/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) CR [EQUIVALENT, 0 ms] (4) HASKELL (5) IFR [EQUIVALENT, 0 ms] (6) HASKELL (7) BR [EQUIVALENT, 0 ms] (8) HASKELL (9) COR [EQUIVALENT, 12 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) AND (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 (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] (30) 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; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (\vv2 ->case vv2 of { x-> if any (eq x) ys then x : [] else []; _-> []; } ) xs; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\vv2->case vv2 of { x -> if any (eq x) ys then x : [] else []; _ -> []} " is transformed to "intersectBy0 eq ys vv2 = case vv2 of { x -> if any (eq x) ys then x : [] else []; _ -> []} ; " ---------------------------------------- (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; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs; intersectBy0 eq ys vv2 = case vv2 of { x-> if any (eq x) ys then x : [] else []; _-> []; } ; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) CR (EQUIVALENT) Case Reductions: The following Case expression "case vv2 of { x -> if any (eq x) ys then x : [] else []; _ -> []} " is transformed to "intersectBy00 eq ys x = if any (eq x) ys then x : [] else []; intersectBy00 eq ys _ = []; " ---------------------------------------- (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; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs; intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2; intersectBy00 eq ys x = if any (eq x) ys then x : [] else []; intersectBy00 eq ys _ = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) IFR (EQUIVALENT) If Reductions: The following If expression "if any (eq x) ys then x : [] else []" is transformed to "intersectBy000 x True = x : []; intersectBy000 x False = []; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs; intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2; intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys); intersectBy00 eq ys _ = []; intersectBy000 x True = x : []; intersectBy000 x False = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (8) 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; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs; intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2; intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys); intersectBy00 eq ys xw = []; intersectBy000 x True = x : []; intersectBy000 x False = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (9) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (10) 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; intersect :: Eq a => [a] -> [a] -> [a]; intersect = intersectBy (==); intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]; intersectBy eq xs ys = concatMap (intersectBy0 eq ys) xs; intersectBy0 eq ys vv2 = intersectBy00 eq ys vv2; intersectBy00 eq ys x = intersectBy000 x (any (eq x) ys); intersectBy00 eq ys xw = []; intersectBy000 x True = x : []; intersectBy000 x False = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.intersect",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.intersect xx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="List.intersect xx3 xx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="List.intersectBy (==) xx3 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xx40",fontsize=16,color="burlywood",shape="box"];743[label="xx40/Nothing",fontsize=10,color="white",style="solid",shape="box"];55 -> 743[label="",style="solid", color="burlywood", weight=9]; 743 -> 78[label="",style="solid", color="burlywood", weight=3]; 744[label="xx40/Just xx400",fontsize=10,color="white",style="solid",shape="box"];55 -> 744[label="",style="solid", color="burlywood", weight=9]; 744 -> 79[label="",style="solid", color="burlywood", weight=3]; 56[label="(==) () xx40",fontsize=16,color="burlywood",shape="box"];745[label="xx40/()",fontsize=10,color="white",style="solid",shape="box"];56 -> 745[label="",style="solid", color="burlywood", weight=9]; 745 -> 80[label="",style="solid", color="burlywood", weight=3]; 57[label="(==) (xx300,xx301,xx302) xx40",fontsize=16,color="burlywood",shape="box"];746[label="xx40/(xx400,xx401,xx402)",fontsize=10,color="white",style="solid",shape="box"];57 -> 746[label="",style="solid", color="burlywood", weight=9]; 746 -> 81[label="",style="solid", color="burlywood", weight=3]; 58[label="primEqChar xx30 xx40",fontsize=16,color="burlywood",shape="box"];747[label="xx30/Char xx300",fontsize=10,color="white",style="solid",shape="box"];58 -> 747[label="",style="solid", color="burlywood", weight=9]; 747 -> 82[label="",style="solid", color="burlywood", weight=3]; 59[label="(==) Integer xx300 xx40",fontsize=16,color="burlywood",shape="box"];748[label="xx40/Integer xx400",fontsize=10,color="white",style="solid",shape="box"];59 -> 748[label="",style="solid", color="burlywood", weight=9]; 748 -> 83[label="",style="solid", color="burlywood", weight=3]; 60[label="(==) LT xx40",fontsize=16,color="burlywood",shape="box"];749[label="xx40/LT",fontsize=10,color="white",style="solid",shape="box"];60 -> 749[label="",style="solid", color="burlywood", weight=9]; 749 -> 84[label="",style="solid", color="burlywood", weight=3]; 750[label="xx40/EQ",fontsize=10,color="white",style="solid",shape="box"];60 -> 750[label="",style="solid", color="burlywood", weight=9]; 750 -> 85[label="",style="solid", color="burlywood", weight=3]; 751[label="xx40/GT",fontsize=10,color="white",style="solid",shape="box"];60 -> 751[label="",style="solid", color="burlywood", weight=9]; 751 -> 86[label="",style="solid", color="burlywood", weight=3]; 61[label="(==) EQ xx40",fontsize=16,color="burlywood",shape="box"];752[label="xx40/LT",fontsize=10,color="white",style="solid",shape="box"];61 -> 752[label="",style="solid", color="burlywood", weight=9]; 752 -> 87[label="",style="solid", color="burlywood", weight=3]; 753[label="xx40/EQ",fontsize=10,color="white",style="solid",shape="box"];61 -> 753[label="",style="solid", color="burlywood", weight=9]; 753 -> 88[label="",style="solid", color="burlywood", weight=3]; 754[label="xx40/GT",fontsize=10,color="white",style="solid",shape="box"];61 -> 754[label="",style="solid", color="burlywood", weight=9]; 754 -> 89[label="",style="solid", color="burlywood", weight=3]; 62[label="(==) GT xx40",fontsize=16,color="burlywood",shape="box"];755[label="xx40/LT",fontsize=10,color="white",style="solid",shape="box"];62 -> 755[label="",style="solid", color="burlywood", weight=9]; 755 -> 90[label="",style="solid", color="burlywood", weight=3]; 756[label="xx40/EQ",fontsize=10,color="white",style="solid",shape="box"];62 -> 756[label="",style="solid", color="burlywood", weight=9]; 756 -> 91[label="",style="solid", color="burlywood", weight=3]; 757[label="xx40/GT",fontsize=10,color="white",style="solid",shape="box"];62 -> 757[label="",style="solid", color="burlywood", weight=9]; 757 -> 92[label="",style="solid", color="burlywood", weight=3]; 63[label="primEqDouble xx30 xx40",fontsize=16,color="burlywood",shape="box"];758[label="xx30/Double xx300 xx301",fontsize=10,color="white",style="solid",shape="box"];63 -> 758[label="",style="solid", color="burlywood", weight=9]; 758 -> 93[label="",style="solid", color="burlywood", weight=3]; 64[label="primEqFloat xx30 xx40",fontsize=16,color="burlywood",shape="box"];759[label="xx30/Float xx300 xx301",fontsize=10,color="white",style="solid",shape="box"];64 -> 759[label="",style="solid", color="burlywood", weight=9]; 759 -> 94[label="",style="solid", color="burlywood", weight=3]; 65[label="primEqInt xx30 xx40",fontsize=16,color="burlywood",shape="triangle"];760[label="xx30/Pos xx300",fontsize=10,color="white",style="solid",shape="box"];65 -> 760[label="",style="solid", color="burlywood", weight=9]; 760 -> 95[label="",style="solid", color="burlywood", weight=3]; 761[label="xx30/Neg xx300",fontsize=10,color="white",style="solid",shape="box"];65 -> 761[label="",style="solid", color="burlywood", weight=9]; 761 -> 96[label="",style="solid", color="burlywood", weight=3]; 66[label="(==) xx300 : xx301 xx40",fontsize=16,color="burlywood",shape="box"];762[label="xx40/xx400 : xx401",fontsize=10,color="white",style="solid",shape="box"];66 -> 762[label="",style="solid", color="burlywood", weight=9]; 762 -> 97[label="",style="solid", color="burlywood", weight=3]; 763[label="xx40/[]",fontsize=10,color="white",style="solid",shape="box"];66 -> 763[label="",style="solid", color="burlywood", weight=9]; 763 -> 98[label="",style="solid", color="burlywood", weight=3]; 67[label="(==) [] xx40",fontsize=16,color="burlywood",shape="box"];764[label="xx40/xx400 : xx401",fontsize=10,color="white",style="solid",shape="box"];67 -> 764[label="",style="solid", color="burlywood", weight=9]; 764 -> 99[label="",style="solid", color="burlywood", weight=3]; 765[label="xx40/[]",fontsize=10,color="white",style="solid",shape="box"];67 -> 765[label="",style="solid", color="burlywood", weight=9]; 765 -> 100[label="",style="solid", color="burlywood", weight=3]; 68[label="(==) False xx40",fontsize=16,color="burlywood",shape="box"];766[label="xx40/False",fontsize=10,color="white",style="solid",shape="box"];68 -> 766[label="",style="solid", color="burlywood", weight=9]; 766 -> 101[label="",style="solid", color="burlywood", weight=3]; 767[label="xx40/True",fontsize=10,color="white",style="solid",shape="box"];68 -> 767[label="",style="solid", color="burlywood", weight=9]; 767 -> 102[label="",style="solid", color="burlywood", weight=3]; 69[label="(==) True xx40",fontsize=16,color="burlywood",shape="box"];768[label="xx40/False",fontsize=10,color="white",style="solid",shape="box"];69 -> 768[label="",style="solid", color="burlywood", weight=9]; 768 -> 103[label="",style="solid", color="burlywood", weight=3]; 769[label="xx40/True",fontsize=10,color="white",style="solid",shape="box"];69 -> 769[label="",style="solid", color="burlywood", weight=9]; 769 -> 104[label="",style="solid", color="burlywood", weight=3]; 70[label="(==) Left xx300 xx40",fontsize=16,color="burlywood",shape="box"];770[label="xx40/Left xx400",fontsize=10,color="white",style="solid",shape="box"];70 -> 770[label="",style="solid", color="burlywood", weight=9]; 770 -> 105[label="",style="solid", color="burlywood", weight=3]; 771[label="xx40/Right xx400",fontsize=10,color="white",style="solid",shape="box"];70 -> 771[label="",style="solid", color="burlywood", weight=9]; 771 -> 106[label="",style="solid", color="burlywood", weight=3]; 71[label="(==) Right xx300 xx40",fontsize=16,color="burlywood",shape="box"];772[label="xx40/Left xx400",fontsize=10,color="white",style="solid",shape="box"];71 -> 772[label="",style="solid", color="burlywood", weight=9]; 772 -> 107[label="",style="solid", color="burlywood", weight=3]; 773[label="xx40/Right xx400",fontsize=10,color="white",style="solid",shape="box"];71 -> 773[label="",style="solid", color="burlywood", weight=9]; 773 -> 108[label="",style="solid", color="burlywood", weight=3]; 72[label="(==) (xx300,xx301) xx40",fontsize=16,color="burlywood",shape="box"];774[label="xx40/(xx400,xx401)",fontsize=10,color="white",style="solid",shape="box"];72 -> 774[label="",style="solid", color="burlywood", weight=9]; 774 -> 109[label="",style="solid", color="burlywood", weight=3]; 73 -> 23[label="",style="dashed", color="red", weight=0]; 73[label="(++) List.intersectBy000 xx11 (foldr (||) False (map ((==) xx11) xx13)) xx14",fontsize=16,color="magenta"];73 -> 110[label="",style="dashed", color="magenta", weight=3]; 73 -> 111[label="",style="dashed", color="magenta", weight=3]; 73 -> 112[label="",style="dashed", color="magenta", weight=3]; 74[label="(++) List.intersectBy000 xx11 True xx14",fontsize=16,color="black",shape="box"];74 -> 113[label="",style="solid", color="black", weight=3]; 75[label="(==) xx300 :% xx301 xx400 :% xx401",fontsize=16,color="black",shape="box"];75 -> 114[label="",style="solid", color="black", weight=3]; 76[label="(==) Nothing Nothing",fontsize=16,color="black",shape="box"];76 -> 115[label="",style="solid", color="black", weight=3]; 77[label="(==) Nothing Just xx400",fontsize=16,color="black",shape="box"];77 -> 116[label="",style="solid", color="black", weight=3]; 78[label="(==) Just xx300 Nothing",fontsize=16,color="black",shape="box"];78 -> 117[label="",style="solid", color="black", weight=3]; 79[label="(==) Just xx300 Just xx400",fontsize=16,color="black",shape="box"];79 -> 118[label="",style="solid", color="black", weight=3]; 80[label="(==) () ()",fontsize=16,color="black",shape="box"];80 -> 119[label="",style="solid", color="black", weight=3]; 81[label="(==) (xx300,xx301,xx302) (xx400,xx401,xx402)",fontsize=16,color="black",shape="box"];81 -> 120[label="",style="solid", color="black", weight=3]; 82[label="primEqChar (Char xx300) xx40",fontsize=16,color="burlywood",shape="box"];775[label="xx40/Char xx400",fontsize=10,color="white",style="solid",shape="box"];82 -> 775[label="",style="solid", color="burlywood", weight=9]; 775 -> 121[label="",style="solid", color="burlywood", weight=3]; 83[label="(==) Integer xx300 Integer xx400",fontsize=16,color="black",shape="box"];83 -> 122[label="",style="solid", color="black", weight=3]; 84[label="(==) LT LT",fontsize=16,color="black",shape="box"];84 -> 123[label="",style="solid", color="black", weight=3]; 85[label="(==) LT EQ",fontsize=16,color="black",shape="box"];85 -> 124[label="",style="solid", color="black", weight=3]; 86[label="(==) LT GT",fontsize=16,color="black",shape="box"];86 -> 125[label="",style="solid", color="black", weight=3]; 87[label="(==) EQ LT",fontsize=16,color="black",shape="box"];87 -> 126[label="",style="solid", color="black", weight=3]; 88[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];88 -> 127[label="",style="solid", color="black", weight=3]; 89[label="(==) EQ GT",fontsize=16,color="black",shape="box"];89 -> 128[label="",style="solid", color="black", weight=3]; 90[label="(==) GT LT",fontsize=16,color="black",shape="box"];90 -> 129[label="",style="solid", color="black", weight=3]; 91[label="(==) GT EQ",fontsize=16,color="black",shape="box"];91 -> 130[label="",style="solid", color="black", weight=3]; 92[label="(==) GT GT",fontsize=16,color="black",shape="box"];92 -> 131[label="",style="solid", color="black", weight=3]; 93[label="primEqDouble (Double xx300 xx301) xx40",fontsize=16,color="burlywood",shape="box"];776[label="xx40/Double xx400 xx401",fontsize=10,color="white",style="solid",shape="box"];93 -> 776[label="",style="solid", color="burlywood", weight=9]; 776 -> 132[label="",style="solid", color="burlywood", weight=3]; 94[label="primEqFloat (Float xx300 xx301) xx40",fontsize=16,color="burlywood",shape="box"];777[label="xx40/Float xx400 xx401",fontsize=10,color="white",style="solid",shape="box"];94 -> 777[label="",style="solid", color="burlywood", weight=9]; 777 -> 133[label="",style="solid", color="burlywood", weight=3]; 95[label="primEqInt (Pos xx300) xx40",fontsize=16,color="burlywood",shape="box"];778[label="xx300/Succ xx3000",fontsize=10,color="white",style="solid",shape="box"];95 -> 778[label="",style="solid", color="burlywood", weight=9]; 778 -> 134[label="",style="solid", color="burlywood", weight=3]; 779[label="xx300/Zero",fontsize=10,color="white",style="solid",shape="box"];95 -> 779[label="",style="solid", color="burlywood", weight=9]; 779 -> 135[label="",style="solid", color="burlywood", weight=3]; 96[label="primEqInt (Neg xx300) xx40",fontsize=16,color="burlywood",shape="box"];780[label="xx300/Succ xx3000",fontsize=10,color="white",style="solid",shape="box"];96 -> 780[label="",style="solid", color="burlywood", weight=9]; 780 -> 136[label="",style="solid", color="burlywood", weight=3]; 781[label="xx300/Zero",fontsize=10,color="white",style="solid",shape="box"];96 -> 781[label="",style="solid", color="burlywood", weight=9]; 781 -> 137[label="",style="solid", color="burlywood", weight=3]; 97[label="(==) xx300 : xx301 xx400 : xx401",fontsize=16,color="black",shape="box"];97 -> 138[label="",style="solid", color="black", weight=3]; 98[label="(==) xx300 : xx301 []",fontsize=16,color="black",shape="box"];98 -> 139[label="",style="solid", color="black", weight=3]; 99[label="(==) [] xx400 : xx401",fontsize=16,color="black",shape="box"];99 -> 140[label="",style="solid", color="black", weight=3]; 100[label="(==) [] []",fontsize=16,color="black",shape="box"];100 -> 141[label="",style="solid", color="black", weight=3]; 101[label="(==) False False",fontsize=16,color="black",shape="box"];101 -> 142[label="",style="solid", color="black", weight=3]; 102[label="(==) False True",fontsize=16,color="black",shape="box"];102 -> 143[label="",style="solid", color="black", weight=3]; 103[label="(==) True False",fontsize=16,color="black",shape="box"];103 -> 144[label="",style="solid", color="black", weight=3]; 104[label="(==) True True",fontsize=16,color="black",shape="box"];104 -> 145[label="",style="solid", color="black", weight=3]; 105[label="(==) Left xx300 Left xx400",fontsize=16,color="black",shape="box"];105 -> 146[label="",style="solid", color="black", weight=3]; 106[label="(==) Left xx300 Right xx400",fontsize=16,color="black",shape="box"];106 -> 147[label="",style="solid", color="black", weight=3]; 107[label="(==) Right xx300 Left xx400",fontsize=16,color="black",shape="box"];107 -> 148[label="",style="solid", color="black", weight=3]; 108[label="(==) Right xx300 Right xx400",fontsize=16,color="black",shape="box"];108 -> 149[label="",style="solid", color="black", weight=3]; 109[label="(==) (xx300,xx301) (xx400,xx401)",fontsize=16,color="black",shape="box"];109 -> 150[label="",style="solid", color="black", weight=3]; 110[label="xx13",fontsize=16,color="green",shape="box"];111[label="xx11",fontsize=16,color="green",shape="box"];112[label="xx14",fontsize=16,color="green",shape="box"];113[label="(++) (xx11 : []) xx14",fontsize=16,color="black",shape="box"];113 -> 151[label="",style="solid", color="black", weight=3]; 114 -> 231[label="",style="dashed", color="red", weight=0]; 114[label="xx300 == xx400 && xx301 == xx401",fontsize=16,color="magenta"];114 -> 232[label="",style="dashed", color="magenta", weight=3]; 114 -> 233[label="",style="dashed", color="magenta", weight=3]; 115[label="True",fontsize=16,color="green",shape="box"];116[label="False",fontsize=16,color="green",shape="box"];117[label="False",fontsize=16,color="green",shape="box"];118[label="xx300 == xx400",fontsize=16,color="blue",shape="box"];782[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 782[label="",style="solid", color="blue", weight=9]; 782 -> 162[label="",style="solid", color="blue", weight=3]; 783[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 783[label="",style="solid", color="blue", weight=9]; 783 -> 163[label="",style="solid", color="blue", weight=3]; 784[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 784[label="",style="solid", color="blue", weight=9]; 784 -> 164[label="",style="solid", color="blue", weight=3]; 785[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 785[label="",style="solid", color="blue", weight=9]; 785 -> 165[label="",style="solid", color="blue", weight=3]; 786[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 786[label="",style="solid", color="blue", weight=9]; 786 -> 166[label="",style="solid", color="blue", weight=3]; 787[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 787[label="",style="solid", color="blue", weight=9]; 787 -> 167[label="",style="solid", color="blue", weight=3]; 788[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 788[label="",style="solid", color="blue", weight=9]; 788 -> 168[label="",style="solid", color="blue", weight=3]; 789[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 789[label="",style="solid", color="blue", weight=9]; 789 -> 169[label="",style="solid", color="blue", weight=3]; 790[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 790[label="",style="solid", color="blue", weight=9]; 790 -> 170[label="",style="solid", color="blue", weight=3]; 791[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 791[label="",style="solid", color="blue", weight=9]; 791 -> 171[label="",style="solid", color="blue", weight=3]; 792[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 792[label="",style="solid", color="blue", weight=9]; 792 -> 172[label="",style="solid", color="blue", weight=3]; 793[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 793[label="",style="solid", color="blue", weight=9]; 793 -> 173[label="",style="solid", color="blue", weight=3]; 794[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 794[label="",style="solid", color="blue", weight=9]; 794 -> 174[label="",style="solid", color="blue", weight=3]; 795[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];118 -> 795[label="",style="solid", color="blue", weight=9]; 795 -> 175[label="",style="solid", color="blue", weight=3]; 119[label="True",fontsize=16,color="green",shape="box"];120 -> 231[label="",style="dashed", color="red", weight=0]; 120[label="xx300 == xx400 && xx301 == xx401 && xx302 == xx402",fontsize=16,color="magenta"];120 -> 234[label="",style="dashed", color="magenta", weight=3]; 120 -> 235[label="",style="dashed", color="magenta", weight=3]; 121[label="primEqChar (Char xx300) (Char xx400)",fontsize=16,color="black",shape="box"];121 -> 187[label="",style="solid", color="black", weight=3]; 122 -> 65[label="",style="dashed", color="red", weight=0]; 122[label="primEqInt xx300 xx400",fontsize=16,color="magenta"];122 -> 188[label="",style="dashed", color="magenta", weight=3]; 122 -> 189[label="",style="dashed", color="magenta", weight=3]; 123[label="True",fontsize=16,color="green",shape="box"];124[label="False",fontsize=16,color="green",shape="box"];125[label="False",fontsize=16,color="green",shape="box"];126[label="False",fontsize=16,color="green",shape="box"];127[label="True",fontsize=16,color="green",shape="box"];128[label="False",fontsize=16,color="green",shape="box"];129[label="False",fontsize=16,color="green",shape="box"];130[label="False",fontsize=16,color="green",shape="box"];131[label="True",fontsize=16,color="green",shape="box"];132[label="primEqDouble (Double xx300 xx301) (Double xx400 xx401)",fontsize=16,color="black",shape="box"];132 -> 190[label="",style="solid", color="black", weight=3]; 133[label="primEqFloat (Float xx300 xx301) (Float xx400 xx401)",fontsize=16,color="black",shape="box"];133 -> 191[label="",style="solid", color="black", weight=3]; 134[label="primEqInt (Pos (Succ xx3000)) xx40",fontsize=16,color="burlywood",shape="box"];796[label="xx40/Pos xx400",fontsize=10,color="white",style="solid",shape="box"];134 -> 796[label="",style="solid", color="burlywood", weight=9]; 796 -> 192[label="",style="solid", color="burlywood", weight=3]; 797[label="xx40/Neg xx400",fontsize=10,color="white",style="solid",shape="box"];134 -> 797[label="",style="solid", color="burlywood", weight=9]; 797 -> 193[label="",style="solid", color="burlywood", weight=3]; 135[label="primEqInt (Pos Zero) xx40",fontsize=16,color="burlywood",shape="box"];798[label="xx40/Pos xx400",fontsize=10,color="white",style="solid",shape="box"];135 -> 798[label="",style="solid", color="burlywood", weight=9]; 798 -> 194[label="",style="solid", color="burlywood", weight=3]; 799[label="xx40/Neg xx400",fontsize=10,color="white",style="solid",shape="box"];135 -> 799[label="",style="solid", color="burlywood", weight=9]; 799 -> 195[label="",style="solid", color="burlywood", weight=3]; 136[label="primEqInt (Neg (Succ xx3000)) xx40",fontsize=16,color="burlywood",shape="box"];800[label="xx40/Pos xx400",fontsize=10,color="white",style="solid",shape="box"];136 -> 800[label="",style="solid", color="burlywood", weight=9]; 800 -> 196[label="",style="solid", color="burlywood", weight=3]; 801[label="xx40/Neg xx400",fontsize=10,color="white",style="solid",shape="box"];136 -> 801[label="",style="solid", color="burlywood", weight=9]; 801 -> 197[label="",style="solid", color="burlywood", weight=3]; 137[label="primEqInt (Neg Zero) xx40",fontsize=16,color="burlywood",shape="box"];802[label="xx40/Pos xx400",fontsize=10,color="white",style="solid",shape="box"];137 -> 802[label="",style="solid", color="burlywood", weight=9]; 802 -> 198[label="",style="solid", color="burlywood", weight=3]; 803[label="xx40/Neg xx400",fontsize=10,color="white",style="solid",shape="box"];137 -> 803[label="",style="solid", color="burlywood", weight=9]; 803 -> 199[label="",style="solid", color="burlywood", weight=3]; 138 -> 231[label="",style="dashed", color="red", weight=0]; 138[label="xx300 == xx400 && xx301 == xx401",fontsize=16,color="magenta"];138 -> 236[label="",style="dashed", color="magenta", weight=3]; 138 -> 237[label="",style="dashed", color="magenta", weight=3]; 139[label="False",fontsize=16,color="green",shape="box"];140[label="False",fontsize=16,color="green",shape="box"];141[label="True",fontsize=16,color="green",shape="box"];142[label="True",fontsize=16,color="green",shape="box"];143[label="False",fontsize=16,color="green",shape="box"];144[label="False",fontsize=16,color="green",shape="box"];145[label="True",fontsize=16,color="green",shape="box"];146[label="xx300 == xx400",fontsize=16,color="blue",shape="box"];804[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];146 -> 804[label="",style="solid", color="blue", weight=9]; 804 -> 200[label="",style="solid", color="blue", weight=3]; 805[label="== :: (Maybe a) -> (Maybe a) -> 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205[label="",style="solid", color="blue", weight=3]; 810[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];146 -> 810[label="",style="solid", color="blue", weight=9]; 810 -> 206[label="",style="solid", color="blue", weight=3]; 811[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];146 -> 811[label="",style="solid", color="blue", weight=9]; 811 -> 207[label="",style="solid", color="blue", weight=3]; 812[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];146 -> 812[label="",style="solid", color="blue", weight=9]; 812 -> 208[label="",style="solid", color="blue", weight=3]; 813[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];146 -> 813[label="",style="solid", color="blue", weight=9]; 813 -> 209[label="",style="solid", color="blue", weight=3]; 814[label="== :: ([] a) -> ([] a) -> 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Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 822[label="",style="solid", color="blue", weight=9]; 822 -> 218[label="",style="solid", color="blue", weight=3]; 823[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 823[label="",style="solid", color="blue", weight=9]; 823 -> 219[label="",style="solid", color="blue", weight=3]; 824[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 824[label="",style="solid", color="blue", weight=9]; 824 -> 220[label="",style="solid", color="blue", weight=3]; 825[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 825[label="",style="solid", color="blue", weight=9]; 825 -> 221[label="",style="solid", color="blue", weight=3]; 826[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 826[label="",style="solid", color="blue", weight=9]; 826 -> 222[label="",style="solid", color="blue", weight=3]; 827[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 827[label="",style="solid", color="blue", weight=9]; 827 -> 223[label="",style="solid", color="blue", weight=3]; 828[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 828[label="",style="solid", color="blue", weight=9]; 828 -> 224[label="",style="solid", color="blue", weight=3]; 829[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 829[label="",style="solid", color="blue", weight=9]; 829 -> 225[label="",style="solid", color="blue", weight=3]; 830[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];149 -> 830[label="",style="solid", color="blue", weight=9]; 830 -> 226[label="",style="solid", color="blue", weight=3]; 831[label="== :: ((@2) a b) -> ((@2) a b) -> 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174 -> 48[label="",style="dashed", color="red", weight=0]; 174[label="xx300 == xx400",fontsize=16,color="magenta"];174 -> 274[label="",style="dashed", color="magenta", weight=3]; 174 -> 275[label="",style="dashed", color="magenta", weight=3]; 175 -> 49[label="",style="dashed", color="red", weight=0]; 175[label="xx300 == xx400",fontsize=16,color="magenta"];175 -> 276[label="",style="dashed", color="magenta", weight=3]; 175 -> 277[label="",style="dashed", color="magenta", weight=3]; 234[label="xx300 == xx400",fontsize=16,color="blue",shape="box"];838[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 838[label="",style="solid", color="blue", weight=9]; 838 -> 278[label="",style="solid", color="blue", weight=3]; 839[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 839[label="",style="solid", color="blue", weight=9]; 839 -> 279[label="",style="solid", color="blue", weight=3]; 840[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 840[label="",style="solid", color="blue", weight=9]; 840 -> 280[label="",style="solid", color="blue", weight=3]; 841[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 841[label="",style="solid", color="blue", weight=9]; 841 -> 281[label="",style="solid", color="blue", weight=3]; 842[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 842[label="",style="solid", color="blue", weight=9]; 842 -> 282[label="",style="solid", color="blue", weight=3]; 843[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 843[label="",style="solid", color="blue", weight=9]; 843 -> 283[label="",style="solid", color="blue", weight=3]; 844[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];234 -> 844[label="",style="solid", 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857[label="xx400/Zero",fontsize=10,color="white",style="solid",shape="box"];194 -> 857[label="",style="solid", color="burlywood", weight=9]; 857 -> 304[label="",style="solid", color="burlywood", weight=3]; 195[label="primEqInt (Pos Zero) (Neg xx400)",fontsize=16,color="burlywood",shape="box"];858[label="xx400/Succ xx4000",fontsize=10,color="white",style="solid",shape="box"];195 -> 858[label="",style="solid", color="burlywood", weight=9]; 858 -> 305[label="",style="solid", color="burlywood", weight=3]; 859[label="xx400/Zero",fontsize=10,color="white",style="solid",shape="box"];195 -> 859[label="",style="solid", color="burlywood", weight=9]; 859 -> 306[label="",style="solid", color="burlywood", weight=3]; 196[label="primEqInt (Neg (Succ xx3000)) (Pos xx400)",fontsize=16,color="black",shape="box"];196 -> 307[label="",style="solid", color="black", weight=3]; 197[label="primEqInt (Neg (Succ xx3000)) (Neg xx400)",fontsize=16,color="burlywood",shape="box"];860[label="xx400/Succ 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-> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 868[label="",style="solid", color="blue", weight=9]; 868 -> 316[label="",style="solid", color="blue", weight=3]; 869[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 869[label="",style="solid", color="blue", weight=9]; 869 -> 317[label="",style="solid", color="blue", weight=3]; 870[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 870[label="",style="solid", color="blue", weight=9]; 870 -> 318[label="",style="solid", color="blue", weight=3]; 871[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 871[label="",style="solid", color="blue", weight=9]; 871 -> 319[label="",style="solid", color="blue", weight=3]; 872[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 872[label="",style="solid", color="blue", weight=9]; 872 -> 320[label="",style="solid", color="blue", weight=3]; 873[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 873[label="",style="solid", color="blue", weight=9]; 873 -> 321[label="",style="solid", color="blue", weight=3]; 874[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 874[label="",style="solid", color="blue", weight=9]; 874 -> 322[label="",style="solid", color="blue", weight=3]; 875[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 875[label="",style="solid", color="blue", weight=9]; 875 -> 323[label="",style="solid", color="blue", weight=3]; 876[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 876[label="",style="solid", color="blue", weight=9]; 876 -> 324[label="",style="solid", color="blue", weight=3]; 877[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 877[label="",style="solid", color="blue", weight=9]; 877 -> 325[label="",style="solid", color="blue", weight=3]; 878[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 878[label="",style="solid", color="blue", weight=9]; 878 -> 326[label="",style="solid", color="blue", weight=3]; 879[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];236 -> 879[label="",style="solid", color="blue", weight=9]; 879 -> 327[label="",style="solid", color="blue", weight=3]; 237 -> 46[label="",style="dashed", color="red", weight=0]; 237[label="xx301 == xx401",fontsize=16,color="magenta"];237 -> 328[label="",style="dashed", color="magenta", weight=3]; 237 -> 329[label="",style="dashed", color="magenta", weight=3]; 200 -> 36[label="",style="dashed", color="red", weight=0]; 200[label="xx300 == xx400",fontsize=16,color="magenta"];200 -> 330[label="",style="dashed", color="magenta", weight=3]; 200 -> 331[label="",style="dashed", color="magenta", weight=3]; 201 -> 37[label="",style="dashed", color="red", weight=0]; 201[label="xx300 == xx400",fontsize=16,color="magenta"];201 -> 332[label="",style="dashed", color="magenta", weight=3]; 201 -> 333[label="",style="dashed", color="magenta", weight=3]; 202 -> 38[label="",style="dashed", color="red", weight=0]; 202[label="xx300 == xx400",fontsize=16,color="magenta"];202 -> 334[label="",style="dashed", color="magenta", weight=3]; 202 -> 335[label="",style="dashed", color="magenta", weight=3]; 203 -> 39[label="",style="dashed", color="red", weight=0]; 203[label="xx300 == xx400",fontsize=16,color="magenta"];203 -> 336[label="",style="dashed", color="magenta", weight=3]; 203 -> 337[label="",style="dashed", color="magenta", weight=3]; 204 -> 40[label="",style="dashed", color="red", weight=0]; 204[label="xx300 == xx400",fontsize=16,color="magenta"];204 -> 338[label="",style="dashed", 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208 -> 347[label="",style="dashed", color="magenta", weight=3]; 209 -> 45[label="",style="dashed", color="red", weight=0]; 209[label="xx300 == xx400",fontsize=16,color="magenta"];209 -> 348[label="",style="dashed", color="magenta", weight=3]; 209 -> 349[label="",style="dashed", color="magenta", weight=3]; 210 -> 46[label="",style="dashed", color="red", weight=0]; 210[label="xx300 == xx400",fontsize=16,color="magenta"];210 -> 350[label="",style="dashed", color="magenta", weight=3]; 210 -> 351[label="",style="dashed", color="magenta", weight=3]; 211 -> 47[label="",style="dashed", color="red", weight=0]; 211[label="xx300 == xx400",fontsize=16,color="magenta"];211 -> 352[label="",style="dashed", color="magenta", weight=3]; 211 -> 353[label="",style="dashed", color="magenta", weight=3]; 212 -> 48[label="",style="dashed", color="red", weight=0]; 212[label="xx300 == xx400",fontsize=16,color="magenta"];212 -> 354[label="",style="dashed", color="magenta", weight=3]; 212 -> 355[label="",style="dashed", color="magenta", weight=3]; 213 -> 49[label="",style="dashed", color="red", weight=0]; 213[label="xx300 == xx400",fontsize=16,color="magenta"];213 -> 356[label="",style="dashed", color="magenta", weight=3]; 213 -> 357[label="",style="dashed", color="magenta", weight=3]; 214 -> 36[label="",style="dashed", color="red", weight=0]; 214[label="xx300 == xx400",fontsize=16,color="magenta"];214 -> 358[label="",style="dashed", color="magenta", weight=3]; 214 -> 359[label="",style="dashed", color="magenta", weight=3]; 215 -> 37[label="",style="dashed", color="red", weight=0]; 215[label="xx300 == xx400",fontsize=16,color="magenta"];215 -> 360[label="",style="dashed", color="magenta", weight=3]; 215 -> 361[label="",style="dashed", color="magenta", weight=3]; 216 -> 38[label="",style="dashed", color="red", weight=0]; 216[label="xx300 == xx400",fontsize=16,color="magenta"];216 -> 362[label="",style="dashed", color="magenta", weight=3]; 216 -> 363[label="",style="dashed", 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221 -> 43[label="",style="dashed", color="red", weight=0]; 221[label="xx300 == xx400",fontsize=16,color="magenta"];221 -> 372[label="",style="dashed", color="magenta", weight=3]; 221 -> 373[label="",style="dashed", color="magenta", weight=3]; 222 -> 44[label="",style="dashed", color="red", weight=0]; 222[label="xx300 == xx400",fontsize=16,color="magenta"];222 -> 374[label="",style="dashed", color="magenta", weight=3]; 222 -> 375[label="",style="dashed", color="magenta", weight=3]; 223 -> 45[label="",style="dashed", color="red", weight=0]; 223[label="xx300 == xx400",fontsize=16,color="magenta"];223 -> 376[label="",style="dashed", color="magenta", weight=3]; 223 -> 377[label="",style="dashed", color="magenta", weight=3]; 224 -> 46[label="",style="dashed", color="red", weight=0]; 224[label="xx300 == xx400",fontsize=16,color="magenta"];224 -> 378[label="",style="dashed", color="magenta", weight=3]; 224 -> 379[label="",style="dashed", color="magenta", weight=3]; 225 -> 47[label="",style="dashed", color="red", weight=0]; 225[label="xx300 == xx400",fontsize=16,color="magenta"];225 -> 380[label="",style="dashed", color="magenta", weight=3]; 225 -> 381[label="",style="dashed", color="magenta", weight=3]; 226 -> 48[label="",style="dashed", color="red", weight=0]; 226[label="xx300 == xx400",fontsize=16,color="magenta"];226 -> 382[label="",style="dashed", color="magenta", weight=3]; 226 -> 383[label="",style="dashed", color="magenta", weight=3]; 227 -> 49[label="",style="dashed", color="red", weight=0]; 227[label="xx300 == xx400",fontsize=16,color="magenta"];227 -> 384[label="",style="dashed", color="magenta", weight=3]; 227 -> 385[label="",style="dashed", color="magenta", weight=3]; 238[label="xx300 == xx400",fontsize=16,color="blue",shape="box"];880[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 880[label="",style="solid", color="blue", weight=9]; 880 -> 386[label="",style="solid", color="blue", weight=3]; 881[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 881[label="",style="solid", color="blue", weight=9]; 881 -> 387[label="",style="solid", color="blue", weight=3]; 882[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 882[label="",style="solid", color="blue", weight=9]; 882 -> 388[label="",style="solid", color="blue", weight=3]; 883[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 883[label="",style="solid", color="blue", weight=9]; 883 -> 389[label="",style="solid", color="blue", weight=3]; 884[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 884[label="",style="solid", color="blue", weight=9]; 884 -> 390[label="",style="solid", color="blue", weight=3]; 885[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 885[label="",style="solid", color="blue", weight=9]; 885 -> 391[label="",style="solid", color="blue", weight=3]; 886[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 886[label="",style="solid", color="blue", weight=9]; 886 -> 392[label="",style="solid", color="blue", weight=3]; 887[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 887[label="",style="solid", color="blue", weight=9]; 887 -> 393[label="",style="solid", color="blue", weight=3]; 888[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 888[label="",style="solid", color="blue", weight=9]; 888 -> 394[label="",style="solid", color="blue", weight=3]; 889[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 889[label="",style="solid", color="blue", weight=9]; 889 -> 395[label="",style="solid", color="blue", weight=3]; 890[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 890[label="",style="solid", color="blue", weight=9]; 890 -> 396[label="",style="solid", color="blue", weight=3]; 891[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 891[label="",style="solid", color="blue", weight=9]; 891 -> 397[label="",style="solid", color="blue", weight=3]; 892[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 892[label="",style="solid", color="blue", weight=9]; 892 -> 398[label="",style="solid", color="blue", weight=3]; 893[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];238 -> 893[label="",style="solid", color="blue", weight=9]; 893 -> 399[label="",style="solid", color="blue", weight=3]; 239[label="xx301 == xx401",fontsize=16,color="blue",shape="box"];894[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 894[label="",style="solid", color="blue", weight=9]; 894 -> 400[label="",style="solid", color="blue", weight=3]; 895[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 895[label="",style="solid", color="blue", weight=9]; 895 -> 401[label="",style="solid", color="blue", weight=3]; 896[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 896[label="",style="solid", color="blue", weight=9]; 896 -> 402[label="",style="solid", color="blue", weight=3]; 897[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 897[label="",style="solid", color="blue", weight=9]; 897 -> 403[label="",style="solid", color="blue", weight=3]; 898[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 898[label="",style="solid", color="blue", weight=9]; 898 -> 404[label="",style="solid", color="blue", weight=3]; 899[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 899[label="",style="solid", color="blue", weight=9]; 899 -> 405[label="",style="solid", color="blue", weight=3]; 900[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 900[label="",style="solid", color="blue", weight=9]; 900 -> 406[label="",style="solid", color="blue", weight=3]; 901[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 901[label="",style="solid", color="blue", weight=9]; 901 -> 407[label="",style="solid", color="blue", weight=3]; 902[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 902[label="",style="solid", color="blue", weight=9]; 902 -> 408[label="",style="solid", color="blue", weight=3]; 903[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 903[label="",style="solid", color="blue", weight=9]; 903 -> 409[label="",style="solid", color="blue", weight=3]; 904[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 904[label="",style="solid", color="blue", weight=9]; 904 -> 410[label="",style="solid", color="blue", weight=3]; 905[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 905[label="",style="solid", color="blue", weight=9]; 905 -> 411[label="",style="solid", color="blue", weight=3]; 906[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 906[label="",style="solid", color="blue", weight=9]; 906 -> 412[label="",style="solid", color="blue", weight=3]; 907[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];239 -> 907[label="",style="solid", color="blue", weight=9]; 907 -> 413[label="",style="solid", color="blue", weight=3]; 228 -> 35[label="",style="dashed", color="red", weight=0]; 228[label="[] ++ xx14",fontsize=16,color="magenta"];228 -> 414[label="",style="dashed", color="magenta", weight=3]; 244 -> 41[label="",style="dashed", color="red", weight=0]; 244[label="xx300 == xx400",fontsize=16,color="magenta"];244 -> 415[label="",style="dashed", color="magenta", weight=3]; 244 -> 416[label="",style="dashed", color="magenta", weight=3]; 245 -> 45[label="",style="dashed", color="red", weight=0]; 245[label="xx300 == xx400",fontsize=16,color="magenta"];245 -> 417[label="",style="dashed", color="magenta", weight=3]; 245 -> 418[label="",style="dashed", color="magenta", weight=3]; 246 -> 41[label="",style="dashed", color="red", weight=0]; 246[label="xx301 == xx401",fontsize=16,color="magenta"];246 -> 419[label="",style="dashed", color="magenta", weight=3]; 246 -> 420[label="",style="dashed", color="magenta", weight=3]; 247 -> 45[label="",style="dashed", color="red", weight=0]; 247[label="xx301 == xx401",fontsize=16,color="magenta"];247 -> 421[label="",style="dashed", color="magenta", weight=3]; 247 -> 422[label="",style="dashed", color="magenta", weight=3]; 248[label="False && xx27",fontsize=16,color="black",shape="box"];248 -> 423[label="",style="solid", color="black", weight=3]; 249[label="True && xx27",fontsize=16,color="black",shape="box"];249 -> 424[label="",style="solid", color="black", weight=3]; 250[label="xx400",fontsize=16,color="green",shape="box"];251[label="xx300",fontsize=16,color="green",shape="box"];252[label="xx400",fontsize=16,color="green",shape="box"];253[label="xx300",fontsize=16,color="green",shape="box"];254[label="xx400",fontsize=16,color="green",shape="box"];255[label="xx300",fontsize=16,color="green",shape="box"];256[label="xx400",fontsize=16,color="green",shape="box"];257[label="xx300",fontsize=16,color="green",shape="box"];258[label="xx400",fontsize=16,color="green",shape="box"];259[label="xx300",fontsize=16,color="green",shape="box"];260[label="xx400",fontsize=16,color="green",shape="box"];261[label="xx300",fontsize=16,color="green",shape="box"];262[label="xx400",fontsize=16,color="green",shape="box"];263[label="xx300",fontsize=16,color="green",shape="box"];264[label="xx400",fontsize=16,color="green",shape="box"];265[label="xx300",fontsize=16,color="green",shape="box"];266[label="xx400",fontsize=16,color="green",shape="box"];267[label="xx300",fontsize=16,color="green",shape="box"];268[label="xx400",fontsize=16,color="green",shape="box"];269[label="xx300",fontsize=16,color="green",shape="box"];270[label="xx400",fontsize=16,color="green",shape="box"];271[label="xx300",fontsize=16,color="green",shape="box"];272[label="xx400",fontsize=16,color="green",shape="box"];273[label="xx300",fontsize=16,color="green",shape="box"];274[label="xx400",fontsize=16,color="green",shape="box"];275[label="xx300",fontsize=16,color="green",shape="box"];276[label="xx400",fontsize=16,color="green",shape="box"];277[label="xx300",fontsize=16,color="green",shape="box"];278 -> 36[label="",style="dashed", color="red", weight=0]; 278[label="xx300 == xx400",fontsize=16,color="magenta"];278 -> 425[label="",style="dashed", color="magenta", weight=3]; 278 -> 426[label="",style="dashed", color="magenta", weight=3]; 279 -> 37[label="",style="dashed", color="red", weight=0]; 279[label="xx300 == xx400",fontsize=16,color="magenta"];279 -> 427[label="",style="dashed", color="magenta", weight=3]; 279 -> 428[label="",style="dashed", color="magenta", weight=3]; 280 -> 38[label="",style="dashed", color="red", weight=0]; 280[label="xx300 == xx400",fontsize=16,color="magenta"];280 -> 429[label="",style="dashed", color="magenta", weight=3]; 280 -> 430[label="",style="dashed", color="magenta", weight=3]; 281 -> 39[label="",style="dashed", color="red", weight=0]; 281[label="xx300 == xx400",fontsize=16,color="magenta"];281 -> 431[label="",style="dashed", color="magenta", weight=3]; 281 -> 432[label="",style="dashed", color="magenta", weight=3]; 282 -> 40[label="",style="dashed", color="red", weight=0]; 282[label="xx300 == xx400",fontsize=16,color="magenta"];282 -> 433[label="",style="dashed", color="magenta", weight=3]; 282 -> 434[label="",style="dashed", color="magenta", weight=3]; 283 -> 41[label="",style="dashed", color="red", weight=0]; 283[label="xx300 == xx400",fontsize=16,color="magenta"];283 -> 435[label="",style="dashed", color="magenta", weight=3]; 283 -> 436[label="",style="dashed", color="magenta", weight=3]; 284 -> 42[label="",style="dashed", color="red", weight=0]; 284[label="xx300 == xx400",fontsize=16,color="magenta"];284 -> 437[label="",style="dashed", color="magenta", weight=3]; 284 -> 438[label="",style="dashed", color="magenta", weight=3]; 285 -> 43[label="",style="dashed", color="red", weight=0]; 285[label="xx300 == xx400",fontsize=16,color="magenta"];285 -> 439[label="",style="dashed", color="magenta", weight=3]; 285 -> 440[label="",style="dashed", color="magenta", weight=3]; 286 -> 44[label="",style="dashed", color="red", weight=0]; 286[label="xx300 == xx400",fontsize=16,color="magenta"];286 -> 441[label="",style="dashed", color="magenta", weight=3]; 286 -> 442[label="",style="dashed", color="magenta", weight=3]; 287 -> 45[label="",style="dashed", color="red", weight=0]; 287[label="xx300 == xx400",fontsize=16,color="magenta"];287 -> 443[label="",style="dashed", color="magenta", weight=3]; 287 -> 444[label="",style="dashed", color="magenta", weight=3]; 288 -> 46[label="",style="dashed", color="red", weight=0]; 288[label="xx300 == xx400",fontsize=16,color="magenta"];288 -> 445[label="",style="dashed", color="magenta", weight=3]; 288 -> 446[label="",style="dashed", color="magenta", weight=3]; 289 -> 47[label="",style="dashed", color="red", weight=0]; 289[label="xx300 == xx400",fontsize=16,color="magenta"];289 -> 447[label="",style="dashed", color="magenta", weight=3]; 289 -> 448[label="",style="dashed", color="magenta", weight=3]; 290 -> 48[label="",style="dashed", color="red", weight=0]; 290[label="xx300 == xx400",fontsize=16,color="magenta"];290 -> 449[label="",style="dashed", color="magenta", weight=3]; 290 -> 450[label="",style="dashed", color="magenta", weight=3]; 291 -> 49[label="",style="dashed", color="red", weight=0]; 291[label="xx300 == xx400",fontsize=16,color="magenta"];291 -> 451[label="",style="dashed", color="magenta", weight=3]; 291 -> 452[label="",style="dashed", color="magenta", weight=3]; 292[label="xx301 == xx401",fontsize=16,color="blue",shape="box"];908[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];292 -> 908[label="",style="solid", color="blue", weight=9]; 908 -> 453[label="",style="solid", color="blue", weight=3]; 909[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];292 -> 909[label="",style="solid", color="blue", weight=9]; 909 -> 454[label="",style="solid", color="blue", weight=3]; 910[label="== :: () -> () -> 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472[label="",style="solid", color="blue", weight=3]; 928[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 928[label="",style="solid", color="blue", weight=9]; 928 -> 473[label="",style="solid", color="blue", weight=3]; 929[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 929[label="",style="solid", color="blue", weight=9]; 929 -> 474[label="",style="solid", color="blue", weight=3]; 930[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 930[label="",style="solid", color="blue", weight=9]; 930 -> 475[label="",style="solid", color="blue", weight=3]; 931[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 931[label="",style="solid", color="blue", weight=9]; 931 -> 476[label="",style="solid", color="blue", weight=3]; 932[label="== :: ([] a) -> ([] a) -> 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323[label="xx300 == xx400",fontsize=16,color="magenta"];323 -> 522[label="",style="dashed", color="magenta", weight=3]; 323 -> 523[label="",style="dashed", color="magenta", weight=3]; 324 -> 46[label="",style="dashed", color="red", weight=0]; 324[label="xx300 == xx400",fontsize=16,color="magenta"];324 -> 524[label="",style="dashed", color="magenta", weight=3]; 324 -> 525[label="",style="dashed", color="magenta", weight=3]; 325 -> 47[label="",style="dashed", color="red", weight=0]; 325[label="xx300 == xx400",fontsize=16,color="magenta"];325 -> 526[label="",style="dashed", color="magenta", weight=3]; 325 -> 527[label="",style="dashed", color="magenta", weight=3]; 326 -> 48[label="",style="dashed", color="red", weight=0]; 326[label="xx300 == xx400",fontsize=16,color="magenta"];326 -> 528[label="",style="dashed", color="magenta", weight=3]; 326 -> 529[label="",style="dashed", color="magenta", weight=3]; 327 -> 49[label="",style="dashed", color="red", weight=0]; 327[label="xx300 == 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328[label="xx401",fontsize=16,color="green",shape="box"];329[label="xx301",fontsize=16,color="green",shape="box"];330[label="xx400",fontsize=16,color="green",shape="box"];331[label="xx300",fontsize=16,color="green",shape="box"];332[label="xx400",fontsize=16,color="green",shape="box"];333[label="xx300",fontsize=16,color="green",shape="box"];334[label="xx400",fontsize=16,color="green",shape="box"];335[label="xx300",fontsize=16,color="green",shape="box"];336[label="xx400",fontsize=16,color="green",shape="box"];337[label="xx300",fontsize=16,color="green",shape="box"];338[label="xx400",fontsize=16,color="green",shape="box"];339[label="xx300",fontsize=16,color="green",shape="box"];340[label="xx400",fontsize=16,color="green",shape="box"];341[label="xx300",fontsize=16,color="green",shape="box"];342[label="xx400",fontsize=16,color="green",shape="box"];343[label="xx300",fontsize=16,color="green",shape="box"];344[label="xx400",fontsize=16,color="green",shape="box"];345[label="xx300",fontsize=16,color="green",shape="box"];346[label="xx400",fontsize=16,color="green",shape="box"];347[label="xx300",fontsize=16,color="green",shape="box"];348[label="xx400",fontsize=16,color="green",shape="box"];349[label="xx300",fontsize=16,color="green",shape="box"];350[label="xx400",fontsize=16,color="green",shape="box"];351[label="xx300",fontsize=16,color="green",shape="box"];352[label="xx400",fontsize=16,color="green",shape="box"];353[label="xx300",fontsize=16,color="green",shape="box"];354[label="xx400",fontsize=16,color="green",shape="box"];355[label="xx300",fontsize=16,color="green",shape="box"];356[label="xx400",fontsize=16,color="green",shape="box"];357[label="xx300",fontsize=16,color="green",shape="box"];358[label="xx400",fontsize=16,color="green",shape="box"];359[label="xx300",fontsize=16,color="green",shape="box"];360[label="xx400",fontsize=16,color="green",shape="box"];361[label="xx300",fontsize=16,color="green",shape="box"];362[label="xx400",fontsize=16,color="green",shape="box"];363[label="xx300",fontsize=16,color="green",shape="box"];364[label="xx400",fontsize=16,color="green",shape="box"];365[label="xx300",fontsize=16,color="green",shape="box"];366[label="xx400",fontsize=16,color="green",shape="box"];367[label="xx300",fontsize=16,color="green",shape="box"];368[label="xx400",fontsize=16,color="green",shape="box"];369[label="xx300",fontsize=16,color="green",shape="box"];370[label="xx400",fontsize=16,color="green",shape="box"];371[label="xx300",fontsize=16,color="green",shape="box"];372[label="xx400",fontsize=16,color="green",shape="box"];373[label="xx300",fontsize=16,color="green",shape="box"];374[label="xx400",fontsize=16,color="green",shape="box"];375[label="xx300",fontsize=16,color="green",shape="box"];376[label="xx400",fontsize=16,color="green",shape="box"];377[label="xx300",fontsize=16,color="green",shape="box"];378[label="xx400",fontsize=16,color="green",shape="box"];379[label="xx300",fontsize=16,color="green",shape="box"];380[label="xx400",fontsize=16,color="green",shape="box"];381[label="xx300",fontsize=16,color="green",shape="box"];382[label="xx400",fontsize=16,color="green",shape="box"];383[label="xx300",fontsize=16,color="green",shape="box"];384[label="xx400",fontsize=16,color="green",shape="box"];385[label="xx300",fontsize=16,color="green",shape="box"];386 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40[label="",style="dashed", color="red", weight=0]; 390[label="xx300 == xx400",fontsize=16,color="magenta"];390 -> 540[label="",style="dashed", color="magenta", weight=3]; 390 -> 541[label="",style="dashed", color="magenta", weight=3]; 391 -> 41[label="",style="dashed", color="red", weight=0]; 391[label="xx300 == xx400",fontsize=16,color="magenta"];391 -> 542[label="",style="dashed", color="magenta", weight=3]; 391 -> 543[label="",style="dashed", color="magenta", weight=3]; 392 -> 42[label="",style="dashed", color="red", weight=0]; 392[label="xx300 == xx400",fontsize=16,color="magenta"];392 -> 544[label="",style="dashed", color="magenta", weight=3]; 392 -> 545[label="",style="dashed", color="magenta", weight=3]; 393 -> 43[label="",style="dashed", color="red", weight=0]; 393[label="xx300 == xx400",fontsize=16,color="magenta"];393 -> 546[label="",style="dashed", color="magenta", weight=3]; 393 -> 547[label="",style="dashed", color="magenta", weight=3]; 394 -> 44[label="",style="dashed", 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398[label="xx300 == xx400",fontsize=16,color="magenta"];398 -> 556[label="",style="dashed", color="magenta", weight=3]; 398 -> 557[label="",style="dashed", color="magenta", weight=3]; 399 -> 49[label="",style="dashed", color="red", weight=0]; 399[label="xx300 == xx400",fontsize=16,color="magenta"];399 -> 558[label="",style="dashed", color="magenta", weight=3]; 399 -> 559[label="",style="dashed", color="magenta", weight=3]; 400 -> 36[label="",style="dashed", color="red", weight=0]; 400[label="xx301 == xx401",fontsize=16,color="magenta"];400 -> 560[label="",style="dashed", color="magenta", weight=3]; 400 -> 561[label="",style="dashed", color="magenta", weight=3]; 401 -> 37[label="",style="dashed", color="red", weight=0]; 401[label="xx301 == xx401",fontsize=16,color="magenta"];401 -> 562[label="",style="dashed", color="magenta", weight=3]; 401 -> 563[label="",style="dashed", color="magenta", weight=3]; 402 -> 38[label="",style="dashed", color="red", weight=0]; 402[label="xx301 == xx401",fontsize=16,color="magenta"];402 -> 564[label="",style="dashed", color="magenta", weight=3]; 402 -> 565[label="",style="dashed", color="magenta", weight=3]; 403 -> 39[label="",style="dashed", color="red", weight=0]; 403[label="xx301 == xx401",fontsize=16,color="magenta"];403 -> 566[label="",style="dashed", color="magenta", weight=3]; 403 -> 567[label="",style="dashed", color="magenta", weight=3]; 404 -> 40[label="",style="dashed", color="red", weight=0]; 404[label="xx301 == xx401",fontsize=16,color="magenta"];404 -> 568[label="",style="dashed", color="magenta", weight=3]; 404 -> 569[label="",style="dashed", color="magenta", weight=3]; 405 -> 41[label="",style="dashed", color="red", weight=0]; 405[label="xx301 == xx401",fontsize=16,color="magenta"];405 -> 570[label="",style="dashed", color="magenta", weight=3]; 405 -> 571[label="",style="dashed", color="magenta", weight=3]; 406 -> 42[label="",style="dashed", color="red", weight=0]; 406[label="xx301 == 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414[label="xx14",fontsize=16,color="green",shape="box"];415[label="xx400",fontsize=16,color="green",shape="box"];416[label="xx300",fontsize=16,color="green",shape="box"];417[label="xx400",fontsize=16,color="green",shape="box"];418[label="xx300",fontsize=16,color="green",shape="box"];419[label="xx401",fontsize=16,color="green",shape="box"];420[label="xx301",fontsize=16,color="green",shape="box"];421[label="xx401",fontsize=16,color="green",shape="box"];422[label="xx301",fontsize=16,color="green",shape="box"];423[label="False",fontsize=16,color="green",shape="box"];424[label="xx27",fontsize=16,color="green",shape="box"];425[label="xx400",fontsize=16,color="green",shape="box"];426[label="xx300",fontsize=16,color="green",shape="box"];427[label="xx400",fontsize=16,color="green",shape="box"];428[label="xx300",fontsize=16,color="green",shape="box"];429[label="xx400",fontsize=16,color="green",shape="box"];430[label="xx300",fontsize=16,color="green",shape="box"];431[label="xx400",fontsize=16,color="green",shape="box"];432[label="xx300",fontsize=16,color="green",shape="box"];433[label="xx400",fontsize=16,color="green",shape="box"];434[label="xx300",fontsize=16,color="green",shape="box"];435[label="xx400",fontsize=16,color="green",shape="box"];436[label="xx300",fontsize=16,color="green",shape="box"];437[label="xx400",fontsize=16,color="green",shape="box"];438[label="xx300",fontsize=16,color="green",shape="box"];439[label="xx400",fontsize=16,color="green",shape="box"];440[label="xx300",fontsize=16,color="green",shape="box"];441[label="xx400",fontsize=16,color="green",shape="box"];442[label="xx300",fontsize=16,color="green",shape="box"];443[label="xx400",fontsize=16,color="green",shape="box"];444[label="xx300",fontsize=16,color="green",shape="box"];445[label="xx400",fontsize=16,color="green",shape="box"];446[label="xx300",fontsize=16,color="green",shape="box"];447[label="xx400",fontsize=16,color="green",shape="box"];448[label="xx300",fontsize=16,color="green",shape="box"];449[label="xx400",fontsize=16,color="green",shape="box"];450[label="xx300",fontsize=16,color="green",shape="box"];451[label="xx400",fontsize=16,color="green",shape="box"];452[label="xx300",fontsize=16,color="green",shape="box"];453 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486[label="xx300",fontsize=16,color="green",shape="box"];487[label="xx401",fontsize=16,color="green",shape="box"];488[label="xx301",fontsize=16,color="green",shape="box"];489[label="xx400",fontsize=16,color="green",shape="box"];490[label="xx300",fontsize=16,color="green",shape="box"];491[label="xx401",fontsize=16,color="green",shape="box"];492 -> 187[label="",style="dashed", color="red", weight=0]; 492[label="primEqNat xx3000 xx4000",fontsize=16,color="magenta"];492 -> 650[label="",style="dashed", color="magenta", weight=3]; 492 -> 651[label="",style="dashed", color="magenta", weight=3]; 493[label="False",fontsize=16,color="green",shape="box"];494[label="False",fontsize=16,color="green",shape="box"];495[label="True",fontsize=16,color="green",shape="box"];496[label="False",fontsize=16,color="green",shape="box"];497[label="True",fontsize=16,color="green",shape="box"];498 -> 187[label="",style="dashed", color="red", weight=0]; 498[label="primEqNat xx3000 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-> 187[label="",style="dashed", color="red", weight=0]; 644[label="primEqNat xx3000 xx4000",fontsize=16,color="magenta"];644 -> 654[label="",style="dashed", color="magenta", weight=3]; 644 -> 655[label="",style="dashed", color="magenta", weight=3]; 645[label="False",fontsize=16,color="green",shape="box"];646[label="False",fontsize=16,color="green",shape="box"];647[label="True",fontsize=16,color="green",shape="box"];648[label="primMulInt (Pos xx3010) xx400",fontsize=16,color="burlywood",shape="box"];942[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];648 -> 942[label="",style="solid", color="burlywood", weight=9]; 942 -> 656[label="",style="solid", color="burlywood", weight=3]; 943[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];648 -> 943[label="",style="solid", color="burlywood", weight=9]; 943 -> 657[label="",style="solid", color="burlywood", weight=3]; 649[label="primMulInt (Neg xx3010) xx400",fontsize=16,color="burlywood",shape="box"];944[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];649 -> 944[label="",style="solid", color="burlywood", weight=9]; 944 -> 658[label="",style="solid", color="burlywood", weight=3]; 945[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];649 -> 945[label="",style="solid", color="burlywood", weight=9]; 945 -> 659[label="",style="solid", color="burlywood", weight=3]; 650[label="xx4000",fontsize=16,color="green",shape="box"];651[label="xx3000",fontsize=16,color="green",shape="box"];652[label="xx4000",fontsize=16,color="green",shape="box"];653[label="xx3000",fontsize=16,color="green",shape="box"];654[label="xx4000",fontsize=16,color="green",shape="box"];655[label="xx3000",fontsize=16,color="green",shape="box"];656[label="primMulInt (Pos xx3010) (Pos xx4000)",fontsize=16,color="black",shape="box"];656 -> 660[label="",style="solid", color="black", weight=3]; 657[label="primMulInt (Pos xx3010) (Neg xx4000)",fontsize=16,color="black",shape="box"];657 -> 661[label="",style="solid", color="black", weight=3]; 658[label="primMulInt (Neg xx3010) (Pos xx4000)",fontsize=16,color="black",shape="box"];658 -> 662[label="",style="solid", color="black", weight=3]; 659[label="primMulInt (Neg xx3010) (Neg xx4000)",fontsize=16,color="black",shape="box"];659 -> 663[label="",style="solid", color="black", weight=3]; 660[label="Pos (primMulNat xx3010 xx4000)",fontsize=16,color="green",shape="box"];660 -> 664[label="",style="dashed", color="green", weight=3]; 661[label="Neg (primMulNat xx3010 xx4000)",fontsize=16,color="green",shape="box"];661 -> 665[label="",style="dashed", color="green", weight=3]; 662[label="Neg (primMulNat xx3010 xx4000)",fontsize=16,color="green",shape="box"];662 -> 666[label="",style="dashed", color="green", weight=3]; 663[label="Pos (primMulNat xx3010 xx4000)",fontsize=16,color="green",shape="box"];663 -> 667[label="",style="dashed", color="green", weight=3]; 664[label="primMulNat xx3010 xx4000",fontsize=16,color="burlywood",shape="triangle"];946[label="xx3010/Succ xx30100",fontsize=10,color="white",style="solid",shape="box"];664 -> 946[label="",style="solid", color="burlywood", weight=9]; 946 -> 668[label="",style="solid", color="burlywood", weight=3]; 947[label="xx3010/Zero",fontsize=10,color="white",style="solid",shape="box"];664 -> 947[label="",style="solid", color="burlywood", weight=9]; 947 -> 669[label="",style="solid", color="burlywood", weight=3]; 665 -> 664[label="",style="dashed", color="red", weight=0]; 665[label="primMulNat xx3010 xx4000",fontsize=16,color="magenta"];665 -> 670[label="",style="dashed", color="magenta", weight=3]; 666 -> 664[label="",style="dashed", color="red", weight=0]; 666[label="primMulNat xx3010 xx4000",fontsize=16,color="magenta"];666 -> 671[label="",style="dashed", color="magenta", weight=3]; 667 -> 664[label="",style="dashed", color="red", weight=0]; 667[label="primMulNat xx3010 xx4000",fontsize=16,color="magenta"];667 -> 672[label="",style="dashed", color="magenta", weight=3]; 667 -> 673[label="",style="dashed", color="magenta", weight=3]; 668[label="primMulNat (Succ xx30100) xx4000",fontsize=16,color="burlywood",shape="box"];948[label="xx4000/Succ xx40000",fontsize=10,color="white",style="solid",shape="box"];668 -> 948[label="",style="solid", color="burlywood", weight=9]; 948 -> 674[label="",style="solid", color="burlywood", weight=3]; 949[label="xx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];668 -> 949[label="",style="solid", color="burlywood", weight=9]; 949 -> 675[label="",style="solid", color="burlywood", weight=3]; 669[label="primMulNat Zero xx4000",fontsize=16,color="burlywood",shape="box"];950[label="xx4000/Succ xx40000",fontsize=10,color="white",style="solid",shape="box"];669 -> 950[label="",style="solid", color="burlywood", weight=9]; 950 -> 676[label="",style="solid", color="burlywood", weight=3]; 951[label="xx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];669 -> 951[label="",style="solid", color="burlywood", weight=9]; 951 -> 677[label="",style="solid", color="burlywood", weight=3]; 670[label="xx4000",fontsize=16,color="green",shape="box"];671[label="xx3010",fontsize=16,color="green",shape="box"];672[label="xx4000",fontsize=16,color="green",shape="box"];673[label="xx3010",fontsize=16,color="green",shape="box"];674[label="primMulNat (Succ xx30100) (Succ xx40000)",fontsize=16,color="black",shape="box"];674 -> 678[label="",style="solid", color="black", weight=3]; 675[label="primMulNat (Succ xx30100) Zero",fontsize=16,color="black",shape="box"];675 -> 679[label="",style="solid", color="black", weight=3]; 676[label="primMulNat Zero (Succ xx40000)",fontsize=16,color="black",shape="box"];676 -> 680[label="",style="solid", color="black", weight=3]; 677[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];677 -> 681[label="",style="solid", color="black", weight=3]; 678 -> 682[label="",style="dashed", color="red", weight=0]; 678[label="primPlusNat (primMulNat xx30100 (Succ xx40000)) (Succ xx40000)",fontsize=16,color="magenta"];678 -> 683[label="",style="dashed", color="magenta", weight=3]; 679[label="Zero",fontsize=16,color="green",shape="box"];680[label="Zero",fontsize=16,color="green",shape="box"];681[label="Zero",fontsize=16,color="green",shape="box"];683 -> 664[label="",style="dashed", color="red", weight=0]; 683[label="primMulNat xx30100 (Succ xx40000)",fontsize=16,color="magenta"];683 -> 684[label="",style="dashed", color="magenta", weight=3]; 683 -> 685[label="",style="dashed", color="magenta", weight=3]; 682[label="primPlusNat xx28 (Succ xx40000)",fontsize=16,color="burlywood",shape="triangle"];952[label="xx28/Succ xx280",fontsize=10,color="white",style="solid",shape="box"];682 -> 952[label="",style="solid", color="burlywood", weight=9]; 952 -> 686[label="",style="solid", color="burlywood", weight=3]; 953[label="xx28/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 953[label="",style="solid", color="burlywood", weight=9]; 953 -> 687[label="",style="solid", color="burlywood", weight=3]; 684[label="Succ xx40000",fontsize=16,color="green",shape="box"];685[label="xx30100",fontsize=16,color="green",shape="box"];686[label="primPlusNat (Succ xx280) (Succ xx40000)",fontsize=16,color="black",shape="box"];686 -> 688[label="",style="solid", color="black", weight=3]; 687[label="primPlusNat Zero (Succ xx40000)",fontsize=16,color="black",shape="box"];687 -> 689[label="",style="solid", color="black", weight=3]; 688[label="Succ (Succ (primPlusNat xx280 xx40000))",fontsize=16,color="green",shape="box"];688 -> 690[label="",style="dashed", color="green", weight=3]; 689[label="Succ xx40000",fontsize=16,color="green",shape="box"];690[label="primPlusNat xx280 xx40000",fontsize=16,color="burlywood",shape="triangle"];954[label="xx280/Succ xx2800",fontsize=10,color="white",style="solid",shape="box"];690 -> 954[label="",style="solid", color="burlywood", weight=9]; 954 -> 691[label="",style="solid", color="burlywood", weight=3]; 955[label="xx280/Zero",fontsize=10,color="white",style="solid",shape="box"];690 -> 955[label="",style="solid", color="burlywood", weight=9]; 955 -> 692[label="",style="solid", color="burlywood", weight=3]; 691[label="primPlusNat (Succ xx2800) xx40000",fontsize=16,color="burlywood",shape="box"];956[label="xx40000/Succ xx400000",fontsize=10,color="white",style="solid",shape="box"];691 -> 956[label="",style="solid", color="burlywood", weight=9]; 956 -> 693[label="",style="solid", color="burlywood", weight=3]; 957[label="xx40000/Zero",fontsize=10,color="white",style="solid",shape="box"];691 -> 957[label="",style="solid", color="burlywood", weight=9]; 957 -> 694[label="",style="solid", color="burlywood", weight=3]; 692[label="primPlusNat Zero xx40000",fontsize=16,color="burlywood",shape="box"];958[label="xx40000/Succ xx400000",fontsize=10,color="white",style="solid",shape="box"];692 -> 958[label="",style="solid", color="burlywood", weight=9]; 958 -> 695[label="",style="solid", color="burlywood", weight=3]; 959[label="xx40000/Zero",fontsize=10,color="white",style="solid",shape="box"];692 -> 959[label="",style="solid", color="burlywood", weight=9]; 959 -> 696[label="",style="solid", color="burlywood", weight=3]; 693[label="primPlusNat (Succ xx2800) (Succ xx400000)",fontsize=16,color="black",shape="box"];693 -> 697[label="",style="solid", color="black", weight=3]; 694[label="primPlusNat (Succ xx2800) Zero",fontsize=16,color="black",shape="box"];694 -> 698[label="",style="solid", color="black", weight=3]; 695[label="primPlusNat Zero (Succ xx400000)",fontsize=16,color="black",shape="box"];695 -> 699[label="",style="solid", color="black", weight=3]; 696[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];696 -> 700[label="",style="solid", color="black", weight=3]; 697[label="Succ (Succ (primPlusNat xx2800 xx400000))",fontsize=16,color="green",shape="box"];697 -> 701[label="",style="dashed", color="green", weight=3]; 698[label="Succ xx2800",fontsize=16,color="green",shape="box"];699[label="Succ xx400000",fontsize=16,color="green",shape="box"];700[label="Zero",fontsize=16,color="green",shape="box"];701 -> 690[label="",style="dashed", color="red", weight=0]; 701[label="primPlusNat xx2800 xx400000",fontsize=16,color="magenta"];701 -> 702[label="",style="dashed", color="magenta", weight=3]; 701 -> 703[label="",style="dashed", color="magenta", weight=3]; 702[label="xx400000",fontsize=16,color="green",shape="box"];703[label="xx2800",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(xx11, False, xx13, xx14, ba) -> new_psPs0(xx11, xx13, xx14, ba) new_psPs0(xx30, :(xx40, xx41), xx5, bb) -> new_psPs(xx30, new_esEs4(xx30, xx40, bb), xx41, xx5, bb) The TRS R consists of the following rules: new_esEs4(xx30, xx40, ty_Int) -> new_esEs17(xx30, xx40) new_esEs14(GT, GT) -> True new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs7(xx301, xx401, app(app(ty_Either, dg), dh)) -> new_esEs20(xx301, xx401, dg, dh) new_primPlusNat0(Zero, Zero) -> Zero new_esEs12(Char(xx300), Char(xx400)) -> new_primEqNat0(xx300, xx400) new_esEs20(Left(xx300), Left(xx400), app(app(app(ty_@3, baa), bab), bac), gb) -> new_esEs5(xx300, xx400, baa, bab, bac) new_esEs8(xx302, xx402, ty_Char) -> new_esEs12(xx302, xx402) new_esEs8(xx302, xx402, ty_Double) -> new_esEs15(xx302, xx402) new_esEs19(False, True) -> False new_esEs19(True, False) -> False new_esEs10(Nothing, Nothing, fg) -> True new_esEs24(xx301, xx401, app(app(ty_@2, bfg), bfh)) -> new_esEs21(xx301, xx401, bfg, bfh) new_esEs23(xx300, xx400, ty_Int) -> new_esEs17(xx300, xx400) new_esEs20(Left(xx300), Left(xx400), app(app(ty_Either, bae), baf), gb) -> new_esEs20(xx300, xx400, bae, baf) new_esEs10(Nothing, Just(xx400), fg) -> False new_esEs10(Just(xx300), Nothing, fg) -> False new_esEs25(xx300, xx400, ty_Int) -> new_esEs17(xx300, xx400) new_esEs22(xx300, xx400, app(app(app(ty_@3, gg), gh), ha)) -> new_esEs5(xx300, xx400, gg, gh, ha) new_esEs7(xx301, xx401, ty_Float) -> new_esEs16(xx301, xx401) new_esEs14(EQ, EQ) -> True new_esEs20(Left(xx300), Left(xx400), ty_Char, gb) -> new_esEs12(xx300, xx400) new_primMulNat0(Succ(xx30100), Succ(xx40000)) -> new_primPlusNat1(new_primMulNat0(xx30100, Succ(xx40000)), xx40000) new_esEs20(Left(xx300), Left(xx400), app(ty_Maybe, hh), gb) -> new_esEs10(xx300, xx400, hh) new_esEs20(Left(xx300), Left(xx400), ty_Double, gb) -> new_esEs15(xx300, xx400) new_esEs24(xx301, xx401, ty_@0) -> new_esEs11(xx301, xx401) new_esEs14(EQ, GT) -> False new_esEs14(GT, EQ) -> False new_esEs23(xx300, xx400, ty_Bool) -> new_esEs19(xx300, xx400) new_esEs7(xx301, xx401, ty_Ordering) -> new_esEs14(xx301, xx401) new_esEs23(xx300, xx400, app(ty_Maybe, bdf)) -> new_esEs10(xx300, xx400, bdf) new_esEs6(xx300, xx400, ty_Char) -> new_esEs12(xx300, xx400) new_asAs(True, xx27) -> xx27 new_esEs24(xx301, xx401, app(app(ty_Either, bfe), bff)) -> new_esEs20(xx301, xx401, bfe, bff) new_esEs20(Right(xx300), Right(xx400), ga, app(ty_Maybe, bbb)) -> new_esEs10(xx300, xx400, bbb) new_esEs8(xx302, xx402, app(ty_Ratio, ec)) -> new_esEs9(xx302, xx402, ec) new_esEs6(xx300, xx400, ty_Int) -> new_esEs17(xx300, xx400) new_primEqInt(Pos(Succ(xx3000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(xx4000))) -> False new_esEs4(xx30, xx40, ty_Double) -> new_esEs15(xx30, xx40) new_esEs4(xx30, xx40, ty_Integer) -> new_esEs13(xx30, xx40) new_esEs23(xx300, xx400, ty_Integer) -> new_esEs13(xx300, xx400) new_esEs20(Right(xx300), Right(xx400), ga, ty_Char) -> new_esEs12(xx300, xx400) new_esEs7(xx301, xx401, app(ty_[], df)) -> new_esEs18(xx301, xx401, df) new_esEs7(xx301, xx401, app(ty_Maybe, db)) -> new_esEs10(xx301, xx401, db) new_primEqNat0(Succ(xx3000), Succ(xx4000)) -> new_primEqNat0(xx3000, xx4000) new_esEs4(xx30, xx40, app(ty_Maybe, fg)) -> new_esEs10(xx30, xx40, fg) new_esEs18([], [], fh) -> True new_esEs10(Just(xx300), Just(xx400), ty_Double) -> new_esEs15(xx300, xx400) new_esEs7(xx301, xx401, ty_Integer) -> new_esEs13(xx301, xx401) new_esEs22(xx300, xx400, ty_@0) -> new_esEs11(xx300, xx400) new_esEs20(Right(xx300), Right(xx400), ga, app(ty_[], bbf)) -> new_esEs18(xx300, xx400, bbf) new_esEs10(Just(xx300), Just(xx400), app(app(app(ty_@3, bce), bcf), bcg)) -> new_esEs5(xx300, xx400, bce, bcf, bcg) new_esEs4(xx30, xx40, ty_Char) -> new_esEs12(xx30, xx40) new_primMulNat0(Zero, Zero) -> Zero new_esEs10(Just(xx300), Just(xx400), app(ty_Maybe, bcd)) -> new_esEs10(xx300, xx400, bcd) new_esEs18(:(xx300, xx301), :(xx400, xx401), fh) -> new_asAs(new_esEs22(xx300, xx400, fh), new_esEs18(xx301, xx401, fh)) new_esEs25(xx300, xx400, ty_Integer) -> new_esEs13(xx300, xx400) new_esEs23(xx300, xx400, ty_Char) -> new_esEs12(xx300, xx400) new_esEs4(xx30, xx40, ty_Ordering) -> new_esEs14(xx30, xx40) new_esEs7(xx301, xx401, app(app(app(ty_@3, dc), dd), de)) -> new_esEs5(xx301, xx401, dc, dd, de) new_esEs6(xx300, xx400, ty_Integer) -> new_esEs13(xx300, xx400) new_esEs4(xx30, xx40, app(ty_[], fh)) -> new_esEs18(xx30, xx40, fh) new_esEs6(xx300, xx400, ty_Ordering) -> new_esEs14(xx300, xx400) new_esEs21(@2(xx300, xx301), @2(xx400, xx401), gc, gd) -> new_asAs(new_esEs23(xx300, xx400, gc), new_esEs24(xx301, xx401, gd)) new_esEs15(Double(xx300, xx301), Double(xx400, xx401)) -> new_esEs17(new_sr(xx300, xx401), new_sr(xx301, xx400)) new_esEs20(Left(xx300), Left(xx400), app(ty_[], bad), gb) -> new_esEs18(xx300, xx400, bad) new_primEqNat0(Succ(xx3000), Zero) -> False new_primEqNat0(Zero, Succ(xx4000)) -> False new_esEs22(xx300, xx400, ty_Char) -> new_esEs12(xx300, xx400) new_esEs24(xx301, xx401, ty_Float) -> new_esEs16(xx301, xx401) new_esEs22(xx300, xx400, ty_Double) -> new_esEs15(xx300, xx400) new_esEs22(xx300, xx400, app(ty_[], hb)) -> new_esEs18(xx300, xx400, hb) new_esEs24(xx301, xx401, ty_Ordering) -> new_esEs14(xx301, xx401) new_esEs4(xx30, xx40, ty_Bool) -> new_esEs19(xx30, xx40) new_esEs8(xx302, xx402, app(ty_Maybe, ed)) -> new_esEs10(xx302, xx402, ed) new_esEs20(Right(xx300), Right(xx400), ga, ty_Double) -> new_esEs15(xx300, xx400) new_esEs6(xx300, xx400, ty_Float) -> new_esEs16(xx300, xx400) new_esEs5(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), bc, bd, be) -> new_asAs(new_esEs6(xx300, xx400, bc), new_asAs(new_esEs7(xx301, xx401, bd), new_esEs8(xx302, xx402, be))) new_esEs19(False, False) -> True new_primEqInt(Neg(Succ(xx3000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(xx4000))) -> False new_primEqInt(Pos(Succ(xx3000)), Pos(Succ(xx4000))) -> new_primEqNat0(xx3000, xx4000) new_esEs24(xx301, xx401, app(app(app(ty_@3, bfa), bfb), bfc)) -> new_esEs5(xx301, xx401, bfa, bfb, bfc) new_esEs23(xx300, xx400, ty_Ordering) -> new_esEs14(xx300, xx400) new_esEs4(xx30, xx40, app(ty_Ratio, ff)) -> new_esEs9(xx30, xx40, ff) new_sr(Pos(xx3010), Neg(xx4000)) -> Neg(new_primMulNat0(xx3010, xx4000)) new_sr(Neg(xx3010), Pos(xx4000)) -> Neg(new_primMulNat0(xx3010, xx4000)) new_esEs22(xx300, xx400, app(app(ty_@2, he), hf)) -> new_esEs21(xx300, xx400, he, hf) new_esEs10(Just(xx300), Just(xx400), app(app(ty_Either, bda), bdb)) -> new_esEs20(xx300, xx400, bda, bdb) new_esEs20(Right(xx300), Right(xx400), ga, app(app(app(ty_@3, bbc), bbd), bbe)) -> new_esEs5(xx300, xx400, bbc, bbd, bbe) new_primEqInt(Pos(Succ(xx3000)), Neg(xx400)) -> False new_primEqInt(Neg(Succ(xx3000)), Pos(xx400)) -> False new_esEs4(xx30, xx40, app(app(ty_@2, gc), gd)) -> new_esEs21(xx30, xx40, gc, gd) new_esEs22(xx300, xx400, app(ty_Ratio, ge)) -> new_esEs9(xx300, xx400, ge) new_esEs24(xx301, xx401, ty_Integer) -> new_esEs13(xx301, xx401) new_esEs6(xx300, xx400, app(app(app(ty_@3, bh), ca), cb)) -> new_esEs5(xx300, xx400, bh, ca, cb) new_esEs8(xx302, xx402, app(ty_[], eh)) -> new_esEs18(xx302, xx402, eh) new_esEs20(Left(xx300), Left(xx400), ty_Float, gb) -> new_esEs16(xx300, xx400) new_esEs23(xx300, xx400, app(app(ty_@2, bee), bef)) -> new_esEs21(xx300, xx400, bee, bef) new_esEs8(xx302, xx402, ty_Float) -> new_esEs16(xx302, xx402) new_esEs20(Right(xx300), Right(xx400), ga, ty_Ordering) -> new_esEs14(xx300, xx400) new_sr(Neg(xx3010), Neg(xx4000)) -> Pos(new_primMulNat0(xx3010, xx4000)) new_esEs4(xx30, xx40, ty_@0) -> new_esEs11(xx30, xx40) new_esEs22(xx300, xx400, ty_Bool) -> new_esEs19(xx300, xx400) new_esEs23(xx300, xx400, ty_@0) -> new_esEs11(xx300, xx400) new_esEs22(xx300, xx400, app(ty_Maybe, gf)) -> new_esEs10(xx300, xx400, gf) new_esEs22(xx300, xx400, ty_Integer) -> new_esEs13(xx300, xx400) new_esEs6(xx300, xx400, app(app(ty_Either, cd), ce)) -> new_esEs20(xx300, xx400, cd, ce) new_primEqInt(Pos(Zero), Neg(Succ(xx4000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(xx4000))) -> False new_esEs20(Right(xx300), Right(xx400), ga, ty_Float) -> new_esEs16(xx300, xx400) new_primPlusNat0(Succ(xx2800), Succ(xx400000)) -> Succ(Succ(new_primPlusNat0(xx2800, xx400000))) new_esEs22(xx300, xx400, ty_Int) -> new_esEs17(xx300, xx400) new_esEs20(Right(xx300), Right(xx400), ga, app(app(ty_Either, bbg), bbh)) -> new_esEs20(xx300, xx400, bbg, bbh) new_esEs10(Just(xx300), Just(xx400), ty_Float) -> new_esEs16(xx300, xx400) new_primEqInt(Neg(Succ(xx3000)), Neg(Succ(xx4000))) -> new_primEqNat0(xx3000, xx4000) new_esEs16(Float(xx300, xx301), Float(xx400, xx401)) -> new_esEs17(new_sr(xx300, xx401), new_sr(xx301, xx400)) new_esEs6(xx300, xx400, ty_@0) -> new_esEs11(xx300, xx400) new_esEs23(xx300, xx400, app(ty_Ratio, bde)) -> new_esEs9(xx300, xx400, bde) new_esEs24(xx301, xx401, ty_Bool) -> new_esEs19(xx301, xx401) new_esEs20(Left(xx300), Left(xx400), ty_Bool, gb) -> new_esEs19(xx300, xx400) new_esEs20(Left(xx300), Left(xx400), app(ty_Ratio, hg), gb) -> new_esEs9(xx300, xx400, hg) new_esEs8(xx302, xx402, app(app(ty_Either, fa), fb)) -> new_esEs20(xx302, xx402, fa, fb) new_esEs14(LT, GT) -> False new_esEs14(GT, LT) -> False new_esEs20(Right(xx300), Right(xx400), ga, app(app(ty_@2, bca), bcb)) -> new_esEs21(xx300, xx400, bca, bcb) new_esEs20(Right(xx300), Right(xx400), ga, ty_Int) -> new_esEs17(xx300, xx400) new_esEs20(Right(xx300), Right(xx400), ga, ty_Bool) -> new_esEs19(xx300, xx400) new_primMulNat0(Succ(xx30100), Zero) -> Zero new_primMulNat0(Zero, Succ(xx40000)) -> Zero new_sr(Pos(xx3010), Pos(xx4000)) -> Pos(new_primMulNat0(xx3010, xx4000)) new_esEs8(xx302, xx402, ty_Bool) -> new_esEs19(xx302, xx402) new_esEs24(xx301, xx401, ty_Char) -> new_esEs12(xx301, xx401) new_esEs14(LT, LT) -> True new_esEs23(xx300, xx400, app(app(app(ty_@3, bdg), bdh), bea)) -> new_esEs5(xx300, xx400, bdg, bdh, bea) new_esEs7(xx301, xx401, ty_Double) -> new_esEs15(xx301, xx401) new_esEs10(Just(xx300), Just(xx400), app(ty_[], bch)) -> new_esEs18(xx300, xx400, bch) new_esEs18(:(xx300, xx301), [], fh) -> False new_esEs18([], :(xx400, xx401), fh) -> False new_esEs24(xx301, xx401, ty_Int) -> new_esEs17(xx301, xx401) new_primPlusNat1(Succ(xx280), xx40000) -> Succ(Succ(new_primPlusNat0(xx280, xx40000))) new_esEs8(xx302, xx402, app(app(ty_@2, fc), fd)) -> new_esEs21(xx302, xx402, fc, fd) new_esEs22(xx300, xx400, ty_Ordering) -> new_esEs14(xx300, xx400) new_esEs14(LT, EQ) -> False new_esEs14(EQ, LT) -> False new_esEs22(xx300, xx400, app(app(ty_Either, hc), hd)) -> new_esEs20(xx300, xx400, hc, hd) new_esEs13(Integer(xx300), Integer(xx400)) -> new_primEqInt(xx300, xx400) new_esEs10(Just(xx300), Just(xx400), ty_Integer) -> new_esEs13(xx300, xx400) new_primPlusNat0(Succ(xx2800), Zero) -> Succ(xx2800) new_primPlusNat0(Zero, Succ(xx400000)) -> Succ(xx400000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_primPlusNat1(Zero, xx40000) -> Succ(xx40000) new_esEs6(xx300, xx400, app(ty_Maybe, bg)) -> new_esEs10(xx300, xx400, bg) new_esEs23(xx300, xx400, ty_Float) -> new_esEs16(xx300, xx400) new_esEs7(xx301, xx401, ty_Bool) -> new_esEs19(xx301, xx401) new_esEs8(xx302, xx402, ty_@0) -> new_esEs11(xx302, xx402) new_esEs8(xx302, xx402, ty_Int) -> new_esEs17(xx302, xx402) new_esEs10(Just(xx300), Just(xx400), ty_Bool) -> new_esEs19(xx300, xx400) new_esEs23(xx300, xx400, ty_Double) -> new_esEs15(xx300, xx400) new_esEs23(xx300, xx400, app(ty_[], beb)) -> new_esEs18(xx300, xx400, beb) new_esEs7(xx301, xx401, app(app(ty_@2, ea), eb)) -> new_esEs21(xx301, xx401, ea, eb) new_esEs9(:%(xx300, xx301), :%(xx400, xx401), ff) -> new_asAs(new_esEs25(xx300, xx400, ff), new_esEs26(xx301, xx401, ff)) new_esEs24(xx301, xx401, app(ty_Ratio, beg)) -> new_esEs9(xx301, xx401, beg) new_esEs6(xx300, xx400, app(ty_Ratio, bf)) -> new_esEs9(xx300, xx400, bf) new_esEs4(xx30, xx40, ty_Float) -> new_esEs16(xx30, xx40) new_esEs23(xx300, xx400, app(app(ty_Either, bec), bed)) -> new_esEs20(xx300, xx400, bec, bed) new_esEs17(xx30, xx40) -> new_primEqInt(xx30, xx40) new_esEs7(xx301, xx401, app(ty_Ratio, da)) -> new_esEs9(xx301, xx401, da) new_esEs7(xx301, xx401, ty_@0) -> new_esEs11(xx301, xx401) new_esEs20(Left(xx300), Left(xx400), app(app(ty_@2, bag), bah), gb) -> new_esEs21(xx300, xx400, bag, bah) new_esEs10(Just(xx300), Just(xx400), app(ty_Ratio, bcc)) -> new_esEs9(xx300, xx400, bcc) new_esEs8(xx302, xx402, app(app(app(ty_@3, ee), ef), eg)) -> new_esEs5(xx302, xx402, ee, ef, eg) new_esEs11(@0, @0) -> True new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs20(Left(xx300), Left(xx400), ty_Integer, gb) -> new_esEs13(xx300, xx400) new_esEs6(xx300, xx400, app(app(ty_@2, cf), cg)) -> new_esEs21(xx300, xx400, cf, cg) new_esEs6(xx300, xx400, ty_Bool) -> new_esEs19(xx300, xx400) new_esEs20(Left(xx300), Left(xx400), ty_Int, gb) -> new_esEs17(xx300, xx400) new_esEs10(Just(xx300), Just(xx400), ty_Ordering) -> new_esEs14(xx300, xx400) new_esEs4(xx30, xx40, app(app(app(ty_@3, bc), bd), be)) -> new_esEs5(xx30, xx40, bc, bd, be) new_esEs10(Just(xx300), Just(xx400), ty_@0) -> new_esEs11(xx300, xx400) new_esEs26(xx301, xx401, ty_Integer) -> new_esEs13(xx301, xx401) new_esEs10(Just(xx300), Just(xx400), ty_Char) -> new_esEs12(xx300, xx400) new_esEs26(xx301, xx401, ty_Int) -> new_esEs17(xx301, xx401) new_primEqNat0(Zero, Zero) -> True new_esEs10(Just(xx300), Just(xx400), app(app(ty_@2, bdc), bdd)) -> new_esEs21(xx300, xx400, bdc, bdd) new_esEs20(Right(xx300), Right(xx400), ga, ty_@0) -> new_esEs11(xx300, xx400) new_esEs20(Right(xx300), Right(xx400), ga, app(ty_Ratio, bba)) -> new_esEs9(xx300, xx400, bba) new_esEs4(xx30, xx40, app(app(ty_Either, ga), gb)) -> new_esEs20(xx30, xx40, ga, gb) new_esEs6(xx300, xx400, app(ty_[], cc)) -> new_esEs18(xx300, xx400, cc) new_esEs8(xx302, xx402, ty_Integer) -> new_esEs13(xx302, xx402) new_asAs(False, xx27) -> False new_esEs6(xx300, xx400, ty_Double) -> new_esEs15(xx300, xx400) new_esEs8(xx302, xx402, ty_Ordering) -> new_esEs14(xx302, xx402) new_esEs20(Right(xx300), Right(xx400), ga, ty_Integer) -> new_esEs13(xx300, xx400) new_esEs24(xx301, xx401, app(ty_Maybe, beh)) -> new_esEs10(xx301, xx401, beh) new_esEs22(xx300, xx400, ty_Float) -> new_esEs16(xx300, xx400) new_esEs24(xx301, xx401, ty_Double) -> new_esEs15(xx301, xx401) new_esEs7(xx301, xx401, ty_Int) -> new_esEs17(xx301, xx401) new_esEs7(xx301, xx401, ty_Char) -> new_esEs12(xx301, xx401) new_esEs20(Left(xx300), Left(xx400), ty_Ordering, gb) -> new_esEs14(xx300, xx400) new_esEs20(Left(xx300), Left(xx400), ty_@0, gb) -> new_esEs11(xx300, xx400) new_esEs20(Left(xx300), Right(xx400), ga, gb) -> False new_esEs20(Right(xx300), Left(xx400), ga, gb) -> False new_esEs19(True, True) -> True new_esEs10(Just(xx300), Just(xx400), ty_Int) -> new_esEs17(xx300, xx400) new_esEs24(xx301, xx401, app(ty_[], bfd)) -> new_esEs18(xx301, xx401, bfd) The set Q consists of the following terms: new_esEs4(x0, x1, ty_Float) new_esEs6(x0, x1, ty_Float) new_esEs7(x0, x1, app(app(ty_Either, x2), x3)) new_esEs14(EQ, EQ) new_esEs20(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs20(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs6(x0, x1, ty_Double) new_esEs4(x0, x1, app(app(ty_@2, x2), x3)) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, ty_Char) new_esEs6(x0, x1, ty_Ordering) new_primPlusNat1(Succ(x0), x1) new_esEs10(Just(x0), Just(x1), ty_Int) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(x0, x1, ty_Double) new_esEs4(x0, x1, ty_Ordering) new_esEs20(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_primMulNat0(Zero, Zero) new_esEs22(x0, x1, ty_Char) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs6(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(False, False) new_esEs18([], :(x0, x1), x2) new_esEs10(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs7(x0, x1, app(ty_Maybe, x2)) new_esEs7(x0, x1, app(app(ty_@2, x2), x3)) new_primEqInt(Pos(Zero), Pos(Zero)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs7(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs10(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs20(Left(x0), Left(x1), ty_Integer, x2) new_primPlusNat0(Succ(x0), Zero) new_esEs10(Just(x0), Just(x1), ty_Float) new_esEs24(x0, x1, ty_@0) new_esEs8(x0, x1, app(ty_Maybe, x2)) new_esEs8(x0, x1, app(ty_Ratio, x2)) new_esEs10(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs20(Right(x0), Right(x1), x2, ty_@0) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs23(x0, x1, ty_Int) new_primPlusNat0(Zero, Zero) new_esEs22(x0, x1, ty_Bool) new_esEs20(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs20(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs23(x0, x1, ty_Bool) new_primEqNat0(Succ(x0), Zero) new_esEs20(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs22(x0, x1, ty_Double) new_esEs10(Just(x0), Just(x1), app(ty_[], x2)) new_esEs4(x0, x1, ty_Char) new_esEs23(x0, x1, ty_Ordering) new_esEs20(Right(x0), Right(x1), x2, ty_Int) new_esEs23(x0, x1, ty_Double) new_esEs20(Right(x0), Right(x1), x2, ty_Integer) new_esEs14(EQ, GT) new_esEs14(GT, EQ) new_esEs8(x0, x1, ty_Bool) new_esEs4(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(Right(x0), Right(x1), x2, ty_Char) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(Left(x0), Left(x1), ty_Ordering, x2) new_esEs8(x0, x1, ty_Float) new_esEs4(x0, x1, ty_Int) new_esEs6(x0, x1, ty_Int) new_esEs10(Just(x0), Just(x1), ty_Ordering) new_esEs7(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs22(x0, x1, ty_Int) new_esEs20(Right(x0), Right(x1), x2, ty_Bool) new_esEs8(x0, x1, ty_@0) new_esEs8(x0, x1, ty_Char) new_esEs8(x0, x1, ty_Double) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, ty_@0) new_esEs8(x0, x1, app(app(ty_Either, x2), x3)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs25(x0, x1, ty_Int) new_esEs26(x0, x1, ty_Integer) new_esEs15(Double(x0, x1), Double(x2, x3)) new_esEs20(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs19(True, True) new_esEs22(x0, x1, ty_Float) new_primMulNat0(Zero, Succ(x0)) new_esEs8(x0, x1, ty_Int) new_esEs6(x0, x1, ty_Char) new_sr(Neg(x0), Neg(x1)) new_esEs4(x0, x1, ty_Bool) new_esEs6(x0, x1, ty_Bool) new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs7(x0, x1, ty_Integer) new_esEs10(Just(x0), Nothing, x1) new_esEs20(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs10(Just(x0), Just(x1), ty_Integer) new_esEs25(x0, x1, ty_Integer) new_esEs4(x0, x1, ty_@0) new_esEs20(Left(x0), Right(x1), x2, x3) new_esEs20(Right(x0), Left(x1), x2, x3) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs4(x0, x1, app(ty_Maybe, x2)) new_esEs10(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Double) new_esEs6(x0, x1, ty_@0) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs18(:(x0, x1), :(x2, x3), x4) new_esEs7(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, ty_Integer) new_primEqNat0(Zero, Succ(x0)) new_esEs20(Right(x0), Right(x1), x2, ty_Double) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs14(LT, EQ) new_esEs14(EQ, LT) new_esEs20(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs24(x0, x1, ty_Ordering) new_esEs24(x0, x1, ty_Float) new_esEs6(x0, x1, ty_Integer) new_esEs19(False, True) new_esEs19(True, False) new_esEs11(@0, @0) new_esEs12(Char(x0), Char(x1)) new_esEs20(Right(x0), Right(x1), x2, ty_Float) new_esEs14(GT, GT) new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs10(Nothing, Nothing, x0) new_esEs6(x0, x1, app(app(ty_@2, x2), x3)) new_asAs(False, x0) new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs6(x0, x1, app(app(ty_Either, x2), x3)) new_esEs14(LT, GT) new_esEs14(GT, LT) new_esEs9(:%(x0, x1), :%(x2, x3), x4) new_esEs21(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs8(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Int) new_esEs20(Right(x0), Right(x1), x2, ty_Ordering) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Float) new_primEqNat0(Zero, Zero) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs6(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Integer) new_esEs20(Left(x0), Left(x1), ty_Bool, x2) new_esEs26(x0, x1, ty_Int) new_esEs4(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_@0) new_esEs20(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs20(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs6(x0, x1, app(ty_[], x2)) new_esEs8(x0, x1, ty_Ordering) new_esEs18(:(x0, x1), [], x2) new_esEs22(x0, x1, ty_Ordering) new_esEs20(Left(x0), Left(x1), ty_Float, x2) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs20(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs20(Left(x0), Left(x1), ty_@0, x2) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs24(x0, x1, ty_Char) new_esEs7(x0, x1, ty_@0) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_primPlusNat0(Zero, Succ(x0)) new_esEs7(x0, x1, ty_Float) new_esEs4(x0, x1, ty_Integer) new_esEs10(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs14(LT, LT) new_esEs7(x0, x1, ty_Bool) new_sr(Pos(x0), Pos(x1)) new_esEs10(Just(x0), Just(x1), ty_@0) new_esEs13(Integer(x0), Integer(x1)) new_esEs8(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_primPlusNat1(Zero, x0) new_esEs24(x0, x1, ty_Bool) new_primMulNat0(Succ(x0), Zero) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Integer) new_esEs10(Just(x0), Just(x1), ty_Bool) new_esEs7(x0, x1, ty_Double) new_esEs20(Left(x0), Left(x1), ty_Int, x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs17(x0, x1) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs7(x0, x1, ty_Char) new_esEs10(Just(x0), Just(x1), ty_Char) new_esEs20(Left(x0), Left(x1), ty_Char, x2) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs18([], [], x0) new_esEs4(x0, x1, app(ty_[], x2)) new_esEs10(Nothing, Just(x0), x1) new_esEs16(Float(x0, x1), Float(x2, x3)) new_asAs(True, x0) new_esEs10(Just(x0), Just(x1), ty_Double) new_esEs8(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs20(Left(x0), Left(x1), ty_Double, x2) 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_psPs0(xx30, :(xx40, xx41), xx5, bb) -> new_psPs(xx30, new_esEs4(xx30, xx40, bb), xx41, xx5, bb) The graph contains the following edges 1 >= 1, 2 > 3, 3 >= 4, 4 >= 5 *new_psPs(xx11, False, xx13, xx14, ba) -> new_psPs0(xx11, xx13, xx14, ba) The graph contains the following edges 1 >= 1, 3 >= 2, 4 >= 3, 5 >= 4 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(xx4, :(xx30, xx31), ba) -> new_foldr(xx4, xx31, ba) 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_foldr(xx4, :(xx30, xx31), ba) -> new_foldr(xx4, xx31, ba) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 ---------------------------------------- (18) YES ---------------------------------------- (19) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(xx30100), Succ(xx40000)) -> new_primMulNat(xx30100, Succ(xx40000)) 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_primMulNat(Succ(xx30100), Succ(xx40000)) -> new_primMulNat(xx30100, Succ(xx40000)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs2(Left(xx300), Left(xx400), app(app(ty_@2, bad), bae), he) -> new_esEs3(xx300, xx400, bad, bae) new_esEs2(Right(xx300), Right(xx400), baf, app(app(app(ty_@3, bah), bba), bbb)) -> new_esEs0(xx300, xx400, bah, bba, bbb) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(ty_Maybe, eh)) -> new_esEs(xx302, xx402, eh) new_esEs1(:(xx300, xx301), :(xx400, xx401), app(ty_Maybe, gb)) -> new_esEs(xx300, xx400, gb) new_esEs(Just(xx300), Just(xx400), app(ty_[], be)) -> new_esEs1(xx300, xx400, be) new_esEs2(Left(xx300), Left(xx400), app(ty_Maybe, hd), he) -> new_esEs(xx300, xx400, hd) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(app(ty_@3, dh), ea), eb), cd) -> new_esEs0(xx301, xx401, dh, ea, eb) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(app(ty_@3, bcb), bcc), bcd), bca) -> new_esEs0(xx300, xx400, bcb, bcc, bcd) new_esEs(Just(xx300), Just(xx400), app(app(ty_@2, bh), ca)) -> new_esEs3(xx300, xx400, bh, ca) new_esEs2(Right(xx300), Right(xx400), baf, app(app(ty_Either, bbd), bbe)) -> new_esEs2(xx300, xx400, bbd, bbe) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(ty_Either, bdh), bea)) -> new_esEs2(xx301, xx401, bdh, bea) new_esEs2(Left(xx300), Left(xx400), app(ty_[], baa), he) -> new_esEs1(xx300, xx400, baa) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(ty_Either, db), dc), cc, cd) -> new_esEs2(xx300, xx400, db, dc) new_esEs(Just(xx300), Just(xx400), app(ty_Maybe, ba)) -> new_esEs(xx300, xx400, ba) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(ty_@2, ef), eg), cd) -> new_esEs3(xx301, xx401, ef, eg) new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(ty_Either, gg), gh)) -> new_esEs2(xx300, xx400, gg, gh) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(ty_@2, dd), de), cc, cd) -> new_esEs3(xx300, xx400, dd, de) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(ty_Either, bcf), bcg), bca) -> new_esEs2(xx300, xx400, bcf, bcg) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(ty_@2, beb), bec)) -> new_esEs3(xx301, xx401, beb, bec) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(app(ty_@3, fa), fb), fc)) -> new_esEs0(xx302, xx402, fa, fb, fc) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(xx301, xx401, bdd, bde, bdf) new_esEs2(Left(xx300), Left(xx400), app(app(ty_Either, bab), bac), he) -> new_esEs2(xx300, xx400, bab, bac) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(ty_[], bdg)) -> new_esEs1(xx301, xx401, bdg) new_esEs2(Right(xx300), Right(xx400), baf, app(ty_[], bbc)) -> new_esEs1(xx300, xx400, bbc) new_esEs(Just(xx300), Just(xx400), app(app(ty_Either, bf), bg)) -> new_esEs2(xx300, xx400, bf, bg) new_esEs(Just(xx300), Just(xx400), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(xx300, xx400, bb, bc, bd) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(ty_@2, bch), bda), bca) -> new_esEs3(xx300, xx400, bch, bda) new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(app(ty_@3, gc), gd), ge)) -> new_esEs0(xx300, xx400, gc, gd, ge) new_esEs1(:(xx300, xx301), :(xx400, xx401), hc) -> new_esEs1(xx301, xx401, hc) new_esEs2(Right(xx300), Right(xx400), baf, app(app(ty_@2, bbf), bbg)) -> new_esEs3(xx300, xx400, bbf, bbg) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(ty_[], ec), cd) -> new_esEs1(xx301, xx401, ec) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(ty_@2, fh), ga)) -> new_esEs3(xx302, xx402, fh, ga) new_esEs1(:(xx300, xx301), :(xx400, xx401), app(ty_[], gf)) -> new_esEs1(xx300, xx400, gf) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(ty_Maybe, bdc)) -> new_esEs(xx301, xx401, bdc) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(ty_Either, ff), fg)) -> new_esEs2(xx302, xx402, ff, fg) new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(ty_@2, ha), hb)) -> new_esEs3(xx300, xx400, ha, hb) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(ty_[], da), cc, cd) -> new_esEs1(xx300, xx400, da) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(ty_Maybe, bbh), bca) -> new_esEs(xx300, xx400, bbh) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(ty_Maybe, cb), cc, cd) -> new_esEs(xx300, xx400, cb) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(app(ty_@3, ce), cf), cg), cc, cd) -> new_esEs0(xx300, xx400, ce, cf, cg) new_esEs2(Left(xx300), Left(xx400), app(app(app(ty_@3, hf), hg), hh), he) -> new_esEs0(xx300, xx400, hf, hg, hh) new_esEs2(Right(xx300), Right(xx400), baf, app(ty_Maybe, bag)) -> new_esEs(xx300, xx400, bag) new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(ty_[], bce), bca) -> new_esEs1(xx300, xx400, bce) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(ty_Either, ed), ee), cd) -> new_esEs2(xx301, xx401, ed, ee) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(ty_[], fd)) -> new_esEs1(xx302, xx402, fd) new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(ty_Maybe, dg), cd) -> new_esEs(xx301, xx401, dg) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) 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_esEs(Just(xx300), Just(xx400), app(app(ty_Either, bf), bg)) -> new_esEs2(xx300, xx400, bf, bg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(Just(xx300), Just(xx400), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(xx300, xx400, bb, bc, bd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(Just(xx300), Just(xx400), app(ty_[], be)) -> new_esEs1(xx300, xx400, be) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(ty_Either, gg), gh)) -> new_esEs2(xx300, xx400, gg, gh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(Just(xx300), Just(xx400), app(ty_Maybe, ba)) -> new_esEs(xx300, xx400, ba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(Just(xx300), Just(xx400), app(app(ty_@2, bh), ca)) -> new_esEs3(xx300, xx400, bh, ca) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(app(ty_@3, gc), gd), ge)) -> new_esEs0(xx300, xx400, gc, gd, ge) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(:(xx300, xx301), :(xx400, xx401), app(ty_Maybe, gb)) -> new_esEs(xx300, xx400, gb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(:(xx300, xx301), :(xx400, xx401), app(app(ty_@2, ha), hb)) -> new_esEs3(xx300, xx400, ha, hb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(ty_Either, bdh), bea)) -> new_esEs2(xx301, xx401, bdh, bea) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(ty_Either, bcf), bcg), bca) -> new_esEs2(xx300, xx400, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(app(ty_@3, bcb), bcc), bcd), bca) -> new_esEs0(xx300, xx400, bcb, bcc, bcd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(xx301, xx401, bdd, bde, bdf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(ty_[], bdg)) -> new_esEs1(xx301, xx401, bdg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(ty_[], bce), bca) -> new_esEs1(xx300, xx400, bce) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(ty_Maybe, bdc)) -> new_esEs(xx301, xx401, bdc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(ty_Maybe, bbh), bca) -> new_esEs(xx300, xx400, bbh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), bdb, app(app(ty_@2, beb), bec)) -> new_esEs3(xx301, xx401, beb, bec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(@2(xx300, xx301), @2(xx400, xx401), app(app(ty_@2, bch), bda), bca) -> new_esEs3(xx300, xx400, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(ty_Either, db), dc), cc, cd) -> new_esEs2(xx300, xx400, db, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(ty_Either, ff), fg)) -> new_esEs2(xx302, xx402, ff, fg) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(ty_Either, ed), ee), cd) -> new_esEs2(xx301, xx401, ed, ee) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(Right(xx300), Right(xx400), baf, app(app(ty_Either, bbd), bbe)) -> new_esEs2(xx300, xx400, bbd, bbe) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(Left(xx300), Left(xx400), app(app(ty_Either, bab), bac), he) -> new_esEs2(xx300, xx400, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(app(ty_@3, dh), ea), eb), cd) -> new_esEs0(xx301, xx401, dh, ea, eb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(app(ty_@3, fa), fb), fc)) -> new_esEs0(xx302, xx402, fa, fb, fc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(app(ty_@3, ce), cf), cg), cc, cd) -> new_esEs0(xx300, xx400, ce, cf, cg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(ty_[], ec), cd) -> new_esEs1(xx301, xx401, ec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(ty_[], da), cc, cd) -> new_esEs1(xx300, xx400, da) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(ty_[], fd)) -> new_esEs1(xx302, xx402, fd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(ty_Maybe, eh)) -> new_esEs(xx302, xx402, eh) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(ty_Maybe, cb), cc, cd) -> new_esEs(xx300, xx400, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(ty_Maybe, dg), cd) -> new_esEs(xx301, xx401, dg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, app(app(ty_@2, ef), eg), cd) -> new_esEs3(xx301, xx401, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), app(app(ty_@2, dd), de), cc, cd) -> new_esEs3(xx300, xx400, dd, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(xx300, xx301, xx302), @3(xx400, xx401, xx402), df, cc, app(app(ty_@2, fh), ga)) -> new_esEs3(xx302, xx402, fh, ga) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs2(Right(xx300), Right(xx400), baf, app(app(app(ty_@3, bah), bba), bbb)) -> new_esEs0(xx300, xx400, bah, bba, bbb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs2(Left(xx300), Left(xx400), app(app(app(ty_@3, hf), hg), hh), he) -> new_esEs0(xx300, xx400, hf, hg, hh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(:(xx300, xx301), :(xx400, xx401), hc) -> new_esEs1(xx301, xx401, hc) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs1(:(xx300, xx301), :(xx400, xx401), app(ty_[], gf)) -> new_esEs1(xx300, xx400, gf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Left(xx300), Left(xx400), app(ty_[], baa), he) -> new_esEs1(xx300, xx400, baa) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Right(xx300), Right(xx400), baf, app(ty_[], bbc)) -> new_esEs1(xx300, xx400, bbc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(Left(xx300), Left(xx400), app(ty_Maybe, hd), he) -> new_esEs(xx300, xx400, hd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Right(xx300), Right(xx400), baf, app(ty_Maybe, bag)) -> new_esEs(xx300, xx400, bag) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(Left(xx300), Left(xx400), app(app(ty_@2, bad), bae), he) -> new_esEs3(xx300, xx400, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Right(xx300), Right(xx400), baf, app(app(ty_@2, bbf), bbg)) -> new_esEs3(xx300, xx400, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 ---------------------------------------- (24) YES ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(xx2800), Succ(xx400000)) -> new_primPlusNat(xx2800, xx400000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) 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(xx2800), Succ(xx400000)) -> new_primPlusNat(xx2800, xx400000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (27) YES ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(xx3000), Succ(xx4000)) -> new_primEqNat(xx3000, xx4000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) 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(xx3000), Succ(xx4000)) -> new_primEqNat(xx3000, xx4000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (30) YES