_[], bag), hh) -> new_esEs3(xy4001, xy3001, bag) new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_@2, bca), bcb)) -> new_esEs(xy4000, xy3000, bca, bcb) new_esEs0(Left(xy4000), Left(xy3000), app(ty_Maybe, ef), dh) -> new_esEs2(xy4000, xy3000, ef) new_esEs0(Right(xy4000), Right(xy3000), eh, app(ty_[], gb)) -> new_esEs3(xy4000, xy3000, gb) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy4000, xy3000, cc, cd) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_Maybe, beb)) -> new_esEs2(xy4000, xy3000, beb) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(ty_[], cb)) -> new_esEs3(xy4001, xy3001, cb) new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(ty_Either, fc), fd)) -> new_esEs0(xy4000, xy3000, fc, fd) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(app(ty_@3, bbd), bbe), bbf), gd, hh) -> new_esEs1(xy4000, xy3000, bbd, bbe, bbf) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], bbh), gd, hh) -> new_esEs3(xy4000, xy3000, bbh) new_esEs0(Left(xy4000), Left(xy3000), app(app(ty_@2, df), dg), dh) -> new_esEs(xy4000, xy3000, df, dg) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(ty_Maybe, ca)) -> new_esEs2(xy4001, xy3001, ca) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_[], bec)) -> new_esEs3(xy4000, xy3000, bec) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, da), db), dc), ce) -> new_esEs1(xy4000, xy3000, da, db, dc) new_esEs2(Just(xy4000), Just(xy3000), app(ty_Maybe, bch)) -> new_esEs2(xy4000, xy3000, bch) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, dd), ce) -> new_esEs2(xy4000, xy3000, dd) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_@2, hf), hg), hh) -> new_esEs(xy4001, xy3001, hf, hg) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(ty_@2, ge), gf)) -> new_esEs(xy4002, xy3002, ge, gf) new_esEs2(Just(xy4000), Just(xy3000), app(ty_[], bda)) -> new_esEs3(xy4000, xy3000, bda) new_esEs0(Right(xy4000), Right(xy3000), eh, app(ty_Maybe, ga)) -> new_esEs2(xy4000, xy3000, ga) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy4001, xy3001, bb, bc) new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(ty_@2, fa), fb)) -> new_esEs(xy4000, xy3000, fa, fb) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs1(xy4001, xy3001, bf, bg, bh) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, bbg), gd, hh) -> new_esEs2(xy4000, xy3000, bbg) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_@2, bdc), bdd)) -> new_esEs(xy4000, xy3000, bdc, bdd) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs1(xy4000, xy3000, bdg, bdh, bea) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, cf), cg), ce) -> new_esEs0(xy4000, xy3000, cf, cg) new_esEs0(Left(xy4000), Left(xy3000), app(ty_[], eg), dh) -> new_esEs3(xy4000, xy3000, eg) new_esEs0(Left(xy4000), Left(xy3000), app(app(ty_Either, ea), eb), dh) -> new_esEs0(xy4000, xy3000, ea, eb) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(ty_Either, bd), be)) -> new_esEs0(xy4001, xy3001, bd, be) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), bdb) -> new_esEs3(xy4001, xy3001, bdb) new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_Either, bcc), bcd)) -> new_esEs0(xy4000, xy3000, bcc, bcd) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(app(ty_@3, ha), hb), hc)) -> new_esEs1(xy4002, xy3002, ha, hb, hc) new_esEs2(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs1(xy4000, xy3000, bce, bcf, bcg) new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], de), ce) -> new_esEs3(xy4000, xy3000, de) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_@2, bah), bba), gd, hh) -> new_esEs(xy4000, xy3000, bah, bba) new_esEs0(Left(xy4000), Left(xy3000), app(app(app(ty_@3, ec), ed), ee), dh) -> new_esEs1(xy4000, xy3000, ec, ed, ee) new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(app(ty_@3, ff), fg), fh)) -> new_esEs1(xy4000, xy3000, ff, fg, fh) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(ty_[], he)) -> new_esEs3(xy4002, xy3002, he) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(ty_Maybe, hd)) -> new_esEs2(xy4002, xy3002, hd) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(app(ty_@3, bac), bad), bae), hh) -> new_esEs1(xy4001, xy3001, bac, bad, bae) new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_Either, bde), bdf)) -> new_esEs0(xy4000, xy3000, bde, bdf) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_Maybe, baf), hh) -> new_esEs2(xy4001, xy3001, baf) R is empty. Q is empty. 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_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs1(xy4000, xy3000, bdg, bdh, bea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_Maybe, beb)) -> new_esEs2(xy4000, xy3000, beb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs1(xy4000, xy3000, bce, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_Either, bde), bdf)) -> new_esEs0(xy4000, xy3000, bde, bdf) 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(ty_Either, bcc), bcd)) -> new_esEs0(xy4000, xy3000, bcc, bcd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_@2, bdc), bdd)) -> new_esEs(xy4000, xy3000, bdc, bdd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Just(xy4000), Just(xy3000), app(app(ty_@2, 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_[], bda)) -> new_esEs3(xy4000, xy3000, bda) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(Left(xy4000), Left(xy3000), app(app(app(ty_@3, ec), ed), ee), dh) -> new_esEs1(xy4000, xy3000, ec, ed, ee) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(app(ty_@3, ff), fg), fh)) -> new_esEs1(xy4000, xy3000, ff, fg, fh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(Left(xy4000), Left(xy3000), app(ty_Maybe, ef), dh) -> new_esEs2(xy4000, xy3000, ef) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(Right(xy4000), Right(xy3000), eh, app(ty_Maybe, ga)) -> new_esEs2(xy4000, xy3000, ga) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(ty_Either, fc), fd)) -> new_esEs0(xy4000, xy3000, fc, fd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(Left(xy4000), Left(xy3000), app(app(ty_Either, ea), eb), dh) -> new_esEs0(xy4000, xy3000, ea, eb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(Left(xy4000), Left(xy3000), app(app(ty_@2, df), dg), dh) -> new_esEs(xy4000, xy3000, df, dg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(Right(xy4000), Right(xy3000), eh, app(app(ty_@2, fa), fb)) -> new_esEs(xy4000, xy3000, fa, fb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(Right(xy4000), Right(xy3000), eh, app(ty_[], gb)) -> new_esEs3(xy4000, xy3000, gb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(Left(xy4000), Left(xy3000), app(ty_[], eg), dh) -> new_esEs3(xy4000, xy3000, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, da), db), dc), ce) -> new_esEs1(xy4000, xy3000, da, db, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs1(xy4001, xy3001, bf, bg, bh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(app(ty_@3, bbd), bbe), bbf), gd, hh) -> new_esEs1(xy4000, xy3000, bbd, bbe, bbf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(app(ty_@3, ha), hb), hc)) -> new_esEs1(xy4002, xy3002, ha, hb, hc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(app(ty_@3, bac), bad), bae), hh) -> new_esEs1(xy4001, xy3001, bac, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_[], bec)) -> new_esEs3(xy4000, xy3000, bec) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(:(xy4000, xy4001), :(xy3000, xy3001), bdb) -> new_esEs3(xy4001, xy3001, bdb) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(ty_Maybe, ca)) -> new_esEs2(xy4001, xy3001, ca) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, dd), ce) -> new_esEs2(xy4000, xy3000, dd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, cf), cg), ce) -> new_esEs0(xy4000, xy3000, cf, cg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(ty_Either, bd), be)) -> new_esEs0(xy4001, xy3001, bd, be) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy4000, xy3000, cc, cd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy4001, xy3001, bb, bc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), ba, app(ty_[], cb)) -> new_esEs3(xy4001, xy3001, cb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], de), ce) -> new_esEs3(xy4000, xy3000, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, bbg), gd, hh) -> new_esEs2(xy4000, xy3000, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(ty_Maybe, hd)) -> new_esEs2(xy4002, xy3002, hd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_Maybe, baf), hh) -> new_esEs2(xy4001, xy3001, baf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(ty_Either, gg), gh)) -> new_esEs0(xy4002, xy3002, gg, gh) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_Either, baa), bab), hh) -> new_esEs0(xy4001, xy3001, baa, bab) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_Either, bbb), bbc), gd, hh) -> new_esEs0(xy4000, xy3000, bbb, bbc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_@2, hf), hg), hh) -> new_esEs(xy4001, xy3001, hf, hg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(app(ty_@2, ge), gf)) -> new_esEs(xy4002, xy3002, ge, gf) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_@2, bah), bba), gd, hh) -> new_esEs(xy4000, xy3000, bah, bba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_[], bag), hh) -> new_esEs3(xy4001, xy3001, bag) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], bbh), gd, hh) -> new_esEs3(xy4000, xy3000, bbh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, gd, app(ty_[], he)) -> new_esEs3(xy4002, xy3002, he) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 ---------------------------------------- (26) YES ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(xy2700), Succ(xy3001000)) -> new_primPlusNat(xy2700, xy3001000) 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(xy2700), Succ(xy3001000)) -> new_primPlusNat(xy2700, xy3001000) 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