/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 11 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) AND (21) QDP (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] (23) YES (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] (26) YES (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy _ _ [] = []; deleteBy eq x (y : ys) = if x `eq` y then ys else y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if eq x y then ys else y : deleteBy eq x ys" is transformed to "deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy _ _ [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy xw xx [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; infix 5 \\; (\\) :: Eq a => [a] -> [a] -> [a]; (\\) = foldl (flip delete); delete :: Eq a => a -> [a] -> [a]; delete = deleteBy (==); deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]; deleteBy xw xx [] = []; deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y); deleteBy0 ys y eq x True = ys; deleteBy0 ys y eq x False = y : deleteBy eq x ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(List.\\)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="xy3 (List.\\)",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="xy3 (List.\\) xy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="foldl (flip List.delete) xy3 xy4",fontsize=16,color="burlywood",shape="triangle"];758[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 758[label="",style="solid", color="burlywood", weight=9]; 758 -> 6[label="",style="solid", color="burlywood", weight=3]; 759[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 759[label="",style="solid", color="burlywood", weight=9]; 759 -> 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"];760[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];13 -> 760[label="",style="solid", color="burlywood", weight=9]; 760 -> 14[label="",style="solid", color="burlywood", weight=3]; 761[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 761[label="",style="solid", color="burlywood", weight=9]; 761 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="List.deleteBy (==) xy40 (xy30 : xy31)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="List.deleteBy (==) xy40 []",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="List.deleteBy0 xy31 xy30 (==) xy40 ((==) xy40 xy30)",fontsize=16,color="burlywood",shape="box"];762[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];16 -> 762[label="",style="solid", color="burlywood", weight=9]; 762 -> 18[label="",style="solid", color="burlywood", weight=3]; 763[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];16 -> 763[label="",style="solid", color="burlywood", weight=9]; 763 -> 19[label="",style="solid", color="burlywood", weight=3]; 17[label="[]",fontsize=16,color="green",shape="box"];18[label="List.deleteBy0 xy31 xy30 (==) (Left xy400) ((==) Left xy400 xy30)",fontsize=16,color="burlywood",shape="box"];764[label="xy30/Left xy300",fontsize=10,color="white",style="solid",shape="box"];18 -> 764[label="",style="solid", color="burlywood", weight=9]; 764 -> 20[label="",style="solid", color="burlywood", weight=3]; 765[label="xy30/Right xy300",fontsize=10,color="white",style="solid",shape="box"];18 -> 765[label="",style="solid", color="burlywood", weight=9]; 765 -> 21[label="",style="solid", color="burlywood", weight=3]; 19[label="List.deleteBy0 xy31 xy30 (==) (Right xy400) ((==) Right xy400 xy30)",fontsize=16,color="burlywood",shape="box"];766[label="xy30/Left xy300",fontsize=10,color="white",style="solid",shape="box"];19 -> 766[label="",style="solid", color="burlywood", weight=9]; 766 -> 22[label="",style="solid", color="burlywood", weight=3]; 767[label="xy30/Right xy300",fontsize=10,color="white",style="solid",shape="box"];19 -> 767[label="",style="solid", color="burlywood", weight=9]; 767 -> 23[label="",style="solid", color="burlywood", weight=3]; 20[label="List.deleteBy0 xy31 (Left xy300) (==) (Left xy400) ((==) Left xy400 Left xy300)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="List.deleteBy0 xy31 (Right xy300) (==) (Left xy400) ((==) Left xy400 Right xy300)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="List.deleteBy0 xy31 (Left xy300) (==) (Right xy400) ((==) Right xy400 Left xy300)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 23[label="List.deleteBy0 xy31 (Right xy300) (==) (Right xy400) ((==) Right xy400 Right xy300)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24 -> 28[label="",style="dashed", color="red", weight=0]; 24[label="List.deleteBy0 xy31 (Left xy300) (==) (Left xy400) (xy400 == xy300)",fontsize=16,color="magenta"];24 -> 29[label="",style="dashed", color="magenta", weight=3]; 24 -> 30[label="",style="dashed", color="magenta", weight=3]; 24 -> 31[label="",style="dashed", color="magenta", weight=3]; 24 -> 32[label="",style="dashed", color="magenta", weight=3]; 25[label="List.deleteBy0 xy31 (Right xy300) (==) (Left xy400) False",fontsize=16,color="black",shape="box"];25 -> 33[label="",style="solid", color="black", weight=3]; 26[label="List.deleteBy0 xy31 (Left xy300) (==) (Right xy400) False",fontsize=16,color="black",shape="box"];26 -> 34[label="",style="solid", color="black", weight=3]; 27 -> 35[label="",style="dashed", color="red", weight=0]; 27[label="List.deleteBy0 xy31 (Right xy300) (==) (Right xy400) (xy400 == xy300)",fontsize=16,color="magenta"];27 -> 36[label="",style="dashed", color="magenta", weight=3]; 27 -> 37[label="",style="dashed", color="magenta", weight=3]; 27 -> 38[label="",style="dashed", color="magenta", weight=3]; 27 -> 39[label="",style="dashed", color="magenta", weight=3]; 29[label="xy31",fontsize=16,color="green",shape="box"];30[label="xy400 == xy300",fontsize=16,color="blue",shape="box"];768[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 768[label="",style="solid", color="blue", weight=9]; 768 -> 40[label="",style="solid", color="blue", weight=3]; 769[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 769[label="",style="solid", color="blue", weight=9]; 769 -> 41[label="",style="solid", color="blue", weight=3]; 770[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 770[label="",style="solid", color="blue", weight=9]; 770 -> 42[label="",style="solid", color="blue", weight=3]; 771[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 771[label="",style="solid", color="blue", weight=9]; 771 -> 43[label="",style="solid", color="blue", weight=3]; 772[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 772[label="",style="solid", color="blue", weight=9]; 772 -> 44[label="",style="solid", color="blue", weight=3]; 773[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 773[label="",style="solid", color="blue", weight=9]; 773 -> 45[label="",style="solid", color="blue", weight=3]; 774[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 774[label="",style="solid", color="blue", weight=9]; 774 -> 46[label="",style="solid", color="blue", weight=3]; 775[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 775[label="",style="solid", color="blue", weight=9]; 775 -> 47[label="",style="solid", color="blue", weight=3]; 776[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 776[label="",style="solid", color="blue", weight=9]; 776 -> 48[label="",style="solid", color="blue", weight=3]; 777[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 777[label="",style="solid", color="blue", weight=9]; 777 -> 49[label="",style="solid", color="blue", weight=3]; 778[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 778[label="",style="solid", color="blue", weight=9]; 778 -> 50[label="",style="solid", color="blue", weight=3]; 779[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 779[label="",style="solid", color="blue", weight=9]; 779 -> 51[label="",style="solid", color="blue", weight=3]; 780[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 780[label="",style="solid", color="blue", weight=9]; 780 -> 52[label="",style="solid", color="blue", weight=3]; 781[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 781[label="",style="solid", color="blue", weight=9]; 781 -> 53[label="",style="solid", color="blue", weight=3]; 31[label="xy300",fontsize=16,color="green",shape="box"];32[label="xy400",fontsize=16,color="green",shape="box"];28[label="List.deleteBy0 xy10 (Left xy11) (==) (Left xy12) xy13",fontsize=16,color="burlywood",shape="triangle"];782[label="xy13/False",fontsize=10,color="white",style="solid",shape="box"];28 -> 782[label="",style="solid", color="burlywood", weight=9]; 782 -> 54[label="",style="solid", color="burlywood", weight=3]; 783[label="xy13/True",fontsize=10,color="white",style="solid",shape="box"];28 -> 783[label="",style="solid", color="burlywood", weight=9]; 783 -> 55[label="",style="solid", color="burlywood", weight=3]; 33[label="Right xy300 : List.deleteBy (==) (Left xy400) xy31",fontsize=16,color="green",shape="box"];33 -> 56[label="",style="dashed", color="green", weight=3]; 34[label="Left xy300 : List.deleteBy (==) (Right xy400) xy31",fontsize=16,color="green",shape="box"];34 -> 57[label="",style="dashed", color="green", weight=3]; 36[label="xy31",fontsize=16,color="green",shape="box"];37[label="xy400",fontsize=16,color="green",shape="box"];38[label="xy400 == xy300",fontsize=16,color="blue",shape="box"];784[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 784[label="",style="solid", color="blue", weight=9]; 784 -> 58[label="",style="solid", color="blue", weight=3]; 785[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 785[label="",style="solid", color="blue", weight=9]; 785 -> 59[label="",style="solid", color="blue", weight=3]; 786[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 786[label="",style="solid", color="blue", weight=9]; 786 -> 60[label="",style="solid", color="blue", weight=3]; 787[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 787[label="",style="solid", color="blue", weight=9]; 787 -> 61[label="",style="solid", color="blue", weight=3]; 788[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 788[label="",style="solid", color="blue", weight=9]; 788 -> 62[label="",style="solid", color="blue", weight=3]; 789[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 789[label="",style="solid", color="blue", weight=9]; 789 -> 63[label="",style="solid", color="blue", weight=3]; 790[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 790[label="",style="solid", color="blue", weight=9]; 790 -> 64[label="",style="solid", color="blue", weight=3]; 791[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 791[label="",style="solid", color="blue", weight=9]; 791 -> 65[label="",style="solid", color="blue", weight=3]; 792[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 792[label="",style="solid", color="blue", weight=9]; 792 -> 66[label="",style="solid", color="blue", weight=3]; 793[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 793[label="",style="solid", color="blue", weight=9]; 793 -> 67[label="",style="solid", color="blue", weight=3]; 794[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 794[label="",style="solid", color="blue", weight=9]; 794 -> 68[label="",style="solid", color="blue", weight=3]; 795[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 795[label="",style="solid", color="blue", weight=9]; 795 -> 69[label="",style="solid", color="blue", weight=3]; 796[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 796[label="",style="solid", color="blue", weight=9]; 796 -> 70[label="",style="solid", color="blue", weight=3]; 797[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];38 -> 797[label="",style="solid", color="blue", weight=9]; 797 -> 71[label="",style="solid", color="blue", weight=3]; 39[label="xy300",fontsize=16,color="green",shape="box"];35[label="List.deleteBy0 xy19 (Right xy20) (==) (Right xy21) xy22",fontsize=16,color="burlywood",shape="triangle"];798[label="xy22/False",fontsize=10,color="white",style="solid",shape="box"];35 -> 798[label="",style="solid", color="burlywood", weight=9]; 798 -> 72[label="",style="solid", color="burlywood", weight=3]; 799[label="xy22/True",fontsize=10,color="white",style="solid",shape="box"];35 -> 799[label="",style="solid", color="burlywood", weight=9]; 799 -> 73[label="",style="solid", color="burlywood", weight=3]; 40[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];800[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];40 -> 800[label="",style="solid", color="burlywood", weight=9]; 800 -> 74[label="",style="solid", color="burlywood", weight=3]; 801[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];40 -> 801[label="",style="solid", color="burlywood", weight=9]; 801 -> 75[label="",style="solid", color="burlywood", weight=3]; 41[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];802[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];41 -> 802[label="",style="solid", color="burlywood", weight=9]; 802 -> 76[label="",style="solid", color="burlywood", weight=3]; 803[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];41 -> 803[label="",style="solid", color="burlywood", weight=9]; 803 -> 77[label="",style="solid", color="burlywood", weight=3]; 804[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];41 -> 804[label="",style="solid", color="burlywood", weight=9]; 804 -> 78[label="",style="solid", color="burlywood", weight=3]; 42[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];805[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];42 -> 805[label="",style="solid", color="burlywood", weight=9]; 805 -> 79[label="",style="solid", color="burlywood", weight=3]; 43[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];806[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];43 -> 806[label="",style="solid", color="burlywood", weight=9]; 806 -> 80[label="",style="solid", color="burlywood", weight=3]; 44[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];44 -> 81[label="",style="solid", color="black", weight=3]; 45[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];807[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];45 -> 807[label="",style="solid", color="burlywood", weight=9]; 807 -> 82[label="",style="solid", color="burlywood", weight=3]; 46[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];46 -> 83[label="",style="solid", color="black", weight=3]; 47[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];808[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];47 -> 808[label="",style="solid", color="burlywood", weight=9]; 808 -> 84[label="",style="solid", color="burlywood", weight=3]; 48[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];809[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];48 -> 809[label="",style="solid", color="burlywood", weight=9]; 809 -> 85[label="",style="solid", color="burlywood", weight=3]; 810[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];48 -> 810[label="",style="solid", color="burlywood", weight=9]; 810 -> 86[label="",style="solid", color="burlywood", weight=3]; 49[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];49 -> 87[label="",style="solid", color="black", weight=3]; 50[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];811[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];50 -> 811[label="",style="solid", color="burlywood", weight=9]; 811 -> 88[label="",style="solid", color="burlywood", weight=3]; 51[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];812[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];51 -> 812[label="",style="solid", color="burlywood", weight=9]; 812 -> 89[label="",style="solid", color="burlywood", weight=3]; 813[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];51 -> 813[label="",style="solid", color="burlywood", weight=9]; 813 -> 90[label="",style="solid", color="burlywood", weight=3]; 52[label="xy400 == xy300",fontsize=16,color="black",shape="triangle"];52 -> 91[label="",style="solid", color="black", weight=3]; 53[label="xy400 == xy300",fontsize=16,color="burlywood",shape="triangle"];814[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];53 -> 814[label="",style="solid", color="burlywood", weight=9]; 814 -> 92[label="",style="solid", color="burlywood", weight=3]; 815[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];53 -> 815[label="",style="solid", color="burlywood", weight=9]; 815 -> 93[label="",style="solid", color="burlywood", weight=3]; 54[label="List.deleteBy0 xy10 (Left xy11) (==) (Left xy12) False",fontsize=16,color="black",shape="box"];54 -> 94[label="",style="solid", color="black", weight=3]; 55[label="List.deleteBy0 xy10 (Left xy11) (==) (Left xy12) True",fontsize=16,color="black",shape="box"];55 -> 95[label="",style="solid", color="black", weight=3]; 56 -> 13[label="",style="dashed", color="red", weight=0]; 56[label="List.deleteBy (==) (Left xy400) xy31",fontsize=16,color="magenta"];56 -> 96[label="",style="dashed", color="magenta", weight=3]; 56 -> 97[label="",style="dashed", color="magenta", weight=3]; 57 -> 13[label="",style="dashed", color="red", weight=0]; 57[label="List.deleteBy (==) (Right xy400) xy31",fontsize=16,color="magenta"];57 -> 98[label="",style="dashed", color="magenta", weight=3]; 57 -> 99[label="",style="dashed", color="magenta", weight=3]; 58 -> 40[label="",style="dashed", color="red", weight=0]; 58[label="xy400 == xy300",fontsize=16,color="magenta"];58 -> 100[label="",style="dashed", color="magenta", weight=3]; 58 -> 101[label="",style="dashed", color="magenta", weight=3]; 59 -> 41[label="",style="dashed", color="red", weight=0]; 59[label="xy400 == xy300",fontsize=16,color="magenta"];59 -> 102[label="",style="dashed", color="magenta", weight=3]; 59 -> 103[label="",style="dashed", color="magenta", weight=3]; 60 -> 42[label="",style="dashed", color="red", weight=0]; 60[label="xy400 == xy300",fontsize=16,color="magenta"];60 -> 104[label="",style="dashed", color="magenta", weight=3]; 60 -> 105[label="",style="dashed", color="magenta", weight=3]; 61 -> 43[label="",style="dashed", color="red", weight=0]; 61[label="xy400 == xy300",fontsize=16,color="magenta"];61 -> 106[label="",style="dashed", color="magenta", weight=3]; 61 -> 107[label="",style="dashed", color="magenta", weight=3]; 62 -> 44[label="",style="dashed", color="red", weight=0]; 62[label="xy400 == xy300",fontsize=16,color="magenta"];62 -> 108[label="",style="dashed", color="magenta", weight=3]; 62 -> 109[label="",style="dashed", color="magenta", weight=3]; 63 -> 45[label="",style="dashed", color="red", weight=0]; 63[label="xy400 == xy300",fontsize=16,color="magenta"];63 -> 110[label="",style="dashed", color="magenta", weight=3]; 63 -> 111[label="",style="dashed", color="magenta", weight=3]; 64 -> 46[label="",style="dashed", color="red", weight=0]; 64[label="xy400 == xy300",fontsize=16,color="magenta"];64 -> 112[label="",style="dashed", color="magenta", weight=3]; 64 -> 113[label="",style="dashed", color="magenta", weight=3]; 65 -> 47[label="",style="dashed", color="red", weight=0]; 65[label="xy400 == xy300",fontsize=16,color="magenta"];65 -> 114[label="",style="dashed", color="magenta", weight=3]; 65 -> 115[label="",style="dashed", color="magenta", weight=3]; 66 -> 48[label="",style="dashed", color="red", weight=0]; 66[label="xy400 == xy300",fontsize=16,color="magenta"];66 -> 116[label="",style="dashed", color="magenta", weight=3]; 66 -> 117[label="",style="dashed", color="magenta", weight=3]; 67 -> 49[label="",style="dashed", color="red", weight=0]; 67[label="xy400 == xy300",fontsize=16,color="magenta"];67 -> 118[label="",style="dashed", color="magenta", weight=3]; 67 -> 119[label="",style="dashed", color="magenta", weight=3]; 68 -> 50[label="",style="dashed", color="red", weight=0]; 68[label="xy400 == xy300",fontsize=16,color="magenta"];68 -> 120[label="",style="dashed", color="magenta", weight=3]; 68 -> 121[label="",style="dashed", color="magenta", weight=3]; 69 -> 51[label="",style="dashed", color="red", weight=0]; 69[label="xy400 == xy300",fontsize=16,color="magenta"];69 -> 122[label="",style="dashed", color="magenta", weight=3]; 69 -> 123[label="",style="dashed", color="magenta", weight=3]; 70 -> 52[label="",style="dashed", color="red", weight=0]; 70[label="xy400 == xy300",fontsize=16,color="magenta"];70 -> 124[label="",style="dashed", color="magenta", weight=3]; 70 -> 125[label="",style="dashed", color="magenta", weight=3]; 71 -> 53[label="",style="dashed", color="red", weight=0]; 71[label="xy400 == xy300",fontsize=16,color="magenta"];71 -> 126[label="",style="dashed", color="magenta", weight=3]; 71 -> 127[label="",style="dashed", color="magenta", weight=3]; 72[label="List.deleteBy0 xy19 (Right xy20) (==) (Right xy21) False",fontsize=16,color="black",shape="box"];72 -> 128[label="",style="solid", color="black", weight=3]; 73[label="List.deleteBy0 xy19 (Right xy20) (==) (Right xy21) True",fontsize=16,color="black",shape="box"];73 -> 129[label="",style="solid", color="black", weight=3]; 74[label="Nothing == xy300",fontsize=16,color="burlywood",shape="box"];816[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];74 -> 816[label="",style="solid", color="burlywood", weight=9]; 816 -> 130[label="",style="solid", color="burlywood", weight=3]; 817[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];74 -> 817[label="",style="solid", color="burlywood", weight=9]; 817 -> 131[label="",style="solid", color="burlywood", weight=3]; 75[label="Just xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];818[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];75 -> 818[label="",style="solid", color="burlywood", weight=9]; 818 -> 132[label="",style="solid", color="burlywood", weight=3]; 819[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];75 -> 819[label="",style="solid", color="burlywood", weight=9]; 819 -> 133[label="",style="solid", color="burlywood", weight=3]; 76[label="LT == xy300",fontsize=16,color="burlywood",shape="box"];820[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];76 -> 820[label="",style="solid", color="burlywood", weight=9]; 820 -> 134[label="",style="solid", color="burlywood", weight=3]; 821[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];76 -> 821[label="",style="solid", color="burlywood", weight=9]; 821 -> 135[label="",style="solid", color="burlywood", weight=3]; 822[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];76 -> 822[label="",style="solid", color="burlywood", weight=9]; 822 -> 136[label="",style="solid", color="burlywood", weight=3]; 77[label="EQ == xy300",fontsize=16,color="burlywood",shape="box"];823[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];77 -> 823[label="",style="solid", color="burlywood", weight=9]; 823 -> 137[label="",style="solid", color="burlywood", weight=3]; 824[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];77 -> 824[label="",style="solid", color="burlywood", weight=9]; 824 -> 138[label="",style="solid", color="burlywood", weight=3]; 825[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];77 -> 825[label="",style="solid", color="burlywood", weight=9]; 825 -> 139[label="",style="solid", color="burlywood", weight=3]; 78[label="GT == xy300",fontsize=16,color="burlywood",shape="box"];826[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];78 -> 826[label="",style="solid", color="burlywood", weight=9]; 826 -> 140[label="",style="solid", color="burlywood", weight=3]; 827[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];78 -> 827[label="",style="solid", color="burlywood", weight=9]; 827 -> 141[label="",style="solid", color="burlywood", weight=3]; 828[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];78 -> 828[label="",style="solid", color="burlywood", weight=9]; 828 -> 142[label="",style="solid", color="burlywood", weight=3]; 79[label="xy4000 :% xy4001 == xy300",fontsize=16,color="burlywood",shape="box"];829[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];79 -> 829[label="",style="solid", color="burlywood", weight=9]; 829 -> 143[label="",style="solid", color="burlywood", weight=3]; 80[label="Integer xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];830[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];80 -> 830[label="",style="solid", color="burlywood", weight=9]; 830 -> 144[label="",style="solid", color="burlywood", weight=3]; 81[label="primEqDouble xy400 xy300",fontsize=16,color="burlywood",shape="box"];831[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];81 -> 831[label="",style="solid", color="burlywood", weight=9]; 831 -> 145[label="",style="solid", color="burlywood", weight=3]; 82[label="(xy4000,xy4001) == xy300",fontsize=16,color="burlywood",shape="box"];832[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];82 -> 832[label="",style="solid", color="burlywood", weight=9]; 832 -> 146[label="",style="solid", color="burlywood", weight=3]; 83[label="primEqInt xy400 xy300",fontsize=16,color="burlywood",shape="triangle"];833[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];83 -> 833[label="",style="solid", color="burlywood", weight=9]; 833 -> 147[label="",style="solid", color="burlywood", weight=3]; 834[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];83 -> 834[label="",style="solid", color="burlywood", weight=9]; 834 -> 148[label="",style="solid", color="burlywood", weight=3]; 84[label="(xy4000,xy4001,xy4002) == xy300",fontsize=16,color="burlywood",shape="box"];835[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];84 -> 835[label="",style="solid", color="burlywood", weight=9]; 835 -> 149[label="",style="solid", color="burlywood", weight=3]; 85[label="False == xy300",fontsize=16,color="burlywood",shape="box"];836[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];85 -> 836[label="",style="solid", color="burlywood", weight=9]; 836 -> 150[label="",style="solid", color="burlywood", weight=3]; 837[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];85 -> 837[label="",style="solid", color="burlywood", weight=9]; 837 -> 151[label="",style="solid", color="burlywood", weight=3]; 86[label="True == xy300",fontsize=16,color="burlywood",shape="box"];838[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];86 -> 838[label="",style="solid", color="burlywood", weight=9]; 838 -> 152[label="",style="solid", color="burlywood", weight=3]; 839[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];86 -> 839[label="",style="solid", color="burlywood", weight=9]; 839 -> 153[label="",style="solid", color="burlywood", weight=3]; 87[label="primEqChar xy400 xy300",fontsize=16,color="burlywood",shape="box"];840[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];87 -> 840[label="",style="solid", color="burlywood", weight=9]; 840 -> 154[label="",style="solid", color="burlywood", weight=3]; 88[label="() == xy300",fontsize=16,color="burlywood",shape="box"];841[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];88 -> 841[label="",style="solid", color="burlywood", weight=9]; 841 -> 155[label="",style="solid", color="burlywood", weight=3]; 89[label="xy4000 : xy4001 == xy300",fontsize=16,color="burlywood",shape="box"];842[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];89 -> 842[label="",style="solid", color="burlywood", weight=9]; 842 -> 156[label="",style="solid", color="burlywood", weight=3]; 843[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];89 -> 843[label="",style="solid", color="burlywood", weight=9]; 843 -> 157[label="",style="solid", color="burlywood", weight=3]; 90[label="[] == xy300",fontsize=16,color="burlywood",shape="box"];844[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];90 -> 844[label="",style="solid", color="burlywood", weight=9]; 844 -> 158[label="",style="solid", color="burlywood", weight=3]; 845[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];90 -> 845[label="",style="solid", color="burlywood", weight=9]; 845 -> 159[label="",style="solid", color="burlywood", weight=3]; 91[label="primEqFloat xy400 xy300",fontsize=16,color="burlywood",shape="box"];846[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];91 -> 846[label="",style="solid", color="burlywood", weight=9]; 846 -> 160[label="",style="solid", color="burlywood", weight=3]; 92[label="Left xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];847[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];92 -> 847[label="",style="solid", color="burlywood", weight=9]; 847 -> 161[label="",style="solid", color="burlywood", weight=3]; 848[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];92 -> 848[label="",style="solid", color="burlywood", weight=9]; 848 -> 162[label="",style="solid", color="burlywood", weight=3]; 93[label="Right xy4000 == xy300",fontsize=16,color="burlywood",shape="box"];849[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];93 -> 849[label="",style="solid", color="burlywood", weight=9]; 849 -> 163[label="",style="solid", color="burlywood", weight=3]; 850[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];93 -> 850[label="",style="solid", color="burlywood", weight=9]; 850 -> 164[label="",style="solid", color="burlywood", weight=3]; 94[label="Left xy11 : List.deleteBy (==) (Left xy12) xy10",fontsize=16,color="green",shape="box"];94 -> 165[label="",style="dashed", color="green", weight=3]; 95[label="xy10",fontsize=16,color="green",shape="box"];96[label="Left xy400",fontsize=16,color="green",shape="box"];97[label="xy31",fontsize=16,color="green",shape="box"];98[label="Right xy400",fontsize=16,color="green",shape="box"];99[label="xy31",fontsize=16,color="green",shape="box"];100[label="xy300",fontsize=16,color="green",shape="box"];101[label="xy400",fontsize=16,color="green",shape="box"];102[label="xy300",fontsize=16,color="green",shape="box"];103[label="xy400",fontsize=16,color="green",shape="box"];104[label="xy300",fontsize=16,color="green",shape="box"];105[label="xy400",fontsize=16,color="green",shape="box"];106[label="xy300",fontsize=16,color="green",shape="box"];107[label="xy400",fontsize=16,color="green",shape="box"];108[label="xy300",fontsize=16,color="green",shape="box"];109[label="xy400",fontsize=16,color="green",shape="box"];110[label="xy300",fontsize=16,color="green",shape="box"];111[label="xy400",fontsize=16,color="green",shape="box"];112[label="xy300",fontsize=16,color="green",shape="box"];113[label="xy400",fontsize=16,color="green",shape="box"];114[label="xy300",fontsize=16,color="green",shape="box"];115[label="xy400",fontsize=16,color="green",shape="box"];116[label="xy300",fontsize=16,color="green",shape="box"];117[label="xy400",fontsize=16,color="green",shape="box"];118[label="xy300",fontsize=16,color="green",shape="box"];119[label="xy400",fontsize=16,color="green",shape="box"];120[label="xy300",fontsize=16,color="green",shape="box"];121[label="xy400",fontsize=16,color="green",shape="box"];122[label="xy300",fontsize=16,color="green",shape="box"];123[label="xy400",fontsize=16,color="green",shape="box"];124[label="xy300",fontsize=16,color="green",shape="box"];125[label="xy400",fontsize=16,color="green",shape="box"];126[label="xy300",fontsize=16,color="green",shape="box"];127[label="xy400",fontsize=16,color="green",shape="box"];128[label="Right xy20 : List.deleteBy (==) (Right xy21) xy19",fontsize=16,color="green",shape="box"];128 -> 166[label="",style="dashed", color="green", weight=3]; 129[label="xy19",fontsize=16,color="green",shape="box"];130[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];130 -> 167[label="",style="solid", color="black", weight=3]; 131[label="Nothing == Just xy3000",fontsize=16,color="black",shape="box"];131 -> 168[label="",style="solid", color="black", weight=3]; 132[label="Just xy4000 == Nothing",fontsize=16,color="black",shape="box"];132 -> 169[label="",style="solid", color="black", weight=3]; 133[label="Just xy4000 == Just xy3000",fontsize=16,color="black",shape="box"];133 -> 170[label="",style="solid", color="black", weight=3]; 134[label="LT == LT",fontsize=16,color="black",shape="box"];134 -> 171[label="",style="solid", color="black", weight=3]; 135[label="LT == EQ",fontsize=16,color="black",shape="box"];135 -> 172[label="",style="solid", color="black", weight=3]; 136[label="LT == GT",fontsize=16,color="black",shape="box"];136 -> 173[label="",style="solid", color="black", weight=3]; 137[label="EQ == LT",fontsize=16,color="black",shape="box"];137 -> 174[label="",style="solid", color="black", weight=3]; 138[label="EQ == EQ",fontsize=16,color="black",shape="box"];138 -> 175[label="",style="solid", color="black", weight=3]; 139[label="EQ == GT",fontsize=16,color="black",shape="box"];139 -> 176[label="",style="solid", color="black", weight=3]; 140[label="GT == LT",fontsize=16,color="black",shape="box"];140 -> 177[label="",style="solid", color="black", weight=3]; 141[label="GT == EQ",fontsize=16,color="black",shape="box"];141 -> 178[label="",style="solid", color="black", weight=3]; 142[label="GT == GT",fontsize=16,color="black",shape="box"];142 -> 179[label="",style="solid", color="black", weight=3]; 143[label="xy4000 :% xy4001 == xy3000 :% xy3001",fontsize=16,color="black",shape="box"];143 -> 180[label="",style="solid", color="black", weight=3]; 144[label="Integer xy4000 == Integer xy3000",fontsize=16,color="black",shape="box"];144 -> 181[label="",style="solid", color="black", weight=3]; 145[label="primEqDouble (Double xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];851[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];145 -> 851[label="",style="solid", color="burlywood", weight=9]; 851 -> 182[label="",style="solid", color="burlywood", weight=3]; 146[label="(xy4000,xy4001) == (xy3000,xy3001)",fontsize=16,color="black",shape="box"];146 -> 183[label="",style="solid", color="black", weight=3]; 147[label="primEqInt (Pos xy4000) xy300",fontsize=16,color="burlywood",shape="box"];852[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];147 -> 852[label="",style="solid", color="burlywood", weight=9]; 852 -> 184[label="",style="solid", color="burlywood", weight=3]; 853[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];147 -> 853[label="",style="solid", color="burlywood", weight=9]; 853 -> 185[label="",style="solid", color="burlywood", weight=3]; 148[label="primEqInt (Neg xy4000) xy300",fontsize=16,color="burlywood",shape="box"];854[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];148 -> 854[label="",style="solid", color="burlywood", weight=9]; 854 -> 186[label="",style="solid", color="burlywood", weight=3]; 855[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];148 -> 855[label="",style="solid", color="burlywood", weight=9]; 855 -> 187[label="",style="solid", color="burlywood", weight=3]; 149[label="(xy4000,xy4001,xy4002) == (xy3000,xy3001,xy3002)",fontsize=16,color="black",shape="box"];149 -> 188[label="",style="solid", color="black", weight=3]; 150[label="False == False",fontsize=16,color="black",shape="box"];150 -> 189[label="",style="solid", color="black", weight=3]; 151[label="False == True",fontsize=16,color="black",shape="box"];151 -> 190[label="",style="solid", color="black", weight=3]; 152[label="True == False",fontsize=16,color="black",shape="box"];152 -> 191[label="",style="solid", color="black", weight=3]; 153[label="True == True",fontsize=16,color="black",shape="box"];153 -> 192[label="",style="solid", color="black", weight=3]; 154[label="primEqChar (Char xy4000) xy300",fontsize=16,color="burlywood",shape="box"];856[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];154 -> 856[label="",style="solid", color="burlywood", weight=9]; 856 -> 193[label="",style="solid", color="burlywood", weight=3]; 155[label="() == ()",fontsize=16,color="black",shape="box"];155 -> 194[label="",style="solid", color="black", weight=3]; 156[label="xy4000 : xy4001 == xy3000 : xy3001",fontsize=16,color="black",shape="box"];156 -> 195[label="",style="solid", color="black", weight=3]; 157[label="xy4000 : xy4001 == []",fontsize=16,color="black",shape="box"];157 -> 196[label="",style="solid", color="black", weight=3]; 158[label="[] == xy3000 : xy3001",fontsize=16,color="black",shape="box"];158 -> 197[label="",style="solid", color="black", weight=3]; 159[label="[] == []",fontsize=16,color="black",shape="box"];159 -> 198[label="",style="solid", color="black", weight=3]; 160[label="primEqFloat (Float xy4000 xy4001) xy300",fontsize=16,color="burlywood",shape="box"];857[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];160 -> 857[label="",style="solid", color="burlywood", weight=9]; 857 -> 199[label="",style="solid", color="burlywood", weight=3]; 161[label="Left xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];161 -> 200[label="",style="solid", color="black", weight=3]; 162[label="Left xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];162 -> 201[label="",style="solid", color="black", weight=3]; 163[label="Right xy4000 == Left xy3000",fontsize=16,color="black",shape="box"];163 -> 202[label="",style="solid", color="black", weight=3]; 164[label="Right xy4000 == Right xy3000",fontsize=16,color="black",shape="box"];164 -> 203[label="",style="solid", color="black", weight=3]; 165 -> 13[label="",style="dashed", color="red", weight=0]; 165[label="List.deleteBy (==) (Left xy12) xy10",fontsize=16,color="magenta"];165 -> 204[label="",style="dashed", color="magenta", weight=3]; 165 -> 205[label="",style="dashed", color="magenta", weight=3]; 166 -> 13[label="",style="dashed", color="red", weight=0]; 166[label="List.deleteBy (==) (Right xy21) xy19",fontsize=16,color="magenta"];166 -> 206[label="",style="dashed", color="magenta", weight=3]; 166 -> 207[label="",style="dashed", color="magenta", weight=3]; 167[label="True",fontsize=16,color="green",shape="box"];168[label="False",fontsize=16,color="green",shape="box"];169[label="False",fontsize=16,color="green",shape="box"];170[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];858[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 858[label="",style="solid", color="blue", weight=9]; 858 -> 208[label="",style="solid", color="blue", weight=3]; 859[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 859[label="",style="solid", color="blue", weight=9]; 859 -> 209[label="",style="solid", color="blue", weight=3]; 860[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 860[label="",style="solid", color="blue", weight=9]; 860 -> 210[label="",style="solid", color="blue", weight=3]; 861[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 861[label="",style="solid", color="blue", weight=9]; 861 -> 211[label="",style="solid", color="blue", weight=3]; 862[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 862[label="",style="solid", color="blue", weight=9]; 862 -> 212[label="",style="solid", color="blue", weight=3]; 863[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 863[label="",style="solid", color="blue", weight=9]; 863 -> 213[label="",style="solid", color="blue", weight=3]; 864[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 864[label="",style="solid", color="blue", weight=9]; 864 -> 214[label="",style="solid", color="blue", weight=3]; 865[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 865[label="",style="solid", color="blue", weight=9]; 865 -> 215[label="",style="solid", color="blue", weight=3]; 866[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 866[label="",style="solid", color="blue", weight=9]; 866 -> 216[label="",style="solid", color="blue", weight=3]; 867[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 867[label="",style="solid", color="blue", weight=9]; 867 -> 217[label="",style="solid", color="blue", weight=3]; 868[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 868[label="",style="solid", color="blue", weight=9]; 868 -> 218[label="",style="solid", color="blue", weight=3]; 869[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 869[label="",style="solid", color="blue", weight=9]; 869 -> 219[label="",style="solid", color="blue", weight=3]; 870[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 870[label="",style="solid", color="blue", weight=9]; 870 -> 220[label="",style="solid", color="blue", weight=3]; 871[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 871[label="",style="solid", color="blue", weight=9]; 871 -> 221[label="",style="solid", color="blue", weight=3]; 171[label="True",fontsize=16,color="green",shape="box"];172[label="False",fontsize=16,color="green",shape="box"];173[label="False",fontsize=16,color="green",shape="box"];174[label="False",fontsize=16,color="green",shape="box"];175[label="True",fontsize=16,color="green",shape="box"];176[label="False",fontsize=16,color="green",shape="box"];177[label="False",fontsize=16,color="green",shape="box"];178[label="False",fontsize=16,color="green",shape="box"];179[label="True",fontsize=16,color="green",shape="box"];180 -> 314[label="",style="dashed", color="red", weight=0]; 180[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];180 -> 315[label="",style="dashed", color="magenta", weight=3]; 180 -> 316[label="",style="dashed", color="magenta", weight=3]; 181 -> 83[label="",style="dashed", color="red", weight=0]; 181[label="primEqInt xy4000 xy3000",fontsize=16,color="magenta"];181 -> 232[label="",style="dashed", color="magenta", weight=3]; 181 -> 233[label="",style="dashed", color="magenta", weight=3]; 182[label="primEqDouble (Double xy4000 xy4001) (Double xy3000 xy3001)",fontsize=16,color="black",shape="box"];182 -> 234[label="",style="solid", color="black", weight=3]; 183 -> 314[label="",style="dashed", color="red", weight=0]; 183[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];183 -> 317[label="",style="dashed", color="magenta", weight=3]; 183 -> 318[label="",style="dashed", color="magenta", weight=3]; 184[label="primEqInt (Pos (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];872[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];184 -> 872[label="",style="solid", color="burlywood", weight=9]; 872 -> 235[label="",style="solid", color="burlywood", weight=3]; 873[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];184 -> 873[label="",style="solid", color="burlywood", weight=9]; 873 -> 236[label="",style="solid", color="burlywood", weight=3]; 185[label="primEqInt (Pos Zero) xy300",fontsize=16,color="burlywood",shape="box"];874[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];185 -> 874[label="",style="solid", color="burlywood", weight=9]; 874 -> 237[label="",style="solid", color="burlywood", weight=3]; 875[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];185 -> 875[label="",style="solid", color="burlywood", weight=9]; 875 -> 238[label="",style="solid", color="burlywood", weight=3]; 186[label="primEqInt (Neg (Succ xy40000)) xy300",fontsize=16,color="burlywood",shape="box"];876[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];186 -> 876[label="",style="solid", color="burlywood", weight=9]; 876 -> 239[label="",style="solid", color="burlywood", weight=3]; 877[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];186 -> 877[label="",style="solid", color="burlywood", weight=9]; 877 -> 240[label="",style="solid", color="burlywood", weight=3]; 187[label="primEqInt (Neg Zero) xy300",fontsize=16,color="burlywood",shape="box"];878[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];187 -> 878[label="",style="solid", color="burlywood", weight=9]; 878 -> 241[label="",style="solid", color="burlywood", weight=3]; 879[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];187 -> 879[label="",style="solid", color="burlywood", weight=9]; 879 -> 242[label="",style="solid", color="burlywood", weight=3]; 188 -> 314[label="",style="dashed", color="red", weight=0]; 188[label="xy4000 == xy3000 && xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];188 -> 319[label="",style="dashed", color="magenta", weight=3]; 188 -> 320[label="",style="dashed", color="magenta", weight=3]; 189[label="True",fontsize=16,color="green",shape="box"];190[label="False",fontsize=16,color="green",shape="box"];191[label="False",fontsize=16,color="green",shape="box"];192[label="True",fontsize=16,color="green",shape="box"];193[label="primEqChar (Char xy4000) (Char xy3000)",fontsize=16,color="black",shape="box"];193 -> 254[label="",style="solid", color="black", weight=3]; 194[label="True",fontsize=16,color="green",shape="box"];195 -> 314[label="",style="dashed", color="red", weight=0]; 195[label="xy4000 == xy3000 && xy4001 == xy3001",fontsize=16,color="magenta"];195 -> 321[label="",style="dashed", color="magenta", weight=3]; 195 -> 322[label="",style="dashed", color="magenta", weight=3]; 196[label="False",fontsize=16,color="green",shape="box"];197[label="False",fontsize=16,color="green",shape="box"];198[label="True",fontsize=16,color="green",shape="box"];199[label="primEqFloat (Float xy4000 xy4001) (Float xy3000 xy3001)",fontsize=16,color="black",shape="box"];199 -> 255[label="",style="solid", color="black", weight=3]; 200[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];880[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 880[label="",style="solid", color="blue", weight=9]; 880 -> 256[label="",style="solid", color="blue", weight=3]; 881[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 881[label="",style="solid", color="blue", weight=9]; 881 -> 257[label="",style="solid", color="blue", weight=3]; 882[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 882[label="",style="solid", color="blue", weight=9]; 882 -> 258[label="",style="solid", color="blue", weight=3]; 883[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 883[label="",style="solid", color="blue", weight=9]; 883 -> 259[label="",style="solid", color="blue", weight=3]; 884[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 884[label="",style="solid", color="blue", weight=9]; 884 -> 260[label="",style="solid", color="blue", weight=3]; 885[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 885[label="",style="solid", color="blue", weight=9]; 885 -> 261[label="",style="solid", color="blue", weight=3]; 886[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 886[label="",style="solid", color="blue", weight=9]; 886 -> 262[label="",style="solid", color="blue", weight=3]; 887[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 887[label="",style="solid", color="blue", weight=9]; 887 -> 263[label="",style="solid", color="blue", weight=3]; 888[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 888[label="",style="solid", color="blue", weight=9]; 888 -> 264[label="",style="solid", color="blue", weight=3]; 889[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 889[label="",style="solid", color="blue", weight=9]; 889 -> 265[label="",style="solid", color="blue", weight=3]; 890[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 890[label="",style="solid", color="blue", weight=9]; 890 -> 266[label="",style="solid", color="blue", weight=3]; 891[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 891[label="",style="solid", color="blue", weight=9]; 891 -> 267[label="",style="solid", color="blue", weight=3]; 892[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 892[label="",style="solid", color="blue", weight=9]; 892 -> 268[label="",style="solid", color="blue", weight=3]; 893[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 893[label="",style="solid", color="blue", weight=9]; 893 -> 269[label="",style="solid", color="blue", weight=3]; 201[label="False",fontsize=16,color="green",shape="box"];202[label="False",fontsize=16,color="green",shape="box"];203[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];894[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 894[label="",style="solid", color="blue", weight=9]; 894 -> 270[label="",style="solid", color="blue", weight=3]; 895[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 895[label="",style="solid", color="blue", weight=9]; 895 -> 271[label="",style="solid", color="blue", weight=3]; 896[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 896[label="",style="solid", color="blue", weight=9]; 896 -> 272[label="",style="solid", color="blue", weight=3]; 897[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 897[label="",style="solid", color="blue", weight=9]; 897 -> 273[label="",style="solid", color="blue", weight=3]; 898[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 898[label="",style="solid", color="blue", weight=9]; 898 -> 274[label="",style="solid", color="blue", weight=3]; 899[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 899[label="",style="solid", color="blue", weight=9]; 899 -> 275[label="",style="solid", color="blue", weight=3]; 900[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 900[label="",style="solid", color="blue", weight=9]; 900 -> 276[label="",style="solid", color="blue", weight=3]; 901[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 901[label="",style="solid", color="blue", weight=9]; 901 -> 277[label="",style="solid", color="blue", weight=3]; 902[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 902[label="",style="solid", color="blue", weight=9]; 902 -> 278[label="",style="solid", color="blue", weight=3]; 903[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 903[label="",style="solid", color="blue", weight=9]; 903 -> 279[label="",style="solid", color="blue", weight=3]; 904[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 904[label="",style="solid", color="blue", weight=9]; 904 -> 280[label="",style="solid", color="blue", weight=3]; 905[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 905[label="",style="solid", color="blue", weight=9]; 905 -> 281[label="",style="solid", color="blue", weight=3]; 906[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 906[label="",style="solid", color="blue", weight=9]; 906 -> 282[label="",style="solid", color="blue", weight=3]; 907[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];203 -> 907[label="",style="solid", color="blue", weight=9]; 907 -> 283[label="",style="solid", color="blue", weight=3]; 204[label="Left xy12",fontsize=16,color="green",shape="box"];205[label="xy10",fontsize=16,color="green",shape="box"];206[label="Right xy21",fontsize=16,color="green",shape="box"];207[label="xy19",fontsize=16,color="green",shape="box"];208 -> 40[label="",style="dashed", color="red", weight=0]; 208[label="xy4000 == xy3000",fontsize=16,color="magenta"];208 -> 284[label="",style="dashed", color="magenta", weight=3]; 208 -> 285[label="",style="dashed", color="magenta", weight=3]; 209 -> 41[label="",style="dashed", color="red", weight=0]; 209[label="xy4000 == xy3000",fontsize=16,color="magenta"];209 -> 286[label="",style="dashed", color="magenta", weight=3]; 209 -> 287[label="",style="dashed", color="magenta", weight=3]; 210 -> 42[label="",style="dashed", color="red", weight=0]; 210[label="xy4000 == xy3000",fontsize=16,color="magenta"];210 -> 288[label="",style="dashed", color="magenta", weight=3]; 210 -> 289[label="",style="dashed", color="magenta", weight=3]; 211 -> 43[label="",style="dashed", color="red", weight=0]; 211[label="xy4000 == xy3000",fontsize=16,color="magenta"];211 -> 290[label="",style="dashed", color="magenta", weight=3]; 211 -> 291[label="",style="dashed", color="magenta", weight=3]; 212 -> 44[label="",style="dashed", color="red", weight=0]; 212[label="xy4000 == xy3000",fontsize=16,color="magenta"];212 -> 292[label="",style="dashed", color="magenta", weight=3]; 212 -> 293[label="",style="dashed", color="magenta", weight=3]; 213 -> 45[label="",style="dashed", color="red", weight=0]; 213[label="xy4000 == xy3000",fontsize=16,color="magenta"];213 -> 294[label="",style="dashed", color="magenta", weight=3]; 213 -> 295[label="",style="dashed", color="magenta", weight=3]; 214 -> 46[label="",style="dashed", color="red", weight=0]; 214[label="xy4000 == xy3000",fontsize=16,color="magenta"];214 -> 296[label="",style="dashed", color="magenta", weight=3]; 214 -> 297[label="",style="dashed", color="magenta", weight=3]; 215 -> 47[label="",style="dashed", color="red", weight=0]; 215[label="xy4000 == xy3000",fontsize=16,color="magenta"];215 -> 298[label="",style="dashed", color="magenta", weight=3]; 215 -> 299[label="",style="dashed", color="magenta", weight=3]; 216 -> 48[label="",style="dashed", color="red", weight=0]; 216[label="xy4000 == xy3000",fontsize=16,color="magenta"];216 -> 300[label="",style="dashed", color="magenta", weight=3]; 216 -> 301[label="",style="dashed", color="magenta", weight=3]; 217 -> 49[label="",style="dashed", color="red", weight=0]; 217[label="xy4000 == xy3000",fontsize=16,color="magenta"];217 -> 302[label="",style="dashed", color="magenta", weight=3]; 217 -> 303[label="",style="dashed", color="magenta", weight=3]; 218 -> 50[label="",style="dashed", color="red", weight=0]; 218[label="xy4000 == xy3000",fontsize=16,color="magenta"];218 -> 304[label="",style="dashed", color="magenta", weight=3]; 218 -> 305[label="",style="dashed", color="magenta", weight=3]; 219 -> 51[label="",style="dashed", color="red", weight=0]; 219[label="xy4000 == xy3000",fontsize=16,color="magenta"];219 -> 306[label="",style="dashed", color="magenta", weight=3]; 219 -> 307[label="",style="dashed", color="magenta", weight=3]; 220 -> 52[label="",style="dashed", color="red", weight=0]; 220[label="xy4000 == xy3000",fontsize=16,color="magenta"];220 -> 308[label="",style="dashed", color="magenta", weight=3]; 220 -> 309[label="",style="dashed", color="magenta", weight=3]; 221 -> 53[label="",style="dashed", color="red", weight=0]; 221[label="xy4000 == xy3000",fontsize=16,color="magenta"];221 -> 310[label="",style="dashed", color="magenta", weight=3]; 221 -> 311[label="",style="dashed", color="magenta", weight=3]; 315[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];908[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];315 -> 908[label="",style="solid", color="blue", weight=9]; 908 -> 327[label="",style="solid", color="blue", weight=3]; 909[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];315 -> 909[label="",style="solid", color="blue", weight=9]; 909 -> 328[label="",style="solid", color="blue", weight=3]; 316[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];910[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];316 -> 910[label="",style="solid", color="blue", weight=9]; 910 -> 329[label="",style="solid", color="blue", weight=3]; 911[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];316 -> 911[label="",style="solid", color="blue", weight=9]; 911 -> 330[label="",style="solid", color="blue", weight=3]; 314[label="xy34 && xy35",fontsize=16,color="burlywood",shape="triangle"];912[label="xy34/False",fontsize=10,color="white",style="solid",shape="box"];314 -> 912[label="",style="solid", color="burlywood", weight=9]; 912 -> 331[label="",style="solid", color="burlywood", weight=3]; 913[label="xy34/True",fontsize=10,color="white",style="solid",shape="box"];314 -> 913[label="",style="solid", color="burlywood", weight=9]; 913 -> 332[label="",style="solid", color="burlywood", weight=3]; 232[label="xy3000",fontsize=16,color="green",shape="box"];233[label="xy4000",fontsize=16,color="green",shape="box"];234 -> 46[label="",style="dashed", color="red", weight=0]; 234[label="xy4000 * xy3001 == xy4001 * xy3000",fontsize=16,color="magenta"];234 -> 333[label="",style="dashed", color="magenta", weight=3]; 234 -> 334[label="",style="dashed", color="magenta", weight=3]; 317[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];914[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 914[label="",style="solid", color="blue", weight=9]; 914 -> 335[label="",style="solid", color="blue", weight=3]; 915[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 915[label="",style="solid", color="blue", weight=9]; 915 -> 336[label="",style="solid", color="blue", weight=3]; 916[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 916[label="",style="solid", color="blue", weight=9]; 916 -> 337[label="",style="solid", color="blue", weight=3]; 917[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 917[label="",style="solid", color="blue", weight=9]; 917 -> 338[label="",style="solid", color="blue", weight=3]; 918[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 918[label="",style="solid", color="blue", weight=9]; 918 -> 339[label="",style="solid", color="blue", weight=3]; 919[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 919[label="",style="solid", color="blue", weight=9]; 919 -> 340[label="",style="solid", color="blue", weight=3]; 920[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 920[label="",style="solid", color="blue", weight=9]; 920 -> 341[label="",style="solid", color="blue", weight=3]; 921[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 921[label="",style="solid", color="blue", weight=9]; 921 -> 342[label="",style="solid", color="blue", weight=3]; 922[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 922[label="",style="solid", color="blue", weight=9]; 922 -> 343[label="",style="solid", color="blue", weight=3]; 923[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 923[label="",style="solid", color="blue", weight=9]; 923 -> 344[label="",style="solid", color="blue", weight=3]; 924[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 924[label="",style="solid", color="blue", weight=9]; 924 -> 345[label="",style="solid", color="blue", weight=3]; 925[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 925[label="",style="solid", color="blue", weight=9]; 925 -> 346[label="",style="solid", color="blue", weight=3]; 926[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 926[label="",style="solid", color="blue", weight=9]; 926 -> 347[label="",style="solid", color="blue", weight=3]; 927[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];317 -> 927[label="",style="solid", color="blue", weight=9]; 927 -> 348[label="",style="solid", color="blue", weight=3]; 318[label="xy4001 == xy3001",fontsize=16,color="blue",shape="box"];928[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 928[label="",style="solid", color="blue", weight=9]; 928 -> 349[label="",style="solid", color="blue", weight=3]; 929[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 929[label="",style="solid", color="blue", weight=9]; 929 -> 350[label="",style="solid", color="blue", weight=3]; 930[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 930[label="",style="solid", color="blue", weight=9]; 930 -> 351[label="",style="solid", color="blue", weight=3]; 931[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 931[label="",style="solid", color="blue", weight=9]; 931 -> 352[label="",style="solid", color="blue", weight=3]; 932[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 932[label="",style="solid", color="blue", weight=9]; 932 -> 353[label="",style="solid", color="blue", weight=3]; 933[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 933[label="",style="solid", color="blue", weight=9]; 933 -> 354[label="",style="solid", color="blue", weight=3]; 934[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 934[label="",style="solid", color="blue", weight=9]; 934 -> 355[label="",style="solid", color="blue", weight=3]; 935[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 935[label="",style="solid", color="blue", weight=9]; 935 -> 356[label="",style="solid", color="blue", weight=3]; 936[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 936[label="",style="solid", color="blue", weight=9]; 936 -> 357[label="",style="solid", color="blue", weight=3]; 937[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 937[label="",style="solid", color="blue", weight=9]; 937 -> 358[label="",style="solid", color="blue", weight=3]; 938[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 938[label="",style="solid", color="blue", weight=9]; 938 -> 359[label="",style="solid", color="blue", weight=3]; 939[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 939[label="",style="solid", color="blue", weight=9]; 939 -> 360[label="",style="solid", color="blue", weight=3]; 940[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 940[label="",style="solid", color="blue", weight=9]; 940 -> 361[label="",style="solid", color="blue", weight=3]; 941[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];318 -> 941[label="",style="solid", color="blue", weight=9]; 941 -> 362[label="",style="solid", color="blue", weight=3]; 235[label="primEqInt (Pos (Succ xy40000)) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];942[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];235 -> 942[label="",style="solid", color="burlywood", weight=9]; 942 -> 363[label="",style="solid", color="burlywood", weight=3]; 943[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];235 -> 943[label="",style="solid", color="burlywood", weight=9]; 943 -> 364[label="",style="solid", color="burlywood", weight=3]; 236[label="primEqInt (Pos (Succ xy40000)) (Neg xy3000)",fontsize=16,color="black",shape="box"];236 -> 365[label="",style="solid", color="black", weight=3]; 237[label="primEqInt (Pos Zero) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];944[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];237 -> 944[label="",style="solid", color="burlywood", weight=9]; 944 -> 366[label="",style="solid", color="burlywood", weight=3]; 945[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];237 -> 945[label="",style="solid", color="burlywood", weight=9]; 945 -> 367[label="",style="solid", color="burlywood", weight=3]; 238[label="primEqInt (Pos Zero) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];946[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];238 -> 946[label="",style="solid", color="burlywood", weight=9]; 946 -> 368[label="",style="solid", color="burlywood", weight=3]; 947[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];238 -> 947[label="",style="solid", color="burlywood", weight=9]; 947 -> 369[label="",style="solid", color="burlywood", weight=3]; 239[label="primEqInt (Neg (Succ xy40000)) (Pos xy3000)",fontsize=16,color="black",shape="box"];239 -> 370[label="",style="solid", color="black", weight=3]; 240[label="primEqInt (Neg (Succ xy40000)) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];948[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];240 -> 948[label="",style="solid", color="burlywood", weight=9]; 948 -> 371[label="",style="solid", color="burlywood", weight=3]; 949[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];240 -> 949[label="",style="solid", color="burlywood", weight=9]; 949 -> 372[label="",style="solid", color="burlywood", weight=3]; 241[label="primEqInt (Neg Zero) (Pos xy3000)",fontsize=16,color="burlywood",shape="box"];950[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];241 -> 950[label="",style="solid", color="burlywood", weight=9]; 950 -> 373[label="",style="solid", color="burlywood", weight=3]; 951[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];241 -> 951[label="",style="solid", color="burlywood", weight=9]; 951 -> 374[label="",style="solid", color="burlywood", weight=3]; 242[label="primEqInt (Neg Zero) (Neg xy3000)",fontsize=16,color="burlywood",shape="box"];952[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];242 -> 952[label="",style="solid", color="burlywood", weight=9]; 952 -> 375[label="",style="solid", color="burlywood", weight=3]; 953[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];242 -> 953[label="",style="solid", color="burlywood", weight=9]; 953 -> 376[label="",style="solid", color="burlywood", weight=3]; 319[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];954[label="== :: (Maybe 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color="blue", weight=9]; 958 -> 381[label="",style="solid", color="blue", weight=3]; 959[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 959[label="",style="solid", color="blue", weight=9]; 959 -> 382[label="",style="solid", color="blue", weight=3]; 960[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 960[label="",style="solid", color="blue", weight=9]; 960 -> 383[label="",style="solid", color="blue", weight=3]; 961[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 961[label="",style="solid", color="blue", weight=9]; 961 -> 384[label="",style="solid", color="blue", weight=3]; 962[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 962[label="",style="solid", color="blue", weight=9]; 962 -> 385[label="",style="solid", color="blue", weight=3]; 963[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 963[label="",style="solid", color="blue", weight=9]; 963 -> 386[label="",style="solid", color="blue", weight=3]; 964[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 964[label="",style="solid", color="blue", weight=9]; 964 -> 387[label="",style="solid", color="blue", weight=3]; 965[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 965[label="",style="solid", color="blue", weight=9]; 965 -> 388[label="",style="solid", color="blue", weight=3]; 966[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 966[label="",style="solid", color="blue", weight=9]; 966 -> 389[label="",style="solid", color="blue", weight=3]; 967[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];319 -> 967[label="",style="solid", color="blue", weight=9]; 967 -> 390[label="",style="solid", color="blue", weight=3]; 320 -> 314[label="",style="dashed", color="red", weight=0]; 320[label="xy4001 == xy3001 && xy4002 == xy3002",fontsize=16,color="magenta"];320 -> 391[label="",style="dashed", color="magenta", weight=3]; 320 -> 392[label="",style="dashed", color="magenta", weight=3]; 254[label="primEqNat xy4000 xy3000",fontsize=16,color="burlywood",shape="triangle"];968[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];254 -> 968[label="",style="solid", color="burlywood", weight=9]; 968 -> 393[label="",style="solid", color="burlywood", weight=3]; 969[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];254 -> 969[label="",style="solid", color="burlywood", weight=9]; 969 -> 394[label="",style="solid", color="burlywood", weight=3]; 321[label="xy4000 == xy3000",fontsize=16,color="blue",shape="box"];970[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 970[label="",style="solid", color="blue", weight=9]; 970 -> 395[label="",style="solid", color="blue", weight=3]; 971[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 971[label="",style="solid", color="blue", weight=9]; 971 -> 396[label="",style="solid", color="blue", weight=3]; 972[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 972[label="",style="solid", color="blue", weight=9]; 972 -> 397[label="",style="solid", color="blue", weight=3]; 973[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 973[label="",style="solid", color="blue", weight=9]; 973 -> 398[label="",style="solid", color="blue", weight=3]; 974[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 974[label="",style="solid", color="blue", weight=9]; 974 -> 399[label="",style="solid", color="blue", weight=3]; 975[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 975[label="",style="solid", color="blue", weight=9]; 975 -> 400[label="",style="solid", color="blue", weight=3]; 976[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 976[label="",style="solid", color="blue", weight=9]; 976 -> 401[label="",style="solid", color="blue", weight=3]; 977[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 977[label="",style="solid", color="blue", weight=9]; 977 -> 402[label="",style="solid", color="blue", weight=3]; 978[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 978[label="",style="solid", color="blue", weight=9]; 978 -> 403[label="",style="solid", color="blue", weight=3]; 979[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 979[label="",style="solid", color="blue", weight=9]; 979 -> 404[label="",style="solid", color="blue", weight=3]; 980[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 980[label="",style="solid", color="blue", weight=9]; 980 -> 405[label="",style="solid", color="blue", weight=3]; 981[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 981[label="",style="solid", color="blue", weight=9]; 981 -> 406[label="",style="solid", color="blue", weight=3]; 982[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 982[label="",style="solid", color="blue", weight=9]; 982 -> 407[label="",style="solid", color="blue", weight=3]; 983[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];321 -> 983[label="",style="solid", color="blue", weight=9]; 983 -> 408[label="",style="solid", color="blue", weight=3]; 322 -> 51[label="",style="dashed", color="red", weight=0]; 322[label="xy4001 == xy3001",fontsize=16,color="magenta"];322 -> 409[label="",style="dashed", color="magenta", weight=3]; 322 -> 410[label="",style="dashed", color="magenta", weight=3]; 255 -> 46[label="",style="dashed", color="red", weight=0]; 255[label="xy4000 * xy3001 == xy4001 * xy3000",fontsize=16,color="magenta"];255 -> 411[label="",style="dashed", color="magenta", weight=3]; 255 -> 412[label="",style="dashed", color="magenta", weight=3]; 256 -> 40[label="",style="dashed", color="red", weight=0]; 256[label="xy4000 == xy3000",fontsize=16,color="magenta"];256 -> 413[label="",style="dashed", color="magenta", weight=3]; 256 -> 414[label="",style="dashed", color="magenta", weight=3]; 257 -> 41[label="",style="dashed", color="red", weight=0]; 257[label="xy4000 == xy3000",fontsize=16,color="magenta"];257 -> 415[label="",style="dashed", color="magenta", weight=3]; 257 -> 416[label="",style="dashed", color="magenta", weight=3]; 258 -> 42[label="",style="dashed", color="red", weight=0]; 258[label="xy4000 == xy3000",fontsize=16,color="magenta"];258 -> 417[label="",style="dashed", color="magenta", weight=3]; 258 -> 418[label="",style="dashed", color="magenta", weight=3]; 259 -> 43[label="",style="dashed", color="red", weight=0]; 259[label="xy4000 == xy3000",fontsize=16,color="magenta"];259 -> 419[label="",style="dashed", color="magenta", weight=3]; 259 -> 420[label="",style="dashed", color="magenta", weight=3]; 260 -> 44[label="",style="dashed", color="red", weight=0]; 260[label="xy4000 == xy3000",fontsize=16,color="magenta"];260 -> 421[label="",style="dashed", color="magenta", weight=3]; 260 -> 422[label="",style="dashed", color="magenta", weight=3]; 261 -> 45[label="",style="dashed", color="red", weight=0]; 261[label="xy4000 == xy3000",fontsize=16,color="magenta"];261 -> 423[label="",style="dashed", color="magenta", weight=3]; 261 -> 424[label="",style="dashed", color="magenta", weight=3]; 262 -> 46[label="",style="dashed", color="red", weight=0]; 262[label="xy4000 == xy3000",fontsize=16,color="magenta"];262 -> 425[label="",style="dashed", color="magenta", weight=3]; 262 -> 426[label="",style="dashed", color="magenta", weight=3]; 263 -> 47[label="",style="dashed", color="red", weight=0]; 263[label="xy4000 == xy3000",fontsize=16,color="magenta"];263 -> 427[label="",style="dashed", color="magenta", weight=3]; 263 -> 428[label="",style="dashed", color="magenta", weight=3]; 264 -> 48[label="",style="dashed", color="red", weight=0]; 264[label="xy4000 == xy3000",fontsize=16,color="magenta"];264 -> 429[label="",style="dashed", color="magenta", weight=3]; 264 -> 430[label="",style="dashed", color="magenta", weight=3]; 265 -> 49[label="",style="dashed", color="red", weight=0]; 265[label="xy4000 == xy3000",fontsize=16,color="magenta"];265 -> 431[label="",style="dashed", color="magenta", weight=3]; 265 -> 432[label="",style="dashed", color="magenta", weight=3]; 266 -> 50[label="",style="dashed", color="red", weight=0]; 266[label="xy4000 == xy3000",fontsize=16,color="magenta"];266 -> 433[label="",style="dashed", color="magenta", weight=3]; 266 -> 434[label="",style="dashed", color="magenta", weight=3]; 267 -> 51[label="",style="dashed", color="red", weight=0]; 267[label="xy4000 == xy3000",fontsize=16,color="magenta"];267 -> 435[label="",style="dashed", color="magenta", weight=3]; 267 -> 436[label="",style="dashed", color="magenta", weight=3]; 268 -> 52[label="",style="dashed", color="red", weight=0]; 268[label="xy4000 == xy3000",fontsize=16,color="magenta"];268 -> 437[label="",style="dashed", color="magenta", weight=3]; 268 -> 438[label="",style="dashed", color="magenta", weight=3]; 269 -> 53[label="",style="dashed", color="red", weight=0]; 269[label="xy4000 == xy3000",fontsize=16,color="magenta"];269 -> 439[label="",style="dashed", color="magenta", weight=3]; 269 -> 440[label="",style="dashed", color="magenta", weight=3]; 270 -> 40[label="",style="dashed", color="red", weight=0]; 270[label="xy4000 == 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516[label="",style="dashed", color="magenta", weight=3]; 352 -> 517[label="",style="dashed", color="magenta", weight=3]; 353 -> 44[label="",style="dashed", color="red", weight=0]; 353[label="xy4001 == xy3001",fontsize=16,color="magenta"];353 -> 518[label="",style="dashed", color="magenta", weight=3]; 353 -> 519[label="",style="dashed", color="magenta", weight=3]; 354 -> 45[label="",style="dashed", color="red", weight=0]; 354[label="xy4001 == xy3001",fontsize=16,color="magenta"];354 -> 520[label="",style="dashed", color="magenta", weight=3]; 354 -> 521[label="",style="dashed", color="magenta", weight=3]; 355 -> 46[label="",style="dashed", color="red", weight=0]; 355[label="xy4001 == xy3001",fontsize=16,color="magenta"];355 -> 522[label="",style="dashed", color="magenta", weight=3]; 355 -> 523[label="",style="dashed", color="magenta", weight=3]; 356 -> 47[label="",style="dashed", color="red", weight=0]; 356[label="xy4001 == xy3001",fontsize=16,color="magenta"];356 -> 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532[label="",style="dashed", color="magenta", weight=3]; 360 -> 533[label="",style="dashed", color="magenta", weight=3]; 361 -> 52[label="",style="dashed", color="red", weight=0]; 361[label="xy4001 == xy3001",fontsize=16,color="magenta"];361 -> 534[label="",style="dashed", color="magenta", weight=3]; 361 -> 535[label="",style="dashed", color="magenta", weight=3]; 362 -> 53[label="",style="dashed", color="red", weight=0]; 362[label="xy4001 == xy3001",fontsize=16,color="magenta"];362 -> 536[label="",style="dashed", color="magenta", weight=3]; 362 -> 537[label="",style="dashed", color="magenta", weight=3]; 363[label="primEqInt (Pos (Succ xy40000)) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];363 -> 538[label="",style="solid", color="black", weight=3]; 364[label="primEqInt (Pos (Succ xy40000)) (Pos Zero)",fontsize=16,color="black",shape="box"];364 -> 539[label="",style="solid", color="black", weight=3]; 365[label="False",fontsize=16,color="green",shape="box"];366[label="primEqInt (Pos Zero) (Pos (Succ xy30000))",fontsize=16,color="black",shape="box"];366 -> 540[label="",style="solid", color="black", weight=3]; 367[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];367 -> 541[label="",style="solid", color="black", weight=3]; 368[label="primEqInt (Pos Zero) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];368 -> 542[label="",style="solid", color="black", weight=3]; 369[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];369 -> 543[label="",style="solid", color="black", weight=3]; 370[label="False",fontsize=16,color="green",shape="box"];371[label="primEqInt (Neg (Succ xy40000)) (Neg (Succ xy30000))",fontsize=16,color="black",shape="box"];371 -> 544[label="",style="solid", color="black", weight=3]; 372[label="primEqInt (Neg (Succ xy40000)) (Neg Zero)",fontsize=16,color="black",shape="box"];372 -> 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992[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 992[label="",style="solid", color="blue", weight=9]; 992 -> 586[label="",style="solid", color="blue", weight=3]; 993[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 993[label="",style="solid", color="blue", weight=9]; 993 -> 587[label="",style="solid", color="blue", weight=3]; 994[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 994[label="",style="solid", color="blue", weight=9]; 994 -> 588[label="",style="solid", color="blue", weight=3]; 995[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 995[label="",style="solid", color="blue", weight=9]; 995 -> 589[label="",style="solid", color="blue", weight=3]; 996[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 996[label="",style="solid", color="blue", weight=9]; 996 -> 590[label="",style="solid", color="blue", weight=3]; 997[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 997[label="",style="solid", color="blue", weight=9]; 997 -> 591[label="",style="solid", color="blue", weight=3]; 392[label="xy4002 == xy3002",fontsize=16,color="blue",shape="box"];998[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 998[label="",style="solid", color="blue", weight=9]; 998 -> 592[label="",style="solid", color="blue", weight=3]; 999[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 999[label="",style="solid", color="blue", weight=9]; 999 -> 593[label="",style="solid", color="blue", weight=3]; 1000[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1000[label="",style="solid", color="blue", weight=9]; 1000 -> 594[label="",style="solid", color="blue", weight=3]; 1001[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1001[label="",style="solid", color="blue", weight=9]; 1001 -> 595[label="",style="solid", color="blue", weight=3]; 1002[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1002[label="",style="solid", color="blue", weight=9]; 1002 -> 596[label="",style="solid", color="blue", weight=3]; 1003[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1003[label="",style="solid", color="blue", weight=9]; 1003 -> 597[label="",style="solid", color="blue", weight=3]; 1004[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1004[label="",style="solid", color="blue", weight=9]; 1004 -> 598[label="",style="solid", color="blue", weight=3]; 1005[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1005[label="",style="solid", color="blue", weight=9]; 1005 -> 599[label="",style="solid", color="blue", weight=3]; 1006[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1006[label="",style="solid", color="blue", weight=9]; 1006 -> 600[label="",style="solid", color="blue", weight=3]; 1007[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1007[label="",style="solid", color="blue", weight=9]; 1007 -> 601[label="",style="solid", color="blue", weight=3]; 1008[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1008[label="",style="solid", color="blue", weight=9]; 1008 -> 602[label="",style="solid", color="blue", weight=3]; 1009[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1009[label="",style="solid", color="blue", weight=9]; 1009 -> 603[label="",style="solid", color="blue", weight=3]; 1010[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1010[label="",style="solid", color="blue", weight=9]; 1010 -> 604[label="",style="solid", color="blue", weight=3]; 1011[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1011[label="",style="solid", color="blue", weight=9]; 1011 -> 605[label="",style="solid", color="blue", weight=3]; 393[label="primEqNat (Succ xy40000) xy3000",fontsize=16,color="burlywood",shape="box"];1012[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];393 -> 1012[label="",style="solid", color="burlywood", weight=9]; 1012 -> 606[label="",style="solid", color="burlywood", weight=3]; 1013[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];393 -> 1013[label="",style="solid", color="burlywood", weight=9]; 1013 -> 607[label="",style="solid", color="burlywood", weight=3]; 394[label="primEqNat Zero xy3000",fontsize=16,color="burlywood",shape="box"];1014[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];394 -> 1014[label="",style="solid", color="burlywood", weight=9]; 1014 -> 608[label="",style="solid", color="burlywood", weight=3]; 1015[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];394 -> 1015[label="",style="solid", color="burlywood", weight=9]; 1015 -> 609[label="",style="solid", color="burlywood", weight=3]; 395 -> 40[label="",style="dashed", color="red", weight=0]; 395[label="xy4000 == xy3000",fontsize=16,color="magenta"];395 -> 610[label="",style="dashed", color="magenta", weight=3]; 395 -> 611[label="",style="dashed", color="magenta", weight=3]; 396 -> 41[label="",style="dashed", color="red", weight=0]; 396[label="xy4000 == xy3000",fontsize=16,color="magenta"];396 -> 612[label="",style="dashed", color="magenta", weight=3]; 396 -> 613[label="",style="dashed", color="magenta", weight=3]; 397 -> 42[label="",style="dashed", color="red", weight=0]; 397[label="xy4000 == xy3000",fontsize=16,color="magenta"];397 -> 614[label="",style="dashed", color="magenta", weight=3]; 397 -> 615[label="",style="dashed", color="magenta", weight=3]; 398 -> 43[label="",style="dashed", color="red", weight=0]; 398[label="xy4000 == xy3000",fontsize=16,color="magenta"];398 -> 616[label="",style="dashed", color="magenta", weight=3]; 398 -> 617[label="",style="dashed", color="magenta", weight=3]; 399 -> 44[label="",style="dashed", color="red", weight=0]; 399[label="xy4000 == xy3000",fontsize=16,color="magenta"];399 -> 618[label="",style="dashed", color="magenta", weight=3]; 399 -> 619[label="",style="dashed", color="magenta", weight=3]; 400 -> 45[label="",style="dashed", color="red", weight=0]; 400[label="xy4000 == xy3000",fontsize=16,color="magenta"];400 -> 620[label="",style="dashed", color="magenta", weight=3]; 400 -> 621[label="",style="dashed", color="magenta", weight=3]; 401 -> 46[label="",style="dashed", color="red", weight=0]; 401[label="xy4000 == xy3000",fontsize=16,color="magenta"];401 -> 622[label="",style="dashed", color="magenta", weight=3]; 401 -> 623[label="",style="dashed", color="magenta", weight=3]; 402 -> 47[label="",style="dashed", color="red", weight=0]; 402[label="xy4000 == xy3000",fontsize=16,color="magenta"];402 -> 624[label="",style="dashed", color="magenta", weight=3]; 402 -> 625[label="",style="dashed", color="magenta", weight=3]; 403 -> 48[label="",style="dashed", color="red", weight=0]; 403[label="xy4000 == xy3000",fontsize=16,color="magenta"];403 -> 626[label="",style="dashed", color="magenta", weight=3]; 403 -> 627[label="",style="dashed", color="magenta", weight=3]; 404 -> 49[label="",style="dashed", color="red", weight=0]; 404[label="xy4000 == xy3000",fontsize=16,color="magenta"];404 -> 628[label="",style="dashed", color="magenta", weight=3]; 404 -> 629[label="",style="dashed", color="magenta", weight=3]; 405 -> 50[label="",style="dashed", color="red", weight=0]; 405[label="xy4000 == xy3000",fontsize=16,color="magenta"];405 -> 630[label="",style="dashed", color="magenta", weight=3]; 405 -> 631[label="",style="dashed", color="magenta", weight=3]; 406 -> 51[label="",style="dashed", color="red", weight=0]; 406[label="xy4000 == xy3000",fontsize=16,color="magenta"];406 -> 632[label="",style="dashed", color="magenta", weight=3]; 406 -> 633[label="",style="dashed", color="magenta", weight=3]; 407 -> 52[label="",style="dashed", color="red", weight=0]; 407[label="xy4000 == xy3000",fontsize=16,color="magenta"];407 -> 634[label="",style="dashed", color="magenta", weight=3]; 407 -> 635[label="",style="dashed", color="magenta", weight=3]; 408 -> 53[label="",style="dashed", color="red", weight=0]; 408[label="xy4000 == xy3000",fontsize=16,color="magenta"];408 -> 636[label="",style="dashed", color="magenta", weight=3]; 408 -> 637[label="",style="dashed", color="magenta", weight=3]; 409[label="xy3001",fontsize=16,color="green",shape="box"];410[label="xy4001",fontsize=16,color="green",shape="box"];411 -> 333[label="",style="dashed", color="red", weight=0]; 411[label="xy4001 * xy3000",fontsize=16,color="magenta"];411 -> 638[label="",style="dashed", color="magenta", weight=3]; 411 -> 639[label="",style="dashed", color="magenta", weight=3]; 412 -> 333[label="",style="dashed", color="red", weight=0]; 412[label="xy4000 * xy3001",fontsize=16,color="magenta"];412 -> 640[label="",style="dashed", color="magenta", weight=3]; 412 -> 641[label="",style="dashed", color="magenta", weight=3]; 413[label="xy3000",fontsize=16,color="green",shape="box"];414[label="xy4000",fontsize=16,color="green",shape="box"];415[label="xy3000",fontsize=16,color="green",shape="box"];416[label="xy4000",fontsize=16,color="green",shape="box"];417[label="xy3000",fontsize=16,color="green",shape="box"];418[label="xy4000",fontsize=16,color="green",shape="box"];419[label="xy3000",fontsize=16,color="green",shape="box"];420[label="xy4000",fontsize=16,color="green",shape="box"];421[label="xy3000",fontsize=16,color="green",shape="box"];422[label="xy4000",fontsize=16,color="green",shape="box"];423[label="xy3000",fontsize=16,color="green",shape="box"];424[label="xy4000",fontsize=16,color="green",shape="box"];425[label="xy3000",fontsize=16,color="green",shape="box"];426[label="xy4000",fontsize=16,color="green",shape="box"];427[label="xy3000",fontsize=16,color="green",shape="box"];428[label="xy4000",fontsize=16,color="green",shape="box"];429[label="xy3000",fontsize=16,color="green",shape="box"];430[label="xy4000",fontsize=16,color="green",shape="box"];431[label="xy3000",fontsize=16,color="green",shape="box"];432[label="xy4000",fontsize=16,color="green",shape="box"];433[label="xy3000",fontsize=16,color="green",shape="box"];434[label="xy4000",fontsize=16,color="green",shape="box"];435[label="xy3000",fontsize=16,color="green",shape="box"];436[label="xy4000",fontsize=16,color="green",shape="box"];437[label="xy3000",fontsize=16,color="green",shape="box"];438[label="xy4000",fontsize=16,color="green",shape="box"];439[label="xy3000",fontsize=16,color="green",shape="box"];440[label="xy4000",fontsize=16,color="green",shape="box"];441[label="xy3000",fontsize=16,color="green",shape="box"];442[label="xy4000",fontsize=16,color="green",shape="box"];443[label="xy3000",fontsize=16,color="green",shape="box"];444[label="xy4000",fontsize=16,color="green",shape="box"];445[label="xy3000",fontsize=16,color="green",shape="box"];446[label="xy4000",fontsize=16,color="green",shape="box"];447[label="xy3000",fontsize=16,color="green",shape="box"];448[label="xy4000",fontsize=16,color="green",shape="box"];449[label="xy3000",fontsize=16,color="green",shape="box"];450[label="xy4000",fontsize=16,color="green",shape="box"];451[label="xy3000",fontsize=16,color="green",shape="box"];452[label="xy4000",fontsize=16,color="green",shape="box"];453[label="xy3000",fontsize=16,color="green",shape="box"];454[label="xy4000",fontsize=16,color="green",shape="box"];455[label="xy3000",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="xy3001",fontsize=16,color="green",shape="box"];474[label="xy4001",fontsize=16,color="green",shape="box"];475[label="xy3001",fontsize=16,color="green",shape="box"];476[label="xy4001",fontsize=16,color="green",shape="box"];477[label="False",fontsize=16,color="green",shape="box"];478[label="xy35",fontsize=16,color="green",shape="box"];479[label="primMulInt xy4001 xy3000",fontsize=16,color="burlywood",shape="box"];1016[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];479 -> 1016[label="",style="solid", color="burlywood", weight=9]; 1016 -> 642[label="",style="solid", color="burlywood", weight=3]; 1017[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];479 -> 1017[label="",style="solid", color="burlywood", weight=9]; 1017 -> 643[label="",style="solid", color="burlywood", weight=3]; 480[label="xy4000",fontsize=16,color="green",shape="box"];481[label="xy3001",fontsize=16,color="green",shape="box"];482[label="xy3000",fontsize=16,color="green",shape="box"];483[label="xy4000",fontsize=16,color="green",shape="box"];484[label="xy3000",fontsize=16,color="green",shape="box"];485[label="xy4000",fontsize=16,color="green",shape="box"];486[label="xy3000",fontsize=16,color="green",shape="box"];487[label="xy4000",fontsize=16,color="green",shape="box"];488[label="xy3000",fontsize=16,color="green",shape="box"];489[label="xy4000",fontsize=16,color="green",shape="box"];490[label="xy3000",fontsize=16,color="green",shape="box"];491[label="xy4000",fontsize=16,color="green",shape="box"];492[label="xy3000",fontsize=16,color="green",shape="box"];493[label="xy4000",fontsize=16,color="green",shape="box"];494[label="xy3000",fontsize=16,color="green",shape="box"];495[label="xy4000",fontsize=16,color="green",shape="box"];496[label="xy3000",fontsize=16,color="green",shape="box"];497[label="xy4000",fontsize=16,color="green",shape="box"];498[label="xy3000",fontsize=16,color="green",shape="box"];499[label="xy4000",fontsize=16,color="green",shape="box"];500[label="xy3000",fontsize=16,color="green",shape="box"];501[label="xy4000",fontsize=16,color="green",shape="box"];502[label="xy3000",fontsize=16,color="green",shape="box"];503[label="xy4000",fontsize=16,color="green",shape="box"];504[label="xy3000",fontsize=16,color="green",shape="box"];505[label="xy4000",fontsize=16,color="green",shape="box"];506[label="xy3000",fontsize=16,color="green",shape="box"];507[label="xy4000",fontsize=16,color="green",shape="box"];508[label="xy3000",fontsize=16,color="green",shape="box"];509[label="xy4000",fontsize=16,color="green",shape="box"];510[label="xy3001",fontsize=16,color="green",shape="box"];511[label="xy4001",fontsize=16,color="green",shape="box"];512[label="xy3001",fontsize=16,color="green",shape="box"];513[label="xy4001",fontsize=16,color="green",shape="box"];514[label="xy3001",fontsize=16,color="green",shape="box"];515[label="xy4001",fontsize=16,color="green",shape="box"];516[label="xy3001",fontsize=16,color="green",shape="box"];517[label="xy4001",fontsize=16,color="green",shape="box"];518[label="xy3001",fontsize=16,color="green",shape="box"];519[label="xy4001",fontsize=16,color="green",shape="box"];520[label="xy3001",fontsize=16,color="green",shape="box"];521[label="xy4001",fontsize=16,color="green",shape="box"];522[label="xy3001",fontsize=16,color="green",shape="box"];523[label="xy4001",fontsize=16,color="green",shape="box"];524[label="xy3001",fontsize=16,color="green",shape="box"];525[label="xy4001",fontsize=16,color="green",shape="box"];526[label="xy3001",fontsize=16,color="green",shape="box"];527[label="xy4001",fontsize=16,color="green",shape="box"];528[label="xy3001",fontsize=16,color="green",shape="box"];529[label="xy4001",fontsize=16,color="green",shape="box"];530[label="xy3001",fontsize=16,color="green",shape="box"];531[label="xy4001",fontsize=16,color="green",shape="box"];532[label="xy3001",fontsize=16,color="green",shape="box"];533[label="xy4001",fontsize=16,color="green",shape="box"];534[label="xy3001",fontsize=16,color="green",shape="box"];535[label="xy4001",fontsize=16,color="green",shape="box"];536[label="xy3001",fontsize=16,color="green",shape="box"];537[label="xy4001",fontsize=16,color="green",shape="box"];538 -> 254[label="",style="dashed", color="red", weight=0]; 538[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];538 -> 644[label="",style="dashed", color="magenta", weight=3]; 538 -> 645[label="",style="dashed", color="magenta", weight=3]; 539[label="False",fontsize=16,color="green",shape="box"];540[label="False",fontsize=16,color="green",shape="box"];541[label="True",fontsize=16,color="green",shape="box"];542[label="False",fontsize=16,color="green",shape="box"];543[label="True",fontsize=16,color="green",shape="box"];544 -> 254[label="",style="dashed", color="red", weight=0]; 544[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];544 -> 646[label="",style="dashed", color="magenta", weight=3]; 544 -> 647[label="",style="dashed", color="magenta", weight=3]; 545[label="False",fontsize=16,color="green",shape="box"];546[label="False",fontsize=16,color="green",shape="box"];547[label="True",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="xy3000",fontsize=16,color="green",shape="box"];551[label="xy4000",fontsize=16,color="green",shape="box"];552[label="xy3000",fontsize=16,color="green",shape="box"];553[label="xy4000",fontsize=16,color="green",shape="box"];554[label="xy3000",fontsize=16,color="green",shape="box"];555[label="xy4000",fontsize=16,color="green",shape="box"];556[label="xy3000",fontsize=16,color="green",shape="box"];557[label="xy4000",fontsize=16,color="green",shape="box"];558[label="xy3000",fontsize=16,color="green",shape="box"];559[label="xy4000",fontsize=16,color="green",shape="box"];560[label="xy3000",fontsize=16,color="green",shape="box"];561[label="xy4000",fontsize=16,color="green",shape="box"];562[label="xy3000",fontsize=16,color="green",shape="box"];563[label="xy4000",fontsize=16,color="green",shape="box"];564[label="xy3000",fontsize=16,color="green",shape="box"];565[label="xy4000",fontsize=16,color="green",shape="box"];566[label="xy3000",fontsize=16,color="green",shape="box"];567[label="xy4000",fontsize=16,color="green",shape="box"];568[label="xy3000",fontsize=16,color="green",shape="box"];569[label="xy4000",fontsize=16,color="green",shape="box"];570[label="xy3000",fontsize=16,color="green",shape="box"];571[label="xy4000",fontsize=16,color="green",shape="box"];572[label="xy3000",fontsize=16,color="green",shape="box"];573[label="xy4000",fontsize=16,color="green",shape="box"];574[label="xy3000",fontsize=16,color="green",shape="box"];575[label="xy4000",fontsize=16,color="green",shape="box"];576[label="xy3000",fontsize=16,color="green",shape="box"];577[label="xy4000",fontsize=16,color="green",shape="box"];578 -> 40[label="",style="dashed", color="red", weight=0]; 578[label="xy4001 == xy3001",fontsize=16,color="magenta"];578 -> 648[label="",style="dashed", color="magenta", weight=3]; 578 -> 649[label="",style="dashed", color="magenta", weight=3]; 579 -> 41[label="",style="dashed", color="red", weight=0]; 579[label="xy4001 == xy3001",fontsize=16,color="magenta"];579 -> 650[label="",style="dashed", color="magenta", weight=3]; 579 -> 651[label="",style="dashed", color="magenta", weight=3]; 580 -> 42[label="",style="dashed", color="red", weight=0]; 580[label="xy4001 == xy3001",fontsize=16,color="magenta"];580 -> 652[label="",style="dashed", color="magenta", weight=3]; 580 -> 653[label="",style="dashed", color="magenta", weight=3]; 581 -> 43[label="",style="dashed", color="red", weight=0]; 581[label="xy4001 == xy3001",fontsize=16,color="magenta"];581 -> 654[label="",style="dashed", color="magenta", weight=3]; 581 -> 655[label="",style="dashed", color="magenta", weight=3]; 582 -> 44[label="",style="dashed", color="red", weight=0]; 582[label="xy4001 == xy3001",fontsize=16,color="magenta"];582 -> 656[label="",style="dashed", color="magenta", weight=3]; 582 -> 657[label="",style="dashed", color="magenta", weight=3]; 583 -> 45[label="",style="dashed", color="red", weight=0]; 583[label="xy4001 == xy3001",fontsize=16,color="magenta"];583 -> 658[label="",style="dashed", color="magenta", weight=3]; 583 -> 659[label="",style="dashed", color="magenta", weight=3]; 584 -> 46[label="",style="dashed", color="red", weight=0]; 584[label="xy4001 == xy3001",fontsize=16,color="magenta"];584 -> 660[label="",style="dashed", color="magenta", weight=3]; 584 -> 661[label="",style="dashed", color="magenta", weight=3]; 585 -> 47[label="",style="dashed", color="red", weight=0]; 585[label="xy4001 == xy3001",fontsize=16,color="magenta"];585 -> 662[label="",style="dashed", color="magenta", weight=3]; 585 -> 663[label="",style="dashed", color="magenta", weight=3]; 586 -> 48[label="",style="dashed", color="red", weight=0]; 586[label="xy4001 == xy3001",fontsize=16,color="magenta"];586 -> 664[label="",style="dashed", color="magenta", weight=3]; 586 -> 665[label="",style="dashed", color="magenta", weight=3]; 587 -> 49[label="",style="dashed", color="red", weight=0]; 587[label="xy4001 == xy3001",fontsize=16,color="magenta"];587 -> 666[label="",style="dashed", color="magenta", weight=3]; 587 -> 667[label="",style="dashed", color="magenta", weight=3]; 588 -> 50[label="",style="dashed", color="red", weight=0]; 588[label="xy4001 == xy3001",fontsize=16,color="magenta"];588 -> 668[label="",style="dashed", color="magenta", weight=3]; 588 -> 669[label="",style="dashed", color="magenta", weight=3]; 589 -> 51[label="",style="dashed", color="red", weight=0]; 589[label="xy4001 == xy3001",fontsize=16,color="magenta"];589 -> 670[label="",style="dashed", color="magenta", weight=3]; 589 -> 671[label="",style="dashed", color="magenta", weight=3]; 590 -> 52[label="",style="dashed", color="red", weight=0]; 590[label="xy4001 == xy3001",fontsize=16,color="magenta"];590 -> 672[label="",style="dashed", color="magenta", weight=3]; 590 -> 673[label="",style="dashed", color="magenta", weight=3]; 591 -> 53[label="",style="dashed", color="red", weight=0]; 591[label="xy4001 == xy3001",fontsize=16,color="magenta"];591 -> 674[label="",style="dashed", color="magenta", weight=3]; 591 -> 675[label="",style="dashed", color="magenta", weight=3]; 592 -> 40[label="",style="dashed", color="red", weight=0]; 592[label="xy4002 == xy3002",fontsize=16,color="magenta"];592 -> 676[label="",style="dashed", color="magenta", weight=3]; 592 -> 677[label="",style="dashed", color="magenta", weight=3]; 593 -> 41[label="",style="dashed", color="red", weight=0]; 593[label="xy4002 == xy3002",fontsize=16,color="magenta"];593 -> 678[label="",style="dashed", color="magenta", weight=3]; 593 -> 679[label="",style="dashed", color="magenta", weight=3]; 594 -> 42[label="",style="dashed", color="red", weight=0]; 594[label="xy4002 == xy3002",fontsize=16,color="magenta"];594 -> 680[label="",style="dashed", color="magenta", weight=3]; 594 -> 681[label="",style="dashed", color="magenta", weight=3]; 595 -> 43[label="",style="dashed", color="red", weight=0]; 595[label="xy4002 == xy3002",fontsize=16,color="magenta"];595 -> 682[label="",style="dashed", color="magenta", weight=3]; 595 -> 683[label="",style="dashed", color="magenta", weight=3]; 596 -> 44[label="",style="dashed", color="red", weight=0]; 596[label="xy4002 == xy3002",fontsize=16,color="magenta"];596 -> 684[label="",style="dashed", color="magenta", weight=3]; 596 -> 685[label="",style="dashed", color="magenta", weight=3]; 597 -> 45[label="",style="dashed", color="red", weight=0]; 597[label="xy4002 == xy3002",fontsize=16,color="magenta"];597 -> 686[label="",style="dashed", color="magenta", weight=3]; 597 -> 687[label="",style="dashed", color="magenta", weight=3]; 598 -> 46[label="",style="dashed", color="red", weight=0]; 598[label="xy4002 == xy3002",fontsize=16,color="magenta"];598 -> 688[label="",style="dashed", color="magenta", weight=3]; 598 -> 689[label="",style="dashed", color="magenta", weight=3]; 599 -> 47[label="",style="dashed", color="red", weight=0]; 599[label="xy4002 == xy3002",fontsize=16,color="magenta"];599 -> 690[label="",style="dashed", color="magenta", weight=3]; 599 -> 691[label="",style="dashed", color="magenta", weight=3]; 600 -> 48[label="",style="dashed", color="red", weight=0]; 600[label="xy4002 == xy3002",fontsize=16,color="magenta"];600 -> 692[label="",style="dashed", color="magenta", weight=3]; 600 -> 693[label="",style="dashed", color="magenta", weight=3]; 601 -> 49[label="",style="dashed", color="red", weight=0]; 601[label="xy4002 == xy3002",fontsize=16,color="magenta"];601 -> 694[label="",style="dashed", color="magenta", weight=3]; 601 -> 695[label="",style="dashed", color="magenta", weight=3]; 602 -> 50[label="",style="dashed", color="red", weight=0]; 602[label="xy4002 == xy3002",fontsize=16,color="magenta"];602 -> 696[label="",style="dashed", color="magenta", weight=3]; 602 -> 697[label="",style="dashed", color="magenta", weight=3]; 603 -> 51[label="",style="dashed", color="red", weight=0]; 603[label="xy4002 == xy3002",fontsize=16,color="magenta"];603 -> 698[label="",style="dashed", color="magenta", weight=3]; 603 -> 699[label="",style="dashed", color="magenta", weight=3]; 604 -> 52[label="",style="dashed", color="red", weight=0]; 604[label="xy4002 == xy3002",fontsize=16,color="magenta"];604 -> 700[label="",style="dashed", color="magenta", weight=3]; 604 -> 701[label="",style="dashed", color="magenta", weight=3]; 605 -> 53[label="",style="dashed", color="red", weight=0]; 605[label="xy4002 == xy3002",fontsize=16,color="magenta"];605 -> 702[label="",style="dashed", color="magenta", weight=3]; 605 -> 703[label="",style="dashed", color="magenta", weight=3]; 606[label="primEqNat (Succ xy40000) (Succ xy30000)",fontsize=16,color="black",shape="box"];606 -> 704[label="",style="solid", color="black", weight=3]; 607[label="primEqNat (Succ xy40000) Zero",fontsize=16,color="black",shape="box"];607 -> 705[label="",style="solid", color="black", weight=3]; 608[label="primEqNat Zero (Succ xy30000)",fontsize=16,color="black",shape="box"];608 -> 706[label="",style="solid", color="black", weight=3]; 609[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];609 -> 707[label="",style="solid", color="black", weight=3]; 610[label="xy3000",fontsize=16,color="green",shape="box"];611[label="xy4000",fontsize=16,color="green",shape="box"];612[label="xy3000",fontsize=16,color="green",shape="box"];613[label="xy4000",fontsize=16,color="green",shape="box"];614[label="xy3000",fontsize=16,color="green",shape="box"];615[label="xy4000",fontsize=16,color="green",shape="box"];616[label="xy3000",fontsize=16,color="green",shape="box"];617[label="xy4000",fontsize=16,color="green",shape="box"];618[label="xy3000",fontsize=16,color="green",shape="box"];619[label="xy4000",fontsize=16,color="green",shape="box"];620[label="xy3000",fontsize=16,color="green",shape="box"];621[label="xy4000",fontsize=16,color="green",shape="box"];622[label="xy3000",fontsize=16,color="green",shape="box"];623[label="xy4000",fontsize=16,color="green",shape="box"];624[label="xy3000",fontsize=16,color="green",shape="box"];625[label="xy4000",fontsize=16,color="green",shape="box"];626[label="xy3000",fontsize=16,color="green",shape="box"];627[label="xy4000",fontsize=16,color="green",shape="box"];628[label="xy3000",fontsize=16,color="green",shape="box"];629[label="xy4000",fontsize=16,color="green",shape="box"];630[label="xy3000",fontsize=16,color="green",shape="box"];631[label="xy4000",fontsize=16,color="green",shape="box"];632[label="xy3000",fontsize=16,color="green",shape="box"];633[label="xy4000",fontsize=16,color="green",shape="box"];634[label="xy3000",fontsize=16,color="green",shape="box"];635[label="xy4000",fontsize=16,color="green",shape="box"];636[label="xy3000",fontsize=16,color="green",shape="box"];637[label="xy4000",fontsize=16,color="green",shape="box"];638[label="xy4001",fontsize=16,color="green",shape="box"];639[label="xy3000",fontsize=16,color="green",shape="box"];640[label="xy4000",fontsize=16,color="green",shape="box"];641[label="xy3001",fontsize=16,color="green",shape="box"];642[label="primMulInt (Pos xy40010) xy3000",fontsize=16,color="burlywood",shape="box"];1018[label="xy3000/Pos xy30000",fontsize=10,color="white",style="solid",shape="box"];642 -> 1018[label="",style="solid", color="burlywood", weight=9]; 1018 -> 708[label="",style="solid", color="burlywood", weight=3]; 1019[label="xy3000/Neg xy30000",fontsize=10,color="white",style="solid",shape="box"];642 -> 1019[label="",style="solid", color="burlywood", weight=9]; 1019 -> 709[label="",style="solid", color="burlywood", weight=3]; 643[label="primMulInt (Neg xy40010) xy3000",fontsize=16,color="burlywood",shape="box"];1020[label="xy3000/Pos xy30000",fontsize=10,color="white",style="solid",shape="box"];643 -> 1020[label="",style="solid", color="burlywood", weight=9]; 1020 -> 710[label="",style="solid", color="burlywood", weight=3]; 1021[label="xy3000/Neg xy30000",fontsize=10,color="white",style="solid",shape="box"];643 -> 1021[label="",style="solid", color="burlywood", weight=9]; 1021 -> 711[label="",style="solid", color="burlywood", weight=3]; 644[label="xy40000",fontsize=16,color="green",shape="box"];645[label="xy30000",fontsize=16,color="green",shape="box"];646[label="xy40000",fontsize=16,color="green",shape="box"];647[label="xy30000",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[label="xy4001",fontsize=16,color="green",shape="box"];658[label="xy3001",fontsize=16,color="green",shape="box"];659[label="xy4001",fontsize=16,color="green",shape="box"];660[label="xy3001",fontsize=16,color="green",shape="box"];661[label="xy4001",fontsize=16,color="green",shape="box"];662[label="xy3001",fontsize=16,color="green",shape="box"];663[label="xy4001",fontsize=16,color="green",shape="box"];664[label="xy3001",fontsize=16,color="green",shape="box"];665[label="xy4001",fontsize=16,color="green",shape="box"];666[label="xy3001",fontsize=16,color="green",shape="box"];667[label="xy4001",fontsize=16,color="green",shape="box"];668[label="xy3001",fontsize=16,color="green",shape="box"];669[label="xy4001",fontsize=16,color="green",shape="box"];670[label="xy3001",fontsize=16,color="green",shape="box"];671[label="xy4001",fontsize=16,color="green",shape="box"];672[label="xy3001",fontsize=16,color="green",shape="box"];673[label="xy4001",fontsize=16,color="green",shape="box"];674[label="xy3001",fontsize=16,color="green",shape="box"];675[label="xy4001",fontsize=16,color="green",shape="box"];676[label="xy3002",fontsize=16,color="green",shape="box"];677[label="xy4002",fontsize=16,color="green",shape="box"];678[label="xy3002",fontsize=16,color="green",shape="box"];679[label="xy4002",fontsize=16,color="green",shape="box"];680[label="xy3002",fontsize=16,color="green",shape="box"];681[label="xy4002",fontsize=16,color="green",shape="box"];682[label="xy3002",fontsize=16,color="green",shape="box"];683[label="xy4002",fontsize=16,color="green",shape="box"];684[label="xy3002",fontsize=16,color="green",shape="box"];685[label="xy4002",fontsize=16,color="green",shape="box"];686[label="xy3002",fontsize=16,color="green",shape="box"];687[label="xy4002",fontsize=16,color="green",shape="box"];688[label="xy3002",fontsize=16,color="green",shape="box"];689[label="xy4002",fontsize=16,color="green",shape="box"];690[label="xy3002",fontsize=16,color="green",shape="box"];691[label="xy4002",fontsize=16,color="green",shape="box"];692[label="xy3002",fontsize=16,color="green",shape="box"];693[label="xy4002",fontsize=16,color="green",shape="box"];694[label="xy3002",fontsize=16,color="green",shape="box"];695[label="xy4002",fontsize=16,color="green",shape="box"];696[label="xy3002",fontsize=16,color="green",shape="box"];697[label="xy4002",fontsize=16,color="green",shape="box"];698[label="xy3002",fontsize=16,color="green",shape="box"];699[label="xy4002",fontsize=16,color="green",shape="box"];700[label="xy3002",fontsize=16,color="green",shape="box"];701[label="xy4002",fontsize=16,color="green",shape="box"];702[label="xy3002",fontsize=16,color="green",shape="box"];703[label="xy4002",fontsize=16,color="green",shape="box"];704 -> 254[label="",style="dashed", color="red", weight=0]; 704[label="primEqNat xy40000 xy30000",fontsize=16,color="magenta"];704 -> 712[label="",style="dashed", color="magenta", weight=3]; 704 -> 713[label="",style="dashed", color="magenta", weight=3]; 705[label="False",fontsize=16,color="green",shape="box"];706[label="False",fontsize=16,color="green",shape="box"];707[label="True",fontsize=16,color="green",shape="box"];708[label="primMulInt (Pos xy40010) (Pos xy30000)",fontsize=16,color="black",shape="box"];708 -> 714[label="",style="solid", color="black", weight=3]; 709[label="primMulInt (Pos xy40010) (Neg xy30000)",fontsize=16,color="black",shape="box"];709 -> 715[label="",style="solid", color="black", weight=3]; 710[label="primMulInt (Neg xy40010) (Pos xy30000)",fontsize=16,color="black",shape="box"];710 -> 716[label="",style="solid", color="black", weight=3]; 711[label="primMulInt (Neg xy40010) (Neg xy30000)",fontsize=16,color="black",shape="box"];711 -> 717[label="",style="solid", color="black", weight=3]; 712[label="xy40000",fontsize=16,color="green",shape="box"];713[label="xy30000",fontsize=16,color="green",shape="box"];714[label="Pos (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];714 -> 718[label="",style="dashed", color="green", weight=3]; 715[label="Neg (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];715 -> 719[label="",style="dashed", color="green", weight=3]; 716[label="Neg (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];716 -> 720[label="",style="dashed", color="green", weight=3]; 717[label="Pos (primMulNat xy40010 xy30000)",fontsize=16,color="green",shape="box"];717 -> 721[label="",style="dashed", color="green", weight=3]; 718[label="primMulNat xy40010 xy30000",fontsize=16,color="burlywood",shape="triangle"];1022[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];718 -> 1022[label="",style="solid", color="burlywood", weight=9]; 1022 -> 722[label="",style="solid", color="burlywood", weight=3]; 1023[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];718 -> 1023[label="",style="solid", color="burlywood", weight=9]; 1023 -> 723[label="",style="solid", color="burlywood", weight=3]; 719 -> 718[label="",style="dashed", color="red", weight=0]; 719[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];719 -> 724[label="",style="dashed", color="magenta", weight=3]; 720 -> 718[label="",style="dashed", color="red", weight=0]; 720[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];720 -> 725[label="",style="dashed", color="magenta", weight=3]; 721 -> 718[label="",style="dashed", color="red", weight=0]; 721[label="primMulNat xy40010 xy30000",fontsize=16,color="magenta"];721 -> 726[label="",style="dashed", color="magenta", weight=3]; 721 -> 727[label="",style="dashed", color="magenta", weight=3]; 722[label="primMulNat (Succ xy400100) xy30000",fontsize=16,color="burlywood",shape="box"];1024[label="xy30000/Succ xy300000",fontsize=10,color="white",style="solid",shape="box"];722 -> 1024[label="",style="solid", color="burlywood", weight=9]; 1024 -> 728[label="",style="solid", color="burlywood", weight=3]; 1025[label="xy30000/Zero",fontsize=10,color="white",style="solid",shape="box"];722 -> 1025[label="",style="solid", color="burlywood", weight=9]; 1025 -> 729[label="",style="solid", color="burlywood", weight=3]; 723[label="primMulNat Zero xy30000",fontsize=16,color="burlywood",shape="box"];1026[label="xy30000/Succ xy300000",fontsize=10,color="white",style="solid",shape="box"];723 -> 1026[label="",style="solid", color="burlywood", weight=9]; 1026 -> 730[label="",style="solid", color="burlywood", weight=3]; 1027[label="xy30000/Zero",fontsize=10,color="white",style="solid",shape="box"];723 -> 1027[label="",style="solid", color="burlywood", weight=9]; 1027 -> 731[label="",style="solid", color="burlywood", weight=3]; 724[label="xy30000",fontsize=16,color="green",shape="box"];725[label="xy40010",fontsize=16,color="green",shape="box"];726[label="xy30000",fontsize=16,color="green",shape="box"];727[label="xy40010",fontsize=16,color="green",shape="box"];728[label="primMulNat (Succ xy400100) (Succ xy300000)",fontsize=16,color="black",shape="box"];728 -> 732[label="",style="solid", color="black", weight=3]; 729[label="primMulNat (Succ xy400100) Zero",fontsize=16,color="black",shape="box"];729 -> 733[label="",style="solid", color="black", weight=3]; 730[label="primMulNat Zero (Succ xy300000)",fontsize=16,color="black",shape="box"];730 -> 734[label="",style="solid", color="black", weight=3]; 731[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];731 -> 735[label="",style="solid", color="black", weight=3]; 732 -> 736[label="",style="dashed", color="red", weight=0]; 732[label="primPlusNat (primMulNat xy400100 (Succ xy300000)) (Succ xy300000)",fontsize=16,color="magenta"];732 -> 737[label="",style="dashed", color="magenta", weight=3]; 733[label="Zero",fontsize=16,color="green",shape="box"];734[label="Zero",fontsize=16,color="green",shape="box"];735[label="Zero",fontsize=16,color="green",shape="box"];737 -> 718[label="",style="dashed", color="red", weight=0]; 737[label="primMulNat xy400100 (Succ xy300000)",fontsize=16,color="magenta"];737 -> 738[label="",style="dashed", color="magenta", weight=3]; 737 -> 739[label="",style="dashed", color="magenta", weight=3]; 736[label="primPlusNat xy36 (Succ xy300000)",fontsize=16,color="burlywood",shape="triangle"];1028[label="xy36/Succ xy360",fontsize=10,color="white",style="solid",shape="box"];736 -> 1028[label="",style="solid", color="burlywood", weight=9]; 1028 -> 740[label="",style="solid", color="burlywood", weight=3]; 1029[label="xy36/Zero",fontsize=10,color="white",style="solid",shape="box"];736 -> 1029[label="",style="solid", color="burlywood", weight=9]; 1029 -> 741[label="",style="solid", color="burlywood", weight=3]; 738[label="Succ xy300000",fontsize=16,color="green",shape="box"];739[label="xy400100",fontsize=16,color="green",shape="box"];740[label="primPlusNat (Succ xy360) (Succ xy300000)",fontsize=16,color="black",shape="box"];740 -> 742[label="",style="solid", color="black", weight=3]; 741[label="primPlusNat Zero (Succ xy300000)",fontsize=16,color="black",shape="box"];741 -> 743[label="",style="solid", color="black", weight=3]; 742[label="Succ (Succ (primPlusNat xy360 xy300000))",fontsize=16,color="green",shape="box"];742 -> 744[label="",style="dashed", color="green", weight=3]; 743[label="Succ xy300000",fontsize=16,color="green",shape="box"];744[label="primPlusNat xy360 xy300000",fontsize=16,color="burlywood",shape="triangle"];1030[label="xy360/Succ xy3600",fontsize=10,color="white",style="solid",shape="box"];744 -> 1030[label="",style="solid", color="burlywood", weight=9]; 1030 -> 745[label="",style="solid", color="burlywood", weight=3]; 1031[label="xy360/Zero",fontsize=10,color="white",style="solid",shape="box"];744 -> 1031[label="",style="solid", color="burlywood", weight=9]; 1031 -> 746[label="",style="solid", color="burlywood", weight=3]; 745[label="primPlusNat (Succ xy3600) xy300000",fontsize=16,color="burlywood",shape="box"];1032[label="xy300000/Succ xy3000000",fontsize=10,color="white",style="solid",shape="box"];745 -> 1032[label="",style="solid", color="burlywood", weight=9]; 1032 -> 747[label="",style="solid", color="burlywood", weight=3]; 1033[label="xy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 1033[label="",style="solid", color="burlywood", weight=9]; 1033 -> 748[label="",style="solid", color="burlywood", weight=3]; 746[label="primPlusNat Zero xy300000",fontsize=16,color="burlywood",shape="box"];1034[label="xy300000/Succ xy3000000",fontsize=10,color="white",style="solid",shape="box"];746 -> 1034[label="",style="solid", color="burlywood", weight=9]; 1034 -> 749[label="",style="solid", color="burlywood", weight=3]; 1035[label="xy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];746 -> 1035[label="",style="solid", color="burlywood", weight=9]; 1035 -> 750[label="",style="solid", color="burlywood", weight=3]; 747[label="primPlusNat (Succ xy3600) (Succ xy3000000)",fontsize=16,color="black",shape="box"];747 -> 751[label="",style="solid", color="black", weight=3]; 748[label="primPlusNat (Succ xy3600) Zero",fontsize=16,color="black",shape="box"];748 -> 752[label="",style="solid", color="black", weight=3]; 749[label="primPlusNat Zero (Succ xy3000000)",fontsize=16,color="black",shape="box"];749 -> 753[label="",style="solid", color="black", weight=3]; 750[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];750 -> 754[label="",style="solid", color="black", weight=3]; 751[label="Succ (Succ (primPlusNat xy3600 xy3000000))",fontsize=16,color="green",shape="box"];751 -> 755[label="",style="dashed", color="green", weight=3]; 752[label="Succ xy3600",fontsize=16,color="green",shape="box"];753[label="Succ xy3000000",fontsize=16,color="green",shape="box"];754[label="Zero",fontsize=16,color="green",shape="box"];755 -> 744[label="",style="dashed", color="red", weight=0]; 755[label="primPlusNat xy3600 xy3000000",fontsize=16,color="magenta"];755 -> 756[label="",style="dashed", color="magenta", weight=3]; 755 -> 757[label="",style="dashed", color="magenta", weight=3]; 756[label="xy3600",fontsize=16,color="green",shape="box"];757[label="xy3000000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldl(xy3, :(xy40, xy41), ba, bb) -> new_foldl(new_deleteBy1(xy40, xy3, ba, bb), xy41, ba, bb) The TRS R consists of the following rules: new_deleteBy01(xy19, xy20, xy21, True, fg, fh) -> xy19 new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs13(xy4000, xy3000, app(ty_Maybe, be)) -> new_esEs14(xy4000, xy3000, be) new_esEs23(xy4000, xy3000, app(app(ty_@2, dd), de)) -> new_esEs17(xy4000, xy3000, dd, de) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs26(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bde, app(app(ty_Either, bef), beg)) -> new_esEs22(xy4000, xy3000, bef, beg) new_esEs4(xy400, xy300, app(app(ty_@2, cg), da)) -> new_esEs17(xy400, xy300, cg, da) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_esEs5(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bde, app(ty_Ratio, bdg)) -> new_esEs6(xy4000, xy3000, bdg) new_esEs19(False, True) -> False new_esEs19(True, False) -> False new_deleteBy1(xy40, [], ba, bb) -> [] new_esEs15(LT, LT) -> True new_esEs23(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs23(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs12(:(xy4000, xy4001), [], bd) -> False new_esEs12([], :(xy3000, xy3001), bd) -> False new_esEs13(xy4000, xy3000, app(app(app(ty_@3, ca), cb), cc)) -> new_esEs18(xy4000, xy3000, ca, cb, cc) new_esEs4(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs13(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_[], bhd)) -> new_esEs12(xy4000, xy3000, bhd) new_esEs23(xy4000, xy3000, app(app(app(ty_@3, df), dg), dh)) -> new_esEs18(xy4000, xy3000, df, dg, dh) new_esEs25(xy4000, xy3000, app(app(ty_Either, hd), he)) -> new_esEs22(xy4000, xy3000, hd, he) new_esEs27(xy4002, xy3002, app(ty_Ratio, bba)) -> new_esEs6(xy4002, xy3002, bba) new_esEs13(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bde), bcc)) -> new_esEs22(xy400, xy300, bde, bcc) new_asAs(True, xy35) -> xy35 new_esEs26(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs13(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_@2, bg), bh)) -> new_esEs17(xy4000, xy3000, bg, bh) new_esEs26(xy4001, xy3001, app(ty_Maybe, hf)) -> new_esEs14(xy4001, xy3001, hf) new_esEs27(xy4002, xy3002, ty_Integer) -> new_esEs9(xy4002, xy3002) new_esEs5(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs23(xy4000, xy3000, app(app(ty_Either, eb), ec)) -> new_esEs22(xy4000, xy3000, eb, ec) new_deleteBy02(xy10, xy11, xy12, False, bgc, bgd) -> :(Left(xy11), new_deleteBy1(Left(xy12), xy10, bgc, bgd)) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs22(Left(xy4000), Left(xy3000), ty_Ordering, bcc) -> new_esEs15(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_@2, gf), gg)) -> new_esEs17(xy4000, xy3000, gf, gg) new_esEs22(Right(xy4000), Right(xy3000), bde, app(app(app(ty_@3, beb), bec), bed)) -> new_esEs18(xy4000, xy3000, beb, bec, bed) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs23(xy4000, xy3000, app(ty_Maybe, db)) -> new_esEs14(xy4000, xy3000, db) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_@2, bce), bcf), bcc) -> new_esEs17(xy4000, xy3000, bce, bcf) new_esEs5(xy400, xy300, app(ty_Maybe, bfa)) -> new_esEs14(xy400, xy300, bfa) new_esEs22(Left(xy4000), Left(xy3000), app(ty_[], bdb), bcc) -> new_esEs12(xy4000, xy3000, bdb) new_primMulNat0(Zero, Zero) -> Zero new_esEs27(xy4002, xy3002, ty_Double) -> new_esEs16(xy4002, xy3002) new_esEs20(@0, @0) -> True new_esEs4(xy400, xy300, app(ty_[], bd)) -> new_esEs12(xy400, xy300, bd) new_esEs24(xy4001, xy3001, app(ty_Maybe, ed)) -> new_esEs14(xy4001, xy3001, ed) new_esEs13(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_deleteBy1(Right(xy400), :(Right(xy300), xy31), ba, bb) -> new_deleteBy01(xy31, xy300, xy400, new_esEs5(xy400, xy300, bb), ba, bb) new_esEs14(Just(xy4000), Just(xy3000), app(ty_Ratio, bgf)) -> new_esEs6(xy4000, xy3000, bgf) new_esEs5(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_deleteBy01(xy19, xy20, xy21, False, fg, fh) -> :(Right(xy20), new_deleteBy1(Right(xy21), xy19, fg, fh)) new_esEs15(LT, EQ) -> False new_esEs15(EQ, LT) -> False new_esEs22(Left(xy4000), Left(xy3000), ty_Char, bcc) -> new_esEs11(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Bool) -> new_esEs19(xy4002, xy3002) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs27(xy4002, xy3002, app(app(app(ty_@3, bbd), bbe), bbf)) -> new_esEs18(xy4002, xy3002, bbd, bbe, bbf) new_esEs22(Right(xy4000), Right(xy3000), bde, app(app(ty_@2, bdh), bea)) -> new_esEs17(xy4000, xy3000, bdh, bea) new_esEs9(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Int) -> new_esEs10(xy4002, xy3002) new_esEs13(xy4000, xy3000, app(ty_Ratio, bf)) -> new_esEs6(xy4000, xy3000, bf) new_esEs25(xy4000, xy3000, app(ty_Maybe, gd)) -> new_esEs14(xy4000, xy3000, gd) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, ga), gb), gc)) -> new_esEs18(xy400, xy300, ga, gb, gc) new_esEs22(Left(xy4000), Left(xy3000), ty_Double, bcc) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_@2, bgg), bgh)) -> new_esEs17(xy4000, xy3000, bgg, bgh) new_esEs19(False, False) -> True new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_esEs27(xy4002, xy3002, app(ty_[], bbg)) -> new_esEs12(xy4002, xy3002, bbg) new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Bool, bcc) -> new_esEs19(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bcg), bch), bda), bcc) -> new_esEs18(xy4000, xy3000, bcg, bch, bda) new_esEs14(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs15(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3600, xy3000000))) new_esEs27(xy4002, xy3002, app(app(ty_Either, bbh), bca)) -> new_esEs22(xy4002, xy3002, bbh, bca) new_esEs4(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Char) -> new_esEs11(xy4002, xy3002) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs5(xy400, xy300, app(app(ty_@2, bfc), bfd)) -> new_esEs17(xy400, xy300, bfc, bfd) new_esEs25(xy4000, xy3000, app(ty_Ratio, ge)) -> new_esEs6(xy4000, xy3000, ge) new_esEs22(Right(xy4000), Right(xy3000), bde, app(ty_[], bee)) -> new_esEs12(xy4000, xy3000, bee) new_esEs22(Left(xy4000), Left(xy3000), ty_Integer, bcc) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs4(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Int, bcc) -> new_esEs10(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs26(xy4001, xy3001, app(app(ty_Either, baf), bag)) -> new_esEs22(xy4001, xy3001, baf, bag) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs15(EQ, EQ) -> True new_esEs14(Just(xy4000), Just(xy3000), app(ty_Maybe, bge)) -> new_esEs14(xy4000, xy3000, bge) new_esEs26(xy4001, xy3001, app(ty_Ratio, hg)) -> new_esEs6(xy4001, xy3001, hg) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs15(GT, GT) -> True new_deleteBy02(xy10, xy11, xy12, True, bgc, bgd) -> xy10 new_esEs5(xy400, xy300, app(ty_Ratio, bfb)) -> new_esEs6(xy400, xy300, bfb) new_esEs14(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs19(xy4000, xy3000) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs15(EQ, GT) -> False new_esEs15(GT, EQ) -> False new_esEs14(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bha), bhb), bhc)) -> new_esEs18(xy4000, xy3000, bha, bhb, bhc) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs11(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_@0) -> new_esEs20(xy4002, xy3002) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_@2, ef), eg)) -> new_esEs17(xy4001, xy3001, ef, eg) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs5(xy400, xy300, app(app(ty_Either, bga), bgb)) -> new_esEs22(xy400, xy300, bga, bgb) new_esEs22(Left(xy4000), Right(xy3000), bde, bcc) -> False new_esEs22(Right(xy4000), Left(xy3000), bde, bcc) -> False new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs16(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs5(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_Either, bdc), bdd), bcc) -> new_esEs22(xy4000, xy3000, bdc, bdd) new_esEs22(Left(xy4000), Left(xy3000), ty_Float, bcc) -> new_esEs21(xy4000, xy3000) new_esEs5(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs8(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, eh), fa), fb)) -> new_esEs18(xy4001, xy3001, eh, fa, fb) new_esEs4(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs5(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs16(xy4000, xy3000) new_primPlusNat0(Succ(xy360), xy300000) -> Succ(Succ(new_primPlusNat1(xy360, xy300000))) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(ty_Ratio, ee)) -> new_esEs6(xy4001, xy3001, ee) new_esEs5(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs23(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs10(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs5(xy400, xy300, app(app(app(ty_@3, bfe), bff), bfg)) -> new_esEs18(xy400, xy300, bfe, bff, bfg) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_esEs26(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs23(xy4000, xy3000, app(ty_[], ea)) -> new_esEs12(xy4000, xy3000, ea) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs6(:%(xy4000, xy4001), :%(xy3000, xy3001), bc) -> new_asAs(new_esEs7(xy4000, xy3000, bc), new_esEs8(xy4001, xy3001, bc)) new_esEs26(xy4001, xy3001, app(ty_[], bae)) -> new_esEs12(xy4001, xy3001, bae) new_esEs14(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs15(LT, GT) -> False new_esEs15(GT, LT) -> False new_esEs26(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Float) -> new_esEs21(xy4002, xy3002) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4001, xy3001, app(app(app(ty_@3, bab), bac), bad)) -> new_esEs18(xy4001, xy3001, bab, bac, bad) new_esEs5(xy400, xy300, app(ty_[], bfh)) -> new_esEs12(xy400, xy300, bfh) new_esEs24(xy4001, xy3001, app(ty_[], fc)) -> new_esEs12(xy4001, xy3001, fc) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs8(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bde, app(ty_Maybe, bdf)) -> new_esEs14(xy4000, xy3000, bdf) new_esEs22(Right(xy4000), Right(xy3000), bde, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs21(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs14(Nothing, Just(xy3000), beh) -> False new_esEs14(Just(xy4000), Nothing, beh) -> False new_esEs14(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_@0, bcc) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Zero) -> Succ(xy3600) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs25(xy4000, xy3000, app(ty_[], hc)) -> new_esEs12(xy4000, xy3000, hc) new_esEs27(xy4002, xy3002, app(app(ty_@2, bbb), bbc)) -> new_esEs17(xy4002, xy3002, bbb, bbc) new_esEs14(Nothing, Nothing, beh) -> True new_esEs14(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_esEs12([], [], bd) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Maybe, bcb), bcc) -> new_esEs14(xy4000, xy3000, bcb) new_esEs12(:(xy4000, xy4001), :(xy3000, xy3001), bd) -> new_asAs(new_esEs13(xy4000, xy3000, bd), new_esEs12(xy4001, xy3001, bd)) new_esEs18(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), ga, gb, gc) -> new_asAs(new_esEs25(xy4000, xy3000, ga), new_asAs(new_esEs26(xy4001, xy3001, gb), new_esEs27(xy4002, xy3002, gc))) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, beh)) -> new_esEs14(xy400, xy300, beh) new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs23(xy4000, xy3000, app(ty_Ratio, dc)) -> new_esEs6(xy4000, xy3000, dc) new_esEs27(xy4002, xy3002, app(ty_Maybe, bah)) -> new_esEs14(xy4002, xy3002, bah) new_deleteBy1(Left(xy400), :(Left(xy300), xy31), ba, bb) -> new_deleteBy02(xy31, xy300, xy400, new_esEs4(xy400, xy300, ba), ba, bb) new_primEqNat0(Zero, Zero) -> True new_esEs17(@2(xy4000, xy4001), @2(xy3000, xy3001), cg, da) -> new_asAs(new_esEs23(xy4000, xy3000, cg), new_esEs24(xy4001, xy3001, da)) new_esEs27(xy4002, xy3002, ty_Ordering) -> new_esEs15(xy4002, xy3002) new_deleteBy1(Left(xy400), :(Right(xy300), xy31), ba, bb) -> :(Right(xy300), new_deleteBy1(Left(xy400), xy31, ba, bb)) new_esEs26(xy4001, xy3001, app(app(ty_@2, hh), baa)) -> new_esEs17(xy4001, xy3001, hh, baa) new_esEs24(xy4001, xy3001, app(app(ty_Either, fd), ff)) -> new_esEs22(xy4001, xy3001, fd, ff) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs13(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_Either, ce), cf)) -> new_esEs22(xy4000, xy3000, ce, cf) new_asAs(False, xy35) -> False new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, gh), ha), hb)) -> new_esEs18(xy4000, xy3000, gh, ha, hb) new_esEs7(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs5(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_Either, bhe), bhf)) -> new_esEs22(xy4000, xy3000, bhe, bhf) new_esEs13(xy4000, xy3000, app(ty_[], cd)) -> new_esEs12(xy4000, xy3000, cd) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, bc)) -> new_esEs6(xy400, xy300, bc) new_deleteBy1(Right(xy400), :(Left(xy300), xy31), ba, bb) -> :(Left(xy300), new_deleteBy1(Right(xy400), xy31, ba, bb)) new_esEs7(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs19(True, True) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Ratio, bcd), bcc) -> new_esEs6(xy4000, xy3000, bcd) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) The set Q consists of the following terms: new_esEs22(Right(x0), Right(x1), x2, ty_Char) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs14(Nothing, Nothing, x0) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, ty_Char) new_esEs22(Left(x0), Left(x1), ty_Integer, x2) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs27(x0, x1, ty_@0) new_esEs14(Just(x0), Just(x1), ty_Double) new_esEs25(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs13(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs8(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Bool) new_esEs22(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_primPlusNat1(Zero, Zero) new_esEs12([], [], x0) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat0(Zero, x0) new_esEs26(x0, x1, ty_Char) new_esEs15(EQ, EQ) new_asAs(True, x0) new_esEs14(Just(x0), Nothing, x1) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_Integer) new_esEs19(False, False) new_primMulNat0(Succ(x0), Zero) new_esEs20(@0, @0) new_esEs22(Left(x0), Left(x1), ty_Bool, x2) new_esEs25(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs9(Integer(x0), Integer(x1)) new_esEs5(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs13(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_esEs26(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Bool) new_esEs22(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs12([], :(x0, x1), x2) new_esEs4(x0, x1, ty_@0) new_esEs22(Right(x0), Right(x1), x2, ty_Ordering) new_primPlusNat0(Succ(x0), x1) new_esEs22(Right(x0), Right(x1), x2, ty_Int) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs27(x0, x1, ty_Integer) new_esEs5(x0, x1, ty_Integer) new_esEs22(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs15(EQ, GT) new_esEs15(GT, EQ) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, ty_Ordering) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_deleteBy1(Left(x0), :(Left(x1), x2), x3, x4) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs10(x0, x1) new_esEs15(LT, LT) new_esEs26(x0, x1, ty_Ordering) new_esEs22(Right(x0), Right(x1), x2, ty_Double) new_esEs27(x0, x1, ty_Char) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs22(Right(x0), Right(x1), x2, ty_Bool) new_esEs27(x0, x1, ty_Int) new_esEs12(:(x0, x1), :(x2, x3), x4) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_deleteBy02(x0, x1, x2, True, x3, x4) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_deleteBy02(x0, x1, x2, False, x3, x4) new_esEs25(x0, x1, ty_Double) new_esEs11(Char(x0), Char(x1)) new_esEs24(x0, x1, ty_Double) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Char) new_esEs24(x0, x1, ty_@0) new_esEs22(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_deleteBy1(x0, [], x1, x2) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs5(x0, x1, ty_Char) new_esEs14(Just(x0), Just(x1), ty_Ordering) new_esEs22(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs27(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Bool) new_esEs5(x0, x1, ty_Double) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Int) new_esEs19(True, True) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Ordering) new_primEqNat0(Zero, Succ(x0)) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs14(Just(x0), Just(x1), ty_Integer) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs5(x0, x1, ty_Ordering) new_esEs22(Left(x0), Left(x1), ty_Int, x2) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_Integer) new_esEs13(x0, x1, app(ty_[], x2)) new_esEs4(x0, x1, ty_Ordering) new_esEs14(Just(x0), Just(x1), ty_@0) new_esEs27(x0, x1, ty_Double) new_primMulNat0(Zero, Succ(x0)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs15(LT, GT) new_esEs15(GT, LT) new_esEs24(x0, x1, app(ty_[], x2)) new_asAs(False, x0) new_esEs22(Right(x0), Right(x1), x2, ty_Integer) new_deleteBy1(Right(x0), :(Left(x1), x2), x3, x4) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Integer) new_esEs22(Left(x0), Left(x1), ty_Ordering, x2) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs5(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Float) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs26(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs4(x0, x1, ty_Char) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs15(GT, GT) new_esEs27(x0, x1, ty_Ordering) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs4(x0, x1, ty_Double) new_esEs19(False, True) new_esEs19(True, False) new_esEs15(LT, EQ) new_esEs15(EQ, LT) new_esEs5(x0, x1, ty_Float) new_esEs25(x0, x1, ty_@0) new_esEs16(Double(x0, x1), Double(x2, x3)) new_esEs12(:(x0, x1), [], x2) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), ty_Bool) new_esEs22(Left(x0), Left(x1), ty_Char, x2) new_esEs26(x0, x1, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs22(Left(x0), Right(x1), x2, x3) new_esEs22(Right(x0), Left(x1), x2, x3) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, ty_Integer) new_esEs22(Left(x0), Left(x1), ty_Double, x2) new_esEs13(x0, x1, ty_@0) new_primPlusNat1(Zero, Succ(x0)) new_esEs7(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs27(x0, x1, ty_Float) new_esEs13(x0, x1, ty_Integer) new_esEs22(Right(x0), Right(x1), x2, ty_@0) new_primEqNat0(Zero, Zero) new_esEs23(x0, x1, ty_@0) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), ty_Char) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_deleteBy1(Left(x0), :(Right(x1), x2), x3, x4) new_esEs22(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs26(x0, x1, ty_Double) new_esEs22(Left(x0), Left(x1), ty_@0, x2) new_esEs23(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), ty_Int) new_esEs13(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Integer) new_deleteBy01(x0, x1, x2, True, x3, x4) new_esEs23(x0, x1, ty_Float) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Double) new_esEs22(Right(x0), Right(x1), x2, ty_Float) new_deleteBy01(x0, x1, x2, False, x3, x4) new_esEs14(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs7(x0, x1, ty_Int) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_sr(Pos(x0), Pos(x1)) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs21(Float(x0, x1), Float(x2, x3)) new_deleteBy1(Right(x0), :(Right(x1), x2), x3, x4) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs14(Nothing, Just(x0), x1) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Bool) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs22(Left(x0), Left(x1), ty_Float, x2) new_esEs14(Just(x0), Just(x1), app(ty_[], x2)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_Int) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs26(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(ty_Maybe, x2)) new_primEqNat0(Succ(x0), Zero) new_primPlusNat1(Succ(x0), Zero) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Ordering) new_esEs14(Just(x0), Just(x1), ty_Float) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_foldl(xy3, :(xy40, xy41), ba, bb) -> new_foldl(new_deleteBy1(xy40, xy3, ba, bb), xy41, ba, bb) The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs(Just(xy4000), Just(xy3000), app(ty_[], bg)) -> new_esEs2(xy4000, xy3000, bg) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(ty_Maybe, df)) -> new_esEs(xy4001, xy3001, df) new_esEs3(Left(xy4000), Left(xy3000), app(app(ty_Either, bch), bda), bca) -> new_esEs3(xy4000, xy3000, bch, bda) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), bbg) -> new_esEs2(xy4001, xy3001, bbg) new_esEs3(Right(xy4000), Right(xy3000), bdb, app(ty_[], bea)) -> new_esEs2(xy4000, xy3000, bea) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_@2, bag), bah)) -> new_esEs0(xy4000, xy3000, bag, bah) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(ty_@2, dg), dh)) -> new_esEs0(xy4001, xy3001, dg, dh) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(app(ty_@3, fd), ff), fg), eh, fa) -> new_esEs1(xy4000, xy3000, fd, ff, fg) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, dc), dd), cc) -> new_esEs3(xy4000, xy3000, dc, dd) new_esEs3(Right(xy4000), Right(xy3000), bdb, app(ty_Maybe, bdc)) -> new_esEs(xy4000, xy3000, bdc) new_esEs(Just(xy4000), Just(xy3000), app(ty_Maybe, ba)) -> new_esEs(xy4000, xy3000, ba) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(ty_[], bac)) -> new_esEs2(xy4002, xy3002, bac) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_[], hb), fa) -> new_esEs2(xy4001, xy3001, hb) new_esEs3(Left(xy4000), Left(xy3000), app(app(ty_@2, bcb), bcc), bca) -> new_esEs0(xy4000, xy3000, bcb, bcc) new_esEs(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bd), be), bf)) -> new_esEs1(xy4000, xy3000, bd, be, bf) new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(ty_Either, beb), bec)) -> new_esEs3(xy4000, xy3000, beb, bec) new_esEs(Just(xy4000), Just(xy3000), app(app(ty_@2, bb), bc)) -> new_esEs0(xy4000, xy3000, bb, bc) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(ty_Either, ee), ef)) -> new_esEs3(xy4001, xy3001, ee, ef) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], fh), eh, fa) -> new_esEs2(xy4000, xy3000, fh) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(ty_Maybe, he)) -> new_esEs(xy4002, xy3002, he) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, cb), cc) -> new_esEs(xy4000, xy3000, cb) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs1(xy4000, xy3000, bba, bbb, bbc) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_Either, ga), gb), eh, fa) -> new_esEs3(xy4000, xy3000, ga, gb) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(ty_Maybe, gd), fa) -> new_esEs(xy4001, xy3001, gd) new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs1(xy4000, xy3000, bdf, bdg, bdh) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(app(ty_@3, ea), eb), ec)) -> new_esEs1(xy4001, xy3001, ea, eb, ec) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_@2, ge), gf), fa) -> new_esEs0(xy4001, xy3001, ge, gf) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, eg), eh, fa) -> new_esEs(xy4000, xy3000, eg) new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(ty_@2, bdd), bde)) -> new_esEs0(xy4000, xy3000, bdd, bde) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(app(ty_@2, hf), hg)) -> new_esEs0(xy4002, xy3002, hf, hg) new_esEs3(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), bca) -> new_esEs(xy4000, xy3000, bbh) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], db), cc) -> new_esEs2(xy4000, xy3000, db) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(app(app(ty_@3, hh), baa), bab)) -> new_esEs1(xy4002, xy3002, hh, baa, bab) new_esEs(Just(xy4000), Just(xy3000), app(app(ty_Either, bh), ca)) -> new_esEs3(xy4000, xy3000, bh, ca) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(ty_Either, hc), hd), fa) -> new_esEs3(xy4001, xy3001, hc, hd) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_Maybe, baf)) -> new_esEs(xy4000, xy3000, baf) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(ty_[], ed)) -> new_esEs2(xy4001, xy3001, ed) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(app(ty_@2, fb), fc), eh, fa) -> new_esEs0(xy4000, xy3000, fb, fc) new_esEs3(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bcd), bce), bcf), bca) -> new_esEs1(xy4000, xy3000, bcd, bce, bcf) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_[], bbd)) -> new_esEs2(xy4000, xy3000, bbd) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(app(ty_Either, bad), bae)) -> new_esEs3(xy4002, xy3002, bad, bae) new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_Either, bbe), bbf)) -> new_esEs3(xy4000, xy3000, bbe, bbf) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, cd), ce), cc) -> new_esEs0(xy4000, xy3000, cd, ce) new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, app(app(app(ty_@3, gg), gh), ha), fa) -> new_esEs1(xy4001, xy3001, gg, gh, ha) new_esEs3(Left(xy4000), Left(xy3000), app(ty_[], bcg), bca) -> new_esEs2(xy4000, xy3000, bcg) new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, cf), cg), da), cc) -> new_esEs1(xy4000, xy3000, cf, cg, da) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (13) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_Maybe, baf)) -> new_esEs(xy4000, xy3000, baf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_@2, bag), bah)) -> new_esEs0(xy4000, xy3000, bag, bah) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(Just(xy4000), Just(xy3000), app(ty_Maybe, ba)) -> new_esEs(xy4000, xy3000, ba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(Just(xy4000), Just(xy3000), app(app(ty_@2, bb), bc)) -> new_esEs0(xy4000, xy3000, bb, bc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(ty_Either, bbe), bbf)) -> new_esEs3(xy4000, xy3000, bbe, bbf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(Just(xy4000), Just(xy3000), app(app(ty_Either, bh), ca)) -> new_esEs3(xy4000, xy3000, bh, ca) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs1(xy4000, xy3000, bba, bbb, bbc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(Just(xy4000), Just(xy3000), app(ty_[], bg)) -> new_esEs2(xy4000, xy3000, bg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bd), be), bf)) -> new_esEs1(xy4000, xy3000, bd, be, bf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), bbg) -> new_esEs2(xy4001, xy3001, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs2(:(xy4000, xy4001), :(xy3000, xy3001), app(ty_[], bbd)) -> new_esEs2(xy4000, xy3000, bbd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Right(xy4000), Right(xy3000), bdb, app(ty_Maybe, bdc)) -> new_esEs(xy4000, xy3000, bdc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(Left(xy4000), Left(xy3000), app(ty_Maybe, bbh), bca) -> new_esEs(xy4000, xy3000, bbh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(ty_Maybe, df)) -> new_esEs(xy4001, xy3001, df) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_Maybe, cb), cc) -> new_esEs(xy4000, xy3000, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(ty_Maybe, he)) -> new_esEs(xy4002, xy3002, he) 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, gd), fa) -> new_esEs(xy4001, xy3001, gd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_Maybe, eg), eh, fa) -> new_esEs(xy4000, xy3000, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(xy4000), Left(xy3000), app(app(ty_@2, bcb), bcc), bca) -> new_esEs0(xy4000, xy3000, bcb, bcc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(ty_@2, bdd), bde)) -> new_esEs0(xy4000, xy3000, bdd, bde) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(ty_@2, dg), dh)) -> new_esEs0(xy4001, xy3001, dg, dh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_@2, cd), ce), cc) -> new_esEs0(xy4000, xy3000, cd, ce) 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, ge), gf), fa) -> new_esEs0(xy4001, xy3001, ge, gf) 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, eh, app(app(ty_@2, hf), hg)) -> new_esEs0(xy4002, xy3002, hf, hg) 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, fb), fc), eh, fa) -> new_esEs0(xy4000, xy3000, fb, fc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(xy4000), Left(xy3000), app(app(ty_Either, bch), bda), bca) -> new_esEs3(xy4000, xy3000, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(ty_Either, beb), bec)) -> new_esEs3(xy4000, xy3000, beb, bec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(Right(xy4000), Right(xy3000), bdb, app(ty_[], bea)) -> new_esEs2(xy4000, xy3000, bea) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(Left(xy4000), Left(xy3000), app(ty_[], bcg), bca) -> new_esEs2(xy4000, xy3000, bcg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Right(xy4000), Right(xy3000), bdb, app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs1(xy4000, xy3000, bdf, bdg, bdh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs3(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bcd), bce), bcf), bca) -> new_esEs1(xy4000, xy3000, bcd, bce, bcf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(ty_Either, dc), dd), cc) -> new_esEs3(xy4000, xy3000, dc, dd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(ty_Either, ee), ef)) -> new_esEs3(xy4001, xy3001, ee, ef) 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, ga), gb), eh, fa) -> new_esEs3(xy4000, xy3000, ga, gb) 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_Either, hc), hd), fa) -> new_esEs3(xy4001, xy3001, hc, hd) 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, eh, app(app(ty_Either, bad), bae)) -> new_esEs3(xy4002, xy3002, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(ty_[], db), cc) -> new_esEs2(xy4000, xy3000, db) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(ty_[], ed)) -> new_esEs2(xy4001, xy3001, ed) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), gc, eh, app(ty_[], bac)) -> new_esEs2(xy4002, xy3002, bac) 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_[], hb), fa) -> new_esEs2(xy4001, xy3001, hb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), app(ty_[], fh), eh, fa) -> new_esEs2(xy4000, xy3000, fh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), de, app(app(app(ty_@3, ea), eb), ec)) -> new_esEs1(xy4001, xy3001, ea, eb, ec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(@2(xy4000, xy4001), @2(xy3000, xy3001), app(app(app(ty_@3, cf), cg), da), cc) -> new_esEs1(xy4000, xy3000, cf, cg, da) 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), app(app(app(ty_@3, fd), ff), fg), eh, fa) -> new_esEs1(xy4000, xy3000, fd, ff, fg) 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, eh, app(app(app(ty_@3, hh), baa), bab)) -> new_esEs1(xy4002, xy3002, hh, baa, bab) 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, gg), gh), ha), fa) -> new_esEs1(xy4001, xy3001, gg, gh, ha) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 ---------------------------------------- (14) YES ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(xy400100), Succ(xy300000)) -> new_primMulNat(xy400100, Succ(xy300000)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primMulNat(Succ(xy400100), Succ(xy300000)) -> new_primMulNat(xy400100, Succ(xy300000)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy00(xy19, xy20, xy21, False, be, bf) -> new_deleteBy(Right(xy21), xy19, be, bf) new_deleteBy(Left(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy(Left(xy400), xy31, bc, bd) new_deleteBy(Right(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy(Right(xy400), xy31, bc, bd) new_deleteBy(Left(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, bc), bc, bd) new_deleteBy0(xy10, xy11, xy12, False, ba, bb) -> new_deleteBy(Left(xy12), xy10, ba, bb) new_deleteBy(Right(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy00(xy31, xy300, xy400, new_esEs5(xy400, xy300, bd), bc, bd) The TRS R consists of the following rules: new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs13(xy4000, xy3000, app(ty_Maybe, ca)) -> new_esEs14(xy4000, xy3000, ca) new_esEs23(xy4000, xy3000, app(app(ty_@2, dh), ea)) -> new_esEs17(xy4000, xy3000, dh, ea) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs26(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_Either, bgb), bgc)) -> new_esEs22(xy4000, xy3000, bgb, bgc) new_esEs4(xy400, xy300, app(app(ty_@2, dd), de)) -> new_esEs17(xy400, xy300, dd, de) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_esEs5(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Ratio, bfc)) -> new_esEs6(xy4000, xy3000, bfc) new_esEs19(False, True) -> False new_esEs19(True, False) -> False new_esEs15(LT, LT) -> True new_esEs23(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs23(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs12(:(xy4000, xy4001), [], bh) -> False new_esEs12([], :(xy3000, xy3001), bh) -> False new_esEs13(xy4000, xy3000, app(app(app(ty_@3, ce), cf), cg)) -> new_esEs18(xy4000, xy3000, ce, cf, cg) new_esEs4(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs13(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_[], bhd)) -> new_esEs12(xy4000, xy3000, bhd) new_esEs23(xy4000, xy3000, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs18(xy4000, xy3000, eb, ec, ed) new_esEs25(xy4000, xy3000, app(app(ty_Either, bah), bba)) -> new_esEs22(xy4000, xy3000, bah, bba) new_esEs27(xy4002, xy3002, app(ty_Ratio, bce)) -> new_esEs6(xy4002, xy3002, bce) new_esEs13(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bfa), bdg)) -> new_esEs22(xy400, xy300, bfa, bdg) new_asAs(True, xy35) -> xy35 new_esEs26(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs13(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_@2, cc), cd)) -> new_esEs17(xy4000, xy3000, cc, cd) new_esEs26(xy4001, xy3001, app(ty_Maybe, bbb)) -> new_esEs14(xy4001, xy3001, bbb) new_esEs5(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Integer) -> new_esEs9(xy4002, xy3002) new_esEs23(xy4000, xy3000, app(app(ty_Either, ef), eg)) -> new_esEs22(xy4000, xy3000, ef, eg) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs22(Left(xy4000), Left(xy3000), ty_Ordering, bdg) -> new_esEs15(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_@2, bab), bac)) -> new_esEs17(xy4000, xy3000, bab, bac) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs18(xy4000, xy3000, bff, bfg, bfh) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs23(xy4000, xy3000, app(ty_Maybe, df)) -> new_esEs14(xy4000, xy3000, df) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_@2, bea), beb), bdg) -> new_esEs17(xy4000, xy3000, bea, beb) new_esEs5(xy400, xy300, app(ty_Maybe, gc)) -> new_esEs14(xy400, xy300, gc) new_esEs22(Left(xy4000), Left(xy3000), app(ty_[], bef), bdg) -> new_esEs12(xy4000, xy3000, bef) new_primMulNat0(Zero, Zero) -> Zero new_esEs27(xy4002, xy3002, ty_Double) -> new_esEs16(xy4002, xy3002) new_esEs20(@0, @0) -> True new_esEs4(xy400, xy300, app(ty_[], bh)) -> new_esEs12(xy400, xy300, bh) new_esEs24(xy4001, xy3001, app(ty_Maybe, eh)) -> new_esEs14(xy4001, xy3001, eh) new_esEs13(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_Ratio, bgf)) -> new_esEs6(xy4000, xy3000, bgf) new_esEs5(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs15(LT, EQ) -> False new_esEs15(EQ, LT) -> False new_esEs22(Left(xy4000), Left(xy3000), ty_Char, bdg) -> new_esEs11(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Bool) -> new_esEs19(xy4002, xy3002) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs27(xy4002, xy3002, app(app(app(ty_@3, bch), bda), bdb)) -> new_esEs18(xy4002, xy3002, bch, bda, bdb) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_@2, bfd), bfe)) -> new_esEs17(xy4000, xy3000, bfd, bfe) new_esEs9(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Int) -> new_esEs10(xy4002, xy3002) new_esEs13(xy4000, xy3000, app(ty_Ratio, cb)) -> new_esEs6(xy4000, xy3000, cb) new_esEs25(xy4000, xy3000, app(ty_Maybe, hh)) -> new_esEs14(xy4000, xy3000, hh) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, he), hf), hg)) -> new_esEs18(xy400, xy300, he, hf, hg) new_esEs22(Left(xy4000), Left(xy3000), ty_Double, bdg) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_@2, bgg), bgh)) -> new_esEs17(xy4000, xy3000, bgg, bgh) new_esEs19(False, False) -> True new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_esEs27(xy4002, xy3002, app(ty_[], bdc)) -> new_esEs12(xy4002, xy3002, bdc) new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Bool, bdg) -> new_esEs19(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bec), bed), bee), bdg) -> new_esEs18(xy4000, xy3000, bec, bed, bee) new_esEs14(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs15(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3600, xy3000000))) new_esEs27(xy4002, xy3002, app(app(ty_Either, bdd), bde)) -> new_esEs22(xy4002, xy3002, bdd, bde) new_esEs4(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Char) -> new_esEs11(xy4002, xy3002) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs5(xy400, xy300, app(app(ty_@2, ge), gf)) -> new_esEs17(xy400, xy300, ge, gf) new_esEs25(xy4000, xy3000, app(ty_Ratio, baa)) -> new_esEs6(xy4000, xy3000, baa) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_[], bga)) -> new_esEs12(xy4000, xy3000, bga) new_esEs22(Left(xy4000), Left(xy3000), ty_Integer, bdg) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs4(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Int, bdg) -> new_esEs10(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs26(xy4001, xy3001, app(app(ty_Either, bcb), bcc)) -> new_esEs22(xy4001, xy3001, bcb, bcc) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs15(EQ, EQ) -> True new_esEs14(Just(xy4000), Just(xy3000), app(ty_Maybe, bge)) -> new_esEs14(xy4000, xy3000, bge) new_esEs26(xy4001, xy3001, app(ty_Ratio, bbc)) -> new_esEs6(xy4001, xy3001, bbc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs15(GT, GT) -> True new_esEs5(xy400, xy300, app(ty_Ratio, gd)) -> new_esEs6(xy400, xy300, gd) new_esEs14(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs19(xy4000, xy3000) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs15(EQ, GT) -> False new_esEs15(GT, EQ) -> False new_esEs14(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bha), bhb), bhc)) -> new_esEs18(xy4000, xy3000, bha, bhb, bhc) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs11(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_@0) -> new_esEs20(xy4002, xy3002) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_@2, fb), fc)) -> new_esEs17(xy4001, xy3001, fb, fc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs5(xy400, xy300, app(app(ty_Either, hc), hd)) -> new_esEs22(xy400, xy300, hc, hd) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs22(Left(xy4000), Right(xy3000), bfa, bdg) -> False new_esEs22(Right(xy4000), Left(xy3000), bfa, bdg) -> False new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs5(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs16(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_Either, beg), beh), bdg) -> new_esEs22(xy4000, xy3000, beg, beh) new_esEs22(Left(xy4000), Left(xy3000), ty_Float, bdg) -> new_esEs21(xy4000, xy3000) new_esEs5(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs8(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs18(xy4001, xy3001, fd, ff, fg) new_esEs4(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs5(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs16(xy4000, xy3000) new_primPlusNat0(Succ(xy360), xy300000) -> Succ(Succ(new_primPlusNat1(xy360, xy300000))) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs6(xy4001, xy3001, fa) new_esEs5(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs23(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs10(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs5(xy400, xy300, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs18(xy400, xy300, gg, gh, ha) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_esEs26(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs23(xy4000, xy3000, app(ty_[], ee)) -> new_esEs12(xy4000, xy3000, ee) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs6(:%(xy4000, xy4001), :%(xy3000, xy3001), bg) -> new_asAs(new_esEs7(xy4000, xy3000, bg), new_esEs8(xy4001, xy3001, bg)) new_esEs26(xy4001, xy3001, app(ty_[], bca)) -> new_esEs12(xy4001, xy3001, bca) new_esEs14(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs15(LT, GT) -> False new_esEs15(GT, LT) -> False new_esEs26(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Float) -> new_esEs21(xy4002, xy3002) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4001, xy3001, app(app(app(ty_@3, bbf), bbg), bbh)) -> new_esEs18(xy4001, xy3001, bbf, bbg, bbh) new_esEs5(xy400, xy300, app(ty_[], hb)) -> new_esEs12(xy400, xy300, hb) new_esEs24(xy4001, xy3001, app(ty_[], fh)) -> new_esEs12(xy4001, xy3001, fh) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs8(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Maybe, bfb)) -> new_esEs14(xy4000, xy3000, bfb) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs21(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs14(Nothing, Just(xy3000), bgd) -> False new_esEs14(Just(xy4000), Nothing, bgd) -> False new_esEs14(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_@0, bdg) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Zero) -> Succ(xy3600) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs25(xy4000, xy3000, app(ty_[], bag)) -> new_esEs12(xy4000, xy3000, bag) new_esEs27(xy4002, xy3002, app(app(ty_@2, bcf), bcg)) -> new_esEs17(xy4002, xy3002, bcf, bcg) new_esEs14(Nothing, Nothing, bgd) -> True new_esEs14(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_esEs12([], [], bh) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Maybe, bdf), bdg) -> new_esEs14(xy4000, xy3000, bdf) new_esEs12(:(xy4000, xy4001), :(xy3000, xy3001), bh) -> new_asAs(new_esEs13(xy4000, xy3000, bh), new_esEs12(xy4001, xy3001, bh)) new_esEs18(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), he, hf, hg) -> new_asAs(new_esEs25(xy4000, xy3000, he), new_asAs(new_esEs26(xy4001, xy3001, hf), new_esEs27(xy4002, xy3002, hg))) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bgd)) -> new_esEs14(xy400, xy300, bgd) new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs23(xy4000, xy3000, app(ty_Ratio, dg)) -> new_esEs6(xy4000, xy3000, dg) new_esEs27(xy4002, xy3002, app(ty_Maybe, bcd)) -> new_esEs14(xy4002, xy3002, bcd) new_primEqNat0(Zero, Zero) -> True new_esEs17(@2(xy4000, xy4001), @2(xy3000, xy3001), dd, de) -> new_asAs(new_esEs23(xy4000, xy3000, dd), new_esEs24(xy4001, xy3001, de)) new_esEs27(xy4002, xy3002, ty_Ordering) -> new_esEs15(xy4002, xy3002) new_esEs26(xy4001, xy3001, app(app(ty_@2, bbd), bbe)) -> new_esEs17(xy4001, xy3001, bbd, bbe) new_esEs24(xy4001, xy3001, app(app(ty_Either, ga), gb)) -> new_esEs22(xy4001, xy3001, ga, gb) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs13(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_Either, db), dc)) -> new_esEs22(xy4000, xy3000, db, dc) new_asAs(False, xy35) -> False new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bad), bae), baf)) -> new_esEs18(xy4000, xy3000, bad, bae, baf) new_esEs7(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs5(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_Either, bhe), bhf)) -> new_esEs22(xy4000, xy3000, bhe, bhf) new_esEs13(xy4000, xy3000, app(ty_[], da)) -> new_esEs12(xy4000, xy3000, da) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, bg)) -> new_esEs6(xy400, xy300, bg) new_esEs7(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs19(True, True) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Ratio, bdh), bdg) -> new_esEs6(xy4000, xy3000, bdh) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(Left(x0), Left(x1), ty_Int, x2) new_esEs22(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Char) new_esEs27(x0, x1, ty_@0) new_esEs14(Just(x0), Just(x1), ty_Double) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Int) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Int) new_esEs22(Left(x0), Left(x1), ty_Char, x2) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs13(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs8(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_primPlusNat0(Zero, x0) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Char) new_esEs15(EQ, EQ) new_asAs(True, x0) new_esEs14(Nothing, Nothing, x0) new_esEs4(x0, x1, ty_Integer) new_esEs19(False, False) new_esEs13(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Zero) new_esEs20(@0, @0) new_esEs25(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs22(Left(x0), Left(x1), ty_Ordering, x2) new_esEs22(Left(x0), Left(x1), ty_Float, x2) new_esEs9(Integer(x0), Integer(x1)) new_esEs5(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_esEs26(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Bool) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_@0) new_esEs22(Right(x0), Right(x1), x2, ty_Float) new_primPlusNat0(Succ(x0), x1) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Integer) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5(x0, x1, ty_Integer) new_esEs15(EQ, GT) new_esEs15(GT, EQ) new_esEs14(Just(x0), Nothing, x1) new_esEs13(x0, x1, ty_Ordering) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs10(x0, x1) new_esEs15(LT, LT) new_esEs26(x0, x1, ty_Ordering) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12([], :(x0, x1), x2) new_esEs27(x0, x1, ty_Char) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs22(Right(x0), Right(x1), x2, ty_Bool) new_esEs27(x0, x1, ty_Int) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_Double, x2) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs22(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs25(x0, x1, ty_Double) new_esEs11(Char(x0), Char(x1)) new_esEs24(x0, x1, ty_Double) new_esEs12([], [], x0) new_esEs22(Right(x0), Right(x1), x2, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs24(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs5(x0, x1, ty_Char) new_esEs14(Just(x0), Just(x1), ty_Ordering) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs27(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Bool) new_esEs5(x0, x1, ty_Double) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Int) new_esEs19(True, True) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Ordering) new_primEqNat0(Zero, Succ(x0)) new_esEs22(Right(x0), Right(x1), x2, ty_Char) new_esEs22(Right(x0), Right(x1), x2, ty_Double) new_esEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Left(x0), Left(x1), ty_Bool, x2) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs14(Just(x0), Just(x1), ty_Integer) new_esEs22(Left(x0), Left(x1), ty_Integer, x2) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Ordering) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Integer) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Ordering) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs22(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs14(Just(x0), Just(x1), ty_@0) new_esEs27(x0, x1, ty_Double) new_primMulNat0(Zero, Succ(x0)) new_esEs15(LT, GT) new_esEs15(GT, LT) new_esEs22(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_asAs(False, x0) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Float) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs26(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs15(GT, GT) new_esEs27(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Double) new_esEs19(False, True) new_esEs19(True, False) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(LT, EQ) new_esEs15(EQ, LT) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_@0, x2) new_esEs5(x0, x1, ty_Float) new_esEs25(x0, x1, ty_@0) new_esEs16(Double(x0, x1), Double(x2, x3)) new_esEs4(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), ty_Bool) new_esEs26(x0, x1, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, ty_Integer) new_esEs13(x0, x1, ty_@0) new_primPlusNat1(Zero, Succ(x0)) new_esEs7(x0, x1, ty_Integer) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Float) new_esEs13(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs22(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs23(x0, x1, ty_@0) new_esEs12(:(x0, x1), [], x2) new_esEs22(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs13(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs14(Just(x0), Just(x1), ty_Char) new_esEs26(x0, x1, ty_Double) new_esEs23(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), ty_Int) new_esEs13(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Float) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs23(x0, x1, ty_Double) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs22(Right(x0), Right(x1), x2, ty_Ordering) new_esEs14(Just(x0), Just(x1), app(ty_Ratio, x2)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs12(:(x0, x1), :(x2, x3), x4) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_sr(Pos(x0), Pos(x1)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs21(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Right(x1), x2, x3) new_esEs22(Right(x0), Left(x1), x2, x3) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Bool) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs14(Nothing, Just(x0), x1) new_esEs14(Just(x0), Just(x1), app(ty_[], x2)) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, ty_Int) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs22(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_primEqNat0(Succ(x0), Zero) new_primPlusNat1(Succ(x0), Zero) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Ordering) new_esEs14(Just(x0), Just(x1), ty_Float) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. ---------------------------------------- (20) Complex Obligation (AND) ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy(Left(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, bc), bc, bd) new_deleteBy0(xy10, xy11, xy12, False, ba, bb) -> new_deleteBy(Left(xy12), xy10, ba, bb) new_deleteBy(Left(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy(Left(xy400), xy31, bc, bd) The TRS R consists of the following rules: new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs13(xy4000, xy3000, app(ty_Maybe, ca)) -> new_esEs14(xy4000, xy3000, ca) new_esEs23(xy4000, xy3000, app(app(ty_@2, dh), ea)) -> new_esEs17(xy4000, xy3000, dh, ea) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs26(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_Either, bgb), bgc)) -> new_esEs22(xy4000, xy3000, bgb, bgc) new_esEs4(xy400, xy300, app(app(ty_@2, dd), de)) -> new_esEs17(xy400, xy300, dd, de) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_esEs5(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Ratio, bfc)) -> new_esEs6(xy4000, xy3000, bfc) new_esEs19(False, True) -> False new_esEs19(True, False) -> False new_esEs15(LT, LT) -> True new_esEs23(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs23(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs12(:(xy4000, xy4001), [], bh) -> False new_esEs12([], :(xy3000, xy3001), bh) -> False new_esEs13(xy4000, xy3000, app(app(app(ty_@3, ce), cf), cg)) -> new_esEs18(xy4000, xy3000, ce, cf, cg) new_esEs4(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs13(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_[], bhd)) -> new_esEs12(xy4000, xy3000, bhd) new_esEs23(xy4000, xy3000, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs18(xy4000, xy3000, eb, ec, ed) new_esEs25(xy4000, xy3000, app(app(ty_Either, bah), bba)) -> new_esEs22(xy4000, xy3000, bah, bba) new_esEs27(xy4002, xy3002, app(ty_Ratio, bce)) -> new_esEs6(xy4002, xy3002, bce) new_esEs13(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bfa), bdg)) -> new_esEs22(xy400, xy300, bfa, bdg) new_asAs(True, xy35) -> xy35 new_esEs26(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs13(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_@2, cc), cd)) -> new_esEs17(xy4000, xy3000, cc, cd) new_esEs26(xy4001, xy3001, app(ty_Maybe, bbb)) -> new_esEs14(xy4001, xy3001, bbb) new_esEs5(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Integer) -> new_esEs9(xy4002, xy3002) new_esEs23(xy4000, xy3000, app(app(ty_Either, ef), eg)) -> new_esEs22(xy4000, xy3000, ef, eg) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs22(Left(xy4000), Left(xy3000), ty_Ordering, bdg) -> new_esEs15(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_@2, bab), bac)) -> new_esEs17(xy4000, xy3000, bab, bac) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs18(xy4000, xy3000, bff, bfg, bfh) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs23(xy4000, xy3000, app(ty_Maybe, df)) -> new_esEs14(xy4000, xy3000, df) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_@2, bea), beb), bdg) -> new_esEs17(xy4000, xy3000, bea, beb) new_esEs5(xy400, xy300, app(ty_Maybe, gc)) -> new_esEs14(xy400, xy300, gc) new_esEs22(Left(xy4000), Left(xy3000), app(ty_[], bef), bdg) -> new_esEs12(xy4000, xy3000, bef) new_primMulNat0(Zero, Zero) -> Zero new_esEs27(xy4002, xy3002, ty_Double) -> new_esEs16(xy4002, xy3002) new_esEs20(@0, @0) -> True new_esEs4(xy400, xy300, app(ty_[], bh)) -> new_esEs12(xy400, xy300, bh) new_esEs24(xy4001, xy3001, app(ty_Maybe, eh)) -> new_esEs14(xy4001, xy3001, eh) new_esEs13(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_Ratio, bgf)) -> new_esEs6(xy4000, xy3000, bgf) new_esEs5(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs15(LT, EQ) -> False new_esEs15(EQ, LT) -> False new_esEs22(Left(xy4000), Left(xy3000), ty_Char, bdg) -> new_esEs11(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Bool) -> new_esEs19(xy4002, xy3002) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs27(xy4002, xy3002, app(app(app(ty_@3, bch), bda), bdb)) -> new_esEs18(xy4002, xy3002, bch, bda, bdb) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_@2, bfd), bfe)) -> new_esEs17(xy4000, xy3000, bfd, bfe) new_esEs9(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Int) -> new_esEs10(xy4002, xy3002) new_esEs13(xy4000, xy3000, app(ty_Ratio, cb)) -> new_esEs6(xy4000, xy3000, cb) new_esEs25(xy4000, xy3000, app(ty_Maybe, hh)) -> new_esEs14(xy4000, xy3000, hh) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, he), hf), hg)) -> new_esEs18(xy400, xy300, he, hf, hg) new_esEs22(Left(xy4000), Left(xy3000), ty_Double, bdg) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_@2, bgg), bgh)) -> new_esEs17(xy4000, xy3000, bgg, bgh) new_esEs19(False, False) -> True new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_esEs27(xy4002, xy3002, app(ty_[], bdc)) -> new_esEs12(xy4002, xy3002, bdc) new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Bool, bdg) -> new_esEs19(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bec), bed), bee), bdg) -> new_esEs18(xy4000, xy3000, bec, bed, bee) new_esEs14(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs15(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3600, xy3000000))) new_esEs27(xy4002, xy3002, app(app(ty_Either, bdd), bde)) -> new_esEs22(xy4002, xy3002, bdd, bde) new_esEs4(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Char) -> new_esEs11(xy4002, xy3002) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs5(xy400, xy300, app(app(ty_@2, ge), gf)) -> new_esEs17(xy400, xy300, ge, gf) new_esEs25(xy4000, xy3000, app(ty_Ratio, baa)) -> new_esEs6(xy4000, xy3000, baa) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_[], bga)) -> new_esEs12(xy4000, xy3000, bga) new_esEs22(Left(xy4000), Left(xy3000), ty_Integer, bdg) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs4(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Int, bdg) -> new_esEs10(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs26(xy4001, xy3001, app(app(ty_Either, bcb), bcc)) -> new_esEs22(xy4001, xy3001, bcb, bcc) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs15(EQ, EQ) -> True new_esEs14(Just(xy4000), Just(xy3000), app(ty_Maybe, bge)) -> new_esEs14(xy4000, xy3000, bge) new_esEs26(xy4001, xy3001, app(ty_Ratio, bbc)) -> new_esEs6(xy4001, xy3001, bbc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs15(GT, GT) -> True new_esEs5(xy400, xy300, app(ty_Ratio, gd)) -> new_esEs6(xy400, xy300, gd) new_esEs14(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs19(xy4000, xy3000) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs15(EQ, GT) -> False new_esEs15(GT, EQ) -> False new_esEs14(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bha), bhb), bhc)) -> new_esEs18(xy4000, xy3000, bha, bhb, bhc) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs11(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_@0) -> new_esEs20(xy4002, xy3002) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_@2, fb), fc)) -> new_esEs17(xy4001, xy3001, fb, fc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs5(xy400, xy300, app(app(ty_Either, hc), hd)) -> new_esEs22(xy400, xy300, hc, hd) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs22(Left(xy4000), Right(xy3000), bfa, bdg) -> False new_esEs22(Right(xy4000), Left(xy3000), bfa, bdg) -> False new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs5(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs16(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_Either, beg), beh), bdg) -> new_esEs22(xy4000, xy3000, beg, beh) new_esEs22(Left(xy4000), Left(xy3000), ty_Float, bdg) -> new_esEs21(xy4000, xy3000) new_esEs5(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs8(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs18(xy4001, xy3001, fd, ff, fg) new_esEs4(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs5(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs16(xy4000, xy3000) new_primPlusNat0(Succ(xy360), xy300000) -> Succ(Succ(new_primPlusNat1(xy360, xy300000))) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs6(xy4001, xy3001, fa) new_esEs5(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs23(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs10(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs5(xy400, xy300, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs18(xy400, xy300, gg, gh, ha) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_esEs26(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs23(xy4000, xy3000, app(ty_[], ee)) -> new_esEs12(xy4000, xy3000, ee) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs6(:%(xy4000, xy4001), :%(xy3000, xy3001), bg) -> new_asAs(new_esEs7(xy4000, xy3000, bg), new_esEs8(xy4001, xy3001, bg)) new_esEs26(xy4001, xy3001, app(ty_[], bca)) -> new_esEs12(xy4001, xy3001, bca) new_esEs14(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs15(LT, GT) -> False new_esEs15(GT, LT) -> False new_esEs26(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Float) -> new_esEs21(xy4002, xy3002) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4001, xy3001, app(app(app(ty_@3, bbf), bbg), bbh)) -> new_esEs18(xy4001, xy3001, bbf, bbg, bbh) new_esEs5(xy400, xy300, app(ty_[], hb)) -> new_esEs12(xy400, xy300, hb) new_esEs24(xy4001, xy3001, app(ty_[], fh)) -> new_esEs12(xy4001, xy3001, fh) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs8(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Maybe, bfb)) -> new_esEs14(xy4000, xy3000, bfb) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs21(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs14(Nothing, Just(xy3000), bgd) -> False new_esEs14(Just(xy4000), Nothing, bgd) -> False new_esEs14(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_@0, bdg) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Zero) -> Succ(xy3600) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs25(xy4000, xy3000, app(ty_[], bag)) -> new_esEs12(xy4000, xy3000, bag) new_esEs27(xy4002, xy3002, app(app(ty_@2, bcf), bcg)) -> new_esEs17(xy4002, xy3002, bcf, bcg) new_esEs14(Nothing, Nothing, bgd) -> True new_esEs14(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_esEs12([], [], bh) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Maybe, bdf), bdg) -> new_esEs14(xy4000, xy3000, bdf) new_esEs12(:(xy4000, xy4001), :(xy3000, xy3001), bh) -> new_asAs(new_esEs13(xy4000, xy3000, bh), new_esEs12(xy4001, xy3001, bh)) new_esEs18(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), he, hf, hg) -> new_asAs(new_esEs25(xy4000, xy3000, he), new_asAs(new_esEs26(xy4001, xy3001, hf), new_esEs27(xy4002, xy3002, hg))) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bgd)) -> new_esEs14(xy400, xy300, bgd) new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs23(xy4000, xy3000, app(ty_Ratio, dg)) -> new_esEs6(xy4000, xy3000, dg) new_esEs27(xy4002, xy3002, app(ty_Maybe, bcd)) -> new_esEs14(xy4002, xy3002, bcd) new_primEqNat0(Zero, Zero) -> True new_esEs17(@2(xy4000, xy4001), @2(xy3000, xy3001), dd, de) -> new_asAs(new_esEs23(xy4000, xy3000, dd), new_esEs24(xy4001, xy3001, de)) new_esEs27(xy4002, xy3002, ty_Ordering) -> new_esEs15(xy4002, xy3002) new_esEs26(xy4001, xy3001, app(app(ty_@2, bbd), bbe)) -> new_esEs17(xy4001, xy3001, bbd, bbe) new_esEs24(xy4001, xy3001, app(app(ty_Either, ga), gb)) -> new_esEs22(xy4001, xy3001, ga, gb) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs13(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_Either, db), dc)) -> new_esEs22(xy4000, xy3000, db, dc) new_asAs(False, xy35) -> False new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bad), bae), baf)) -> new_esEs18(xy4000, xy3000, bad, bae, baf) new_esEs7(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs5(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_Either, bhe), bhf)) -> new_esEs22(xy4000, xy3000, bhe, bhf) new_esEs13(xy4000, xy3000, app(ty_[], da)) -> new_esEs12(xy4000, xy3000, da) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, bg)) -> new_esEs6(xy400, xy300, bg) new_esEs7(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs19(True, True) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Ratio, bdh), bdg) -> new_esEs6(xy4000, xy3000, bdh) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(Left(x0), Left(x1), ty_Int, x2) new_esEs22(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Char) new_esEs27(x0, x1, ty_@0) new_esEs14(Just(x0), Just(x1), ty_Double) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Int) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Int) new_esEs22(Left(x0), Left(x1), ty_Char, x2) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs13(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs8(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_primPlusNat0(Zero, x0) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Char) new_esEs15(EQ, EQ) new_asAs(True, x0) new_esEs14(Nothing, Nothing, x0) new_esEs4(x0, x1, ty_Integer) new_esEs19(False, False) new_esEs13(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Zero) new_esEs20(@0, @0) new_esEs25(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs22(Left(x0), Left(x1), ty_Ordering, x2) new_esEs22(Left(x0), Left(x1), ty_Float, x2) new_esEs9(Integer(x0), Integer(x1)) new_esEs5(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_esEs26(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Bool) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_@0) new_esEs22(Right(x0), Right(x1), x2, ty_Float) new_primPlusNat0(Succ(x0), x1) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Integer) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5(x0, x1, ty_Integer) new_esEs15(EQ, GT) new_esEs15(GT, EQ) new_esEs14(Just(x0), Nothing, x1) new_esEs13(x0, x1, ty_Ordering) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs10(x0, x1) new_esEs15(LT, LT) new_esEs26(x0, x1, ty_Ordering) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12([], :(x0, x1), x2) new_esEs27(x0, x1, ty_Char) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs22(Right(x0), Right(x1), x2, ty_Bool) new_esEs27(x0, x1, ty_Int) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_Double, x2) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs22(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs25(x0, x1, ty_Double) new_esEs11(Char(x0), Char(x1)) new_esEs24(x0, x1, ty_Double) new_esEs12([], [], x0) new_esEs22(Right(x0), Right(x1), x2, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs24(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs5(x0, x1, ty_Char) new_esEs14(Just(x0), Just(x1), ty_Ordering) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs27(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Bool) new_esEs5(x0, x1, ty_Double) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Int) new_esEs19(True, True) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Ordering) new_primEqNat0(Zero, Succ(x0)) new_esEs22(Right(x0), Right(x1), x2, ty_Char) new_esEs22(Right(x0), Right(x1), x2, ty_Double) new_esEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Left(x0), Left(x1), ty_Bool, x2) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs14(Just(x0), Just(x1), ty_Integer) new_esEs22(Left(x0), Left(x1), ty_Integer, x2) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Ordering) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Integer) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Ordering) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs22(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs14(Just(x0), Just(x1), ty_@0) new_esEs27(x0, x1, ty_Double) new_primMulNat0(Zero, Succ(x0)) new_esEs15(LT, GT) new_esEs15(GT, LT) new_esEs22(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_asAs(False, x0) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Float) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs26(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs15(GT, GT) new_esEs27(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Double) new_esEs19(False, True) new_esEs19(True, False) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(LT, EQ) new_esEs15(EQ, LT) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_@0, x2) new_esEs5(x0, x1, ty_Float) new_esEs25(x0, x1, ty_@0) new_esEs16(Double(x0, x1), Double(x2, x3)) new_esEs4(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), ty_Bool) new_esEs26(x0, x1, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, ty_Integer) new_esEs13(x0, x1, ty_@0) new_primPlusNat1(Zero, Succ(x0)) new_esEs7(x0, x1, ty_Integer) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Float) new_esEs13(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs22(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs23(x0, x1, ty_@0) new_esEs12(:(x0, x1), [], x2) new_esEs22(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs13(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs14(Just(x0), Just(x1), ty_Char) new_esEs26(x0, x1, ty_Double) new_esEs23(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), ty_Int) new_esEs13(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Float) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs23(x0, x1, ty_Double) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs22(Right(x0), Right(x1), x2, ty_Ordering) new_esEs14(Just(x0), Just(x1), app(ty_Ratio, x2)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs12(:(x0, x1), :(x2, x3), x4) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_sr(Pos(x0), Pos(x1)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs21(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Right(x1), x2, x3) new_esEs22(Right(x0), Left(x1), x2, x3) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Bool) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs14(Nothing, Just(x0), x1) new_esEs14(Just(x0), Just(x1), app(ty_[], x2)) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, ty_Int) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs22(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_primEqNat0(Succ(x0), Zero) new_primPlusNat1(Succ(x0), Zero) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Ordering) new_esEs14(Just(x0), Just(x1), ty_Float) 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_deleteBy0(xy10, xy11, xy12, False, ba, bb) -> new_deleteBy(Left(xy12), xy10, ba, bb) The graph contains the following edges 1 >= 2, 5 >= 3, 6 >= 4 *new_deleteBy(Left(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy(Left(xy400), xy31, bc, bd) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_deleteBy(Left(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy0(xy31, xy300, xy400, new_esEs4(xy400, xy300, bc), bc, bd) The graph contains the following edges 2 > 1, 2 > 2, 1 > 3, 3 >= 5, 4 >= 6 ---------------------------------------- (23) YES ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_deleteBy(Right(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy(Right(xy400), xy31, bc, bd) new_deleteBy(Right(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy00(xy31, xy300, xy400, new_esEs5(xy400, xy300, bd), bc, bd) new_deleteBy00(xy19, xy20, xy21, False, be, bf) -> new_deleteBy(Right(xy21), xy19, be, bf) The TRS R consists of the following rules: new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs13(xy4000, xy3000, app(ty_Maybe, ca)) -> new_esEs14(xy4000, xy3000, ca) new_esEs23(xy4000, xy3000, app(app(ty_@2, dh), ea)) -> new_esEs17(xy4000, xy3000, dh, ea) new_esEs24(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs26(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_Either, bgb), bgc)) -> new_esEs22(xy4000, xy3000, bgb, bgc) new_esEs4(xy400, xy300, app(app(ty_@2, dd), de)) -> new_esEs17(xy400, xy300, dd, de) new_esEs24(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_esEs5(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Ratio, bfc)) -> new_esEs6(xy4000, xy3000, bfc) new_esEs19(False, True) -> False new_esEs19(True, False) -> False new_esEs15(LT, LT) -> True new_esEs23(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs23(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs12(:(xy4000, xy4001), [], bh) -> False new_esEs12([], :(xy3000, xy3001), bh) -> False new_esEs13(xy4000, xy3000, app(app(app(ty_@3, ce), cf), cg)) -> new_esEs18(xy4000, xy3000, ce, cf, cg) new_esEs4(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs13(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_[], bhd)) -> new_esEs12(xy4000, xy3000, bhd) new_esEs23(xy4000, xy3000, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs18(xy4000, xy3000, eb, ec, ed) new_esEs25(xy4000, xy3000, app(app(ty_Either, bah), bba)) -> new_esEs22(xy4000, xy3000, bah, bba) new_esEs27(xy4002, xy3002, app(ty_Ratio, bce)) -> new_esEs6(xy4002, xy3002, bce) new_esEs13(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs25(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Char) -> new_esEs11(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(ty_Either, bfa), bdg)) -> new_esEs22(xy400, xy300, bfa, bdg) new_asAs(True, xy35) -> xy35 new_esEs26(xy4001, xy3001, ty_Ordering) -> new_esEs15(xy4001, xy3001) new_primEqInt(Pos(Succ(xy40000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xy30000))) -> False new_esEs13(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_@2, cc), cd)) -> new_esEs17(xy4000, xy3000, cc, cd) new_esEs26(xy4001, xy3001, app(ty_Maybe, bbb)) -> new_esEs14(xy4001, xy3001, bbb) new_esEs5(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Integer) -> new_esEs9(xy4002, xy3002) new_esEs23(xy4000, xy3000, app(app(ty_Either, ef), eg)) -> new_esEs22(xy4000, xy3000, ef, eg) new_primEqNat0(Succ(xy40000), Succ(xy30000)) -> new_primEqNat0(xy40000, xy30000) new_esEs22(Left(xy4000), Left(xy3000), ty_Ordering, bdg) -> new_esEs15(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(ty_@2, bab), bac)) -> new_esEs17(xy4000, xy3000, bab, bac) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs18(xy4000, xy3000, bff, bfg, bfh) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs23(xy4000, xy3000, app(ty_Maybe, df)) -> new_esEs14(xy4000, xy3000, df) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_@2, bea), beb), bdg) -> new_esEs17(xy4000, xy3000, bea, beb) new_esEs5(xy400, xy300, app(ty_Maybe, gc)) -> new_esEs14(xy400, xy300, gc) new_esEs22(Left(xy4000), Left(xy3000), app(ty_[], bef), bdg) -> new_esEs12(xy4000, xy3000, bef) new_primMulNat0(Zero, Zero) -> Zero new_esEs27(xy4002, xy3002, ty_Double) -> new_esEs16(xy4002, xy3002) new_esEs20(@0, @0) -> True new_esEs4(xy400, xy300, app(ty_[], bh)) -> new_esEs12(xy400, xy300, bh) new_esEs24(xy4001, xy3001, app(ty_Maybe, eh)) -> new_esEs14(xy4001, xy3001, eh) new_esEs13(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(ty_Ratio, bgf)) -> new_esEs6(xy4000, xy3000, bgf) new_esEs5(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs15(LT, EQ) -> False new_esEs15(EQ, LT) -> False new_esEs22(Left(xy4000), Left(xy3000), ty_Char, bdg) -> new_esEs11(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Bool) -> new_esEs19(xy4002, xy3002) new_primEqNat0(Succ(xy40000), Zero) -> False new_primEqNat0(Zero, Succ(xy30000)) -> False new_esEs27(xy4002, xy3002, app(app(app(ty_@3, bch), bda), bdb)) -> new_esEs18(xy4002, xy3002, bch, bda, bdb) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(app(ty_@2, bfd), bfe)) -> new_esEs17(xy4000, xy3000, bfd, bfe) new_esEs9(Integer(xy4000), Integer(xy3000)) -> new_primEqInt(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Int) -> new_esEs10(xy4002, xy3002) new_esEs13(xy4000, xy3000, app(ty_Ratio, cb)) -> new_esEs6(xy4000, xy3000, cb) new_esEs25(xy4000, xy3000, app(ty_Maybe, hh)) -> new_esEs14(xy4000, xy3000, hh) new_esEs4(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs4(xy400, xy300, app(app(app(ty_@3, he), hf), hg)) -> new_esEs18(xy400, xy300, he, hf, hg) new_esEs22(Left(xy4000), Left(xy3000), ty_Double, bdg) -> new_esEs16(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_@2, bgg), bgh)) -> new_esEs17(xy4000, xy3000, bgg, bgh) new_esEs19(False, False) -> True new_primEqInt(Neg(Succ(xy40000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xy30000))) -> False new_esEs27(xy4002, xy3002, app(ty_[], bdc)) -> new_esEs12(xy4002, xy3002, bdc) new_primEqInt(Pos(Succ(xy40000)), Pos(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs13(xy4000, xy3000, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Bool, bdg) -> new_esEs19(xy4000, xy3000) new_esEs24(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_sr(Pos(xy40010), Neg(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_sr(Neg(xy40010), Pos(xy30000)) -> Neg(new_primMulNat0(xy40010, xy30000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(app(ty_@3, bec), bed), bee), bdg) -> new_esEs18(xy4000, xy3000, bec, bed, bee) new_esEs14(Just(xy4000), Just(xy3000), ty_Ordering) -> new_esEs15(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Succ(xy3000000)) -> Succ(Succ(new_primPlusNat1(xy3600, xy3000000))) new_esEs27(xy4002, xy3002, app(app(ty_Either, bdd), bde)) -> new_esEs22(xy4002, xy3002, bdd, bde) new_esEs4(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs27(xy4002, xy3002, ty_Char) -> new_esEs11(xy4002, xy3002) new_primEqInt(Pos(Succ(xy40000)), Neg(xy3000)) -> False new_primEqInt(Neg(Succ(xy40000)), Pos(xy3000)) -> False new_esEs5(xy400, xy300, app(app(ty_@2, ge), gf)) -> new_esEs17(xy400, xy300, ge, gf) new_esEs25(xy4000, xy3000, app(ty_Ratio, baa)) -> new_esEs6(xy4000, xy3000, baa) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_[], bga)) -> new_esEs12(xy4000, xy3000, bga) new_esEs22(Left(xy4000), Left(xy3000), ty_Integer, bdg) -> new_esEs9(xy4000, xy3000) new_esEs4(xy400, xy300, ty_Int) -> new_esEs10(xy400, xy300) new_esEs4(xy400, xy300, ty_Char) -> new_esEs11(xy400, xy300) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_Int, bdg) -> new_esEs10(xy4000, xy3000) new_esEs14(Just(xy4000), Just(xy3000), ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs26(xy4001, xy3001, app(app(ty_Either, bcb), bcc)) -> new_esEs22(xy4001, xy3001, bcb, bcc) new_esEs4(xy400, xy300, ty_Ordering) -> new_esEs15(xy400, xy300) new_esEs15(EQ, EQ) -> True new_esEs14(Just(xy4000), Just(xy3000), app(ty_Maybe, bge)) -> new_esEs14(xy4000, xy3000, bge) new_esEs26(xy4001, xy3001, app(ty_Ratio, bbc)) -> new_esEs6(xy4001, xy3001, bbc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Float) -> new_esEs21(xy4000, xy3000) new_esEs15(GT, GT) -> True new_esEs5(xy400, xy300, app(ty_Ratio, gd)) -> new_esEs6(xy400, xy300, gd) new_esEs14(Just(xy4000), Just(xy3000), ty_Bool) -> new_esEs19(xy4000, xy3000) new_sr(Neg(xy40010), Neg(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs15(EQ, GT) -> False new_esEs15(GT, EQ) -> False new_esEs14(Just(xy4000), Just(xy3000), app(app(app(ty_@3, bha), bhb), bhc)) -> new_esEs18(xy4000, xy3000, bha, bhb, bhc) new_esEs25(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs11(Char(xy4000), Char(xy3000)) -> new_primEqNat0(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_@0) -> new_esEs20(xy4002, xy3002) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs24(xy4001, xy3001, app(app(ty_@2, fb), fc)) -> new_esEs17(xy4001, xy3001, fb, fc) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs5(xy400, xy300, app(app(ty_Either, hc), hd)) -> new_esEs22(xy400, xy300, hc, hd) new_esEs25(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs22(Left(xy4000), Right(xy3000), bfa, bdg) -> False new_esEs22(Right(xy4000), Left(xy3000), bfa, bdg) -> False new_primEqInt(Pos(Zero), Neg(Succ(xy30000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xy30000))) -> False new_esEs5(xy400, xy300, ty_Integer) -> new_esEs9(xy400, xy300) new_esEs16(Double(xy4000, xy4001), Double(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs22(Left(xy4000), Left(xy3000), app(app(ty_Either, beg), beh), bdg) -> new_esEs22(xy4000, xy3000, beg, beh) new_esEs22(Left(xy4000), Left(xy3000), ty_Float, bdg) -> new_esEs21(xy4000, xy3000) new_esEs5(xy400, xy300, ty_Float) -> new_esEs21(xy400, xy300) new_esEs8(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs24(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_primEqInt(Neg(Succ(xy40000)), Neg(Succ(xy30000))) -> new_primEqNat0(xy40000, xy30000) new_esEs24(xy4001, xy3001, app(app(app(ty_@3, fd), ff), fg)) -> new_esEs18(xy4001, xy3001, fd, ff, fg) new_esEs4(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs5(xy400, xy300, ty_Double) -> new_esEs16(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), ty_Double) -> new_esEs16(xy4000, xy3000) new_primPlusNat0(Succ(xy360), xy300000) -> Succ(Succ(new_primPlusNat1(xy360, xy300000))) new_esEs24(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs24(xy4001, xy3001, app(ty_Ratio, fa)) -> new_esEs6(xy4001, xy3001, fa) new_esEs5(xy400, xy300, ty_Bool) -> new_esEs19(xy400, xy300) new_esEs24(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs23(xy4000, xy3000, ty_Ordering) -> new_esEs15(xy4000, xy3000) new_esEs10(xy400, xy300) -> new_primEqInt(xy400, xy300) new_esEs5(xy400, xy300, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs18(xy400, xy300, gg, gh, ha) new_primPlusNat1(Zero, Zero) -> Zero new_primMulNat0(Succ(xy400100), Zero) -> Zero new_primMulNat0(Zero, Succ(xy300000)) -> Zero new_esEs26(xy4001, xy3001, ty_Double) -> new_esEs16(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_sr(Pos(xy40010), Pos(xy30000)) -> Pos(new_primMulNat0(xy40010, xy30000)) new_esEs23(xy4000, xy3000, app(ty_[], ee)) -> new_esEs12(xy4000, xy3000, ee) new_primPlusNat0(Zero, xy300000) -> Succ(xy300000) new_esEs24(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs6(:%(xy4000, xy4001), :%(xy3000, xy3001), bg) -> new_asAs(new_esEs7(xy4000, xy3000, bg), new_esEs8(xy4001, xy3001, bg)) new_esEs26(xy4001, xy3001, app(ty_[], bca)) -> new_esEs12(xy4001, xy3001, bca) new_esEs14(Just(xy4000), Just(xy3000), ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs23(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs15(LT, GT) -> False new_esEs15(GT, LT) -> False new_esEs26(xy4001, xy3001, ty_Bool) -> new_esEs19(xy4001, xy3001) new_esEs25(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs27(xy4002, xy3002, ty_Float) -> new_esEs21(xy4002, xy3002) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs26(xy4001, xy3001, app(app(app(ty_@3, bbf), bbg), bbh)) -> new_esEs18(xy4001, xy3001, bbf, bbg, bbh) new_esEs5(xy400, xy300, app(ty_[], hb)) -> new_esEs12(xy400, xy300, hb) new_esEs24(xy4001, xy3001, app(ty_[], fh)) -> new_esEs12(xy4001, xy3001, fh) new_primMulNat0(Succ(xy400100), Succ(xy300000)) -> new_primPlusNat0(new_primMulNat0(xy400100, Succ(xy300000)), xy300000) new_esEs8(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs22(Right(xy4000), Right(xy3000), bfa, app(ty_Maybe, bfb)) -> new_esEs14(xy4000, xy3000, bfb) new_esEs22(Right(xy4000), Right(xy3000), bfa, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs21(Float(xy4000, xy4001), Float(xy3000, xy3001)) -> new_esEs10(new_sr(xy4000, xy3001), new_sr(xy4001, xy3000)) new_esEs14(Nothing, Just(xy3000), bgd) -> False new_esEs14(Just(xy4000), Nothing, bgd) -> False new_esEs14(Just(xy4000), Just(xy3000), ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs22(Left(xy4000), Left(xy3000), ty_@0, bdg) -> new_esEs20(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_primPlusNat1(Succ(xy3600), Zero) -> Succ(xy3600) new_primPlusNat1(Zero, Succ(xy3000000)) -> Succ(xy3000000) new_esEs23(xy4000, xy3000, ty_@0) -> new_esEs20(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Int) -> new_esEs10(xy4001, xy3001) new_esEs25(xy4000, xy3000, app(ty_[], bag)) -> new_esEs12(xy4000, xy3000, bag) new_esEs27(xy4002, xy3002, app(app(ty_@2, bcf), bcg)) -> new_esEs17(xy4002, xy3002, bcf, bcg) new_esEs14(Nothing, Nothing, bgd) -> True new_esEs14(Just(xy4000), Just(xy3000), ty_Char) -> new_esEs11(xy4000, xy3000) new_esEs26(xy4001, xy3001, ty_Float) -> new_esEs21(xy4001, xy3001) new_esEs12([], [], bh) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Maybe, bdf), bdg) -> new_esEs14(xy4000, xy3000, bdf) new_esEs12(:(xy4000, xy4001), :(xy3000, xy3001), bh) -> new_asAs(new_esEs13(xy4000, xy3000, bh), new_esEs12(xy4001, xy3001, bh)) new_esEs18(@3(xy4000, xy4001, xy4002), @3(xy3000, xy3001, xy3002), he, hf, hg) -> new_asAs(new_esEs25(xy4000, xy3000, he), new_asAs(new_esEs26(xy4001, xy3001, hf), new_esEs27(xy4002, xy3002, hg))) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(xy400, xy300, app(ty_Maybe, bgd)) -> new_esEs14(xy400, xy300, bgd) new_esEs26(xy4001, xy3001, ty_Integer) -> new_esEs9(xy4001, xy3001) new_esEs23(xy4000, xy3000, app(ty_Ratio, dg)) -> new_esEs6(xy4000, xy3000, dg) new_esEs27(xy4002, xy3002, app(ty_Maybe, bcd)) -> new_esEs14(xy4002, xy3002, bcd) new_primEqNat0(Zero, Zero) -> True new_esEs17(@2(xy4000, xy4001), @2(xy3000, xy3001), dd, de) -> new_asAs(new_esEs23(xy4000, xy3000, dd), new_esEs24(xy4001, xy3001, de)) new_esEs27(xy4002, xy3002, ty_Ordering) -> new_esEs15(xy4002, xy3002) new_esEs26(xy4001, xy3001, app(app(ty_@2, bbd), bbe)) -> new_esEs17(xy4001, xy3001, bbd, bbe) new_esEs24(xy4001, xy3001, app(app(ty_Either, ga), gb)) -> new_esEs22(xy4001, xy3001, ga, gb) new_esEs24(xy4001, xy3001, ty_@0) -> new_esEs20(xy4001, xy3001) new_esEs13(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs13(xy4000, xy3000, app(app(ty_Either, db), dc)) -> new_esEs22(xy4000, xy3000, db, dc) new_asAs(False, xy35) -> False new_esEs25(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs25(xy4000, xy3000, app(app(app(ty_@3, bad), bae), baf)) -> new_esEs18(xy4000, xy3000, bad, bae, baf) new_esEs7(xy4000, xy3000, ty_Int) -> new_esEs10(xy4000, xy3000) new_esEs5(xy400, xy300, ty_@0) -> new_esEs20(xy400, xy300) new_esEs14(Just(xy4000), Just(xy3000), app(app(ty_Either, bhe), bhf)) -> new_esEs22(xy4000, xy3000, bhe, bhf) new_esEs13(xy4000, xy3000, app(ty_[], da)) -> new_esEs12(xy4000, xy3000, da) new_esEs25(xy4000, xy3000, ty_Double) -> new_esEs16(xy4000, xy3000) new_esEs4(xy400, xy300, app(ty_Ratio, bg)) -> new_esEs6(xy400, xy300, bg) new_esEs7(xy4000, xy3000, ty_Integer) -> new_esEs9(xy4000, xy3000) new_esEs19(True, True) -> True new_esEs22(Left(xy4000), Left(xy3000), app(ty_Ratio, bdh), bdg) -> new_esEs6(xy4000, xy3000, bdh) new_esEs25(xy4000, xy3000, ty_Bool) -> new_esEs19(xy4000, xy3000) new_esEs13(xy4000, xy3000, ty_Char) -> new_esEs11(xy4000, xy3000) The set Q consists of the following terms: new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(Left(x0), Left(x1), ty_Int, x2) new_esEs22(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Char) new_esEs27(x0, x1, ty_@0) new_esEs14(Just(x0), Just(x1), ty_Double) new_esEs13(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Int) new_esEs5(x0, x1, app(ty_[], x2)) new_esEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Int) new_esEs22(Left(x0), Left(x1), ty_Char, x2) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs13(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs25(x0, x1, ty_Char) new_esEs8(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Bool) new_primPlusNat1(Zero, Zero) new_primPlusNat0(Zero, x0) new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Char) new_esEs15(EQ, EQ) new_asAs(True, x0) new_esEs14(Nothing, Nothing, x0) new_esEs4(x0, x1, ty_Integer) new_esEs19(False, False) new_esEs13(x0, x1, app(ty_[], x2)) new_primMulNat0(Succ(x0), Zero) new_esEs20(@0, @0) new_esEs25(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs22(Left(x0), Left(x1), ty_Ordering, x2) new_esEs22(Left(x0), Left(x1), ty_Float, x2) new_esEs9(Integer(x0), Integer(x1)) new_esEs5(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_esEs26(x0, x1, ty_@0) new_esEs24(x0, x1, ty_Bool) new_esEs27(x0, x1, app(ty_Maybe, x2)) new_esEs4(x0, x1, ty_@0) new_esEs22(Right(x0), Right(x1), x2, ty_Float) new_primPlusNat0(Succ(x0), x1) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Integer) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs5(x0, x1, ty_Integer) new_esEs15(EQ, GT) new_esEs15(GT, EQ) new_esEs14(Just(x0), Nothing, x1) new_esEs13(x0, x1, ty_Ordering) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs10(x0, x1) new_esEs15(LT, LT) new_esEs26(x0, x1, ty_Ordering) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12([], :(x0, x1), x2) new_esEs27(x0, x1, ty_Char) new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs22(Right(x0), Right(x1), x2, ty_Bool) new_esEs27(x0, x1, ty_Int) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_Double, x2) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs22(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs25(x0, x1, ty_Double) new_esEs11(Char(x0), Char(x1)) new_esEs24(x0, x1, ty_Double) new_esEs12([], [], x0) new_esEs22(Right(x0), Right(x1), x2, ty_@0) new_esEs24(x0, x1, ty_Char) new_esEs24(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Bool) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs5(x0, x1, ty_Char) new_esEs14(Just(x0), Just(x1), ty_Ordering) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primMulNat0(Succ(x0), Succ(x1)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs27(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Bool) new_esEs5(x0, x1, ty_Double) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs24(x0, x1, ty_Int) new_esEs19(True, True) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs23(x0, x1, ty_Ordering) new_primEqNat0(Zero, Succ(x0)) new_esEs22(Right(x0), Right(x1), x2, ty_Char) new_esEs22(Right(x0), Right(x1), x2, ty_Double) new_esEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs22(Left(x0), Left(x1), ty_Bool, x2) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs14(Just(x0), Just(x1), ty_Integer) new_esEs22(Left(x0), Left(x1), ty_Integer, x2) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs5(x0, x1, ty_Ordering) new_esEs27(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, ty_Integer) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_Ordering) new_esEs5(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs22(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs14(Just(x0), Just(x1), ty_@0) new_esEs27(x0, x1, ty_Double) new_primMulNat0(Zero, Succ(x0)) new_esEs15(LT, GT) new_esEs15(GT, LT) new_esEs22(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_asAs(False, x0) new_esEs23(x0, x1, ty_Integer) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, ty_Int) new_esEs4(x0, x1, ty_Float) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs26(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs4(x0, x1, ty_Char) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs13(x0, x1, app(ty_Ratio, x2)) new_esEs15(GT, GT) new_esEs27(x0, x1, ty_Ordering) new_esEs4(x0, x1, ty_Double) new_esEs19(False, True) new_esEs19(True, False) new_esEs13(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(LT, EQ) new_esEs15(EQ, LT) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Left(x1), ty_@0, x2) new_esEs5(x0, x1, ty_Float) new_esEs25(x0, x1, ty_@0) new_esEs16(Double(x0, x1), Double(x2, x3)) new_esEs4(x0, x1, ty_Int) new_esEs14(Just(x0), Just(x1), ty_Bool) new_esEs26(x0, x1, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs27(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, ty_Integer) new_esEs13(x0, x1, ty_@0) new_primPlusNat1(Zero, Succ(x0)) new_esEs7(x0, x1, ty_Integer) new_esEs27(x0, x1, app(app(ty_@2, x2), x3)) new_esEs27(x0, x1, ty_Float) new_esEs13(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs22(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs22(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs23(x0, x1, ty_@0) new_esEs12(:(x0, x1), [], x2) new_esEs22(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs13(x0, x1, ty_Int) new_esEs27(x0, x1, app(app(ty_Either, x2), x3)) new_esEs14(Just(x0), Just(x1), ty_Char) new_esEs26(x0, x1, ty_Double) new_esEs23(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), ty_Int) new_esEs13(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Integer) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs5(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Float) new_primPlusNat1(Succ(x0), Succ(x1)) new_esEs23(x0, x1, ty_Double) new_esEs22(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs22(Right(x0), Right(x1), x2, ty_Ordering) new_esEs14(Just(x0), Just(x1), app(ty_Ratio, x2)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs12(:(x0, x1), :(x2, x3), x4) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_sr(Pos(x0), Pos(x1)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs21(Float(x0, x1), Float(x2, x3)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(Left(x0), Right(x1), x2, x3) new_esEs22(Right(x0), Left(x1), x2, x3) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs13(x0, x1, ty_Bool) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs13(x0, x1, app(app(ty_@2, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs14(Nothing, Just(x0), x1) new_esEs14(Just(x0), Just(x1), app(ty_[], x2)) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, ty_Int) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, ty_Bool) new_esEs14(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs22(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_primEqNat0(Succ(x0), Zero) new_primPlusNat1(Succ(x0), Zero) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs5(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Ordering) new_esEs14(Just(x0), Just(x1), ty_Float) 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_deleteBy(Right(xy400), :(Left(xy300), xy31), bc, bd) -> new_deleteBy(Right(xy400), xy31, bc, bd) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 *new_deleteBy(Right(xy400), :(Right(xy300), xy31), bc, bd) -> new_deleteBy00(xy31, xy300, xy400, new_esEs5(xy400, xy300, bd), bc, bd) The graph contains the following edges 2 > 1, 2 > 2, 1 > 3, 3 >= 5, 4 >= 6 *new_deleteBy00(xy19, xy20, xy21, False, be, bf) -> new_deleteBy(Right(xy21), xy19, be, bf) The graph contains the following edges 1 >= 2, 5 >= 3, 6 >= 4 ---------------------------------------- (26) YES ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(xy3600), Succ(xy3000000)) -> new_primPlusNat(xy3600, xy3000000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primPlusNat(Succ(xy3600), Succ(xy3000000)) -> new_primPlusNat(xy3600, xy3000000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (29) YES ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(xy40000), Succ(xy30000)) -> new_primEqNat(xy40000, xy30000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primEqNat(Succ(xy40000), Succ(xy30000)) -> new_primEqNat(xy40000, xy30000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (32) YES