/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 8 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] (21) 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; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] _ = True; isPrefixOf _ [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (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; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] xw = True; isPrefixOf xx [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (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; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] xw = True; isPrefixOf xx [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.isPrefixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.isPrefixOf xy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="List.isPrefixOf xy3 xy4",fontsize=16,color="burlywood",shape="triangle"];629[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 629[label="",style="solid", color="burlywood", weight=9]; 629 -> 5[label="",style="solid", color="burlywood", weight=3]; 630[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 630[label="",style="solid", color="burlywood", weight=9]; 630 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="List.isPrefixOf (xy30 : xy31) xy4",fontsize=16,color="burlywood",shape="box"];631[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 631[label="",style="solid", color="burlywood", weight=9]; 631 -> 7[label="",style="solid", color="burlywood", weight=3]; 632[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 632[label="",style="solid", color="burlywood", weight=9]; 632 -> 8[label="",style="solid", color="burlywood", weight=3]; 6[label="List.isPrefixOf [] xy4",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 7[label="List.isPrefixOf (xy30 : xy31) (xy40 : xy41)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 8[label="List.isPrefixOf (xy30 : xy31) []",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 9[label="True",fontsize=16,color="green",shape="box"];10 -> 26[label="",style="dashed", color="red", weight=0]; 10[label="xy30 == xy40 && List.isPrefixOf xy31 xy41",fontsize=16,color="magenta"];10 -> 27[label="",style="dashed", color="magenta", weight=3]; 10 -> 28[label="",style="dashed", color="magenta", weight=3]; 11[label="False",fontsize=16,color="green",shape="box"];27 -> 4[label="",style="dashed", color="red", weight=0]; 27[label="List.isPrefixOf xy31 xy41",fontsize=16,color="magenta"];27 -> 39[label="",style="dashed", color="magenta", weight=3]; 27 -> 40[label="",style="dashed", color="magenta", weight=3]; 28[label="xy30 == xy40",fontsize=16,color="burlywood",shape="triangle"];633[label="xy30/Left xy300",fontsize=10,color="white",style="solid",shape="box"];28 -> 633[label="",style="solid", color="burlywood", weight=9]; 633 -> 41[label="",style="solid", color="burlywood", weight=3]; 634[label="xy30/Right xy300",fontsize=10,color="white",style="solid",shape="box"];28 -> 634[label="",style="solid", color="burlywood", weight=9]; 634 -> 42[label="",style="solid", color="burlywood", weight=3]; 26[label="xy9 && xy10",fontsize=16,color="burlywood",shape="triangle"];635[label="xy9/False",fontsize=10,color="white",style="solid",shape="box"];26 -> 635[label="",style="solid", color="burlywood", weight=9]; 635 -> 43[label="",style="solid", color="burlywood", weight=3]; 636[label="xy9/True",fontsize=10,color="white",style="solid",shape="box"];26 -> 636[label="",style="solid", color="burlywood", weight=9]; 636 -> 44[label="",style="solid", color="burlywood", weight=3]; 39[label="xy31",fontsize=16,color="green",shape="box"];40[label="xy41",fontsize=16,color="green",shape="box"];41[label="Left xy300 == xy40",fontsize=16,color="burlywood",shape="box"];637[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];41 -> 637[label="",style="solid", color="burlywood", weight=9]; 637 -> 45[label="",style="solid", color="burlywood", weight=3]; 638[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];41 -> 638[label="",style="solid", color="burlywood", weight=9]; 638 -> 46[label="",style="solid", color="burlywood", weight=3]; 42[label="Right xy300 == xy40",fontsize=16,color="burlywood",shape="box"];639[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];42 -> 639[label="",style="solid", color="burlywood", weight=9]; 639 -> 47[label="",style="solid", color="burlywood", weight=3]; 640[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];42 -> 640[label="",style="solid", color="burlywood", weight=9]; 640 -> 48[label="",style="solid", color="burlywood", weight=3]; 43[label="False && xy10",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3]; 44[label="True && xy10",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3]; 45[label="Left xy300 == Left xy400",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3]; 46[label="Left xy300 == Right xy400",fontsize=16,color="black",shape="box"];46 -> 52[label="",style="solid", color="black", weight=3]; 47[label="Right xy300 == Left xy400",fontsize=16,color="black",shape="box"];47 -> 53[label="",style="solid", color="black", weight=3]; 48[label="Right xy300 == Right xy400",fontsize=16,color="black",shape="box"];48 -> 54[label="",style="solid", color="black", weight=3]; 49[label="False",fontsize=16,color="green",shape="box"];50[label="xy10",fontsize=16,color="green",shape="box"];51[label="xy300 == xy400",fontsize=16,color="blue",shape="box"];641[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 641[label="",style="solid", color="blue", weight=9]; 641 -> 55[label="",style="solid", color="blue", weight=3]; 642[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 642[label="",style="solid", color="blue", weight=9]; 642 -> 56[label="",style="solid", color="blue", weight=3]; 643[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 643[label="",style="solid", color="blue", weight=9]; 643 -> 57[label="",style="solid", color="blue", weight=3]; 644[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 644[label="",style="solid", color="blue", weight=9]; 644 -> 58[label="",style="solid", color="blue", weight=3]; 645[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 645[label="",style="solid", color="blue", weight=9]; 645 -> 59[label="",style="solid", color="blue", weight=3]; 646[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 646[label="",style="solid", color="blue", weight=9]; 646 -> 60[label="",style="solid", color="blue", weight=3]; 647[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 647[label="",style="solid", color="blue", weight=9]; 647 -> 61[label="",style="solid", color="blue", weight=3]; 648[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 648[label="",style="solid", color="blue", weight=9]; 648 -> 62[label="",style="solid", color="blue", weight=3]; 649[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 649[label="",style="solid", color="blue", weight=9]; 649 -> 63[label="",style="solid", color="blue", weight=3]; 650[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 650[label="",style="solid", color="blue", weight=9]; 650 -> 64[label="",style="solid", color="blue", weight=3]; 651[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 651[label="",style="solid", color="blue", weight=9]; 651 -> 65[label="",style="solid", color="blue", weight=3]; 652[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 652[label="",style="solid", color="blue", weight=9]; 652 -> 66[label="",style="solid", color="blue", weight=3]; 653[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 653[label="",style="solid", color="blue", weight=9]; 653 -> 67[label="",style="solid", color="blue", weight=3]; 654[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 654[label="",style="solid", color="blue", weight=9]; 654 -> 68[label="",style="solid", color="blue", weight=3]; 52[label="False",fontsize=16,color="green",shape="box"];53[label="False",fontsize=16,color="green",shape="box"];54[label="xy300 == xy400",fontsize=16,color="blue",shape="box"];655[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 655[label="",style="solid", color="blue", weight=9]; 655 -> 69[label="",style="solid", color="blue", weight=3]; 656[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 656[label="",style="solid", color="blue", weight=9]; 656 -> 70[label="",style="solid", color="blue", weight=3]; 657[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 657[label="",style="solid", color="blue", weight=9]; 657 -> 71[label="",style="solid", color="blue", weight=3]; 658[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 658[label="",style="solid", color="blue", weight=9]; 658 -> 72[label="",style="solid", color="blue", weight=3]; 659[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 659[label="",style="solid", color="blue", weight=9]; 659 -> 73[label="",style="solid", color="blue", weight=3]; 660[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 660[label="",style="solid", color="blue", weight=9]; 660 -> 74[label="",style="solid", color="blue", weight=3]; 661[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 661[label="",style="solid", color="blue", weight=9]; 661 -> 75[label="",style="solid", color="blue", weight=3]; 662[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 662[label="",style="solid", color="blue", weight=9]; 662 -> 76[label="",style="solid", color="blue", weight=3]; 663[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 663[label="",style="solid", color="blue", weight=9]; 663 -> 77[label="",style="solid", color="blue", weight=3]; 664[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 664[label="",style="solid", color="blue", weight=9]; 664 -> 78[label="",style="solid", color="blue", weight=3]; 665[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 665[label="",style="solid", color="blue", weight=9]; 665 -> 79[label="",style="solid", color="blue", weight=3]; 666[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 666[label="",style="solid", color="blue", weight=9]; 666 -> 80[label="",style="solid", color="blue", weight=3]; 667[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 667[label="",style="solid", color="blue", weight=9]; 667 -> 81[label="",style="solid", color="blue", weight=3]; 668[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];54 -> 668[label="",style="solid", color="blue", weight=9]; 668 -> 82[label="",style="solid", color="blue", weight=3]; 55[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];669[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];55 -> 669[label="",style="solid", color="burlywood", weight=9]; 669 -> 83[label="",style="solid", color="burlywood", weight=3]; 670[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];55 -> 670[label="",style="solid", color="burlywood", weight=9]; 670 -> 84[label="",style="solid", color="burlywood", weight=3]; 671[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];55 -> 671[label="",style="solid", color="burlywood", weight=9]; 671 -> 85[label="",style="solid", color="burlywood", weight=3]; 56[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];672[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];56 -> 672[label="",style="solid", color="burlywood", weight=9]; 672 -> 86[label="",style="solid", color="burlywood", weight=3]; 673[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];56 -> 673[label="",style="solid", color="burlywood", weight=9]; 673 -> 87[label="",style="solid", color="burlywood", weight=3]; 57[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];57 -> 88[label="",style="solid", color="black", weight=3]; 58[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];674[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];58 -> 674[label="",style="solid", color="burlywood", weight=9]; 674 -> 89[label="",style="solid", color="burlywood", weight=3]; 59[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];675[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];59 -> 675[label="",style="solid", color="burlywood", weight=9]; 675 -> 90[label="",style="solid", color="burlywood", weight=3]; 676[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];59 -> 676[label="",style="solid", color="burlywood", weight=9]; 676 -> 91[label="",style="solid", color="burlywood", weight=3]; 60[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];677[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];60 -> 677[label="",style="solid", color="burlywood", weight=9]; 677 -> 92[label="",style="solid", color="burlywood", weight=3]; 61[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];61 -> 93[label="",style="solid", color="black", weight=3]; 62[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];678[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];62 -> 678[label="",style="solid", color="burlywood", weight=9]; 678 -> 94[label="",style="solid", color="burlywood", weight=3]; 63[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];679[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];63 -> 679[label="",style="solid", color="burlywood", weight=9]; 679 -> 95[label="",style="solid", color="burlywood", weight=3]; 64[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];64 -> 96[label="",style="solid", color="black", weight=3]; 65[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];680[label="xy300/Nothing",fontsize=10,color="white",style="solid",shape="box"];65 -> 680[label="",style="solid", color="burlywood", weight=9]; 680 -> 97[label="",style="solid", color="burlywood", weight=3]; 681[label="xy300/Just xy3000",fontsize=10,color="white",style="solid",shape="box"];65 -> 681[label="",style="solid", color="burlywood", weight=9]; 681 -> 98[label="",style="solid", color="burlywood", weight=3]; 66[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];66 -> 99[label="",style="solid", color="black", weight=3]; 67 -> 28[label="",style="dashed", color="red", weight=0]; 67[label="xy300 == xy400",fontsize=16,color="magenta"];67 -> 100[label="",style="dashed", color="magenta", weight=3]; 67 -> 101[label="",style="dashed", color="magenta", weight=3]; 68[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];682[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];68 -> 682[label="",style="solid", color="burlywood", weight=9]; 682 -> 102[label="",style="solid", color="burlywood", weight=3]; 69 -> 55[label="",style="dashed", color="red", weight=0]; 69[label="xy300 == xy400",fontsize=16,color="magenta"];69 -> 103[label="",style="dashed", color="magenta", weight=3]; 69 -> 104[label="",style="dashed", color="magenta", weight=3]; 70 -> 56[label="",style="dashed", color="red", weight=0]; 70[label="xy300 == xy400",fontsize=16,color="magenta"];70 -> 105[label="",style="dashed", color="magenta", weight=3]; 70 -> 106[label="",style="dashed", color="magenta", weight=3]; 71 -> 57[label="",style="dashed", color="red", weight=0]; 71[label="xy300 == xy400",fontsize=16,color="magenta"];71 -> 107[label="",style="dashed", color="magenta", weight=3]; 71 -> 108[label="",style="dashed", color="magenta", weight=3]; 72 -> 58[label="",style="dashed", color="red", weight=0]; 72[label="xy300 == xy400",fontsize=16,color="magenta"];72 -> 109[label="",style="dashed", color="magenta", weight=3]; 72 -> 110[label="",style="dashed", color="magenta", weight=3]; 73 -> 59[label="",style="dashed", color="red", weight=0]; 73[label="xy300 == xy400",fontsize=16,color="magenta"];73 -> 111[label="",style="dashed", color="magenta", weight=3]; 73 -> 112[label="",style="dashed", color="magenta", weight=3]; 74 -> 60[label="",style="dashed", color="red", weight=0]; 74[label="xy300 == xy400",fontsize=16,color="magenta"];74 -> 113[label="",style="dashed", color="magenta", weight=3]; 74 -> 114[label="",style="dashed", color="magenta", weight=3]; 75 -> 61[label="",style="dashed", color="red", weight=0]; 75[label="xy300 == xy400",fontsize=16,color="magenta"];75 -> 115[label="",style="dashed", color="magenta", weight=3]; 75 -> 116[label="",style="dashed", color="magenta", weight=3]; 76 -> 62[label="",style="dashed", color="red", weight=0]; 76[label="xy300 == xy400",fontsize=16,color="magenta"];76 -> 117[label="",style="dashed", color="magenta", weight=3]; 76 -> 118[label="",style="dashed", color="magenta", weight=3]; 77 -> 63[label="",style="dashed", color="red", weight=0]; 77[label="xy300 == xy400",fontsize=16,color="magenta"];77 -> 119[label="",style="dashed", color="magenta", weight=3]; 77 -> 120[label="",style="dashed", color="magenta", weight=3]; 78 -> 64[label="",style="dashed", color="red", weight=0]; 78[label="xy300 == xy400",fontsize=16,color="magenta"];78 -> 121[label="",style="dashed", color="magenta", weight=3]; 78 -> 122[label="",style="dashed", color="magenta", weight=3]; 79 -> 65[label="",style="dashed", color="red", weight=0]; 79[label="xy300 == xy400",fontsize=16,color="magenta"];79 -> 123[label="",style="dashed", color="magenta", weight=3]; 79 -> 124[label="",style="dashed", color="magenta", weight=3]; 80 -> 66[label="",style="dashed", color="red", weight=0]; 80[label="xy300 == xy400",fontsize=16,color="magenta"];80 -> 125[label="",style="dashed", color="magenta", weight=3]; 80 -> 126[label="",style="dashed", color="magenta", weight=3]; 81 -> 28[label="",style="dashed", color="red", weight=0]; 81[label="xy300 == xy400",fontsize=16,color="magenta"];81 -> 127[label="",style="dashed", color="magenta", weight=3]; 81 -> 128[label="",style="dashed", color="magenta", weight=3]; 82 -> 68[label="",style="dashed", color="red", weight=0]; 82[label="xy300 == xy400",fontsize=16,color="magenta"];82 -> 129[label="",style="dashed", color="magenta", weight=3]; 82 -> 130[label="",style="dashed", color="magenta", weight=3]; 83[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];683[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];83 -> 683[label="",style="solid", color="burlywood", weight=9]; 683 -> 131[label="",style="solid", color="burlywood", weight=3]; 684[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];83 -> 684[label="",style="solid", color="burlywood", weight=9]; 684 -> 132[label="",style="solid", color="burlywood", weight=3]; 685[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];83 -> 685[label="",style="solid", color="burlywood", weight=9]; 685 -> 133[label="",style="solid", color="burlywood", weight=3]; 84[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];686[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];84 -> 686[label="",style="solid", color="burlywood", weight=9]; 686 -> 134[label="",style="solid", color="burlywood", weight=3]; 687[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];84 -> 687[label="",style="solid", color="burlywood", weight=9]; 687 -> 135[label="",style="solid", color="burlywood", weight=3]; 688[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];84 -> 688[label="",style="solid", color="burlywood", weight=9]; 688 -> 136[label="",style="solid", color="burlywood", weight=3]; 85[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];689[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];85 -> 689[label="",style="solid", color="burlywood", weight=9]; 689 -> 137[label="",style="solid", color="burlywood", weight=3]; 690[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];85 -> 690[label="",style="solid", color="burlywood", weight=9]; 690 -> 138[label="",style="solid", color="burlywood", weight=3]; 691[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];85 -> 691[label="",style="solid", color="burlywood", weight=9]; 691 -> 139[label="",style="solid", color="burlywood", weight=3]; 86[label="False == xy400",fontsize=16,color="burlywood",shape="box"];692[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];86 -> 692[label="",style="solid", color="burlywood", weight=9]; 692 -> 140[label="",style="solid", color="burlywood", weight=3]; 693[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];86 -> 693[label="",style="solid", color="burlywood", weight=9]; 693 -> 141[label="",style="solid", color="burlywood", weight=3]; 87[label="True == xy400",fontsize=16,color="burlywood",shape="box"];694[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];87 -> 694[label="",style="solid", color="burlywood", weight=9]; 694 -> 142[label="",style="solid", color="burlywood", weight=3]; 695[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];87 -> 695[label="",style="solid", color="burlywood", weight=9]; 695 -> 143[label="",style="solid", color="burlywood", weight=3]; 88[label="primEqDouble xy300 xy400",fontsize=16,color="burlywood",shape="box"];696[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];88 -> 696[label="",style="solid", color="burlywood", weight=9]; 696 -> 144[label="",style="solid", color="burlywood", weight=3]; 89[label="(xy3000,xy3001) == xy400",fontsize=16,color="burlywood",shape="box"];697[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];89 -> 697[label="",style="solid", color="burlywood", weight=9]; 697 -> 145[label="",style="solid", color="burlywood", weight=3]; 90[label="xy3000 : xy3001 == xy400",fontsize=16,color="burlywood",shape="box"];698[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];90 -> 698[label="",style="solid", color="burlywood", weight=9]; 698 -> 146[label="",style="solid", color="burlywood", weight=3]; 699[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];90 -> 699[label="",style="solid", color="burlywood", weight=9]; 699 -> 147[label="",style="solid", color="burlywood", weight=3]; 91[label="[] == xy400",fontsize=16,color="burlywood",shape="box"];700[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];91 -> 700[label="",style="solid", color="burlywood", weight=9]; 700 -> 148[label="",style="solid", color="burlywood", weight=3]; 701[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];91 -> 701[label="",style="solid", color="burlywood", weight=9]; 701 -> 149[label="",style="solid", color="burlywood", weight=3]; 92[label="() == xy400",fontsize=16,color="burlywood",shape="box"];702[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];92 -> 702[label="",style="solid", color="burlywood", weight=9]; 702 -> 150[label="",style="solid", color="burlywood", weight=3]; 93[label="primEqInt xy300 xy400",fontsize=16,color="burlywood",shape="triangle"];703[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];93 -> 703[label="",style="solid", color="burlywood", weight=9]; 703 -> 151[label="",style="solid", color="burlywood", weight=3]; 704[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];93 -> 704[label="",style="solid", color="burlywood", weight=9]; 704 -> 152[label="",style="solid", color="burlywood", weight=3]; 94[label="Integer xy3000 == xy400",fontsize=16,color="burlywood",shape="box"];705[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];94 -> 705[label="",style="solid", color="burlywood", weight=9]; 705 -> 153[label="",style="solid", color="burlywood", weight=3]; 95[label="(xy3000,xy3001,xy3002) == xy400",fontsize=16,color="burlywood",shape="box"];706[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];95 -> 706[label="",style="solid", color="burlywood", weight=9]; 706 -> 154[label="",style="solid", color="burlywood", weight=3]; 96[label="primEqFloat xy300 xy400",fontsize=16,color="burlywood",shape="box"];707[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];96 -> 707[label="",style="solid", color="burlywood", weight=9]; 707 -> 155[label="",style="solid", color="burlywood", weight=3]; 97[label="Nothing == xy400",fontsize=16,color="burlywood",shape="box"];708[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];97 -> 708[label="",style="solid", color="burlywood", weight=9]; 708 -> 156[label="",style="solid", color="burlywood", weight=3]; 709[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];97 -> 709[label="",style="solid", color="burlywood", weight=9]; 709 -> 157[label="",style="solid", color="burlywood", weight=3]; 98[label="Just xy3000 == xy400",fontsize=16,color="burlywood",shape="box"];710[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];98 -> 710[label="",style="solid", color="burlywood", weight=9]; 710 -> 158[label="",style="solid", color="burlywood", weight=3]; 711[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];98 -> 711[label="",style="solid", color="burlywood", weight=9]; 711 -> 159[label="",style="solid", color="burlywood", weight=3]; 99[label="primEqChar xy300 xy400",fontsize=16,color="burlywood",shape="box"];712[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];99 -> 712[label="",style="solid", color="burlywood", weight=9]; 712 -> 160[label="",style="solid", color="burlywood", weight=3]; 100[label="xy300",fontsize=16,color="green",shape="box"];101[label="xy400",fontsize=16,color="green",shape="box"];102[label="xy3000 :% xy3001 == xy400",fontsize=16,color="burlywood",shape="box"];713[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];102 -> 713[label="",style="solid", color="burlywood", weight=9]; 713 -> 161[label="",style="solid", color="burlywood", weight=3]; 103[label="xy300",fontsize=16,color="green",shape="box"];104[label="xy400",fontsize=16,color="green",shape="box"];105[label="xy300",fontsize=16,color="green",shape="box"];106[label="xy400",fontsize=16,color="green",shape="box"];107[label="xy300",fontsize=16,color="green",shape="box"];108[label="xy400",fontsize=16,color="green",shape="box"];109[label="xy300",fontsize=16,color="green",shape="box"];110[label="xy400",fontsize=16,color="green",shape="box"];111[label="xy300",fontsize=16,color="green",shape="box"];112[label="xy400",fontsize=16,color="green",shape="box"];113[label="xy300",fontsize=16,color="green",shape="box"];114[label="xy400",fontsize=16,color="green",shape="box"];115[label="xy300",fontsize=16,color="green",shape="box"];116[label="xy400",fontsize=16,color="green",shape="box"];117[label="xy300",fontsize=16,color="green",shape="box"];118[label="xy400",fontsize=16,color="green",shape="box"];119[label="xy300",fontsize=16,color="green",shape="box"];120[label="xy400",fontsize=16,color="green",shape="box"];121[label="xy300",fontsize=16,color="green",shape="box"];122[label="xy400",fontsize=16,color="green",shape="box"];123[label="xy300",fontsize=16,color="green",shape="box"];124[label="xy400",fontsize=16,color="green",shape="box"];125[label="xy300",fontsize=16,color="green",shape="box"];126[label="xy400",fontsize=16,color="green",shape="box"];127[label="xy300",fontsize=16,color="green",shape="box"];128[label="xy400",fontsize=16,color="green",shape="box"];129[label="xy300",fontsize=16,color="green",shape="box"];130[label="xy400",fontsize=16,color="green",shape="box"];131[label="LT == LT",fontsize=16,color="black",shape="box"];131 -> 162[label="",style="solid", color="black", weight=3]; 132[label="LT == EQ",fontsize=16,color="black",shape="box"];132 -> 163[label="",style="solid", color="black", weight=3]; 133[label="LT == GT",fontsize=16,color="black",shape="box"];133 -> 164[label="",style="solid", color="black", weight=3]; 134[label="EQ == LT",fontsize=16,color="black",shape="box"];134 -> 165[label="",style="solid", color="black", weight=3]; 135[label="EQ == EQ",fontsize=16,color="black",shape="box"];135 -> 166[label="",style="solid", color="black", weight=3]; 136[label="EQ == GT",fontsize=16,color="black",shape="box"];136 -> 167[label="",style="solid", color="black", weight=3]; 137[label="GT == LT",fontsize=16,color="black",shape="box"];137 -> 168[label="",style="solid", color="black", weight=3]; 138[label="GT == EQ",fontsize=16,color="black",shape="box"];138 -> 169[label="",style="solid", color="black", weight=3]; 139[label="GT == GT",fontsize=16,color="black",shape="box"];139 -> 170[label="",style="solid", color="black", weight=3]; 140[label="False == False",fontsize=16,color="black",shape="box"];140 -> 171[label="",style="solid", color="black", weight=3]; 141[label="False == True",fontsize=16,color="black",shape="box"];141 -> 172[label="",style="solid", color="black", weight=3]; 142[label="True == False",fontsize=16,color="black",shape="box"];142 -> 173[label="",style="solid", color="black", weight=3]; 143[label="True == True",fontsize=16,color="black",shape="box"];143 -> 174[label="",style="solid", color="black", weight=3]; 144[label="primEqDouble (Double xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];714[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];144 -> 714[label="",style="solid", color="burlywood", weight=9]; 714 -> 175[label="",style="solid", color="burlywood", weight=3]; 145[label="(xy3000,xy3001) == (xy4000,xy4001)",fontsize=16,color="black",shape="box"];145 -> 176[label="",style="solid", color="black", weight=3]; 146[label="xy3000 : xy3001 == xy4000 : xy4001",fontsize=16,color="black",shape="box"];146 -> 177[label="",style="solid", color="black", weight=3]; 147[label="xy3000 : xy3001 == []",fontsize=16,color="black",shape="box"];147 -> 178[label="",style="solid", color="black", weight=3]; 148[label="[] == xy4000 : xy4001",fontsize=16,color="black",shape="box"];148 -> 179[label="",style="solid", color="black", weight=3]; 149[label="[] == []",fontsize=16,color="black",shape="box"];149 -> 180[label="",style="solid", color="black", weight=3]; 150[label="() == ()",fontsize=16,color="black",shape="box"];150 -> 181[label="",style="solid", color="black", weight=3]; 151[label="primEqInt (Pos xy3000) xy400",fontsize=16,color="burlywood",shape="box"];715[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];151 -> 715[label="",style="solid", color="burlywood", weight=9]; 715 -> 182[label="",style="solid", color="burlywood", weight=3]; 716[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];151 -> 716[label="",style="solid", color="burlywood", weight=9]; 716 -> 183[label="",style="solid", color="burlywood", weight=3]; 152[label="primEqInt (Neg xy3000) xy400",fontsize=16,color="burlywood",shape="box"];717[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];152 -> 717[label="",style="solid", color="burlywood", weight=9]; 717 -> 184[label="",style="solid", color="burlywood", weight=3]; 718[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];152 -> 718[label="",style="solid", color="burlywood", weight=9]; 718 -> 185[label="",style="solid", color="burlywood", weight=3]; 153[label="Integer xy3000 == Integer xy4000",fontsize=16,color="black",shape="box"];153 -> 186[label="",style="solid", color="black", weight=3]; 154[label="(xy3000,xy3001,xy3002) == (xy4000,xy4001,xy4002)",fontsize=16,color="black",shape="box"];154 -> 187[label="",style="solid", color="black", weight=3]; 155[label="primEqFloat (Float xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];719[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];155 -> 719[label="",style="solid", color="burlywood", weight=9]; 719 -> 188[label="",style="solid", color="burlywood", weight=3]; 156[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];156 -> 189[label="",style="solid", color="black", weight=3]; 157[label="Nothing == Just xy4000",fontsize=16,color="black",shape="box"];157 -> 190[label="",style="solid", color="black", weight=3]; 158[label="Just xy3000 == Nothing",fontsize=16,color="black",shape="box"];158 -> 191[label="",style="solid", color="black", weight=3]; 159[label="Just xy3000 == Just xy4000",fontsize=16,color="black",shape="box"];159 -> 192[label="",style="solid", color="black", weight=3]; 160[label="primEqChar (Char xy3000) xy400",fontsize=16,color="burlywood",shape="box"];720[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];160 -> 720[label="",style="solid", color="burlywood", weight=9]; 720 -> 193[label="",style="solid", color="burlywood", weight=3]; 161[label="xy3000 :% xy3001 == xy4000 :% xy4001",fontsize=16,color="black",shape="box"];161 -> 194[label="",style="solid", color="black", weight=3]; 162[label="True",fontsize=16,color="green",shape="box"];163[label="False",fontsize=16,color="green",shape="box"];164[label="False",fontsize=16,color="green",shape="box"];165[label="False",fontsize=16,color="green",shape="box"];166[label="True",fontsize=16,color="green",shape="box"];167[label="False",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="True",fontsize=16,color="green",shape="box"];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="True",fontsize=16,color="green",shape="box"];175[label="primEqDouble (Double xy3000 xy3001) (Double xy4000 xy4001)",fontsize=16,color="black",shape="box"];175 -> 195[label="",style="solid", color="black", weight=3]; 176 -> 26[label="",style="dashed", color="red", weight=0]; 176[label="xy3000 == xy4000 && xy3001 == xy4001",fontsize=16,color="magenta"];176 -> 196[label="",style="dashed", color="magenta", weight=3]; 176 -> 197[label="",style="dashed", color="magenta", weight=3]; 177 -> 26[label="",style="dashed", color="red", weight=0]; 177[label="xy3000 == xy4000 && xy3001 == xy4001",fontsize=16,color="magenta"];177 -> 198[label="",style="dashed", color="magenta", weight=3]; 177 -> 199[label="",style="dashed", color="magenta", weight=3]; 178[label="False",fontsize=16,color="green",shape="box"];179[label="False",fontsize=16,color="green",shape="box"];180[label="True",fontsize=16,color="green",shape="box"];181[label="True",fontsize=16,color="green",shape="box"];182[label="primEqInt (Pos (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];721[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];182 -> 721[label="",style="solid", color="burlywood", weight=9]; 721 -> 200[label="",style="solid", color="burlywood", weight=3]; 722[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];182 -> 722[label="",style="solid", color="burlywood", weight=9]; 722 -> 201[label="",style="solid", color="burlywood", weight=3]; 183[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];723[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];183 -> 723[label="",style="solid", color="burlywood", weight=9]; 723 -> 202[label="",style="solid", color="burlywood", weight=3]; 724[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];183 -> 724[label="",style="solid", color="burlywood", weight=9]; 724 -> 203[label="",style="solid", color="burlywood", weight=3]; 184[label="primEqInt (Neg (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];725[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];184 -> 725[label="",style="solid", color="burlywood", weight=9]; 725 -> 204[label="",style="solid", color="burlywood", weight=3]; 726[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];184 -> 726[label="",style="solid", color="burlywood", weight=9]; 726 -> 205[label="",style="solid", color="burlywood", weight=3]; 185[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];727[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];185 -> 727[label="",style="solid", color="burlywood", weight=9]; 727 -> 206[label="",style="solid", color="burlywood", weight=3]; 728[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];185 -> 728[label="",style="solid", color="burlywood", weight=9]; 728 -> 207[label="",style="solid", color="burlywood", weight=3]; 186 -> 93[label="",style="dashed", color="red", weight=0]; 186[label="primEqInt xy3000 xy4000",fontsize=16,color="magenta"];186 -> 208[label="",style="dashed", color="magenta", weight=3]; 186 -> 209[label="",style="dashed", color="magenta", weight=3]; 187 -> 26[label="",style="dashed", color="red", weight=0]; 187[label="xy3000 == xy4000 && xy3001 == xy4001 && xy3002 == xy4002",fontsize=16,color="magenta"];187 -> 210[label="",style="dashed", color="magenta", weight=3]; 187 -> 211[label="",style="dashed", color="magenta", weight=3]; 188[label="primEqFloat (Float xy3000 xy3001) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];188 -> 212[label="",style="solid", color="black", 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="xy3000 == xy4000",fontsize=16,color="blue",shape="box"];729[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 729[label="",style="solid", color="blue", weight=9]; 729 -> 213[label="",style="solid", color="blue", weight=3]; 730[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 730[label="",style="solid", color="blue", weight=9]; 730 -> 214[label="",style="solid", color="blue", weight=3]; 731[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 731[label="",style="solid", color="blue", weight=9]; 731 -> 215[label="",style="solid", color="blue", weight=3]; 732[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 732[label="",style="solid", color="blue", weight=9]; 732 -> 216[label="",style="solid", color="blue", weight=3]; 733[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 733[label="",style="solid", color="blue", weight=9]; 733 -> 217[label="",style="solid", color="blue", weight=3]; 734[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 734[label="",style="solid", color="blue", weight=9]; 734 -> 218[label="",style="solid", color="blue", weight=3]; 735[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 735[label="",style="solid", color="blue", weight=9]; 735 -> 219[label="",style="solid", color="blue", weight=3]; 736[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 736[label="",style="solid", color="blue", weight=9]; 736 -> 220[label="",style="solid", color="blue", weight=3]; 737[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 737[label="",style="solid", color="blue", weight=9]; 737 -> 221[label="",style="solid", color="blue", weight=3]; 738[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 738[label="",style="solid", color="blue", weight=9]; 738 -> 222[label="",style="solid", color="blue", weight=3]; 739[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 739[label="",style="solid", color="blue", weight=9]; 739 -> 223[label="",style="solid", color="blue", weight=3]; 740[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 740[label="",style="solid", color="blue", weight=9]; 740 -> 224[label="",style="solid", color="blue", weight=3]; 741[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 741[label="",style="solid", color="blue", weight=9]; 741 -> 225[label="",style="solid", color="blue", weight=3]; 742[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];192 -> 742[label="",style="solid", color="blue", weight=9]; 742 -> 226[label="",style="solid", color="blue", weight=3]; 193[label="primEqChar (Char xy3000) (Char xy4000)",fontsize=16,color="black",shape="box"];193 -> 227[label="",style="solid", color="black", weight=3]; 194 -> 26[label="",style="dashed", color="red", weight=0]; 194[label="xy3000 == xy4000 && xy3001 == xy4001",fontsize=16,color="magenta"];194 -> 228[label="",style="dashed", color="magenta", weight=3]; 194 -> 229[label="",style="dashed", color="magenta", weight=3]; 195 -> 61[label="",style="dashed", color="red", weight=0]; 195[label="xy3000 * xy4001 == xy3001 * xy4000",fontsize=16,color="magenta"];195 -> 230[label="",style="dashed", color="magenta", weight=3]; 195 -> 231[label="",style="dashed", color="magenta", weight=3]; 196[label="xy3001 == xy4001",fontsize=16,color="blue",shape="box"];743[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 743[label="",style="solid", color="blue", weight=9]; 743 -> 232[label="",style="solid", color="blue", weight=3]; 744[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 744[label="",style="solid", color="blue", weight=9]; 744 -> 233[label="",style="solid", color="blue", weight=3]; 745[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 745[label="",style="solid", color="blue", weight=9]; 745 -> 234[label="",style="solid", color="blue", weight=3]; 746[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 746[label="",style="solid", color="blue", weight=9]; 746 -> 235[label="",style="solid", color="blue", weight=3]; 747[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 747[label="",style="solid", color="blue", weight=9]; 747 -> 236[label="",style="solid", color="blue", weight=3]; 748[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 748[label="",style="solid", color="blue", weight=9]; 748 -> 237[label="",style="solid", color="blue", weight=3]; 749[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 749[label="",style="solid", color="blue", weight=9]; 749 -> 238[label="",style="solid", color="blue", weight=3]; 750[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 750[label="",style="solid", color="blue", weight=9]; 750 -> 239[label="",style="solid", color="blue", weight=3]; 751[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 751[label="",style="solid", color="blue", weight=9]; 751 -> 240[label="",style="solid", color="blue", weight=3]; 752[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 752[label="",style="solid", color="blue", weight=9]; 752 -> 241[label="",style="solid", color="blue", weight=3]; 753[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 753[label="",style="solid", color="blue", weight=9]; 753 -> 242[label="",style="solid", color="blue", weight=3]; 754[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 754[label="",style="solid", color="blue", weight=9]; 754 -> 243[label="",style="solid", color="blue", weight=3]; 755[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 755[label="",style="solid", color="blue", weight=9]; 755 -> 244[label="",style="solid", color="blue", weight=3]; 756[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 756[label="",style="solid", color="blue", weight=9]; 756 -> 245[label="",style="solid", color="blue", weight=3]; 197[label="xy3000 == xy4000",fontsize=16,color="blue",shape="box"];757[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 757[label="",style="solid", color="blue", weight=9]; 757 -> 246[label="",style="solid", color="blue", weight=3]; 758[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 758[label="",style="solid", color="blue", weight=9]; 758 -> 247[label="",style="solid", color="blue", weight=3]; 759[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 759[label="",style="solid", color="blue", weight=9]; 759 -> 248[label="",style="solid", color="blue", weight=3]; 760[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 760[label="",style="solid", color="blue", weight=9]; 760 -> 249[label="",style="solid", color="blue", weight=3]; 761[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 761[label="",style="solid", color="blue", weight=9]; 761 -> 250[label="",style="solid", color="blue", weight=3]; 762[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 762[label="",style="solid", color="blue", weight=9]; 762 -> 251[label="",style="solid", color="blue", weight=3]; 763[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 763[label="",style="solid", color="blue", weight=9]; 763 -> 252[label="",style="solid", color="blue", weight=3]; 764[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 764[label="",style="solid", color="blue", weight=9]; 764 -> 253[label="",style="solid", color="blue", weight=3]; 765[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 765[label="",style="solid", color="blue", weight=9]; 765 -> 254[label="",style="solid", color="blue", weight=3]; 766[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 766[label="",style="solid", color="blue", weight=9]; 766 -> 255[label="",style="solid", color="blue", weight=3]; 767[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 767[label="",style="solid", color="blue", weight=9]; 767 -> 256[label="",style="solid", color="blue", weight=3]; 768[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 768[label="",style="solid", color="blue", weight=9]; 768 -> 257[label="",style="solid", color="blue", weight=3]; 769[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 769[label="",style="solid", color="blue", weight=9]; 769 -> 258[label="",style="solid", color="blue", weight=3]; 770[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];197 -> 770[label="",style="solid", color="blue", weight=9]; 770 -> 259[label="",style="solid", color="blue", weight=3]; 198 -> 59[label="",style="dashed", color="red", weight=0]; 198[label="xy3001 == xy4001",fontsize=16,color="magenta"];198 -> 260[label="",style="dashed", color="magenta", weight=3]; 198 -> 261[label="",style="dashed", color="magenta", weight=3]; 199[label="xy3000 == xy4000",fontsize=16,color="blue",shape="box"];771[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 771[label="",style="solid", color="blue", weight=9]; 771 -> 262[label="",style="solid", color="blue", weight=3]; 772[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 772[label="",style="solid", color="blue", weight=9]; 772 -> 263[label="",style="solid", color="blue", weight=3]; 773[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 773[label="",style="solid", color="blue", weight=9]; 773 -> 264[label="",style="solid", color="blue", weight=3]; 774[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 774[label="",style="solid", color="blue", weight=9]; 774 -> 265[label="",style="solid", color="blue", weight=3]; 775[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 775[label="",style="solid", color="blue", weight=9]; 775 -> 266[label="",style="solid", color="blue", weight=3]; 776[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 776[label="",style="solid", color="blue", weight=9]; 776 -> 267[label="",style="solid", color="blue", weight=3]; 777[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 777[label="",style="solid", color="blue", weight=9]; 777 -> 268[label="",style="solid", color="blue", weight=3]; 778[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 778[label="",style="solid", color="blue", weight=9]; 778 -> 269[label="",style="solid", color="blue", weight=3]; 779[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 779[label="",style="solid", color="blue", weight=9]; 779 -> 270[label="",style="solid", color="blue", weight=3]; 780[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 780[label="",style="solid", color="blue", weight=9]; 780 -> 271[label="",style="solid", color="blue", weight=3]; 781[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 781[label="",style="solid", color="blue", weight=9]; 781 -> 272[label="",style="solid", color="blue", weight=3]; 782[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 782[label="",style="solid", color="blue", weight=9]; 782 -> 273[label="",style="solid", color="blue", weight=3]; 783[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 783[label="",style="solid", color="blue", weight=9]; 783 -> 274[label="",style="solid", color="blue", weight=3]; 784[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];199 -> 784[label="",style="solid", color="blue", weight=9]; 784 -> 275[label="",style="solid", color="blue", weight=3]; 200[label="primEqInt (Pos (Succ xy30000)) (Pos xy4000)",fontsize=16,color="burlywood",shape="box"];785[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];200 -> 785[label="",style="solid", color="burlywood", weight=9]; 785 -> 276[label="",style="solid", color="burlywood", weight=3]; 786[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];200 -> 786[label="",style="solid", color="burlywood", weight=9]; 786 -> 277[label="",style="solid", color="burlywood", weight=3]; 201[label="primEqInt (Pos (Succ xy30000)) (Neg xy4000)",fontsize=16,color="black",shape="box"];201 -> 278[label="",style="solid", color="black", weight=3]; 202[label="primEqInt (Pos Zero) (Pos xy4000)",fontsize=16,color="burlywood",shape="box"];787[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];202 -> 787[label="",style="solid", color="burlywood", weight=9]; 787 -> 279[label="",style="solid", color="burlywood", weight=3]; 788[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];202 -> 788[label="",style="solid", color="burlywood", weight=9]; 788 -> 280[label="",style="solid", color="burlywood", weight=3]; 203[label="primEqInt (Pos Zero) (Neg xy4000)",fontsize=16,color="burlywood",shape="box"];789[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];203 -> 789[label="",style="solid", color="burlywood", weight=9]; 789 -> 281[label="",style="solid", color="burlywood", weight=3]; 790[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];203 -> 790[label="",style="solid", color="burlywood", weight=9]; 790 -> 282[label="",style="solid", color="burlywood", weight=3]; 204[label="primEqInt (Neg (Succ xy30000)) (Pos xy4000)",fontsize=16,color="black",shape="box"];204 -> 283[label="",style="solid", color="black", weight=3]; 205[label="primEqInt (Neg (Succ xy30000)) (Neg xy4000)",fontsize=16,color="burlywood",shape="box"];791[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];205 -> 791[label="",style="solid", color="burlywood", weight=9]; 791 -> 284[label="",style="solid", color="burlywood", weight=3]; 792[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];205 -> 792[label="",style="solid", color="burlywood", weight=9]; 792 -> 285[label="",style="solid", color="burlywood", weight=3]; 206[label="primEqInt (Neg Zero) (Pos xy4000)",fontsize=16,color="burlywood",shape="box"];793[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];206 -> 793[label="",style="solid", color="burlywood", weight=9]; 793 -> 286[label="",style="solid", color="burlywood", weight=3]; 794[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];206 -> 794[label="",style="solid", color="burlywood", weight=9]; 794 -> 287[label="",style="solid", color="burlywood", weight=3]; 207[label="primEqInt (Neg Zero) (Neg xy4000)",fontsize=16,color="burlywood",shape="box"];795[label="xy4000/Succ xy40000",fontsize=10,color="white",style="solid",shape="box"];207 -> 795[label="",style="solid", color="burlywood", weight=9]; 795 -> 288[label="",style="solid", color="burlywood", weight=3]; 796[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];207 -> 796[label="",style="solid", color="burlywood", weight=9]; 796 -> 289[label="",style="solid", color="burlywood", weight=3]; 208[label="xy3000",fontsize=16,color="green",shape="box"];209[label="xy4000",fontsize=16,color="green",shape="box"];210 -> 26[label="",style="dashed", color="red", weight=0]; 210[label="xy3001 == xy4001 && xy3002 == xy4002",fontsize=16,color="magenta"];210 -> 290[label="",style="dashed", color="magenta", weight=3]; 210 -> 291[label="",style="dashed", color="magenta", weight=3]; 211[label="xy3000 == xy4000",fontsize=16,color="blue",shape="box"];797[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 797[label="",style="solid", color="blue", weight=9]; 797 -> 292[label="",style="solid", color="blue", weight=3]; 798[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 798[label="",style="solid", color="blue", weight=9]; 798 -> 293[label="",style="solid", color="blue", weight=3]; 799[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 799[label="",style="solid", color="blue", weight=9]; 799 -> 294[label="",style="solid", color="blue", weight=3]; 800[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 800[label="",style="solid", color="blue", weight=9]; 800 -> 295[label="",style="solid", color="blue", weight=3]; 801[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 801[label="",style="solid", color="blue", weight=9]; 801 -> 296[label="",style="solid", color="blue", weight=3]; 802[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 802[label="",style="solid", color="blue", weight=9]; 802 -> 297[label="",style="solid", color="blue", weight=3]; 803[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 803[label="",style="solid", color="blue", weight=9]; 803 -> 298[label="",style="solid", color="blue", weight=3]; 804[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 804[label="",style="solid", color="blue", weight=9]; 804 -> 299[label="",style="solid", color="blue", weight=3]; 805[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 805[label="",style="solid", color="blue", weight=9]; 805 -> 300[label="",style="solid", color="blue", weight=3]; 806[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 806[label="",style="solid", color="blue", weight=9]; 806 -> 301[label="",style="solid", color="blue", weight=3]; 807[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 807[label="",style="solid", color="blue", weight=9]; 807 -> 302[label="",style="solid", color="blue", weight=3]; 808[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 808[label="",style="solid", color="blue", weight=9]; 808 -> 303[label="",style="solid", color="blue", weight=3]; 809[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 809[label="",style="solid", color="blue", weight=9]; 809 -> 304[label="",style="solid", color="blue", weight=3]; 810[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 810[label="",style="solid", color="blue", weight=9]; 810 -> 305[label="",style="solid", color="blue", weight=3]; 212 -> 61[label="",style="dashed", color="red", weight=0]; 212[label="xy3000 * xy4001 == xy3001 * xy4000",fontsize=16,color="magenta"];212 -> 306[label="",style="dashed", color="magenta", weight=3]; 212 -> 307[label="",style="dashed", color="magenta", weight=3]; 213 -> 55[label="",style="dashed", color="red", weight=0]; 213[label="xy3000 == xy4000",fontsize=16,color="magenta"];213 -> 308[label="",style="dashed", color="magenta", weight=3]; 213 -> 309[label="",style="dashed", color="magenta", weight=3]; 214 -> 56[label="",style="dashed", color="red", weight=0]; 214[label="xy3000 == xy4000",fontsize=16,color="magenta"];214 -> 310[label="",style="dashed", color="magenta", weight=3]; 214 -> 311[label="",style="dashed", color="magenta", weight=3]; 215 -> 57[label="",style="dashed", color="red", weight=0]; 215[label="xy3000 == xy4000",fontsize=16,color="magenta"];215 -> 312[label="",style="dashed", color="magenta", weight=3]; 215 -> 313[label="",style="dashed", color="magenta", weight=3]; 216 -> 58[label="",style="dashed", color="red", weight=0]; 216[label="xy3000 == xy4000",fontsize=16,color="magenta"];216 -> 314[label="",style="dashed", color="magenta", weight=3]; 216 -> 315[label="",style="dashed", color="magenta", weight=3]; 217 -> 59[label="",style="dashed", color="red", weight=0]; 217[label="xy3000 == xy4000",fontsize=16,color="magenta"];217 -> 316[label="",style="dashed", color="magenta", weight=3]; 217 -> 317[label="",style="dashed", color="magenta", weight=3]; 218 -> 60[label="",style="dashed", color="red", weight=0]; 218[label="xy3000 == xy4000",fontsize=16,color="magenta"];218 -> 318[label="",style="dashed", color="magenta", weight=3]; 218 -> 319[label="",style="dashed", color="magenta", weight=3]; 219 -> 61[label="",style="dashed", color="red", weight=0]; 219[label="xy3000 == xy4000",fontsize=16,color="magenta"];219 -> 320[label="",style="dashed", color="magenta", weight=3]; 219 -> 321[label="",style="dashed", color="magenta", weight=3]; 220 -> 62[label="",style="dashed", color="red", weight=0]; 220[label="xy3000 == xy4000",fontsize=16,color="magenta"];220 -> 322[label="",style="dashed", color="magenta", weight=3]; 220 -> 323[label="",style="dashed", color="magenta", weight=3]; 221 -> 63[label="",style="dashed", color="red", weight=0]; 221[label="xy3000 == xy4000",fontsize=16,color="magenta"];221 -> 324[label="",style="dashed", color="magenta", weight=3]; 221 -> 325[label="",style="dashed", color="magenta", weight=3]; 222 -> 64[label="",style="dashed", color="red", weight=0]; 222[label="xy3000 == xy4000",fontsize=16,color="magenta"];222 -> 326[label="",style="dashed", color="magenta", weight=3]; 222 -> 327[label="",style="dashed", color="magenta", weight=3]; 223 -> 65[label="",style="dashed", color="red", weight=0]; 223[label="xy3000 == xy4000",fontsize=16,color="magenta"];223 -> 328[label="",style="dashed", color="magenta", weight=3]; 223 -> 329[label="",style="dashed", color="magenta", weight=3]; 224 -> 66[label="",style="dashed", color="red", weight=0]; 224[label="xy3000 == xy4000",fontsize=16,color="magenta"];224 -> 330[label="",style="dashed", color="magenta", weight=3]; 224 -> 331[label="",style="dashed", color="magenta", weight=3]; 225 -> 28[label="",style="dashed", color="red", weight=0]; 225[label="xy3000 == xy4000",fontsize=16,color="magenta"];225 -> 332[label="",style="dashed", color="magenta", weight=3]; 225 -> 333[label="",style="dashed", color="magenta", weight=3]; 226 -> 68[label="",style="dashed", color="red", weight=0]; 226[label="xy3000 == xy4000",fontsize=16,color="magenta"];226 -> 334[label="",style="dashed", color="magenta", weight=3]; 226 -> 335[label="",style="dashed", color="magenta", weight=3]; 227[label="primEqNat xy3000 xy4000",fontsize=16,color="burlywood",shape="triangle"];811[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];227 -> 811[label="",style="solid", color="burlywood", weight=9]; 811 -> 336[label="",style="solid", color="burlywood", weight=3]; 812[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];227 -> 812[label="",style="solid", color="burlywood", weight=9]; 812 -> 337[label="",style="solid", color="burlywood", weight=3]; 228[label="xy3001 == xy4001",fontsize=16,color="blue",shape="box"];813[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];228 -> 813[label="",style="solid", color="blue", weight=9]; 813 -> 338[label="",style="solid", color="blue", weight=3]; 814[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];228 -> 814[label="",style="solid", color="blue", weight=9]; 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weight=9]; 844 -> 468[label="",style="solid", color="blue", weight=3]; 292 -> 55[label="",style="dashed", color="red", weight=0]; 292[label="xy3000 == xy4000",fontsize=16,color="magenta"];292 -> 469[label="",style="dashed", color="magenta", weight=3]; 292 -> 470[label="",style="dashed", color="magenta", weight=3]; 293 -> 56[label="",style="dashed", color="red", weight=0]; 293[label="xy3000 == xy4000",fontsize=16,color="magenta"];293 -> 471[label="",style="dashed", color="magenta", weight=3]; 293 -> 472[label="",style="dashed", color="magenta", weight=3]; 294 -> 57[label="",style="dashed", color="red", weight=0]; 294[label="xy3000 == xy4000",fontsize=16,color="magenta"];294 -> 473[label="",style="dashed", color="magenta", weight=3]; 294 -> 474[label="",style="dashed", color="magenta", weight=3]; 295 -> 58[label="",style="dashed", color="red", weight=0]; 295[label="xy3000 == xy4000",fontsize=16,color="magenta"];295 -> 475[label="",style="dashed", color="magenta", weight=3]; 295 -> 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308[label="xy3000",fontsize=16,color="green",shape="box"];309[label="xy4000",fontsize=16,color="green",shape="box"];310[label="xy3000",fontsize=16,color="green",shape="box"];311[label="xy4000",fontsize=16,color="green",shape="box"];312[label="xy3000",fontsize=16,color="green",shape="box"];313[label="xy4000",fontsize=16,color="green",shape="box"];314[label="xy3000",fontsize=16,color="green",shape="box"];315[label="xy4000",fontsize=16,color="green",shape="box"];316[label="xy3000",fontsize=16,color="green",shape="box"];317[label="xy4000",fontsize=16,color="green",shape="box"];318[label="xy3000",fontsize=16,color="green",shape="box"];319[label="xy4000",fontsize=16,color="green",shape="box"];320[label="xy3000",fontsize=16,color="green",shape="box"];321[label="xy4000",fontsize=16,color="green",shape="box"];322[label="xy3000",fontsize=16,color="green",shape="box"];323[label="xy4000",fontsize=16,color="green",shape="box"];324[label="xy3000",fontsize=16,color="green",shape="box"];325[label="xy4000",fontsize=16,color="green",shape="box"];326[label="xy3000",fontsize=16,color="green",shape="box"];327[label="xy4000",fontsize=16,color="green",shape="box"];328[label="xy3000",fontsize=16,color="green",shape="box"];329[label="xy4000",fontsize=16,color="green",shape="box"];330[label="xy3000",fontsize=16,color="green",shape="box"];331[label="xy4000",fontsize=16,color="green",shape="box"];332[label="xy3000",fontsize=16,color="green",shape="box"];333[label="xy4000",fontsize=16,color="green",shape="box"];334[label="xy3000",fontsize=16,color="green",shape="box"];335[label="xy4000",fontsize=16,color="green",shape="box"];336[label="primEqNat 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xy3000 xy4001",fontsize=16,color="burlywood",shape="box"];849[label="xy3000/Pos xy30000",fontsize=10,color="white",style="solid",shape="box"];342 -> 849[label="",style="solid", color="burlywood", weight=9]; 849 -> 513[label="",style="solid", color="burlywood", weight=3]; 850[label="xy3000/Neg xy30000",fontsize=10,color="white",style="solid",shape="box"];342 -> 850[label="",style="solid", color="burlywood", weight=9]; 850 -> 514[label="",style="solid", color="burlywood", weight=3]; 343[label="xy3001",fontsize=16,color="green",shape="box"];344[label="xy4000",fontsize=16,color="green",shape="box"];345[label="xy3001",fontsize=16,color="green",shape="box"];346[label="xy4001",fontsize=16,color="green",shape="box"];347[label="xy3001",fontsize=16,color="green",shape="box"];348[label="xy4001",fontsize=16,color="green",shape="box"];349[label="xy3001",fontsize=16,color="green",shape="box"];350[label="xy4001",fontsize=16,color="green",shape="box"];351[label="xy3001",fontsize=16,color="green",shape="box"];352[label="xy4001",fontsize=16,color="green",shape="box"];353[label="xy3001",fontsize=16,color="green",shape="box"];354[label="xy4001",fontsize=16,color="green",shape="box"];355[label="xy3001",fontsize=16,color="green",shape="box"];356[label="xy4001",fontsize=16,color="green",shape="box"];357[label="xy3001",fontsize=16,color="green",shape="box"];358[label="xy4001",fontsize=16,color="green",shape="box"];359[label="xy3001",fontsize=16,color="green",shape="box"];360[label="xy4001",fontsize=16,color="green",shape="box"];361[label="xy3001",fontsize=16,color="green",shape="box"];362[label="xy4001",fontsize=16,color="green",shape="box"];363[label="xy3001",fontsize=16,color="green",shape="box"];364[label="xy4001",fontsize=16,color="green",shape="box"];365[label="xy3001",fontsize=16,color="green",shape="box"];366[label="xy4001",fontsize=16,color="green",shape="box"];367[label="xy3001",fontsize=16,color="green",shape="box"];368[label="xy4001",fontsize=16,color="green",shape="box"];369[label="xy3001",fontsize=16,color="green",shape="box"];370[label="xy4001",fontsize=16,color="green",shape="box"];371[label="xy3001",fontsize=16,color="green",shape="box"];372[label="xy4001",fontsize=16,color="green",shape="box"];373[label="xy3000",fontsize=16,color="green",shape="box"];374[label="xy4000",fontsize=16,color="green",shape="box"];375[label="xy3000",fontsize=16,color="green",shape="box"];376[label="xy4000",fontsize=16,color="green",shape="box"];377[label="xy3000",fontsize=16,color="green",shape="box"];378[label="xy4000",fontsize=16,color="green",shape="box"];379[label="xy3000",fontsize=16,color="green",shape="box"];380[label="xy4000",fontsize=16,color="green",shape="box"];381[label="xy3000",fontsize=16,color="green",shape="box"];382[label="xy4000",fontsize=16,color="green",shape="box"];383[label="xy3000",fontsize=16,color="green",shape="box"];384[label="xy4000",fontsize=16,color="green",shape="box"];385[label="xy3000",fontsize=16,color="green",shape="box"];386[label="xy4000",fontsize=16,color="green",shape="box"];387[label="xy3000",fontsize=16,color="green",shape="box"];388[label="xy4000",fontsize=16,color="green",shape="box"];389[label="xy3000",fontsize=16,color="green",shape="box"];390[label="xy4000",fontsize=16,color="green",shape="box"];391[label="xy3000",fontsize=16,color="green",shape="box"];392[label="xy4000",fontsize=16,color="green",shape="box"];393[label="xy3000",fontsize=16,color="green",shape="box"];394[label="xy4000",fontsize=16,color="green",shape="box"];395[label="xy3000",fontsize=16,color="green",shape="box"];396[label="xy4000",fontsize=16,color="green",shape="box"];397[label="xy3000",fontsize=16,color="green",shape="box"];398[label="xy4000",fontsize=16,color="green",shape="box"];399[label="xy3000",fontsize=16,color="green",shape="box"];400[label="xy4000",fontsize=16,color="green",shape="box"];401[label="xy3000",fontsize=16,color="green",shape="box"];402[label="xy4000",fontsize=16,color="green",shape="box"];403[label="xy3000",fontsize=16,color="green",shape="box"];404[label="xy4000",fontsize=16,color="green",shape="box"];405[label="xy3000",fontsize=16,color="green",shape="box"];406[label="xy4000",fontsize=16,color="green",shape="box"];407[label="xy3000",fontsize=16,color="green",shape="box"];408[label="xy4000",fontsize=16,color="green",shape="box"];409[label="xy3000",fontsize=16,color="green",shape="box"];410[label="xy4000",fontsize=16,color="green",shape="box"];411[label="xy3000",fontsize=16,color="green",shape="box"];412[label="xy4000",fontsize=16,color="green",shape="box"];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 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436[label="False",fontsize=16,color="green",shape="box"];437[label="False",fontsize=16,color="green",shape="box"];438[label="True",fontsize=16,color="green",shape="box"];439[label="False",fontsize=16,color="green",shape="box"];440[label="True",fontsize=16,color="green",shape="box"];441 -> 55[label="",style="dashed", color="red", weight=0]; 441[label="xy3002 == xy4002",fontsize=16,color="magenta"];441 -> 519[label="",style="dashed", color="magenta", weight=3]; 441 -> 520[label="",style="dashed", color="magenta", weight=3]; 442 -> 56[label="",style="dashed", color="red", weight=0]; 442[label="xy3002 == xy4002",fontsize=16,color="magenta"];442 -> 521[label="",style="dashed", color="magenta", weight=3]; 442 -> 522[label="",style="dashed", color="magenta", weight=3]; 443 -> 57[label="",style="dashed", color="red", weight=0]; 443[label="xy3002 == xy4002",fontsize=16,color="magenta"];443 -> 523[label="",style="dashed", color="magenta", weight=3]; 443 -> 524[label="",style="dashed", 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weight=3]; 448 -> 62[label="",style="dashed", color="red", weight=0]; 448[label="xy3002 == xy4002",fontsize=16,color="magenta"];448 -> 533[label="",style="dashed", color="magenta", weight=3]; 448 -> 534[label="",style="dashed", color="magenta", weight=3]; 449 -> 63[label="",style="dashed", color="red", weight=0]; 449[label="xy3002 == xy4002",fontsize=16,color="magenta"];449 -> 535[label="",style="dashed", color="magenta", weight=3]; 449 -> 536[label="",style="dashed", color="magenta", weight=3]; 450 -> 64[label="",style="dashed", color="red", weight=0]; 450[label="xy3002 == xy4002",fontsize=16,color="magenta"];450 -> 537[label="",style="dashed", color="magenta", weight=3]; 450 -> 538[label="",style="dashed", color="magenta", weight=3]; 451 -> 65[label="",style="dashed", color="red", weight=0]; 451[label="xy3002 == xy4002",fontsize=16,color="magenta"];451 -> 539[label="",style="dashed", color="magenta", weight=3]; 451 -> 540[label="",style="dashed", color="magenta", weight=3]; 452 -> 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469[label="xy3000",fontsize=16,color="green",shape="box"];470[label="xy4000",fontsize=16,color="green",shape="box"];471[label="xy3000",fontsize=16,color="green",shape="box"];472[label="xy4000",fontsize=16,color="green",shape="box"];473[label="xy3000",fontsize=16,color="green",shape="box"];474[label="xy4000",fontsize=16,color="green",shape="box"];475[label="xy3000",fontsize=16,color="green",shape="box"];476[label="xy4000",fontsize=16,color="green",shape="box"];477[label="xy3000",fontsize=16,color="green",shape="box"];478[label="xy4000",fontsize=16,color="green",shape="box"];479[label="xy3000",fontsize=16,color="green",shape="box"];480[label="xy4000",fontsize=16,color="green",shape="box"];481[label="xy3000",fontsize=16,color="green",shape="box"];482[label="xy4000",fontsize=16,color="green",shape="box"];483[label="xy3000",fontsize=16,color="green",shape="box"];484[label="xy4000",fontsize=16,color="green",shape="box"];485[label="xy3000",fontsize=16,color="green",shape="box"];486[label="xy4000",fontsize=16,color="green",shape="box"];487[label="xy3000",fontsize=16,color="green",shape="box"];488[label="xy4000",fontsize=16,color="green",shape="box"];489[label="xy3000",fontsize=16,color="green",shape="box"];490[label="xy4000",fontsize=16,color="green",shape="box"];491[label="xy3000",fontsize=16,color="green",shape="box"];492[label="xy4000",fontsize=16,color="green",shape="box"];493[label="xy3000",fontsize=16,color="green",shape="box"];494[label="xy4000",fontsize=16,color="green",shape="box"];495[label="xy3000",fontsize=16,color="green",shape="box"];496[label="xy4000",fontsize=16,color="green",shape="box"];497[label="xy3000",fontsize=16,color="green",shape="box"];498[label="xy4001",fontsize=16,color="green",shape="box"];499[label="xy3001",fontsize=16,color="green",shape="box"];500[label="xy4000",fontsize=16,color="green",shape="box"];501[label="primEqNat (Succ xy30000) (Succ xy40000)",fontsize=16,color="black",shape="box"];501 -> 575[label="",style="solid", color="black", weight=3]; 502[label="primEqNat (Succ xy30000) Zero",fontsize=16,color="black",shape="box"];502 -> 576[label="",style="solid", color="black", weight=3]; 503[label="primEqNat Zero (Succ xy40000)",fontsize=16,color="black",shape="box"];503 -> 577[label="",style="solid", color="black", weight=3]; 504[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];504 -> 578[label="",style="solid", color="black", weight=3]; 505[label="xy3001",fontsize=16,color="green",shape="box"];506[label="xy4001",fontsize=16,color="green",shape="box"];507[label="xy3001",fontsize=16,color="green",shape="box"];508[label="xy4001",fontsize=16,color="green",shape="box"];509[label="xy3000",fontsize=16,color="green",shape="box"];510[label="xy4000",fontsize=16,color="green",shape="box"];511[label="xy3000",fontsize=16,color="green",shape="box"];512[label="xy4000",fontsize=16,color="green",shape="box"];513[label="primMulInt (Pos xy30000) xy4001",fontsize=16,color="burlywood",shape="box"];851[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];513 -> 851[label="",style="solid", color="burlywood", weight=9]; 851 -> 579[label="",style="solid", color="burlywood", weight=3]; 852[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];513 -> 852[label="",style="solid", color="burlywood", weight=9]; 852 -> 580[label="",style="solid", color="burlywood", weight=3]; 514[label="primMulInt (Neg xy30000) xy4001",fontsize=16,color="burlywood",shape="box"];853[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];514 -> 853[label="",style="solid", color="burlywood", weight=9]; 853 -> 581[label="",style="solid", color="burlywood", weight=3]; 854[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];514 -> 854[label="",style="solid", color="burlywood", weight=9]; 854 -> 582[label="",style="solid", color="burlywood", weight=3]; 515[label="xy40000",fontsize=16,color="green",shape="box"];516[label="xy30000",fontsize=16,color="green",shape="box"];517[label="xy40000",fontsize=16,color="green",shape="box"];518[label="xy30000",fontsize=16,color="green",shape="box"];519[label="xy3002",fontsize=16,color="green",shape="box"];520[label="xy4002",fontsize=16,color="green",shape="box"];521[label="xy3002",fontsize=16,color="green",shape="box"];522[label="xy4002",fontsize=16,color="green",shape="box"];523[label="xy3002",fontsize=16,color="green",shape="box"];524[label="xy4002",fontsize=16,color="green",shape="box"];525[label="xy3002",fontsize=16,color="green",shape="box"];526[label="xy4002",fontsize=16,color="green",shape="box"];527[label="xy3002",fontsize=16,color="green",shape="box"];528[label="xy4002",fontsize=16,color="green",shape="box"];529[label="xy3002",fontsize=16,color="green",shape="box"];530[label="xy4002",fontsize=16,color="green",shape="box"];531[label="xy3002",fontsize=16,color="green",shape="box"];532[label="xy4002",fontsize=16,color="green",shape="box"];533[label="xy3002",fontsize=16,color="green",shape="box"];534[label="xy4002",fontsize=16,color="green",shape="box"];535[label="xy3002",fontsize=16,color="green",shape="box"];536[label="xy4002",fontsize=16,color="green",shape="box"];537[label="xy3002",fontsize=16,color="green",shape="box"];538[label="xy4002",fontsize=16,color="green",shape="box"];539[label="xy3002",fontsize=16,color="green",shape="box"];540[label="xy4002",fontsize=16,color="green",shape="box"];541[label="xy3002",fontsize=16,color="green",shape="box"];542[label="xy4002",fontsize=16,color="green",shape="box"];543[label="xy3002",fontsize=16,color="green",shape="box"];544[label="xy4002",fontsize=16,color="green",shape="box"];545[label="xy3002",fontsize=16,color="green",shape="box"];546[label="xy4002",fontsize=16,color="green",shape="box"];547[label="xy3001",fontsize=16,color="green",shape="box"];548[label="xy4001",fontsize=16,color="green",shape="box"];549[label="xy3001",fontsize=16,color="green",shape="box"];550[label="xy4001",fontsize=16,color="green",shape="box"];551[label="xy3001",fontsize=16,color="green",shape="box"];552[label="xy4001",fontsize=16,color="green",shape="box"];553[label="xy3001",fontsize=16,color="green",shape="box"];554[label="xy4001",fontsize=16,color="green",shape="box"];555[label="xy3001",fontsize=16,color="green",shape="box"];556[label="xy4001",fontsize=16,color="green",shape="box"];557[label="xy3001",fontsize=16,color="green",shape="box"];558[label="xy4001",fontsize=16,color="green",shape="box"];559[label="xy3001",fontsize=16,color="green",shape="box"];560[label="xy4001",fontsize=16,color="green",shape="box"];561[label="xy3001",fontsize=16,color="green",shape="box"];562[label="xy4001",fontsize=16,color="green",shape="box"];563[label="xy3001",fontsize=16,color="green",shape="box"];564[label="xy4001",fontsize=16,color="green",shape="box"];565[label="xy3001",fontsize=16,color="green",shape="box"];566[label="xy4001",fontsize=16,color="green",shape="box"];567[label="xy3001",fontsize=16,color="green",shape="box"];568[label="xy4001",fontsize=16,color="green",shape="box"];569[label="xy3001",fontsize=16,color="green",shape="box"];570[label="xy4001",fontsize=16,color="green",shape="box"];571[label="xy3001",fontsize=16,color="green",shape="box"];572[label="xy4001",fontsize=16,color="green",shape="box"];573[label="xy3001",fontsize=16,color="green",shape="box"];574[label="xy4001",fontsize=16,color="green",shape="box"];575 -> 227[label="",style="dashed", color="red", weight=0]; 575[label="primEqNat xy30000 xy40000",fontsize=16,color="magenta"];575 -> 583[label="",style="dashed", color="magenta", weight=3]; 575 -> 584[label="",style="dashed", color="magenta", weight=3]; 576[label="False",fontsize=16,color="green",shape="box"];577[label="False",fontsize=16,color="green",shape="box"];578[label="True",fontsize=16,color="green",shape="box"];579[label="primMulInt (Pos xy30000) (Pos xy40010)",fontsize=16,color="black",shape="box"];579 -> 585[label="",style="solid", color="black", weight=3]; 580[label="primMulInt (Pos xy30000) (Neg xy40010)",fontsize=16,color="black",shape="box"];580 -> 586[label="",style="solid", color="black", weight=3]; 581[label="primMulInt (Neg xy30000) (Pos xy40010)",fontsize=16,color="black",shape="box"];581 -> 587[label="",style="solid", color="black", weight=3]; 582[label="primMulInt (Neg xy30000) (Neg xy40010)",fontsize=16,color="black",shape="box"];582 -> 588[label="",style="solid", color="black", weight=3]; 583[label="xy40000",fontsize=16,color="green",shape="box"];584[label="xy30000",fontsize=16,color="green",shape="box"];585[label="Pos (primMulNat xy30000 xy40010)",fontsize=16,color="green",shape="box"];585 -> 589[label="",style="dashed", color="green", weight=3]; 586[label="Neg (primMulNat xy30000 xy40010)",fontsize=16,color="green",shape="box"];586 -> 590[label="",style="dashed", color="green", weight=3]; 587[label="Neg (primMulNat xy30000 xy40010)",fontsize=16,color="green",shape="box"];587 -> 591[label="",style="dashed", color="green", weight=3]; 588[label="Pos (primMulNat xy30000 xy40010)",fontsize=16,color="green",shape="box"];588 -> 592[label="",style="dashed", color="green", weight=3]; 589[label="primMulNat xy30000 xy40010",fontsize=16,color="burlywood",shape="triangle"];855[label="xy30000/Succ xy300000",fontsize=10,color="white",style="solid",shape="box"];589 -> 855[label="",style="solid", color="burlywood", weight=9]; 855 -> 593[label="",style="solid", color="burlywood", weight=3]; 856[label="xy30000/Zero",fontsize=10,color="white",style="solid",shape="box"];589 -> 856[label="",style="solid", color="burlywood", weight=9]; 856 -> 594[label="",style="solid", color="burlywood", weight=3]; 590 -> 589[label="",style="dashed", color="red", weight=0]; 590[label="primMulNat xy30000 xy40010",fontsize=16,color="magenta"];590 -> 595[label="",style="dashed", color="magenta", weight=3]; 591 -> 589[label="",style="dashed", color="red", weight=0]; 591[label="primMulNat xy30000 xy40010",fontsize=16,color="magenta"];591 -> 596[label="",style="dashed", color="magenta", weight=3]; 592 -> 589[label="",style="dashed", color="red", weight=0]; 592[label="primMulNat xy30000 xy40010",fontsize=16,color="magenta"];592 -> 597[label="",style="dashed", color="magenta", weight=3]; 592 -> 598[label="",style="dashed", color="magenta", weight=3]; 593[label="primMulNat (Succ xy300000) xy40010",fontsize=16,color="burlywood",shape="box"];857[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];593 -> 857[label="",style="solid", color="burlywood", weight=9]; 857 -> 599[label="",style="solid", color="burlywood", weight=3]; 858[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];593 -> 858[label="",style="solid", color="burlywood", weight=9]; 858 -> 600[label="",style="solid", color="burlywood", weight=3]; 594[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];859[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];594 -> 859[label="",style="solid", color="burlywood", weight=9]; 859 -> 601[label="",style="solid", color="burlywood", weight=3]; 860[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];594 -> 860[label="",style="solid", color="burlywood", weight=9]; 860 -> 602[label="",style="solid", color="burlywood", weight=3]; 595[label="xy40010",fontsize=16,color="green",shape="box"];596[label="xy30000",fontsize=16,color="green",shape="box"];597[label="xy30000",fontsize=16,color="green",shape="box"];598[label="xy40010",fontsize=16,color="green",shape="box"];599[label="primMulNat (Succ xy300000) (Succ xy400100)",fontsize=16,color="black",shape="box"];599 -> 603[label="",style="solid", color="black", weight=3]; 600[label="primMulNat (Succ xy300000) Zero",fontsize=16,color="black",shape="box"];600 -> 604[label="",style="solid", color="black", weight=3]; 601[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];601 -> 605[label="",style="solid", color="black", weight=3]; 602[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];602 -> 606[label="",style="solid", color="black", weight=3]; 603 -> 607[label="",style="dashed", color="red", weight=0]; 603[label="primPlusNat (primMulNat xy300000 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];603 -> 608[label="",style="dashed", color="magenta", weight=3]; 604[label="Zero",fontsize=16,color="green",shape="box"];605[label="Zero",fontsize=16,color="green",shape="box"];606[label="Zero",fontsize=16,color="green",shape="box"];608 -> 589[label="",style="dashed", color="red", weight=0]; 608[label="primMulNat xy300000 (Succ xy400100)",fontsize=16,color="magenta"];608 -> 609[label="",style="dashed", color="magenta", weight=3]; 608 -> 610[label="",style="dashed", color="magenta", weight=3]; 607[label="primPlusNat xy11 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];861[label="xy11/Succ xy110",fontsize=10,color="white",style="solid",shape="box"];607 -> 861[label="",style="solid", color="burlywood", weight=9]; 861 -> 611[label="",style="solid", color="burlywood", weight=3]; 862[label="xy11/Zero",fontsize=10,color="white",style="solid",shape="box"];607 -> 862[label="",style="solid", color="burlywood", weight=9]; 862 -> 612[label="",style="solid", color="burlywood", weight=3]; 609[label="xy300000",fontsize=16,color="green",shape="box"];610[label="Succ xy400100",fontsize=16,color="green",shape="box"];611[label="primPlusNat (Succ xy110) (Succ xy400100)",fontsize=16,color="black",shape="box"];611 -> 613[label="",style="solid", color="black", weight=3]; 612[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];612 -> 614[label="",style="solid", color="black", weight=3]; 613[label="Succ (Succ (primPlusNat xy110 xy400100))",fontsize=16,color="green",shape="box"];613 -> 615[label="",style="dashed", color="green", weight=3]; 614[label="Succ xy400100",fontsize=16,color="green",shape="box"];615[label="primPlusNat xy110 xy400100",fontsize=16,color="burlywood",shape="triangle"];863[label="xy110/Succ xy1100",fontsize=10,color="white",style="solid",shape="box"];615 -> 863[label="",style="solid", color="burlywood", weight=9]; 863 -> 616[label="",style="solid", color="burlywood", weight=3]; 864[label="xy110/Zero",fontsize=10,color="white",style="solid",shape="box"];615 -> 864[label="",style="solid", color="burlywood", weight=9]; 864 -> 617[label="",style="solid", color="burlywood", weight=3]; 616[label="primPlusNat (Succ xy1100) xy400100",fontsize=16,color="burlywood",shape="box"];865[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];616 -> 865[label="",style="solid", color="burlywood", weight=9]; 865 -> 618[label="",style="solid", color="burlywood", weight=3]; 866[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];616 -> 866[label="",style="solid", color="burlywood", weight=9]; 866 -> 619[label="",style="solid", color="burlywood", weight=3]; 617[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];867[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];617 -> 867[label="",style="solid", color="burlywood", weight=9]; 867 -> 620[label="",style="solid", color="burlywood", weight=3]; 868[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];617 -> 868[label="",style="solid", color="burlywood", weight=9]; 868 -> 621[label="",style="solid", color="burlywood", weight=3]; 618[label="primPlusNat (Succ xy1100) (Succ xy4001000)",fontsize=16,color="black",shape="box"];618 -> 622[label="",style="solid", color="black", weight=3]; 619[label="primPlusNat (Succ xy1100) Zero",fontsize=16,color="black",shape="box"];619 -> 623[label="",style="solid", color="black", weight=3]; 620[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];620 -> 624[label="",style="solid", color="black", weight=3]; 621[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];621 -> 625[label="",style="solid", color="black", weight=3]; 622[label="Succ (Succ (primPlusNat xy1100 xy4001000))",fontsize=16,color="green",shape="box"];622 -> 626[label="",style="dashed", color="green", weight=3]; 623[label="Succ xy1100",fontsize=16,color="green",shape="box"];624[label="Succ xy4001000",fontsize=16,color="green",shape="box"];625[label="Zero",fontsize=16,color="green",shape="box"];626 -> 615[label="",style="dashed", color="red", weight=0]; 626[label="primPlusNat xy1100 xy4001000",fontsize=16,color="magenta"];626 -> 627[label="",style="dashed", color="magenta", weight=3]; 626 -> 628[label="",style="dashed", color="magenta", weight=3]; 627[label="xy1100",fontsize=16,color="green",shape="box"];628[label="xy4001000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(app(ty_@3, be), bf), bg)), bbh) -> new_esEs1(xy3001, xy4001, be, bf, bg) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], cf), ce) -> new_esEs0(xy3000, xy4000, cf) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_[], cf)), ce), bbh) -> new_esEs0(xy3000, xy4000, cf) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(ty_[], fd)), bbh) -> new_esEs0(xy3002, xy4002, fd) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_[], bd)) -> new_esEs0(xy3001, xy4001, bd) new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_@2, bag), bah)) -> new_esEs(xy3000, xy4000, bag, bah) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy3000, xy4000, cc, cd) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, baa), bab), bac), fa, gf) -> new_esEs1(xy3000, xy4000, baa, bab, bac) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_@2, dg), dh)) -> new_esEs(xy3000, xy4000, dg, dh) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_Maybe, bh)) -> new_esEs2(xy3001, xy4001, bh) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, cg), da), db), ce) -> new_esEs1(xy3000, xy4000, cg, da, db) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, dd), de), ce) -> new_esEs3(xy3000, xy4000, dd, de) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(app(ty_@3, eb), ec), ed)) -> new_esEs1(xy3000, xy4000, eb, ec, ed) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_Either, ca), cb)), bbh) -> new_esEs3(xy3001, xy4001, ca, cb) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, dc), ce) -> new_esEs2(xy3000, xy4000, dc) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_[], ea)) -> new_esEs0(xy3000, xy4000, ea) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(app(ty_@3, baa), bab), bac)), fa), gf), bbh) -> new_esEs1(xy3000, xy4000, baa, bab, bac) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(ty_@2, fb), fc)) -> new_esEs(xy3002, xy4002, fb, fc) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_Either, dd), de)), ce), bbh) -> new_esEs3(xy3000, xy4000, dd, de) new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_Either, bdc), bdd)) -> new_esEs3(xy300, xy400, bdc, bdd) new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_[], bba)), bbh) -> new_esEs0(xy3000, xy4000, bba) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(ty_Either, gb), gc)), bbh) -> new_esEs3(xy3002, xy4002, gb, gc) new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(app(ty_@3, bbb), bbc), bbd)), bbh) -> new_esEs1(xy3000, xy4000, bbb, bbc, bbd) new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_Either, bbf), bbg)) -> new_esEs3(xy3000, xy4000, bbf, bbg) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bad), fa, gf) -> new_esEs2(xy3000, xy4000, bad) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(ty_Maybe, hc)), gf), bbh) -> new_esEs2(xy3001, xy4001, hc) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(ty_Either, hd), he), gf) -> new_esEs3(xy3001, xy4001, hd, he) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(ty_[], fd)) -> new_esEs0(xy3002, xy4002, fd) new_esEs2(Just(xy3000), Just(xy4000), app(app(app(ty_@3, bbb), bbc), bbd)) -> new_esEs1(xy3000, xy4000, bbb, bbc, bbd) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(ty_@2, fb), fc)), bbh) -> new_esEs(xy3002, xy4002, fb, fc) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(ty_@2, gd), ge)), gf), bbh) -> new_esEs(xy3001, xy4001, gd, ge) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], hh), fa, gf) -> new_esEs0(xy3000, xy4000, hh) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(ty_[], gg)), gf), bbh) -> new_esEs0(xy3001, xy4001, gg) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(ty_Maybe, ga)) -> new_esEs2(xy3002, xy4002, ga) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(app(ty_@3, cg), da), db)), ce), bbh) -> new_esEs1(xy3000, xy4000, cg, da, db) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_[], ea)), bbh) -> new_esEs0(xy3000, xy4000, ea) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], df), bbh) -> new_esEs0(xy3001, xy4001, df) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_Either, ef), eg)) -> new_esEs3(xy3000, xy4000, ef, eg) new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_Maybe, bdb)) -> new_esEs2(xy300, xy400, bdb) new_esEs3(Left(xy300), Left(xy400), app(app(ty_Either, bca), bcb), bbh) -> new_esEs3(xy300, xy400, bca, bcb) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(app(ty_@3, eb), ec), ed)), bbh) -> new_esEs1(xy3000, xy4000, eb, ec, ed) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(app(ty_@3, ff), fg), fh)), bbh) -> new_esEs1(xy3002, xy4002, ff, fg, fh) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_Either, bae), baf)), fa), gf), bbh) -> new_esEs3(xy3000, xy4000, bae, baf) new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_[], bcf)) -> new_esEs0(xy300, xy400, bcf) new_esEs2(Just(xy3000), Just(xy4000), app(ty_[], bba)) -> new_esEs0(xy3000, xy4000, bba) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_[], bd)), bbh) -> new_esEs0(xy3001, xy4001, bd) new_esEs2(Just(xy3000), Just(xy4000), app(ty_Maybe, bbe)) -> new_esEs2(xy3000, xy4000, bbe) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_@2, hf), hg)), fa), gf), bbh) -> new_esEs(xy3000, xy4000, hf, hg) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_Either, ef), eg)), bbh) -> new_esEs3(xy3000, xy4000, ef, eg) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(ty_@2, gd), ge), gf) -> new_esEs(xy3001, xy4001, gd, ge) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_Maybe, dc)), ce), bbh) -> new_esEs2(xy3000, xy4000, dc) new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_Maybe, bbe)), bbh) -> new_esEs2(xy3000, xy4000, bbe) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(app(ty_@3, gh), ha), hb)), gf), bbh) -> new_esEs1(xy3001, xy4001, gh, ha, hb) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy3001, xy4001, bb, bc) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), df) -> new_esEs0(xy3001, xy4001, df) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(app(ty_@3, be), bf), bg)) -> new_esEs1(xy3001, xy4001, be, bf, bg) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bae), baf), fa, gf) -> new_esEs3(xy3000, xy4000, bae, baf) new_esEs3(Right(xy300), Right(xy400), bcc, app(app(app(ty_@3, bcg), bch), bda)) -> new_esEs1(xy300, xy400, bcg, bch, bda) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_@2, dg), dh)), bbh) -> new_esEs(xy3000, xy4000, dg, dh) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(ty_Either, hd), he)), gf), bbh) -> new_esEs3(xy3001, xy4001, hd, he) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_[], hh)), fa), gf), bbh) -> new_esEs0(xy3000, xy4000, hh) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_Maybe, bh)), bbh) -> new_esEs2(xy3001, xy4001, bh) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_@2, bb), bc)), bbh) -> new_esEs(xy3001, xy4001, bb, bc) new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_Maybe, ee)) -> new_esEs2(xy3000, xy4000, ee) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(ty_[], gg), gf) -> new_esEs0(xy3001, xy4001, gg) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(app(ty_@3, ff), fg), fh)) -> new_esEs1(xy3002, xy4002, ff, fg, fh) new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_Either, bbf), bbg)), bbh) -> new_esEs3(xy3000, xy4000, bbf, bbg) new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_Either, ca), cb)) -> new_esEs3(xy3001, xy4001, ca, cb) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(ty_Either, gb), gc)) -> new_esEs3(xy3002, xy4002, gb, gc) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, hf), hg), fa, gf) -> new_esEs(xy3000, xy4000, hf, hg) new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_@2, bcd), bce)) -> new_esEs(xy300, xy400, bcd, bce) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(ty_Maybe, ga)), bbh) -> new_esEs2(xy3002, xy4002, ga) new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_Maybe, bad)), fa), gf), bbh) -> new_esEs2(xy3000, xy4000, bad) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(app(ty_@3, gh), ha), hb), gf) -> new_esEs1(xy3001, xy4001, gh, ha, hb) new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_@2, bag), bah)), bbh) -> new_esEs(xy3000, xy4000, bag, bah) new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(ty_Maybe, hc), gf) -> new_esEs2(xy3001, xy4001, hc) new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_@2, cc), cd)), ce), bbh) -> new_esEs(xy3000, xy4000, cc, cd) new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_Maybe, ee)), bbh) -> new_esEs2(xy3000, xy4000, ee) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (8) 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_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_Either, ef), eg)) -> new_esEs3(xy3000, xy4000, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_@2, dg), dh)) -> new_esEs(xy3000, xy4000, dg, dh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_Maybe, ee)) -> new_esEs2(xy3000, xy4000, ee) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(app(app(ty_@3, eb), ec), ed)) -> new_esEs1(xy3000, xy4000, eb, ec, ed) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_Either, bbf), bbg)) -> new_esEs3(xy3000, xy4000, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Just(xy3000), Just(xy4000), app(app(ty_@2, bag), bah)) -> new_esEs(xy3000, xy4000, bag, bah) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Just(xy3000), Just(xy4000), app(ty_Maybe, bbe)) -> new_esEs2(xy3000, xy4000, bbe) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Just(xy3000), Just(xy4000), app(app(app(ty_@3, bbb), bbc), bbd)) -> new_esEs1(xy3000, xy4000, bbb, bbc, bbd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(Just(xy3000), Just(xy4000), app(ty_[], bba)) -> new_esEs0(xy3000, xy4000, bba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(ty_Either, hd), he), gf) -> new_esEs3(xy3001, xy4001, hd, he) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bae), baf), fa, gf) -> new_esEs3(xy3000, xy4000, bae, baf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(ty_Either, gb), gc)) -> new_esEs3(xy3002, xy4002, gb, gc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(ty_@2, fb), fc)) -> new_esEs(xy3002, xy4002, fb, fc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(ty_@2, gd), ge), gf) -> new_esEs(xy3001, xy4001, gd, ge) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, hf), hg), fa, gf) -> new_esEs(xy3000, xy4000, hf, hg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bad), fa, gf) -> new_esEs2(xy3000, xy4000, bad) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(ty_Maybe, ga)) -> new_esEs2(xy3002, xy4002, ga) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(ty_Maybe, hc), gf) -> new_esEs2(xy3001, xy4001, hc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, baa), bab), bac), fa, gf) -> new_esEs1(xy3000, xy4000, baa, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(app(app(ty_@3, ff), fg), fh)) -> new_esEs1(xy3002, xy4002, ff, fg, fh) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(app(app(ty_@3, gh), ha), hb), gf) -> new_esEs1(xy3001, xy4001, gh, ha, hb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, fa, app(ty_[], fd)) -> new_esEs0(xy3002, xy4002, fd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], hh), fa, gf) -> new_esEs0(xy3000, xy4000, hh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), eh, app(ty_[], gg), gf) -> new_esEs0(xy3001, xy4001, gg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, dd), de), ce) -> new_esEs3(xy3000, xy4000, dd, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_Either, ca), cb)) -> new_esEs3(xy3001, xy4001, ca, cb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_Either, ca), cb)), bbh) -> new_esEs3(xy3001, xy4001, ca, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_Either, dd), de)), ce), bbh) -> new_esEs3(xy3000, xy4000, dd, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_Either, bdc), bdd)) -> new_esEs3(xy300, xy400, bdc, bdd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(ty_Either, gb), gc)), bbh) -> new_esEs3(xy3002, xy4002, gb, gc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(xy300), Left(xy400), app(app(ty_Either, bca), bcb), bbh) -> new_esEs3(xy300, xy400, bca, bcb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_Either, bae), baf)), fa), gf), bbh) -> new_esEs3(xy3000, xy4000, bae, baf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_Either, ef), eg)), bbh) -> new_esEs3(xy3000, xy4000, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(ty_Either, hd), he)), gf), bbh) -> new_esEs3(xy3001, xy4001, hd, he) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_Either, bbf), bbg)), bbh) -> new_esEs3(xy3000, xy4000, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_[], ea)) -> new_esEs0(xy3000, xy4000, ea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(:(xy3000, xy3001), :(xy4000, xy4001), df) -> new_esEs0(xy3001, xy4001, df) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy3000, xy4000, cc, cd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy3001, xy4001, bb, bc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(ty_@2, fb), fc)), bbh) -> new_esEs(xy3002, xy4002, fb, fc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(ty_@2, gd), ge)), gf), bbh) -> new_esEs(xy3001, xy4001, gd, ge) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_@2, hf), hg)), fa), gf), bbh) -> new_esEs(xy3000, xy4000, hf, hg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(ty_@2, dg), dh)), bbh) -> new_esEs(xy3000, xy4000, dg, dh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_@2, bb), bc)), bbh) -> new_esEs(xy3001, xy4001, bb, bc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Right(xy300), Right(xy400), bcc, app(app(ty_@2, bcd), bce)) -> new_esEs(xy300, xy400, bcd, bce) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(ty_@2, bag), bah)), bbh) -> new_esEs(xy3000, xy4000, bag, bah) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_@2, cc), cd)), ce), bbh) -> new_esEs(xy3000, xy4000, cc, cd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_Maybe, bh)) -> new_esEs2(xy3001, xy4001, bh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, dc), ce) -> new_esEs2(xy3000, xy4000, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, cg), da), db), ce) -> new_esEs1(xy3000, xy4000, cg, da, db) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(app(ty_@3, be), bf), bg)) -> new_esEs1(xy3001, xy4001, be, bf, bg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], cf), ce) -> new_esEs0(xy3000, xy4000, cf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_[], bd)) -> new_esEs0(xy3001, xy4001, bd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(ty_Maybe, hc)), gf), bbh) -> new_esEs2(xy3001, xy4001, hc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_Maybe, bdb)) -> new_esEs2(xy300, xy400, bdb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_Maybe, dc)), ce), bbh) -> new_esEs2(xy3000, xy4000, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_Maybe, bbe)), bbh) -> new_esEs2(xy3000, xy4000, bbe) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_Maybe, bh)), bbh) -> new_esEs2(xy3001, xy4001, bh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(ty_Maybe, ga)), bbh) -> new_esEs2(xy3002, xy4002, ga) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_Maybe, bad)), fa), gf), bbh) -> new_esEs2(xy3000, xy4000, bad) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_Maybe, ee)), bbh) -> new_esEs2(xy3000, xy4000, ee) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(app(ty_@3, be), bf), bg)), bbh) -> new_esEs1(xy3001, xy4001, be, bf, bg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(app(ty_@3, baa), bab), bac)), fa), gf), bbh) -> new_esEs1(xy3000, xy4000, baa, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(app(app(ty_@3, bbb), bbc), bbd)), bbh) -> new_esEs1(xy3000, xy4000, bbb, bbc, bbd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(app(app(ty_@3, cg), da), db)), ce), bbh) -> new_esEs1(xy3000, xy4000, cg, da, db) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(app(app(ty_@3, eb), ec), ed)), bbh) -> new_esEs1(xy3000, xy4000, eb, ec, ed) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(app(app(ty_@3, ff), fg), fh)), bbh) -> new_esEs1(xy3002, xy4002, ff, fg, fh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(app(app(ty_@3, gh), ha), hb)), gf), bbh) -> new_esEs1(xy3001, xy4001, gh, ha, hb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Right(xy300), Right(xy400), bcc, app(app(app(ty_@3, bcg), bch), bda)) -> new_esEs1(xy300, xy400, bcg, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_[], cf)), ce), bbh) -> new_esEs0(xy3000, xy4000, cf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), fa), app(ty_[], fd)), bbh) -> new_esEs0(xy3002, xy4002, fd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(Just(xy3000)), Left(Just(xy4000)), app(ty_Maybe, app(ty_[], bba)), bbh) -> new_esEs0(xy3000, xy4000, bba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, eh), app(ty_[], gg)), gf), bbh) -> new_esEs0(xy3001, xy4001, gg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], app(ty_[], ea)), bbh) -> new_esEs0(xy3000, xy4000, ea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(:(xy3000, xy3001)), Left(:(xy4000, xy4001)), app(ty_[], df), bbh) -> new_esEs0(xy3001, xy4001, df) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Right(xy300), Right(xy400), bcc, app(ty_[], bcf)) -> new_esEs0(xy300, xy400, bcf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(Left(@2(xy3000, xy3001)), Left(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_[], bd)), bbh) -> new_esEs0(xy3001, xy4001, bd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Left(@3(xy3000, xy3001, xy3002)), Left(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_[], hh)), fa), gf), bbh) -> new_esEs0(xy3000, xy4000, hh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 ---------------------------------------- (9) YES ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba, bb) -> new_isPrefixOf(xy31, xy41, ba, bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) 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_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba, bb) -> new_isPrefixOf(xy31, xy41, ba, bb) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (12) YES ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(xy300000), Succ(xy400100)) -> new_primMulNat(xy300000, Succ(xy400100)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) 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(xy300000), Succ(xy400100)) -> new_primMulNat(xy300000, Succ(xy400100)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(xy1100), Succ(xy4001000)) -> new_primPlusNat(xy1100, xy4001000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) 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(xy1100), Succ(xy4001000)) -> new_primPlusNat(xy1100, xy4001000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (18) YES ---------------------------------------- (19) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(xy30000), Succ(xy40000)) -> new_primEqNat(xy30000, xy40000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (20) 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(xy30000), Succ(xy40000)) -> new_primEqNat(xy30000, xy40000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (21) YES