/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 13 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) AND (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 415 ms] (13) YES (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 7 ms] (16) YES (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] (25) YES (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) 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; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy _ [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = (\(ys,_) ->ys) vv10; zs = (\(_,zs) ->zs) vv10; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\(_,zs)->zs" is transformed to "zs0 (_,zs) = zs; " The following Lambda expression "\(ys,_)->ys" is transformed to "ys0 (ys,_) = ys; " The following Lambda expression "\(_,zs)->zs" is transformed to "zs1 (_,zs) = zs; " The following Lambda expression "\(ys,_)->ys" is transformed to "ys1 (ys,_) = ys; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy _ [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,_) = ys; zs = zs1 vv10; zs1 (_,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. Binding Reductions: The bind variable of the following binding Pattern "xs@(xw : xx)" is replaced by the following term "xw : xx" ---------------------------------------- (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; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,yv) = ys; zs = zs1 vv10; zs1 (yw,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "span p [] = ([],[]); span p (xw : xx)|p xw(xw : ys,zs)|otherwise([],xw : xx) where { vu43 = span p xx; ; ys = ys0 vu43; ; ys0 (ys,xz) = ys; ; zs = zs0 vu43; ; zs0 (xy,zs) = zs; } ; " is transformed to "span p [] = span3 p []; span p (xw : xx) = span2 p (xw : xx); " "span2 p (xw : xx) = span1 p xw xx (p xw) where { span0 p xw xx True = ([],xw : xx); ; span1 p xw xx True = (xw : ys,zs); span1 p xw xx False = span0 p xw xx otherwise; ; vu43 = span p xx; ; ys = ys0 vu43; ; ys0 (ys,xz) = ys; ; zs = zs0 vu43; ; zs0 (xy,zs) = zs; } ; " "span3 p [] = ([],[]); span3 yz zu = span2 yz zu; " ---------------------------------------- (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; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ys = ys1 vv10; ys1 (ys,yv) = ys; zs = zs1 vv10; zs1 (yw,zs) = zs; }; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "span1 p xw xx (p xw) where { span0 p xw xx True = ([],xw : xx); ; span1 p xw xx True = (xw : ys,zs); span1 p xw xx False = span0 p xw xx otherwise; ; vu43 = span p xx; ; ys = ys0 vu43; ; ys0 (ys,xz) = ys; ; zs = zs0 vu43; ; zs0 (xy,zs) = zs; } " are unpacked to the following functions on top level "span2Zs zv zw = span2Zs0 zv zw (span2Vu43 zv zw); " "span2Ys0 zv zw (ys,xz) = ys; " "span2Vu43 zv zw = span zv zw; " "span2Span0 zv zw p xw xx True = ([],xw : xx); " "span2Zs0 zv zw (xy,zs) = zs; " "span2Ys zv zw = span2Ys0 zv zw (span2Vu43 zv zw); " "span2Span1 zv zw p xw xx True = (xw : span2Ys zv zw,span2Zs zv zw); span2Span1 zv zw p xw xx False = span2Span0 zv zw p xw xx otherwise; " The bindings of the following Let/Where expression "(x : ys) : groupBy eq zs where { vv10 = span (eq x) xs; ; ys = ys1 vv10; ; ys1 (ys,yv) = ys; ; zs = zs1 vv10; ; zs1 (yw,zs) = zs; } " are unpacked to the following functions on top level "groupByYs1 zx zy zz (ys,yv) = ys; " "groupByYs zx zy zz = groupByYs1 zx zy zz (groupByVv10 zx zy zz); " "groupByZs1 zx zy zz (yw,zs) = zs; " "groupByZs zx zy zz = groupByZs1 zx zy zz (groupByVv10 zx zy zz); " "groupByVv10 zx zy zz = span (zx zy) zz; " ---------------------------------------- (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; group :: Eq a => [a] -> [[a]]; group = groupBy (==); groupBy :: (a -> a -> Bool) -> [a] -> [[a]]; groupBy yu [] = []; groupBy eq (x : xs) = (x : groupByYs eq x xs) : groupBy eq (groupByZs eq x xs); groupByVv10 zx zy zz = span (zx zy) zz; groupByYs zx zy zz = groupByYs1 zx zy zz (groupByVv10 zx zy zz); groupByYs1 zx zy zz (ys,yv) = ys; groupByZs zx zy zz = groupByZs1 zx zy zz (groupByVv10 zx zy zz); groupByZs1 zx zy zz (yw,zs) = zs; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.group",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.group vuu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="List.groupBy (==) vuu3",fontsize=16,color="burlywood",shape="triangle"];880[label="vuu3/vuu30 : vuu31",fontsize=10,color="white",style="solid",shape="box"];4 -> 880[label="",style="solid", color="burlywood", weight=9]; 880 -> 5[label="",style="solid", color="burlywood", weight=3]; 881[label="vuu3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 881[label="",style="solid", color="burlywood", weight=9]; 881 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="List.groupBy (==) (vuu30 : vuu31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="List.groupBy (==) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="(vuu30 : List.groupByYs (==) vuu30 vuu31) : List.groupBy (==) (List.groupByZs (==) vuu30 vuu31)",fontsize=16,color="green",shape="box"];7 -> 9[label="",style="dashed", color="green", weight=3]; 7 -> 10[label="",style="dashed", color="green", weight=3]; 8[label="[]",fontsize=16,color="green",shape="box"];9[label="List.groupByYs (==) vuu30 vuu31",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10 -> 4[label="",style="dashed", color="red", weight=0]; 10[label="List.groupBy (==) (List.groupByZs (==) vuu30 vuu31)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3]; 11[label="List.groupByYs1 (==) vuu30 vuu31 (List.groupByVv10 (==) vuu30 vuu31)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="List.groupByZs (==) vuu30 vuu31",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="List.groupByYs1 (==) vuu30 vuu31 (span ((==) vuu30) vuu31)",fontsize=16,color="burlywood",shape="box"];882[label="vuu31/vuu310 : vuu311",fontsize=10,color="white",style="solid",shape="box"];13 -> 882[label="",style="solid", color="burlywood", weight=9]; 882 -> 15[label="",style="solid", color="burlywood", weight=3]; 883[label="vuu31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 883[label="",style="solid", color="burlywood", weight=9]; 883 -> 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885[label="",style="solid", color="burlywood", weight=9]; 885 -> 21[label="",style="solid", color="burlywood", weight=3]; 18[label="List.groupByYs1 (==) vuu30 (vuu310 : vuu311) (span2 ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="List.groupByYs1 (==) vuu30 [] (span3 ((==) vuu30) [])",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="List.groupByZs1 (==) vuu30 [] (span ((==) vuu30) [])",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="List.groupByYs1 (==) vuu30 (vuu310 : vuu311) (span2Span1 ((==) vuu30) vuu311 ((==) vuu30) vuu310 vuu311 ((==) vuu30 vuu310))",fontsize=16,color="burlywood",shape="box"];886[label="vuu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];22 -> 886[label="",style="solid", color="burlywood", weight=9]; 886 -> 26[label="",style="solid", color="burlywood", weight=3]; 887[label="vuu30/Just vuu300",fontsize=10,color="white",style="solid",shape="box"];22 -> 887[label="",style="solid", color="burlywood", weight=9]; 887 -> 27[label="",style="solid", color="burlywood", weight=3]; 23[label="List.groupByYs1 (==) vuu30 [] ([],[])",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3]; 24[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span2 ((==) vuu30) (vuu310 : vuu311))",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3]; 25[label="List.groupByZs1 (==) vuu30 [] (span3 ((==) vuu30) [])",fontsize=16,color="black",shape="box"];25 -> 30[label="",style="solid", color="black", weight=3]; 26[label="List.groupByYs1 (==) Nothing (vuu310 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) vuu310 vuu311 ((==) Nothing vuu310))",fontsize=16,color="burlywood",shape="box"];888[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];26 -> 888[label="",style="solid", color="burlywood", weight=9]; 888 -> 31[label="",style="solid", color="burlywood", weight=3]; 889[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];26 -> 889[label="",style="solid", color="burlywood", weight=9]; 889 -> 32[label="",style="solid", color="burlywood", weight=3]; 27[label="List.groupByYs1 (==) (Just vuu300) (vuu310 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) vuu310 vuu311 ((==) Just vuu300 vuu310))",fontsize=16,color="burlywood",shape="box"];890[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];27 -> 890[label="",style="solid", color="burlywood", weight=9]; 890 -> 33[label="",style="solid", color="burlywood", weight=3]; 891[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];27 -> 891[label="",style="solid", color="burlywood", weight=9]; 891 -> 34[label="",style="solid", color="burlywood", weight=3]; 28[label="[]",fontsize=16,color="green",shape="box"];29[label="List.groupByZs1 (==) vuu30 (vuu310 : vuu311) (span2Span1 ((==) vuu30) vuu311 ((==) vuu30) vuu310 vuu311 ((==) vuu30 vuu310))",fontsize=16,color="burlywood",shape="box"];892[label="vuu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];29 -> 892[label="",style="solid", color="burlywood", weight=9]; 892 -> 35[label="",style="solid", color="burlywood", weight=3]; 893[label="vuu30/Just vuu300",fontsize=10,color="white",style="solid",shape="box"];29 -> 893[label="",style="solid", color="burlywood", weight=9]; 893 -> 36[label="",style="solid", color="burlywood", weight=3]; 30[label="List.groupByZs1 (==) vuu30 [] ([],[])",fontsize=16,color="black",shape="box"];30 -> 37[label="",style="solid", color="black", weight=3]; 31[label="List.groupByYs1 (==) Nothing (Nothing : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) Nothing vuu311 ((==) Nothing Nothing))",fontsize=16,color="black",shape="box"];31 -> 38[label="",style="solid", color="black", weight=3]; 32[label="List.groupByYs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 ((==) Nothing Just vuu3100))",fontsize=16,color="black",shape="box"];32 -> 39[label="",style="solid", color="black", weight=3]; 33[label="List.groupByYs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 ((==) Just vuu300 Nothing))",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3]; 34[label="List.groupByYs1 (==) (Just vuu300) (Just vuu3100 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) (Just vuu3100) vuu311 ((==) Just vuu300 Just vuu3100))",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3]; 35[label="List.groupByZs1 (==) Nothing (vuu310 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) vuu310 vuu311 ((==) Nothing vuu310))",fontsize=16,color="burlywood",shape="box"];894[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];35 -> 894[label="",style="solid", color="burlywood", weight=9]; 894 -> 42[label="",style="solid", color="burlywood", weight=3]; 895[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 895[label="",style="solid", color="burlywood", weight=9]; 895 -> 43[label="",style="solid", color="burlywood", weight=3]; 36[label="List.groupByZs1 (==) (Just vuu300) (vuu310 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) vuu310 vuu311 ((==) Just vuu300 vuu310))",fontsize=16,color="burlywood",shape="box"];896[label="vuu310/Nothing",fontsize=10,color="white",style="solid",shape="box"];36 -> 896[label="",style="solid", color="burlywood", weight=9]; 896 -> 44[label="",style="solid", color="burlywood", weight=3]; 897[label="vuu310/Just vuu3100",fontsize=10,color="white",style="solid",shape="box"];36 -> 897[label="",style="solid", color="burlywood", weight=9]; 897 -> 45[label="",style="solid", color="burlywood", weight=3]; 37[label="[]",fontsize=16,color="green",shape="box"];38[label="List.groupByYs1 (==) Nothing (Nothing : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) Nothing vuu311 True)",fontsize=16,color="black",shape="box"];38 -> 46[label="",style="solid", color="black", weight=3]; 39[label="List.groupByYs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 False)",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 40[label="List.groupByYs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 False)",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 41 -> 49[label="",style="dashed", color="red", weight=0]; 41[label="List.groupByYs1 (==) (Just vuu300) (Just vuu3100 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) (Just vuu3100) vuu311 (vuu300 == vuu3100))",fontsize=16,color="magenta"];41 -> 50[label="",style="dashed", color="magenta", weight=3]; 41 -> 51[label="",style="dashed", color="magenta", weight=3]; 41 -> 52[label="",style="dashed", color="magenta", weight=3]; 41 -> 53[label="",style="dashed", color="magenta", weight=3]; 42[label="List.groupByZs1 (==) Nothing (Nothing : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) Nothing vuu311 ((==) Nothing Nothing))",fontsize=16,color="black",shape="box"];42 -> 54[label="",style="solid", color="black", weight=3]; 43[label="List.groupByZs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 ((==) Nothing Just vuu3100))",fontsize=16,color="black",shape="box"];43 -> 55[label="",style="solid", color="black", weight=3]; 44[label="List.groupByZs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 ((==) Just vuu300 Nothing))",fontsize=16,color="black",shape="box"];44 -> 56[label="",style="solid", color="black", weight=3]; 45[label="List.groupByZs1 (==) (Just vuu300) (Just vuu3100 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) (Just vuu3100) vuu311 ((==) Just vuu300 Just vuu3100))",fontsize=16,color="black",shape="box"];45 -> 57[label="",style="solid", color="black", weight=3]; 46[label="List.groupByYs1 (==) Nothing (Nothing : vuu311) (Nothing : span2Ys ((==) Nothing) vuu311,span2Zs ((==) Nothing) vuu311)",fontsize=16,color="black",shape="box"];46 -> 58[label="",style="solid", color="black", weight=3]; 47[label="List.groupByYs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span0 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 otherwise)",fontsize=16,color="black",shape="box"];47 -> 59[label="",style="solid", color="black", weight=3]; 48[label="List.groupByYs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span0 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 otherwise)",fontsize=16,color="black",shape="box"];48 -> 60[label="",style="solid", color="black", weight=3]; 50[label="vuu3100",fontsize=16,color="green",shape="box"];51[label="vuu300 == vuu3100",fontsize=16,color="blue",shape="box"];898[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 898[label="",style="solid", color="blue", weight=9]; 898 -> 61[label="",style="solid", color="blue", weight=3]; 899[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 899[label="",style="solid", color="blue", weight=9]; 899 -> 62[label="",style="solid", color="blue", weight=3]; 900[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 900[label="",style="solid", color="blue", weight=9]; 900 -> 63[label="",style="solid", color="blue", weight=3]; 901[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 901[label="",style="solid", color="blue", weight=9]; 901 -> 64[label="",style="solid", color="blue", weight=3]; 902[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 902[label="",style="solid", color="blue", weight=9]; 902 -> 65[label="",style="solid", color="blue", weight=3]; 903[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 903[label="",style="solid", color="blue", weight=9]; 903 -> 66[label="",style="solid", color="blue", weight=3]; 904[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 904[label="",style="solid", color="blue", weight=9]; 904 -> 67[label="",style="solid", color="blue", weight=3]; 905[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 905[label="",style="solid", color="blue", weight=9]; 905 -> 68[label="",style="solid", color="blue", weight=3]; 906[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 906[label="",style="solid", color="blue", weight=9]; 906 -> 69[label="",style="solid", color="blue", weight=3]; 907[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 907[label="",style="solid", color="blue", weight=9]; 907 -> 70[label="",style="solid", color="blue", weight=3]; 908[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 908[label="",style="solid", color="blue", weight=9]; 908 -> 71[label="",style="solid", color="blue", weight=3]; 909[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 909[label="",style="solid", color="blue", weight=9]; 909 -> 72[label="",style="solid", color="blue", weight=3]; 910[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 910[label="",style="solid", color="blue", weight=9]; 910 -> 73[label="",style="solid", color="blue", weight=3]; 911[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];51 -> 911[label="",style="solid", color="blue", weight=9]; 911 -> 74[label="",style="solid", color="blue", weight=3]; 52[label="vuu311",fontsize=16,color="green",shape="box"];53[label="vuu300",fontsize=16,color="green",shape="box"];49[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (span2Span1 ((==) Just vuu9) vuu11 ((==) Just vuu9) (Just vuu10) vuu11 vuu12)",fontsize=16,color="burlywood",shape="triangle"];912[label="vuu12/False",fontsize=10,color="white",style="solid",shape="box"];49 -> 912[label="",style="solid", color="burlywood", weight=9]; 912 -> 75[label="",style="solid", color="burlywood", weight=3]; 913[label="vuu12/True",fontsize=10,color="white",style="solid",shape="box"];49 -> 913[label="",style="solid", color="burlywood", weight=9]; 913 -> 76[label="",style="solid", color="burlywood", weight=3]; 54[label="List.groupByZs1 (==) Nothing (Nothing : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) Nothing vuu311 True)",fontsize=16,color="black",shape="box"];54 -> 77[label="",style="solid", color="black", weight=3]; 55[label="List.groupByZs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span1 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 False)",fontsize=16,color="black",shape="box"];55 -> 78[label="",style="solid", color="black", weight=3]; 56[label="List.groupByZs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 False)",fontsize=16,color="black",shape="box"];56 -> 79[label="",style="solid", color="black", weight=3]; 57 -> 80[label="",style="dashed", color="red", weight=0]; 57[label="List.groupByZs1 (==) (Just vuu300) (Just vuu3100 : vuu311) (span2Span1 ((==) Just vuu300) vuu311 ((==) Just vuu300) (Just vuu3100) vuu311 (vuu300 == vuu3100))",fontsize=16,color="magenta"];57 -> 81[label="",style="dashed", color="magenta", weight=3]; 57 -> 82[label="",style="dashed", color="magenta", weight=3]; 57 -> 83[label="",style="dashed", color="magenta", weight=3]; 57 -> 84[label="",style="dashed", color="magenta", weight=3]; 58[label="Nothing : span2Ys ((==) Nothing) vuu311",fontsize=16,color="green",shape="box"];58 -> 85[label="",style="dashed", color="green", weight=3]; 59[label="List.groupByYs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span0 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 True)",fontsize=16,color="black",shape="box"];59 -> 86[label="",style="solid", color="black", weight=3]; 60[label="List.groupByYs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span0 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 True)",fontsize=16,color="black",shape="box"];60 -> 87[label="",style="solid", color="black", weight=3]; 61[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];914[label="vuu300/Integer vuu3000",fontsize=10,color="white",style="solid",shape="box"];61 -> 914[label="",style="solid", color="burlywood", weight=9]; 914 -> 88[label="",style="solid", color="burlywood", weight=3]; 62[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];915[label="vuu300/(vuu3000,vuu3001,vuu3002)",fontsize=10,color="white",style="solid",shape="box"];62 -> 915[label="",style="solid", color="burlywood", weight=9]; 915 -> 89[label="",style="solid", color="burlywood", weight=3]; 63[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];63 -> 90[label="",style="solid", color="black", weight=3]; 64[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];64 -> 91[label="",style="solid", color="black", weight=3]; 65[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];916[label="vuu300/Nothing",fontsize=10,color="white",style="solid",shape="box"];65 -> 916[label="",style="solid", color="burlywood", weight=9]; 916 -> 92[label="",style="solid", color="burlywood", weight=3]; 917[label="vuu300/Just vuu3000",fontsize=10,color="white",style="solid",shape="box"];65 -> 917[label="",style="solid", color="burlywood", weight=9]; 917 -> 93[label="",style="solid", color="burlywood", weight=3]; 66[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];918[label="vuu300/()",fontsize=10,color="white",style="solid",shape="box"];66 -> 918[label="",style="solid", color="burlywood", weight=9]; 918 -> 94[label="",style="solid", color="burlywood", weight=3]; 67[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];67 -> 95[label="",style="solid", color="black", weight=3]; 68[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];919[label="vuu300/LT",fontsize=10,color="white",style="solid",shape="box"];68 -> 919[label="",style="solid", color="burlywood", weight=9]; 919 -> 96[label="",style="solid", color="burlywood", weight=3]; 920[label="vuu300/EQ",fontsize=10,color="white",style="solid",shape="box"];68 -> 920[label="",style="solid", color="burlywood", weight=9]; 920 -> 97[label="",style="solid", color="burlywood", weight=3]; 921[label="vuu300/GT",fontsize=10,color="white",style="solid",shape="box"];68 -> 921[label="",style="solid", color="burlywood", weight=9]; 921 -> 98[label="",style="solid", color="burlywood", weight=3]; 69[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];922[label="vuu300/vuu3000 :% vuu3001",fontsize=10,color="white",style="solid",shape="box"];69 -> 922[label="",style="solid", color="burlywood", weight=9]; 922 -> 99[label="",style="solid", color="burlywood", weight=3]; 70[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];923[label="vuu300/False",fontsize=10,color="white",style="solid",shape="box"];70 -> 923[label="",style="solid", color="burlywood", weight=9]; 923 -> 100[label="",style="solid", color="burlywood", weight=3]; 924[label="vuu300/True",fontsize=10,color="white",style="solid",shape="box"];70 -> 924[label="",style="solid", color="burlywood", weight=9]; 924 -> 101[label="",style="solid", color="burlywood", weight=3]; 71[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];925[label="vuu300/vuu3000 : vuu3001",fontsize=10,color="white",style="solid",shape="box"];71 -> 925[label="",style="solid", color="burlywood", weight=9]; 925 -> 102[label="",style="solid", color="burlywood", weight=3]; 926[label="vuu300/[]",fontsize=10,color="white",style="solid",shape="box"];71 -> 926[label="",style="solid", color="burlywood", weight=9]; 926 -> 103[label="",style="solid", color="burlywood", weight=3]; 72[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];927[label="vuu300/Left vuu3000",fontsize=10,color="white",style="solid",shape="box"];72 -> 927[label="",style="solid", color="burlywood", weight=9]; 927 -> 104[label="",style="solid", color="burlywood", weight=3]; 928[label="vuu300/Right vuu3000",fontsize=10,color="white",style="solid",shape="box"];72 -> 928[label="",style="solid", color="burlywood", weight=9]; 928 -> 105[label="",style="solid", color="burlywood", weight=3]; 73[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];929[label="vuu300/(vuu3000,vuu3001)",fontsize=10,color="white",style="solid",shape="box"];73 -> 929[label="",style="solid", color="burlywood", weight=9]; 929 -> 106[label="",style="solid", color="burlywood", weight=3]; 74[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];74 -> 107[label="",style="solid", color="black", weight=3]; 75[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (span2Span1 ((==) Just vuu9) vuu11 ((==) Just vuu9) (Just vuu10) vuu11 False)",fontsize=16,color="black",shape="box"];75 -> 108[label="",style="solid", color="black", weight=3]; 76[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (span2Span1 ((==) Just vuu9) vuu11 ((==) Just vuu9) (Just vuu10) vuu11 True)",fontsize=16,color="black",shape="box"];76 -> 109[label="",style="solid", color="black", weight=3]; 77[label="List.groupByZs1 (==) Nothing (Nothing : vuu311) (Nothing : span2Ys ((==) Nothing) vuu311,span2Zs ((==) Nothing) vuu311)",fontsize=16,color="black",shape="box"];77 -> 110[label="",style="solid", color="black", weight=3]; 78[label="List.groupByZs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span0 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 otherwise)",fontsize=16,color="black",shape="box"];78 -> 111[label="",style="solid", color="black", weight=3]; 79[label="List.groupByZs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span0 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 otherwise)",fontsize=16,color="black",shape="box"];79 -> 112[label="",style="solid", color="black", weight=3]; 81[label="vuu3100",fontsize=16,color="green",shape="box"];82[label="vuu300 == vuu3100",fontsize=16,color="blue",shape="box"];930[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 930[label="",style="solid", color="blue", weight=9]; 930 -> 113[label="",style="solid", color="blue", weight=3]; 931[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 931[label="",style="solid", color="blue", weight=9]; 931 -> 114[label="",style="solid", color="blue", weight=3]; 932[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 932[label="",style="solid", color="blue", weight=9]; 932 -> 115[label="",style="solid", color="blue", weight=3]; 933[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 933[label="",style="solid", color="blue", weight=9]; 933 -> 116[label="",style="solid", color="blue", weight=3]; 934[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 934[label="",style="solid", color="blue", weight=9]; 934 -> 117[label="",style="solid", color="blue", weight=3]; 935[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 935[label="",style="solid", color="blue", weight=9]; 935 -> 118[label="",style="solid", color="blue", weight=3]; 936[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 936[label="",style="solid", color="blue", weight=9]; 936 -> 119[label="",style="solid", color="blue", weight=3]; 937[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 937[label="",style="solid", color="blue", weight=9]; 937 -> 120[label="",style="solid", color="blue", weight=3]; 938[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 938[label="",style="solid", color="blue", weight=9]; 938 -> 121[label="",style="solid", color="blue", weight=3]; 939[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 939[label="",style="solid", color="blue", weight=9]; 939 -> 122[label="",style="solid", color="blue", weight=3]; 940[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 940[label="",style="solid", color="blue", weight=9]; 940 -> 123[label="",style="solid", color="blue", weight=3]; 941[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 941[label="",style="solid", color="blue", weight=9]; 941 -> 124[label="",style="solid", color="blue", weight=3]; 942[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 942[label="",style="solid", color="blue", weight=9]; 942 -> 125[label="",style="solid", color="blue", weight=3]; 943[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];82 -> 943[label="",style="solid", color="blue", weight=9]; 943 -> 126[label="",style="solid", color="blue", weight=3]; 83[label="vuu300",fontsize=16,color="green",shape="box"];84[label="vuu311",fontsize=16,color="green",shape="box"];80[label="List.groupByZs1 (==) (Just vuu18) (Just vuu19 : vuu20) (span2Span1 ((==) Just vuu18) vuu20 ((==) Just vuu18) (Just vuu19) vuu20 vuu21)",fontsize=16,color="burlywood",shape="triangle"];944[label="vuu21/False",fontsize=10,color="white",style="solid",shape="box"];80 -> 944[label="",style="solid", color="burlywood", weight=9]; 944 -> 127[label="",style="solid", color="burlywood", weight=3]; 945[label="vuu21/True",fontsize=10,color="white",style="solid",shape="box"];80 -> 945[label="",style="solid", color="burlywood", weight=9]; 945 -> 128[label="",style="solid", color="burlywood", weight=3]; 85[label="span2Ys ((==) Nothing) vuu311",fontsize=16,color="black",shape="triangle"];85 -> 129[label="",style="solid", color="black", weight=3]; 86[label="List.groupByYs1 (==) Nothing (Just vuu3100 : vuu311) ([],Just vuu3100 : vuu311)",fontsize=16,color="black",shape="box"];86 -> 130[label="",style="solid", color="black", weight=3]; 87[label="List.groupByYs1 (==) (Just vuu300) (Nothing : vuu311) ([],Nothing : vuu311)",fontsize=16,color="black",shape="box"];87 -> 131[label="",style="solid", color="black", weight=3]; 88[label="Integer vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];946[label="vuu3100/Integer vuu31000",fontsize=10,color="white",style="solid",shape="box"];88 -> 946[label="",style="solid", color="burlywood", weight=9]; 946 -> 132[label="",style="solid", color="burlywood", weight=3]; 89[label="(vuu3000,vuu3001,vuu3002) == vuu3100",fontsize=16,color="burlywood",shape="box"];947[label="vuu3100/(vuu31000,vuu31001,vuu31002)",fontsize=10,color="white",style="solid",shape="box"];89 -> 947[label="",style="solid", color="burlywood", weight=9]; 947 -> 133[label="",style="solid", color="burlywood", weight=3]; 90[label="primEqDouble vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];948[label="vuu300/Double vuu3000 vuu3001",fontsize=10,color="white",style="solid",shape="box"];90 -> 948[label="",style="solid", color="burlywood", weight=9]; 948 -> 134[label="",style="solid", color="burlywood", weight=3]; 91[label="primEqFloat vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];949[label="vuu300/Float vuu3000 vuu3001",fontsize=10,color="white",style="solid",shape="box"];91 -> 949[label="",style="solid", color="burlywood", weight=9]; 949 -> 135[label="",style="solid", color="burlywood", weight=3]; 92[label="Nothing == vuu3100",fontsize=16,color="burlywood",shape="box"];950[label="vuu3100/Nothing",fontsize=10,color="white",style="solid",shape="box"];92 -> 950[label="",style="solid", color="burlywood", weight=9]; 950 -> 136[label="",style="solid", color="burlywood", weight=3]; 951[label="vuu3100/Just vuu31000",fontsize=10,color="white",style="solid",shape="box"];92 -> 951[label="",style="solid", color="burlywood", weight=9]; 951 -> 137[label="",style="solid", color="burlywood", weight=3]; 93[label="Just vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];952[label="vuu3100/Nothing",fontsize=10,color="white",style="solid",shape="box"];93 -> 952[label="",style="solid", color="burlywood", weight=9]; 952 -> 138[label="",style="solid", color="burlywood", weight=3]; 953[label="vuu3100/Just vuu31000",fontsize=10,color="white",style="solid",shape="box"];93 -> 953[label="",style="solid", color="burlywood", weight=9]; 953 -> 139[label="",style="solid", color="burlywood", weight=3]; 94[label="() == vuu3100",fontsize=16,color="burlywood",shape="box"];954[label="vuu3100/()",fontsize=10,color="white",style="solid",shape="box"];94 -> 954[label="",style="solid", color="burlywood", weight=9]; 954 -> 140[label="",style="solid", color="burlywood", weight=3]; 95[label="primEqInt vuu300 vuu3100",fontsize=16,color="burlywood",shape="triangle"];955[label="vuu300/Pos vuu3000",fontsize=10,color="white",style="solid",shape="box"];95 -> 955[label="",style="solid", color="burlywood", weight=9]; 955 -> 141[label="",style="solid", color="burlywood", weight=3]; 956[label="vuu300/Neg vuu3000",fontsize=10,color="white",style="solid",shape="box"];95 -> 956[label="",style="solid", color="burlywood", weight=9]; 956 -> 142[label="",style="solid", color="burlywood", weight=3]; 96[label="LT == vuu3100",fontsize=16,color="burlywood",shape="box"];957[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];96 -> 957[label="",style="solid", color="burlywood", weight=9]; 957 -> 143[label="",style="solid", color="burlywood", weight=3]; 958[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];96 -> 958[label="",style="solid", color="burlywood", weight=9]; 958 -> 144[label="",style="solid", color="burlywood", weight=3]; 959[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];96 -> 959[label="",style="solid", color="burlywood", weight=9]; 959 -> 145[label="",style="solid", color="burlywood", weight=3]; 97[label="EQ == vuu3100",fontsize=16,color="burlywood",shape="box"];960[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];97 -> 960[label="",style="solid", color="burlywood", weight=9]; 960 -> 146[label="",style="solid", color="burlywood", weight=3]; 961[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];97 -> 961[label="",style="solid", color="burlywood", weight=9]; 961 -> 147[label="",style="solid", color="burlywood", weight=3]; 962[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];97 -> 962[label="",style="solid", color="burlywood", weight=9]; 962 -> 148[label="",style="solid", color="burlywood", weight=3]; 98[label="GT == vuu3100",fontsize=16,color="burlywood",shape="box"];963[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];98 -> 963[label="",style="solid", color="burlywood", weight=9]; 963 -> 149[label="",style="solid", color="burlywood", weight=3]; 964[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];98 -> 964[label="",style="solid", color="burlywood", weight=9]; 964 -> 150[label="",style="solid", color="burlywood", weight=3]; 965[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];98 -> 965[label="",style="solid", color="burlywood", weight=9]; 965 -> 151[label="",style="solid", color="burlywood", weight=3]; 99[label="vuu3000 :% vuu3001 == vuu3100",fontsize=16,color="burlywood",shape="box"];966[label="vuu3100/vuu31000 :% vuu31001",fontsize=10,color="white",style="solid",shape="box"];99 -> 966[label="",style="solid", color="burlywood", weight=9]; 966 -> 152[label="",style="solid", color="burlywood", weight=3]; 100[label="False == vuu3100",fontsize=16,color="burlywood",shape="box"];967[label="vuu3100/False",fontsize=10,color="white",style="solid",shape="box"];100 -> 967[label="",style="solid", color="burlywood", weight=9]; 967 -> 153[label="",style="solid", color="burlywood", weight=3]; 968[label="vuu3100/True",fontsize=10,color="white",style="solid",shape="box"];100 -> 968[label="",style="solid", color="burlywood", weight=9]; 968 -> 154[label="",style="solid", color="burlywood", weight=3]; 101[label="True == vuu3100",fontsize=16,color="burlywood",shape="box"];969[label="vuu3100/False",fontsize=10,color="white",style="solid",shape="box"];101 -> 969[label="",style="solid", color="burlywood", weight=9]; 969 -> 155[label="",style="solid", color="burlywood", weight=3]; 970[label="vuu3100/True",fontsize=10,color="white",style="solid",shape="box"];101 -> 970[label="",style="solid", color="burlywood", weight=9]; 970 -> 156[label="",style="solid", color="burlywood", weight=3]; 102[label="vuu3000 : vuu3001 == vuu3100",fontsize=16,color="burlywood",shape="box"];971[label="vuu3100/vuu31000 : vuu31001",fontsize=10,color="white",style="solid",shape="box"];102 -> 971[label="",style="solid", color="burlywood", weight=9]; 971 -> 157[label="",style="solid", color="burlywood", weight=3]; 972[label="vuu3100/[]",fontsize=10,color="white",style="solid",shape="box"];102 -> 972[label="",style="solid", color="burlywood", weight=9]; 972 -> 158[label="",style="solid", color="burlywood", weight=3]; 103[label="[] == vuu3100",fontsize=16,color="burlywood",shape="box"];973[label="vuu3100/vuu31000 : vuu31001",fontsize=10,color="white",style="solid",shape="box"];103 -> 973[label="",style="solid", color="burlywood", weight=9]; 973 -> 159[label="",style="solid", color="burlywood", weight=3]; 974[label="vuu3100/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 974[label="",style="solid", color="burlywood", weight=9]; 974 -> 160[label="",style="solid", color="burlywood", weight=3]; 104[label="Left vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];975[label="vuu3100/Left vuu31000",fontsize=10,color="white",style="solid",shape="box"];104 -> 975[label="",style="solid", color="burlywood", weight=9]; 975 -> 161[label="",style="solid", color="burlywood", weight=3]; 976[label="vuu3100/Right vuu31000",fontsize=10,color="white",style="solid",shape="box"];104 -> 976[label="",style="solid", color="burlywood", weight=9]; 976 -> 162[label="",style="solid", color="burlywood", weight=3]; 105[label="Right vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];977[label="vuu3100/Left vuu31000",fontsize=10,color="white",style="solid",shape="box"];105 -> 977[label="",style="solid", color="burlywood", weight=9]; 977 -> 163[label="",style="solid", color="burlywood", weight=3]; 978[label="vuu3100/Right vuu31000",fontsize=10,color="white",style="solid",shape="box"];105 -> 978[label="",style="solid", color="burlywood", weight=9]; 978 -> 164[label="",style="solid", color="burlywood", weight=3]; 106[label="(vuu3000,vuu3001) == vuu3100",fontsize=16,color="burlywood",shape="box"];979[label="vuu3100/(vuu31000,vuu31001)",fontsize=10,color="white",style="solid",shape="box"];106 -> 979[label="",style="solid", color="burlywood", weight=9]; 979 -> 165[label="",style="solid", color="burlywood", weight=3]; 107[label="primEqChar vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];980[label="vuu300/Char vuu3000",fontsize=10,color="white",style="solid",shape="box"];107 -> 980[label="",style="solid", color="burlywood", weight=9]; 980 -> 166[label="",style="solid", color="burlywood", weight=3]; 108[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (span2Span0 ((==) Just vuu9) vuu11 ((==) Just vuu9) (Just vuu10) vuu11 otherwise)",fontsize=16,color="black",shape="box"];108 -> 167[label="",style="solid", color="black", weight=3]; 109[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (Just vuu10 : span2Ys ((==) Just vuu9) vuu11,span2Zs ((==) Just vuu9) vuu11)",fontsize=16,color="black",shape="box"];109 -> 168[label="",style="solid", color="black", weight=3]; 110[label="span2Zs ((==) Nothing) vuu311",fontsize=16,color="black",shape="triangle"];110 -> 169[label="",style="solid", color="black", weight=3]; 111[label="List.groupByZs1 (==) Nothing (Just vuu3100 : vuu311) (span2Span0 ((==) Nothing) vuu311 ((==) Nothing) (Just vuu3100) vuu311 True)",fontsize=16,color="black",shape="box"];111 -> 170[label="",style="solid", color="black", weight=3]; 112[label="List.groupByZs1 (==) (Just vuu300) (Nothing : vuu311) (span2Span0 ((==) Just vuu300) vuu311 ((==) Just vuu300) Nothing vuu311 True)",fontsize=16,color="black",shape="box"];112 -> 171[label="",style="solid", color="black", weight=3]; 113 -> 61[label="",style="dashed", color="red", weight=0]; 113[label="vuu300 == vuu3100",fontsize=16,color="magenta"];114 -> 62[label="",style="dashed", color="red", weight=0]; 114[label="vuu300 == vuu3100",fontsize=16,color="magenta"];115 -> 63[label="",style="dashed", color="red", weight=0]; 115[label="vuu300 == vuu3100",fontsize=16,color="magenta"];116 -> 64[label="",style="dashed", color="red", weight=0]; 116[label="vuu300 == vuu3100",fontsize=16,color="magenta"];117 -> 65[label="",style="dashed", color="red", weight=0]; 117[label="vuu300 == vuu3100",fontsize=16,color="magenta"];118 -> 66[label="",style="dashed", color="red", weight=0]; 118[label="vuu300 == vuu3100",fontsize=16,color="magenta"];119 -> 67[label="",style="dashed", color="red", weight=0]; 119[label="vuu300 == vuu3100",fontsize=16,color="magenta"];120 -> 68[label="",style="dashed", color="red", weight=0]; 120[label="vuu300 == vuu3100",fontsize=16,color="magenta"];121 -> 69[label="",style="dashed", color="red", weight=0]; 121[label="vuu300 == vuu3100",fontsize=16,color="magenta"];122 -> 70[label="",style="dashed", color="red", weight=0]; 122[label="vuu300 == vuu3100",fontsize=16,color="magenta"];123 -> 71[label="",style="dashed", color="red", weight=0]; 123[label="vuu300 == vuu3100",fontsize=16,color="magenta"];124 -> 72[label="",style="dashed", color="red", weight=0]; 124[label="vuu300 == vuu3100",fontsize=16,color="magenta"];125 -> 73[label="",style="dashed", color="red", weight=0]; 125[label="vuu300 == vuu3100",fontsize=16,color="magenta"];126 -> 74[label="",style="dashed", color="red", weight=0]; 126[label="vuu300 == vuu3100",fontsize=16,color="magenta"];127[label="List.groupByZs1 (==) (Just vuu18) (Just vuu19 : vuu20) (span2Span1 ((==) Just vuu18) vuu20 ((==) Just vuu18) (Just vuu19) vuu20 False)",fontsize=16,color="black",shape="box"];127 -> 172[label="",style="solid", color="black", weight=3]; 128[label="List.groupByZs1 (==) (Just vuu18) (Just vuu19 : vuu20) (span2Span1 ((==) Just vuu18) vuu20 ((==) Just vuu18) (Just vuu19) vuu20 True)",fontsize=16,color="black",shape="box"];128 -> 173[label="",style="solid", color="black", weight=3]; 129[label="span2Ys0 ((==) Nothing) vuu311 (span2Vu43 ((==) Nothing) vuu311)",fontsize=16,color="black",shape="box"];129 -> 174[label="",style="solid", color="black", weight=3]; 130[label="[]",fontsize=16,color="green",shape="box"];131[label="[]",fontsize=16,color="green",shape="box"];132[label="Integer vuu3000 == Integer vuu31000",fontsize=16,color="black",shape="box"];132 -> 175[label="",style="solid", color="black", weight=3]; 133[label="(vuu3000,vuu3001,vuu3002) == (vuu31000,vuu31001,vuu31002)",fontsize=16,color="black",shape="box"];133 -> 176[label="",style="solid", color="black", weight=3]; 134[label="primEqDouble (Double vuu3000 vuu3001) vuu3100",fontsize=16,color="burlywood",shape="box"];981[label="vuu3100/Double vuu31000 vuu31001",fontsize=10,color="white",style="solid",shape="box"];134 -> 981[label="",style="solid", color="burlywood", weight=9]; 981 -> 177[label="",style="solid", color="burlywood", weight=3]; 135[label="primEqFloat (Float vuu3000 vuu3001) vuu3100",fontsize=16,color="burlywood",shape="box"];982[label="vuu3100/Float vuu31000 vuu31001",fontsize=10,color="white",style="solid",shape="box"];135 -> 982[label="",style="solid", color="burlywood", weight=9]; 982 -> 178[label="",style="solid", color="burlywood", weight=3]; 136[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];136 -> 179[label="",style="solid", color="black", weight=3]; 137[label="Nothing == Just vuu31000",fontsize=16,color="black",shape="box"];137 -> 180[label="",style="solid", color="black", weight=3]; 138[label="Just vuu3000 == Nothing",fontsize=16,color="black",shape="box"];138 -> 181[label="",style="solid", color="black", weight=3]; 139[label="Just vuu3000 == Just vuu31000",fontsize=16,color="black",shape="box"];139 -> 182[label="",style="solid", color="black", weight=3]; 140[label="() == ()",fontsize=16,color="black",shape="box"];140 -> 183[label="",style="solid", color="black", weight=3]; 141[label="primEqInt (Pos vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];983[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];141 -> 983[label="",style="solid", color="burlywood", weight=9]; 983 -> 184[label="",style="solid", color="burlywood", weight=3]; 984[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 984[label="",style="solid", color="burlywood", weight=9]; 984 -> 185[label="",style="solid", color="burlywood", weight=3]; 142[label="primEqInt (Neg vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];985[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];142 -> 985[label="",style="solid", color="burlywood", weight=9]; 985 -> 186[label="",style="solid", color="burlywood", weight=3]; 986[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];142 -> 986[label="",style="solid", color="burlywood", weight=9]; 986 -> 187[label="",style="solid", color="burlywood", weight=3]; 143[label="LT == LT",fontsize=16,color="black",shape="box"];143 -> 188[label="",style="solid", color="black", weight=3]; 144[label="LT == EQ",fontsize=16,color="black",shape="box"];144 -> 189[label="",style="solid", color="black", weight=3]; 145[label="LT == GT",fontsize=16,color="black",shape="box"];145 -> 190[label="",style="solid", color="black", weight=3]; 146[label="EQ == LT",fontsize=16,color="black",shape="box"];146 -> 191[label="",style="solid", color="black", weight=3]; 147[label="EQ == EQ",fontsize=16,color="black",shape="box"];147 -> 192[label="",style="solid", color="black", weight=3]; 148[label="EQ == GT",fontsize=16,color="black",shape="box"];148 -> 193[label="",style="solid", color="black", weight=3]; 149[label="GT == LT",fontsize=16,color="black",shape="box"];149 -> 194[label="",style="solid", color="black", weight=3]; 150[label="GT == EQ",fontsize=16,color="black",shape="box"];150 -> 195[label="",style="solid", color="black", weight=3]; 151[label="GT == GT",fontsize=16,color="black",shape="box"];151 -> 196[label="",style="solid", color="black", weight=3]; 152[label="vuu3000 :% vuu3001 == vuu31000 :% vuu31001",fontsize=16,color="black",shape="box"];152 -> 197[label="",style="solid", color="black", weight=3]; 153[label="False == False",fontsize=16,color="black",shape="box"];153 -> 198[label="",style="solid", color="black", weight=3]; 154[label="False == True",fontsize=16,color="black",shape="box"];154 -> 199[label="",style="solid", color="black", weight=3]; 155[label="True == False",fontsize=16,color="black",shape="box"];155 -> 200[label="",style="solid", color="black", weight=3]; 156[label="True == True",fontsize=16,color="black",shape="box"];156 -> 201[label="",style="solid", color="black", weight=3]; 157[label="vuu3000 : vuu3001 == vuu31000 : vuu31001",fontsize=16,color="black",shape="box"];157 -> 202[label="",style="solid", color="black", weight=3]; 158[label="vuu3000 : vuu3001 == []",fontsize=16,color="black",shape="box"];158 -> 203[label="",style="solid", color="black", weight=3]; 159[label="[] == vuu31000 : vuu31001",fontsize=16,color="black",shape="box"];159 -> 204[label="",style="solid", color="black", weight=3]; 160[label="[] == []",fontsize=16,color="black",shape="box"];160 -> 205[label="",style="solid", color="black", weight=3]; 161[label="Left vuu3000 == Left vuu31000",fontsize=16,color="black",shape="box"];161 -> 206[label="",style="solid", color="black", weight=3]; 162[label="Left vuu3000 == Right vuu31000",fontsize=16,color="black",shape="box"];162 -> 207[label="",style="solid", color="black", weight=3]; 163[label="Right vuu3000 == Left vuu31000",fontsize=16,color="black",shape="box"];163 -> 208[label="",style="solid", color="black", weight=3]; 164[label="Right vuu3000 == Right vuu31000",fontsize=16,color="black",shape="box"];164 -> 209[label="",style="solid", color="black", weight=3]; 165[label="(vuu3000,vuu3001) == (vuu31000,vuu31001)",fontsize=16,color="black",shape="box"];165 -> 210[label="",style="solid", color="black", weight=3]; 166[label="primEqChar (Char vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];987[label="vuu3100/Char vuu31000",fontsize=10,color="white",style="solid",shape="box"];166 -> 987[label="",style="solid", color="burlywood", weight=9]; 987 -> 211[label="",style="solid", color="burlywood", weight=3]; 167[label="List.groupByYs1 (==) (Just vuu9) (Just vuu10 : vuu11) (span2Span0 ((==) Just vuu9) vuu11 ((==) Just vuu9) (Just vuu10) vuu11 True)",fontsize=16,color="black",shape="box"];167 -> 212[label="",style="solid", color="black", weight=3]; 168[label="Just vuu10 : span2Ys ((==) Just vuu9) vuu11",fontsize=16,color="green",shape="box"];168 -> 213[label="",style="dashed", color="green", weight=3]; 169[label="span2Zs0 ((==) Nothing) vuu311 (span2Vu43 ((==) Nothing) vuu311)",fontsize=16,color="black",shape="box"];169 -> 214[label="",style="solid", color="black", weight=3]; 170[label="List.groupByZs1 (==) Nothing (Just vuu3100 : vuu311) ([],Just vuu3100 : vuu311)",fontsize=16,color="black",shape="box"];170 -> 215[label="",style="solid", color="black", weight=3]; 171[label="List.groupByZs1 (==) (Just vuu300) (Nothing : vuu311) ([],Nothing : vuu311)",fontsize=16,color="black",shape="box"];171 -> 216[label="",style="solid", color="black", weight=3]; 172[label="List.groupByZs1 (==) (Just vuu18) (Just vuu19 : vuu20) (span2Span0 ((==) Just vuu18) vuu20 ((==) Just vuu18) (Just vuu19) vuu20 otherwise)",fontsize=16,color="black",shape="box"];172 -> 217[label="",style="solid", color="black", weight=3]; 173[label="List.groupByZs1 (==) (Just vuu18) (Just vuu19 : vuu20) (Just vuu19 : span2Ys ((==) Just vuu18) vuu20,span2Zs ((==) Just vuu18) vuu20)",fontsize=16,color="black",shape="box"];173 -> 218[label="",style="solid", color="black", weight=3]; 174[label="span2Ys0 ((==) Nothing) vuu311 (span ((==) Nothing) vuu311)",fontsize=16,color="burlywood",shape="box"];988[label="vuu311/vuu3110 : vuu3111",fontsize=10,color="white",style="solid",shape="box"];174 -> 988[label="",style="solid", color="burlywood", weight=9]; 988 -> 219[label="",style="solid", color="burlywood", weight=3]; 989[label="vuu311/[]",fontsize=10,color="white",style="solid",shape="box"];174 -> 989[label="",style="solid", color="burlywood", weight=9]; 989 -> 220[label="",style="solid", color="burlywood", weight=3]; 175 -> 95[label="",style="dashed", color="red", weight=0]; 175[label="primEqInt vuu3000 vuu31000",fontsize=16,color="magenta"];175 -> 221[label="",style="dashed", color="magenta", weight=3]; 175 -> 222[label="",style="dashed", color="magenta", weight=3]; 176 -> 314[label="",style="dashed", color="red", weight=0]; 176[label="vuu3000 == vuu31000 && vuu3001 == vuu31001 && vuu3002 == vuu31002",fontsize=16,color="magenta"];176 -> 315[label="",style="dashed", color="magenta", weight=3]; 176 -> 316[label="",style="dashed", color="magenta", weight=3]; 177[label="primEqDouble (Double vuu3000 vuu3001) (Double vuu31000 vuu31001)",fontsize=16,color="black",shape="box"];177 -> 229[label="",style="solid", color="black", weight=3]; 178[label="primEqFloat (Float vuu3000 vuu3001) (Float vuu31000 vuu31001)",fontsize=16,color="black",shape="box"];178 -> 230[label="",style="solid", color="black", weight=3]; 179[label="True",fontsize=16,color="green",shape="box"];180[label="False",fontsize=16,color="green",shape="box"];181[label="False",fontsize=16,color="green",shape="box"];182[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];990[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 990[label="",style="solid", color="blue", weight=9]; 990 -> 231[label="",style="solid", color="blue", weight=3]; 991[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 991[label="",style="solid", color="blue", weight=9]; 991 -> 232[label="",style="solid", color="blue", weight=3]; 992[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 992[label="",style="solid", color="blue", weight=9]; 992 -> 233[label="",style="solid", color="blue", weight=3]; 993[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 993[label="",style="solid", color="blue", weight=9]; 993 -> 234[label="",style="solid", color="blue", weight=3]; 994[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 994[label="",style="solid", color="blue", weight=9]; 994 -> 235[label="",style="solid", color="blue", weight=3]; 995[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 995[label="",style="solid", color="blue", weight=9]; 995 -> 236[label="",style="solid", color="blue", weight=3]; 996[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 996[label="",style="solid", color="blue", weight=9]; 996 -> 237[label="",style="solid", color="blue", weight=3]; 997[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 997[label="",style="solid", color="blue", weight=9]; 997 -> 238[label="",style="solid", color="blue", weight=3]; 998[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 998[label="",style="solid", color="blue", weight=9]; 998 -> 239[label="",style="solid", color="blue", weight=3]; 999[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 999[label="",style="solid", color="blue", weight=9]; 999 -> 240[label="",style="solid", color="blue", weight=3]; 1000[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 1000[label="",style="solid", color="blue", weight=9]; 1000 -> 241[label="",style="solid", color="blue", weight=3]; 1001[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 1001[label="",style="solid", color="blue", weight=9]; 1001 -> 242[label="",style="solid", color="blue", weight=3]; 1002[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 1002[label="",style="solid", color="blue", weight=9]; 1002 -> 243[label="",style="solid", color="blue", weight=3]; 1003[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];182 -> 1003[label="",style="solid", color="blue", weight=9]; 1003 -> 244[label="",style="solid", color="blue", weight=3]; 183[label="True",fontsize=16,color="green",shape="box"];184[label="primEqInt (Pos (Succ vuu30000)) vuu3100",fontsize=16,color="burlywood",shape="box"];1004[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];184 -> 1004[label="",style="solid", color="burlywood", weight=9]; 1004 -> 245[label="",style="solid", color="burlywood", weight=3]; 1005[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];184 -> 1005[label="",style="solid", color="burlywood", weight=9]; 1005 -> 246[label="",style="solid", color="burlywood", weight=3]; 185[label="primEqInt (Pos Zero) vuu3100",fontsize=16,color="burlywood",shape="box"];1006[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];185 -> 1006[label="",style="solid", color="burlywood", weight=9]; 1006 -> 247[label="",style="solid", color="burlywood", weight=3]; 1007[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];185 -> 1007[label="",style="solid", color="burlywood", weight=9]; 1007 -> 248[label="",style="solid", color="burlywood", weight=3]; 186[label="primEqInt (Neg (Succ vuu30000)) vuu3100",fontsize=16,color="burlywood",shape="box"];1008[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];186 -> 1008[label="",style="solid", color="burlywood", weight=9]; 1008 -> 249[label="",style="solid", color="burlywood", weight=3]; 1009[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];186 -> 1009[label="",style="solid", color="burlywood", weight=9]; 1009 -> 250[label="",style="solid", color="burlywood", weight=3]; 187[label="primEqInt (Neg Zero) vuu3100",fontsize=16,color="burlywood",shape="box"];1010[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];187 -> 1010[label="",style="solid", color="burlywood", weight=9]; 1010 -> 251[label="",style="solid", color="burlywood", weight=3]; 1011[label="vuu3100/Neg 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285[label="",style="solid", color="blue", weight=3]; 1035[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];209 -> 1035[label="",style="solid", color="blue", weight=9]; 1035 -> 286[label="",style="solid", color="blue", weight=3]; 1036[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];209 -> 1036[label="",style="solid", color="blue", weight=9]; 1036 -> 287[label="",style="solid", color="blue", weight=3]; 1037[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];209 -> 1037[label="",style="solid", color="blue", weight=9]; 1037 -> 288[label="",style="solid", color="blue", weight=3]; 1038[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];209 -> 1038[label="",style="solid", color="blue", weight=9]; 1038 -> 289[label="",style="solid", color="blue", weight=3]; 1039[label="== :: Char -> Char -> 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494[label="primEqNat (Succ vuu30000) vuu31000",fontsize=16,color="burlywood",shape="box"];1146[label="vuu31000/Succ vuu310000",fontsize=10,color="white",style="solid",shape="box"];494 -> 1146[label="",style="solid", color="burlywood", weight=9]; 1146 -> 672[label="",style="solid", color="burlywood", weight=3]; 1147[label="vuu31000/Zero",fontsize=10,color="white",style="solid",shape="box"];494 -> 1147[label="",style="solid", color="burlywood", weight=9]; 1147 -> 673[label="",style="solid", color="burlywood", weight=3]; 495[label="primEqNat Zero vuu31000",fontsize=16,color="burlywood",shape="box"];1148[label="vuu31000/Succ vuu310000",fontsize=10,color="white",style="solid",shape="box"];495 -> 1148[label="",style="solid", color="burlywood", weight=9]; 1148 -> 674[label="",style="solid", color="burlywood", weight=3]; 1149[label="vuu31000/Zero",fontsize=10,color="white",style="solid",shape="box"];495 -> 1149[label="",style="solid", color="burlywood", weight=9]; 1149 -> 675[label="",style="solid", color="burlywood", weight=3]; 496[label="span2Ys0 ((==) Just vuu9) vuu11 (span ((==) Just vuu9) vuu11)",fontsize=16,color="burlywood",shape="box"];1150[label="vuu11/vuu110 : vuu111",fontsize=10,color="white",style="solid",shape="box"];496 -> 1150[label="",style="solid", color="burlywood", weight=9]; 1150 -> 676[label="",style="solid", color="burlywood", weight=3]; 1151[label="vuu11/[]",fontsize=10,color="white",style="solid",shape="box"];496 -> 1151[label="",style="solid", color="burlywood", weight=9]; 1151 -> 677[label="",style="solid", color="burlywood", weight=3]; 497[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (span2 ((==) Nothing) (vuu3110 : vuu3111))",fontsize=16,color="black",shape="box"];497 -> 678[label="",style="solid", color="black", weight=3]; 498[label="span2Zs0 ((==) Nothing) [] (span3 ((==) Nothing) [])",fontsize=16,color="black",shape="box"];498 -> 679[label="",style="solid", color="black", weight=3]; 499[label="Just vuu19 : 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531[label="vuu3000",fontsize=16,color="green",shape="box"];532[label="vuu31000",fontsize=16,color="green",shape="box"];533[label="vuu3000",fontsize=16,color="green",shape="box"];534[label="vuu31000",fontsize=16,color="green",shape="box"];535[label="vuu3000",fontsize=16,color="green",shape="box"];536[label="vuu31000",fontsize=16,color="green",shape="box"];537[label="vuu3000",fontsize=16,color="green",shape="box"];538[label="vuu31000",fontsize=16,color="green",shape="box"];539[label="vuu3000",fontsize=16,color="green",shape="box"];540[label="vuu31000",fontsize=16,color="green",shape="box"];541[label="vuu3000",fontsize=16,color="green",shape="box"];542[label="vuu31000",fontsize=16,color="green",shape="box"];543[label="vuu3000",fontsize=16,color="green",shape="box"];544[label="vuu31000",fontsize=16,color="green",shape="box"];545[label="vuu3000",fontsize=16,color="green",shape="box"];546[label="vuu31000",fontsize=16,color="green",shape="box"];547[label="vuu3000",fontsize=16,color="green",shape="box"];548[label="vuu31000",fontsize=16,color="green",shape="box"];549[label="vuu3000",fontsize=16,color="green",shape="box"];550[label="vuu31000",fontsize=16,color="green",shape="box"];551[label="vuu3000",fontsize=16,color="green",shape="box"];552[label="vuu31000",fontsize=16,color="green",shape="box"];553[label="vuu3000",fontsize=16,color="green",shape="box"];554[label="vuu31000",fontsize=16,color="green",shape="box"];555[label="vuu3000",fontsize=16,color="green",shape="box"];556[label="vuu31000",fontsize=16,color="green",shape="box"];557[label="vuu3000",fontsize=16,color="green",shape="box"];558[label="vuu31000",fontsize=16,color="green",shape="box"];559[label="False",fontsize=16,color="green",shape="box"];560[label="vuu40",fontsize=16,color="green",shape="box"];561[label="primMulInt 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743[label="",style="dashed", color="magenta", weight=3]; 568 -> 744[label="",style="dashed", color="magenta", weight=3]; 569[label="False",fontsize=16,color="green",shape="box"];570[label="False",fontsize=16,color="green",shape="box"];571[label="True",fontsize=16,color="green",shape="box"];572[label="False",fontsize=16,color="green",shape="box"];573[label="True",fontsize=16,color="green",shape="box"];574 -> 291[label="",style="dashed", color="red", weight=0]; 574[label="primEqNat vuu30000 vuu310000",fontsize=16,color="magenta"];574 -> 745[label="",style="dashed", color="magenta", weight=3]; 574 -> 746[label="",style="dashed", color="magenta", weight=3]; 575[label="False",fontsize=16,color="green",shape="box"];576[label="False",fontsize=16,color="green",shape="box"];577[label="True",fontsize=16,color="green",shape="box"];578[label="False",fontsize=16,color="green",shape="box"];579[label="True",fontsize=16,color="green",shape="box"];580[label="vuu3001",fontsize=16,color="green",shape="box"];581[label="vuu31001",fontsize=16,color="green",shape="box"];582[label="vuu3001",fontsize=16,color="green",shape="box"];583[label="vuu31001",fontsize=16,color="green",shape="box"];584[label="vuu3000",fontsize=16,color="green",shape="box"];585[label="vuu31000",fontsize=16,color="green",shape="box"];586[label="vuu3000",fontsize=16,color="green",shape="box"];587[label="vuu31000",fontsize=16,color="green",shape="box"];588[label="vuu3000",fontsize=16,color="green",shape="box"];589[label="vuu31000",fontsize=16,color="green",shape="box"];590[label="vuu3000",fontsize=16,color="green",shape="box"];591[label="vuu31000",fontsize=16,color="green",shape="box"];592[label="vuu3000",fontsize=16,color="green",shape="box"];593[label="vuu31000",fontsize=16,color="green",shape="box"];594[label="vuu3000",fontsize=16,color="green",shape="box"];595[label="vuu31000",fontsize=16,color="green",shape="box"];596[label="vuu3000",fontsize=16,color="green",shape="box"];597[label="vuu31000",fontsize=16,color="green",shape="box"];598[label="vuu3000",fontsize=16,color="green",shape="box"];599[label="vuu31000",fontsize=16,color="green",shape="box"];600[label="vuu3000",fontsize=16,color="green",shape="box"];601[label="vuu31000",fontsize=16,color="green",shape="box"];602[label="vuu3000",fontsize=16,color="green",shape="box"];603[label="vuu31000",fontsize=16,color="green",shape="box"];604[label="vuu3000",fontsize=16,color="green",shape="box"];605[label="vuu31000",fontsize=16,color="green",shape="box"];606[label="vuu3000",fontsize=16,color="green",shape="box"];607[label="vuu31000",fontsize=16,color="green",shape="box"];608[label="vuu3000",fontsize=16,color="green",shape="box"];609[label="vuu31000",fontsize=16,color="green",shape="box"];610[label="vuu3000",fontsize=16,color="green",shape="box"];611[label="vuu31000",fontsize=16,color="green",shape="box"];612[label="vuu3000",fontsize=16,color="green",shape="box"];613[label="vuu31000",fontsize=16,color="green",shape="box"];614[label="vuu3000",fontsize=16,color="green",shape="box"];615[label="vuu31000",fontsize=16,color="green",shape="box"];616[label="vuu3001",fontsize=16,color="green",shape="box"];617[label="vuu31001",fontsize=16,color="green",shape="box"];618[label="vuu3001",fontsize=16,color="green",shape="box"];619[label="vuu31001",fontsize=16,color="green",shape="box"];620[label="vuu3001",fontsize=16,color="green",shape="box"];621[label="vuu31001",fontsize=16,color="green",shape="box"];622[label="vuu3001",fontsize=16,color="green",shape="box"];623[label="vuu31001",fontsize=16,color="green",shape="box"];624[label="vuu3001",fontsize=16,color="green",shape="box"];625[label="vuu31001",fontsize=16,color="green",shape="box"];626[label="vuu3001",fontsize=16,color="green",shape="box"];627[label="vuu31001",fontsize=16,color="green",shape="box"];628[label="vuu3001",fontsize=16,color="green",shape="box"];629[label="vuu31001",fontsize=16,color="green",shape="box"];630[label="vuu3001",fontsize=16,color="green",shape="box"];631[label="vuu31001",fontsize=16,color="green",shape="box"];632[label="vuu3001",fontsize=16,color="green",shape="box"];633[label="vuu31001",fontsize=16,color="green",shape="box"];634[label="vuu3001",fontsize=16,color="green",shape="box"];635[label="vuu31001",fontsize=16,color="green",shape="box"];636[label="vuu3001",fontsize=16,color="green",shape="box"];637[label="vuu31001",fontsize=16,color="green",shape="box"];638[label="vuu3001",fontsize=16,color="green",shape="box"];639[label="vuu31001",fontsize=16,color="green",shape="box"];640[label="vuu3001",fontsize=16,color="green",shape="box"];641[label="vuu31001",fontsize=16,color="green",shape="box"];642[label="vuu3001",fontsize=16,color="green",shape="box"];643[label="vuu31001",fontsize=16,color="green",shape="box"];644[label="vuu3000",fontsize=16,color="green",shape="box"];645[label="vuu31000",fontsize=16,color="green",shape="box"];646[label="vuu3000",fontsize=16,color="green",shape="box"];647[label="vuu31000",fontsize=16,color="green",shape="box"];648[label="vuu3000",fontsize=16,color="green",shape="box"];649[label="vuu31000",fontsize=16,color="green",shape="box"];650[label="vuu3000",fontsize=16,color="green",shape="box"];651[label="vuu31000",fontsize=16,color="green",shape="box"];652[label="vuu3000",fontsize=16,color="green",shape="box"];653[label="vuu31000",fontsize=16,color="green",shape="box"];654[label="vuu3000",fontsize=16,color="green",shape="box"];655[label="vuu31000",fontsize=16,color="green",shape="box"];656[label="vuu3000",fontsize=16,color="green",shape="box"];657[label="vuu31000",fontsize=16,color="green",shape="box"];658[label="vuu3000",fontsize=16,color="green",shape="box"];659[label="vuu310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((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 ((==) Nothing vuu3110))",fontsize=16,color="magenta"];678 -> 754[label="",style="dashed", color="magenta", weight=3]; 679[label="span2Zs0 ((==) Nothing) [] ([],[])",fontsize=16,color="black",shape="box"];679 -> 755[label="",style="solid", color="black", weight=3]; 680[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span ((==) Just vuu18) (vuu200 : vuu201))",fontsize=16,color="black",shape="box"];680 -> 756[label="",style="solid", color="black", weight=3]; 681[label="span2Zs0 ((==) Just vuu18) [] (span ((==) Just vuu18) [])",fontsize=16,color="black",shape="box"];681 -> 757[label="",style="solid", color="black", weight=3]; 683 -> 65[label="",style="dashed", color="red", weight=0]; 683[label="(==) Nothing vuu3110",fontsize=16,color="magenta"];683 -> 758[label="",style="dashed", color="magenta", weight=3]; 683 -> 759[label="",style="dashed", color="magenta", weight=3]; 682[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 vuu41)",fontsize=16,color="burlywood",shape="triangle"];1156[label="vuu41/False",fontsize=10,color="white",style="solid",shape="box"];682 -> 1156[label="",style="solid", color="burlywood", weight=9]; 1156 -> 760[label="",style="solid", color="burlywood", weight=3]; 1157[label="vuu41/True",fontsize=10,color="white",style="solid",shape="box"];682 -> 1157[label="",style="solid", color="burlywood", weight=9]; 1157 -> 761[label="",style="solid", color="burlywood", weight=3]; 684[label="[]",fontsize=16,color="green",shape="box"];685[label="vuu3002",fontsize=16,color="green",shape="box"];686[label="vuu31002",fontsize=16,color="green",shape="box"];687[label="vuu3002",fontsize=16,color="green",shape="box"];688[label="vuu31002",fontsize=16,color="green",shape="box"];689[label="vuu3002",fontsize=16,color="green",shape="box"];690[label="vuu31002",fontsize=16,color="green",shape="box"];691[label="vuu3002",fontsize=16,color="green",shape="box"];692[label="vuu31002",fontsize=16,color="green",shape="box"];693[label="vuu3002",fontsize=16,color="green",shape="box"];694[label="vuu31002",fontsize=16,color="green",shape="box"];695[label="vuu3002",fontsize=16,color="green",shape="box"];696[label="vuu31002",fontsize=16,color="green",shape="box"];697[label="vuu3002",fontsize=16,color="green",shape="box"];698[label="vuu31002",fontsize=16,color="green",shape="box"];699[label="vuu3002",fontsize=16,color="green",shape="box"];700[label="vuu31002",fontsize=16,color="green",shape="box"];701[label="vuu3002",fontsize=16,color="green",shape="box"];702[label="vuu31002",fontsize=16,color="green",shape="box"];703[label="vuu3002",fontsize=16,color="green",shape="box"];704[label="vuu31002",fontsize=16,color="green",shape="box"];705[label="vuu3002",fontsize=16,color="green",shape="box"];706[label="vuu31002",fontsize=16,color="green",shape="box"];707[label="vuu3002",fontsize=16,color="green",shape="box"];708[label="vuu31002",fontsize=16,color="green",shape="box"];709[label="vuu3002",fontsize=16,color="green",shape="box"];710[label="vuu31002",fontsize=16,color="green",shape="box"];711[label="vuu3002",fontsize=16,color="green",shape="box"];712[label="vuu31002",fontsize=16,color="green",shape="box"];713[label="vuu3001",fontsize=16,color="green",shape="box"];714[label="vuu31001",fontsize=16,color="green",shape="box"];715[label="vuu3001",fontsize=16,color="green",shape="box"];716[label="vuu31001",fontsize=16,color="green",shape="box"];717[label="vuu3001",fontsize=16,color="green",shape="box"];718[label="vuu31001",fontsize=16,color="green",shape="box"];719[label="vuu3001",fontsize=16,color="green",shape="box"];720[label="vuu31001",fontsize=16,color="green",shape="box"];721[label="vuu3001",fontsize=16,color="green",shape="box"];722[label="vuu31001",fontsize=16,color="green",shape="box"];723[label="vuu3001",fontsize=16,color="green",shape="box"];724[label="vuu31001",fontsize=16,color="green",shape="box"];725[label="vuu3001",fontsize=16,color="green",shape="box"];726[label="vuu31001",fontsize=16,color="green",shape="box"];727[label="vuu3001",fontsize=16,color="green",shape="box"];728[label="vuu31001",fontsize=16,color="green",shape="box"];729[label="vuu3001",fontsize=16,color="green",shape="box"];730[label="vuu31001",fontsize=16,color="green",shape="box"];731[label="vuu3001",fontsize=16,color="green",shape="box"];732[label="vuu31001",fontsize=16,color="green",shape="box"];733[label="vuu3001",fontsize=16,color="green",shape="box"];734[label="vuu31001",fontsize=16,color="green",shape="box"];735[label="vuu3001",fontsize=16,color="green",shape="box"];736[label="vuu31001",fontsize=16,color="green",shape="box"];737[label="vuu3001",fontsize=16,color="green",shape="box"];738[label="vuu31001",fontsize=16,color="green",shape="box"];739[label="vuu3001",fontsize=16,color="green",shape="box"];740[label="vuu31001",fontsize=16,color="green",shape="box"];741[label="primMulInt 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765[label="",style="solid", color="burlywood", weight=3]; 743[label="vuu310000",fontsize=16,color="green",shape="box"];744[label="vuu30000",fontsize=16,color="green",shape="box"];745[label="vuu310000",fontsize=16,color="green",shape="box"];746[label="vuu30000",fontsize=16,color="green",shape="box"];747 -> 291[label="",style="dashed", color="red", weight=0]; 747[label="primEqNat vuu30000 vuu310000",fontsize=16,color="magenta"];747 -> 766[label="",style="dashed", color="magenta", weight=3]; 747 -> 767[label="",style="dashed", color="magenta", weight=3]; 748[label="False",fontsize=16,color="green",shape="box"];749[label="False",fontsize=16,color="green",shape="box"];750[label="True",fontsize=16,color="green",shape="box"];751[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2 ((==) Just vuu9) (vuu110 : vuu111))",fontsize=16,color="black",shape="box"];751 -> 768[label="",style="solid", color="black", weight=3]; 752[label="span2Ys0 ((==) Just vuu9) [] (span3 ((==) Just vuu9) 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755[label="[]",fontsize=16,color="green",shape="box"];756[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2 ((==) Just vuu18) (vuu200 : vuu201))",fontsize=16,color="black",shape="box"];756 -> 774[label="",style="solid", color="black", weight=3]; 757[label="span2Zs0 ((==) Just vuu18) [] (span3 ((==) Just vuu18) [])",fontsize=16,color="black",shape="box"];757 -> 775[label="",style="solid", color="black", weight=3]; 758[label="Nothing",fontsize=16,color="green",shape="box"];759[label="vuu3110",fontsize=16,color="green",shape="box"];760[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 False)",fontsize=16,color="black",shape="box"];760 -> 776[label="",style="solid", color="black", weight=3]; 761[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];761 -> 777[label="",style="solid", color="black", weight=3]; 762[label="primMulInt (Pos vuu30000) (Pos vuu310010)",fontsize=16,color="black",shape="box"];762 -> 778[label="",style="solid", color="black", weight=3]; 763[label="primMulInt (Pos vuu30000) (Neg vuu310010)",fontsize=16,color="black",shape="box"];763 -> 779[label="",style="solid", color="black", weight=3]; 764[label="primMulInt (Neg vuu30000) (Pos vuu310010)",fontsize=16,color="black",shape="box"];764 -> 780[label="",style="solid", color="black", weight=3]; 765[label="primMulInt (Neg vuu30000) (Neg vuu310010)",fontsize=16,color="black",shape="box"];765 -> 781[label="",style="solid", color="black", weight=3]; 766[label="vuu310000",fontsize=16,color="green",shape="box"];767[label="vuu30000",fontsize=16,color="green",shape="box"];768 -> 782[label="",style="dashed", color="red", weight=0]; 768[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span1 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 ((==) Just vuu9 vuu110))",fontsize=16,color="magenta"];768 -> 783[label="",style="dashed", color="magenta", weight=3]; 769[label="span2Ys0 ((==) Just vuu9) [] ([],[])",fontsize=16,color="black",shape="box"];769 -> 784[label="",style="solid", color="black", weight=3]; 770[label="Nothing",fontsize=16,color="green",shape="box"];771[label="vuu3110",fontsize=16,color="green",shape="box"];772[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 False)",fontsize=16,color="black",shape="box"];772 -> 785[label="",style="solid", color="black", weight=3]; 773[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span1 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];773 -> 786[label="",style="solid", color="black", weight=3]; 774 -> 787[label="",style="dashed", color="red", weight=0]; 774[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span1 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 ((==) Just vuu18 vuu200))",fontsize=16,color="magenta"];774 -> 788[label="",style="dashed", color="magenta", weight=3]; 775[label="span2Zs0 ((==) Just vuu18) [] ([],[])",fontsize=16,color="black",shape="box"];775 -> 789[label="",style="solid", color="black", weight=3]; 776[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span0 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 otherwise)",fontsize=16,color="black",shape="box"];776 -> 790[label="",style="solid", color="black", weight=3]; 777 -> 791[label="",style="dashed", color="red", weight=0]; 777[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (vuu3110 : span2Ys ((==) Nothing) vuu3111,span2Zs ((==) Nothing) vuu3111)",fontsize=16,color="magenta"];777 -> 792[label="",style="dashed", color="magenta", weight=3]; 777 -> 793[label="",style="dashed", color="magenta", weight=3]; 778[label="Pos (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];778 -> 794[label="",style="dashed", color="green", weight=3]; 779[label="Neg (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];779 -> 795[label="",style="dashed", color="green", weight=3]; 780[label="Neg (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];780 -> 796[label="",style="dashed", color="green", weight=3]; 781[label="Pos (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];781 -> 797[label="",style="dashed", color="green", weight=3]; 783 -> 65[label="",style="dashed", color="red", weight=0]; 783[label="(==) Just vuu9 vuu110",fontsize=16,color="magenta"];783 -> 798[label="",style="dashed", color="magenta", weight=3]; 783 -> 799[label="",style="dashed", color="magenta", weight=3]; 782[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span1 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 vuu43)",fontsize=16,color="burlywood",shape="triangle"];1164[label="vuu43/False",fontsize=10,color="white",style="solid",shape="box"];782 -> 1164[label="",style="solid", color="burlywood", weight=9]; 1164 -> 800[label="",style="solid", color="burlywood", weight=3]; 1165[label="vuu43/True",fontsize=10,color="white",style="solid",shape="box"];782 -> 1165[label="",style="solid", color="burlywood", weight=9]; 1165 -> 801[label="",style="solid", color="burlywood", weight=3]; 784[label="[]",fontsize=16,color="green",shape="box"];785[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span0 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 otherwise)",fontsize=16,color="black",shape="box"];785 -> 802[label="",style="solid", color="black", weight=3]; 786 -> 803[label="",style="dashed", color="red", weight=0]; 786[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (vuu3110 : span2Ys ((==) Nothing) vuu3111,span2Zs ((==) Nothing) vuu3111)",fontsize=16,color="magenta"];786 -> 804[label="",style="dashed", color="magenta", weight=3]; 786 -> 805[label="",style="dashed", color="magenta", weight=3]; 788 -> 65[label="",style="dashed", color="red", weight=0]; 788[label="(==) Just vuu18 vuu200",fontsize=16,color="magenta"];788 -> 806[label="",style="dashed", color="magenta", weight=3]; 788 -> 807[label="",style="dashed", color="magenta", weight=3]; 787[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span1 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 vuu44)",fontsize=16,color="burlywood",shape="triangle"];1166[label="vuu44/False",fontsize=10,color="white",style="solid",shape="box"];787 -> 1166[label="",style="solid", color="burlywood", weight=9]; 1166 -> 808[label="",style="solid", color="burlywood", weight=3]; 1167[label="vuu44/True",fontsize=10,color="white",style="solid",shape="box"];787 -> 1167[label="",style="solid", color="burlywood", weight=9]; 1167 -> 809[label="",style="solid", color="burlywood", weight=3]; 789[label="[]",fontsize=16,color="green",shape="box"];790[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span0 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];790 -> 810[label="",style="solid", color="black", weight=3]; 792 -> 85[label="",style="dashed", color="red", weight=0]; 792[label="span2Ys ((==) Nothing) vuu3111",fontsize=16,color="magenta"];792 -> 811[label="",style="dashed", color="magenta", weight=3]; 793 -> 110[label="",style="dashed", color="red", weight=0]; 793[label="span2Zs ((==) Nothing) vuu3111",fontsize=16,color="magenta"];793 -> 812[label="",style="dashed", color="magenta", weight=3]; 791[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) (vuu3110 : vuu46,vuu45)",fontsize=16,color="black",shape="triangle"];791 -> 813[label="",style="solid", color="black", weight=3]; 794[label="primMulNat vuu30000 vuu310010",fontsize=16,color="burlywood",shape="triangle"];1168[label="vuu30000/Succ vuu300000",fontsize=10,color="white",style="solid",shape="box"];794 -> 1168[label="",style="solid", color="burlywood", weight=9]; 1168 -> 814[label="",style="solid", color="burlywood", weight=3]; 1169[label="vuu30000/Zero",fontsize=10,color="white",style="solid",shape="box"];794 -> 1169[label="",style="solid", color="burlywood", weight=9]; 1169 -> 815[label="",style="solid", color="burlywood", weight=3]; 795 -> 794[label="",style="dashed", color="red", weight=0]; 795[label="primMulNat vuu30000 vuu310010",fontsize=16,color="magenta"];795 -> 816[label="",style="dashed", color="magenta", weight=3]; 796 -> 794[label="",style="dashed", color="red", weight=0]; 796[label="primMulNat vuu30000 vuu310010",fontsize=16,color="magenta"];796 -> 817[label="",style="dashed", color="magenta", weight=3]; 797 -> 794[label="",style="dashed", color="red", weight=0]; 797[label="primMulNat vuu30000 vuu310010",fontsize=16,color="magenta"];797 -> 818[label="",style="dashed", color="magenta", weight=3]; 797 -> 819[label="",style="dashed", color="magenta", weight=3]; 798[label="Just vuu9",fontsize=16,color="green",shape="box"];799[label="vuu110",fontsize=16,color="green",shape="box"];800[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span1 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 False)",fontsize=16,color="black",shape="box"];800 -> 820[label="",style="solid", color="black", weight=3]; 801[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span1 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 True)",fontsize=16,color="black",shape="box"];801 -> 821[label="",style="solid", color="black", weight=3]; 802[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (span2Span0 ((==) Nothing) vuu3111 ((==) Nothing) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];802 -> 822[label="",style="solid", color="black", weight=3]; 804 -> 110[label="",style="dashed", color="red", weight=0]; 804[label="span2Zs ((==) Nothing) vuu3111",fontsize=16,color="magenta"];804 -> 823[label="",style="dashed", color="magenta", weight=3]; 805 -> 85[label="",style="dashed", color="red", weight=0]; 805[label="span2Ys ((==) Nothing) vuu3111",fontsize=16,color="magenta"];805 -> 824[label="",style="dashed", color="magenta", weight=3]; 803[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) (vuu3110 : vuu48,vuu47)",fontsize=16,color="black",shape="triangle"];803 -> 825[label="",style="solid", color="black", weight=3]; 806[label="Just vuu18",fontsize=16,color="green",shape="box"];807[label="vuu200",fontsize=16,color="green",shape="box"];808[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span1 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 False)",fontsize=16,color="black",shape="box"];808 -> 826[label="",style="solid", color="black", weight=3]; 809[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span1 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 True)",fontsize=16,color="black",shape="box"];809 -> 827[label="",style="solid", color="black", weight=3]; 810[label="span2Ys0 ((==) Nothing) (vuu3110 : vuu3111) ([],vuu3110 : vuu3111)",fontsize=16,color="black",shape="box"];810 -> 828[label="",style="solid", color="black", weight=3]; 811[label="vuu3111",fontsize=16,color="green",shape="box"];812[label="vuu3111",fontsize=16,color="green",shape="box"];813[label="vuu3110 : vuu46",fontsize=16,color="green",shape="box"];814[label="primMulNat (Succ vuu300000) vuu310010",fontsize=16,color="burlywood",shape="box"];1170[label="vuu310010/Succ vuu3100100",fontsize=10,color="white",style="solid",shape="box"];814 -> 1170[label="",style="solid", color="burlywood", weight=9]; 1170 -> 829[label="",style="solid", color="burlywood", weight=3]; 1171[label="vuu310010/Zero",fontsize=10,color="white",style="solid",shape="box"];814 -> 1171[label="",style="solid", color="burlywood", weight=9]; 1171 -> 830[label="",style="solid", color="burlywood", weight=3]; 815[label="primMulNat Zero vuu310010",fontsize=16,color="burlywood",shape="box"];1172[label="vuu310010/Succ vuu3100100",fontsize=10,color="white",style="solid",shape="box"];815 -> 1172[label="",style="solid", color="burlywood", weight=9]; 1172 -> 831[label="",style="solid", color="burlywood", weight=3]; 1173[label="vuu310010/Zero",fontsize=10,color="white",style="solid",shape="box"];815 -> 1173[label="",style="solid", color="burlywood", weight=9]; 1173 -> 832[label="",style="solid", color="burlywood", weight=3]; 816[label="vuu310010",fontsize=16,color="green",shape="box"];817[label="vuu30000",fontsize=16,color="green",shape="box"];818[label="vuu310010",fontsize=16,color="green",shape="box"];819[label="vuu30000",fontsize=16,color="green",shape="box"];820[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span0 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 otherwise)",fontsize=16,color="black",shape="box"];820 -> 833[label="",style="solid", color="black", weight=3]; 821 -> 834[label="",style="dashed", color="red", weight=0]; 821[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (vuu110 : span2Ys ((==) Just vuu9) vuu111,span2Zs ((==) Just vuu9) vuu111)",fontsize=16,color="magenta"];821 -> 835[label="",style="dashed", color="magenta", weight=3]; 821 -> 836[label="",style="dashed", color="magenta", weight=3]; 822[label="span2Zs0 ((==) Nothing) (vuu3110 : vuu3111) ([],vuu3110 : vuu3111)",fontsize=16,color="black",shape="box"];822 -> 837[label="",style="solid", color="black", weight=3]; 823[label="vuu3111",fontsize=16,color="green",shape="box"];824[label="vuu3111",fontsize=16,color="green",shape="box"];825[label="vuu47",fontsize=16,color="green",shape="box"];826[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span0 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 otherwise)",fontsize=16,color="black",shape="box"];826 -> 838[label="",style="solid", color="black", weight=3]; 827 -> 839[label="",style="dashed", color="red", weight=0]; 827[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (vuu200 : span2Ys ((==) Just vuu18) vuu201,span2Zs ((==) Just vuu18) vuu201)",fontsize=16,color="magenta"];827 -> 840[label="",style="dashed", color="magenta", weight=3]; 827 -> 841[label="",style="dashed", color="magenta", weight=3]; 828[label="[]",fontsize=16,color="green",shape="box"];829[label="primMulNat (Succ vuu300000) (Succ vuu3100100)",fontsize=16,color="black",shape="box"];829 -> 842[label="",style="solid", color="black", weight=3]; 830[label="primMulNat (Succ vuu300000) Zero",fontsize=16,color="black",shape="box"];830 -> 843[label="",style="solid", color="black", weight=3]; 831[label="primMulNat Zero (Succ vuu3100100)",fontsize=16,color="black",shape="box"];831 -> 844[label="",style="solid", color="black", weight=3]; 832[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];832 -> 845[label="",style="solid", color="black", weight=3]; 833[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (span2Span0 ((==) Just vuu9) vuu111 ((==) Just vuu9) vuu110 vuu111 True)",fontsize=16,color="black",shape="box"];833 -> 846[label="",style="solid", color="black", weight=3]; 835 -> 218[label="",style="dashed", color="red", weight=0]; 835[label="span2Zs ((==) Just vuu9) vuu111",fontsize=16,color="magenta"];835 -> 847[label="",style="dashed", color="magenta", weight=3]; 835 -> 848[label="",style="dashed", color="magenta", weight=3]; 836 -> 213[label="",style="dashed", color="red", weight=0]; 836[label="span2Ys ((==) Just vuu9) vuu111",fontsize=16,color="magenta"];836 -> 849[label="",style="dashed", color="magenta", weight=3]; 834[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) (vuu110 : vuu50,vuu49)",fontsize=16,color="black",shape="triangle"];834 -> 850[label="",style="solid", color="black", weight=3]; 837[label="vuu3110 : vuu3111",fontsize=16,color="green",shape="box"];838[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (span2Span0 ((==) Just vuu18) vuu201 ((==) Just vuu18) vuu200 vuu201 True)",fontsize=16,color="black",shape="box"];838 -> 851[label="",style="solid", color="black", weight=3]; 840 -> 213[label="",style="dashed", color="red", weight=0]; 840[label="span2Ys ((==) Just vuu18) vuu201",fontsize=16,color="magenta"];840 -> 852[label="",style="dashed", color="magenta", weight=3]; 840 -> 853[label="",style="dashed", color="magenta", weight=3]; 841 -> 218[label="",style="dashed", color="red", weight=0]; 841[label="span2Zs ((==) Just vuu18) vuu201",fontsize=16,color="magenta"];841 -> 854[label="",style="dashed", color="magenta", weight=3]; 839[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) (vuu200 : vuu52,vuu51)",fontsize=16,color="black",shape="triangle"];839 -> 855[label="",style="solid", color="black", weight=3]; 842 -> 856[label="",style="dashed", color="red", weight=0]; 842[label="primPlusNat (primMulNat vuu300000 (Succ vuu3100100)) (Succ vuu3100100)",fontsize=16,color="magenta"];842 -> 857[label="",style="dashed", color="magenta", weight=3]; 843[label="Zero",fontsize=16,color="green",shape="box"];844[label="Zero",fontsize=16,color="green",shape="box"];845[label="Zero",fontsize=16,color="green",shape="box"];846[label="span2Ys0 ((==) Just vuu9) (vuu110 : vuu111) ([],vuu110 : vuu111)",fontsize=16,color="black",shape="box"];846 -> 858[label="",style="solid", color="black", weight=3]; 847[label="vuu9",fontsize=16,color="green",shape="box"];848[label="vuu111",fontsize=16,color="green",shape="box"];849[label="vuu111",fontsize=16,color="green",shape="box"];850[label="vuu110 : vuu50",fontsize=16,color="green",shape="box"];851[label="span2Zs0 ((==) Just vuu18) (vuu200 : vuu201) ([],vuu200 : vuu201)",fontsize=16,color="black",shape="box"];851 -> 859[label="",style="solid", color="black", weight=3]; 852[label="vuu201",fontsize=16,color="green",shape="box"];853[label="vuu18",fontsize=16,color="green",shape="box"];854[label="vuu201",fontsize=16,color="green",shape="box"];855[label="vuu51",fontsize=16,color="green",shape="box"];857 -> 794[label="",style="dashed", color="red", weight=0]; 857[label="primMulNat vuu300000 (Succ vuu3100100)",fontsize=16,color="magenta"];857 -> 860[label="",style="dashed", color="magenta", weight=3]; 857 -> 861[label="",style="dashed", color="magenta", weight=3]; 856[label="primPlusNat vuu53 (Succ vuu3100100)",fontsize=16,color="burlywood",shape="triangle"];1174[label="vuu53/Succ vuu530",fontsize=10,color="white",style="solid",shape="box"];856 -> 1174[label="",style="solid", color="burlywood", weight=9]; 1174 -> 862[label="",style="solid", color="burlywood", weight=3]; 1175[label="vuu53/Zero",fontsize=10,color="white",style="solid",shape="box"];856 -> 1175[label="",style="solid", color="burlywood", weight=9]; 1175 -> 863[label="",style="solid", color="burlywood", weight=3]; 858[label="[]",fontsize=16,color="green",shape="box"];859[label="vuu200 : vuu201",fontsize=16,color="green",shape="box"];860[label="Succ vuu3100100",fontsize=16,color="green",shape="box"];861[label="vuu300000",fontsize=16,color="green",shape="box"];862[label="primPlusNat (Succ vuu530) (Succ vuu3100100)",fontsize=16,color="black",shape="box"];862 -> 864[label="",style="solid", color="black", weight=3]; 863[label="primPlusNat Zero (Succ vuu3100100)",fontsize=16,color="black",shape="box"];863 -> 865[label="",style="solid", color="black", weight=3]; 864[label="Succ (Succ (primPlusNat vuu530 vuu3100100))",fontsize=16,color="green",shape="box"];864 -> 866[label="",style="dashed", color="green", weight=3]; 865[label="Succ vuu3100100",fontsize=16,color="green",shape="box"];866[label="primPlusNat vuu530 vuu3100100",fontsize=16,color="burlywood",shape="triangle"];1176[label="vuu530/Succ vuu5300",fontsize=10,color="white",style="solid",shape="box"];866 -> 1176[label="",style="solid", color="burlywood", weight=9]; 1176 -> 867[label="",style="solid", color="burlywood", weight=3]; 1177[label="vuu530/Zero",fontsize=10,color="white",style="solid",shape="box"];866 -> 1177[label="",style="solid", color="burlywood", weight=9]; 1177 -> 868[label="",style="solid", color="burlywood", weight=3]; 867[label="primPlusNat (Succ vuu5300) vuu3100100",fontsize=16,color="burlywood",shape="box"];1178[label="vuu3100100/Succ vuu31001000",fontsize=10,color="white",style="solid",shape="box"];867 -> 1178[label="",style="solid", color="burlywood", weight=9]; 1178 -> 869[label="",style="solid", color="burlywood", weight=3]; 1179[label="vuu3100100/Zero",fontsize=10,color="white",style="solid",shape="box"];867 -> 1179[label="",style="solid", color="burlywood", weight=9]; 1179 -> 870[label="",style="solid", color="burlywood", weight=3]; 868[label="primPlusNat Zero vuu3100100",fontsize=16,color="burlywood",shape="box"];1180[label="vuu3100100/Succ vuu31001000",fontsize=10,color="white",style="solid",shape="box"];868 -> 1180[label="",style="solid", color="burlywood", weight=9]; 1180 -> 871[label="",style="solid", color="burlywood", weight=3]; 1181[label="vuu3100100/Zero",fontsize=10,color="white",style="solid",shape="box"];868 -> 1181[label="",style="solid", color="burlywood", weight=9]; 1181 -> 872[label="",style="solid", color="burlywood", weight=3]; 869[label="primPlusNat (Succ vuu5300) (Succ vuu31001000)",fontsize=16,color="black",shape="box"];869 -> 873[label="",style="solid", color="black", weight=3]; 870[label="primPlusNat (Succ vuu5300) Zero",fontsize=16,color="black",shape="box"];870 -> 874[label="",style="solid", color="black", weight=3]; 871[label="primPlusNat Zero (Succ vuu31001000)",fontsize=16,color="black",shape="box"];871 -> 875[label="",style="solid", color="black", weight=3]; 872[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];872 -> 876[label="",style="solid", color="black", weight=3]; 873[label="Succ (Succ (primPlusNat vuu5300 vuu31001000))",fontsize=16,color="green",shape="box"];873 -> 877[label="",style="dashed", color="green", weight=3]; 874[label="Succ vuu5300",fontsize=16,color="green",shape="box"];875[label="Succ vuu31001000",fontsize=16,color="green",shape="box"];876[label="Zero",fontsize=16,color="green",shape="box"];877 -> 866[label="",style="dashed", color="red", weight=0]; 877[label="primPlusNat vuu5300 vuu31001000",fontsize=16,color="magenta"];877 -> 878[label="",style="dashed", color="magenta", weight=3]; 877 -> 879[label="",style="dashed", color="magenta", weight=3]; 878[label="vuu31001000",fontsize=16,color="green",shape="box"];879[label="vuu5300",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_groupBy(:(vuu30, vuu31), ba) -> new_groupBy(new_groupByZs1(vuu30, vuu31, ba), ba) The TRS R consists of the following rules: new_esEs15(Left(vuu3000), Left(vuu31000), ty_Double, hg) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Int) -> new_esEs6(vuu3002, vuu31002) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bah), bba), hg) -> new_esEs16(vuu3000, vuu31000, bah, bba) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(Left(vuu3000), Right(vuu31000), hf, hg) -> False new_esEs15(Right(vuu3000), Left(vuu31000), hf, hg) -> False new_esEs23(vuu3002, vuu31002, ty_Char) -> new_esEs17(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_Maybe, bea)) -> new_esEs4(vuu3001, vuu31001, bea) new_esEs22(vuu3000, vuu31000, app(app(ty_Either, df), dg)) -> new_esEs15(vuu3000, vuu31000, df, dg) new_esEs12(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), fg) -> new_asAs(new_esEs19(vuu3000, vuu31000, fg), new_esEs18(vuu3001, vuu31001, fg)) new_esEs26(vuu300, vuu3100, ty_Float) -> new_esEs5(vuu300, vuu3100) new_esEs26(vuu300, vuu3100, ty_Ordering) -> new_esEs11(vuu300, vuu3100) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs14(:(vuu3000, vuu3001), :(vuu31000, vuu31001), fh) -> new_asAs(new_esEs20(vuu3000, vuu31000, fh), new_esEs14(vuu3001, vuu31001, fh)) new_span2Ys04(vuu3110, vuu3111, vuu46, vuu45, ba) -> :(vuu3110, vuu46) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs26(vuu300, vuu3100, app(app(app(ty_@3, hc), hd), he)) -> new_esEs8(vuu300, vuu3100, hc, hd, he) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Maybe, bac), hg) -> new_esEs4(vuu3000, vuu31000, bac) new_esEs13(False, False) -> True new_esEs22(vuu3000, vuu31000, app(ty_Ratio, dd)) -> new_esEs12(vuu3000, vuu31000, dd) new_esEs26(vuu300, vuu3100, ty_@0) -> new_esEs10(vuu300, vuu3100) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs15(Left(vuu3000), Left(vuu31000), ty_@0, hg) -> new_esEs10(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(ty_Ratio, bbf)) -> new_esEs12(vuu3000, vuu31000, bbf) new_esEs25(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_asAs(True, vuu40) -> vuu40 new_esEs23(vuu3002, vuu31002, ty_Double) -> new_esEs9(vuu3002, vuu31002) new_esEs21(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, bed), bee)) -> new_esEs15(vuu3001, vuu31001, bed, bee) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(app(app(ty_@3, bbb), bbc), bbd)) -> new_esEs8(vuu3000, vuu31000, bbb, bbc, bbd) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) -> False new_span2Ys2(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys01(vuu9, vuu110, vuu111, new_esEs4(Just(vuu9), vuu110, bb), bb) new_span2Zs3([], ba) -> [] new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, beb)) -> new_esEs12(vuu3001, vuu31001, beb) new_esEs19(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, dc)) -> new_esEs4(vuu3000, vuu31000, dc) new_esEs5(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Ratio, bad), hg) -> new_esEs12(vuu3000, vuu31000, bad) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Float, hg) -> new_esEs5(vuu3000, vuu31000) new_span2Zs02(vuu3110, vuu3111, vuu48, vuu47, ba) -> vuu47 new_span2Ys02(vuu3110, vuu3111, True, ba) -> new_span2Ys04(vuu3110, vuu3111, new_span2Ys3(vuu3111, ba), new_span2Zs3(vuu3111, ba), ba) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs17(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Ordering, hg) -> new_esEs11(vuu3000, vuu31000) new_primMulNat0(Zero, Zero) -> Zero new_esEs14([], [], fh) -> True new_esEs20(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_@0) -> new_esEs10(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_[], bec)) -> new_esEs14(vuu3001, vuu31001, bec) new_esEs25(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(app(app(ty_@3, be), bf), bg)) -> new_esEs8(vuu3001, vuu31001, be, bf, bg) new_esEs20(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(ty_@2, bdd), bde)) -> new_esEs16(vuu3002, vuu31002, bdd, bde) new_esEs26(vuu300, vuu3100, app(app(ty_Either, hf), hg)) -> new_esEs15(vuu300, vuu3100, hf, hg) new_groupByZs1(Just(vuu300), :(Just(vuu3100), vuu311), ba) -> new_groupByZs10(vuu300, vuu3100, vuu311, new_esEs26(vuu300, vuu3100, ba), ba) new_esEs4(Nothing, Nothing, ec) -> True new_esEs26(vuu300, vuu3100, ty_Char) -> new_esEs17(vuu300, vuu3100) new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(Left(vuu3000), Left(vuu31000), ty_Integer, hg) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_Either, baf), bag), hg) -> new_esEs15(vuu3000, vuu31000, baf, bag) new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs4(Nothing, Just(vuu31000), ec) -> False new_esEs4(Just(vuu3000), Nothing, ec) -> False new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(ty_[], bda)) -> new_esEs14(vuu3002, vuu31002, bda) new_esEs26(vuu300, vuu3100, ty_Int) -> new_esEs6(vuu300, vuu3100) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, dh), ea)) -> new_esEs16(vuu3000, vuu31000, dh, ea) new_esEs25(vuu3000, vuu31000, app(app(ty_Either, bff), bfg)) -> new_esEs15(vuu3000, vuu31000, bff, bfg) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, cg), da), db)) -> new_esEs8(vuu3000, vuu31000, cg, da, db) new_groupByZs10(vuu18, vuu19, vuu20, True, eb) -> new_span2Zs2(vuu18, vuu20, eb) new_span2Zs2(vuu18, [], eb) -> [] new_esEs26(vuu300, vuu3100, ty_Integer) -> new_esEs7(vuu300, vuu3100) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Int, hg) -> new_esEs6(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(app(ty_Either, gg), gh)) -> new_esEs15(vuu3000, vuu31000, gg, gh) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Char, hg) -> new_esEs17(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, ed), ee), ef)) -> new_esEs8(vuu3000, vuu31000, ed, ee, ef) new_span2Zs04(vuu18, vuu200, vuu201, False, eb) -> :(vuu200, vuu201) new_span2Ys3(:(vuu3110, vuu3111), ba) -> new_span2Ys02(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hh), baa), bab), hg) -> new_esEs8(vuu3000, vuu31000, hh, baa, bab) new_esEs11(EQ, EQ) -> True new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs23(vuu3002, vuu31002, ty_Float) -> new_esEs5(vuu3002, vuu31002) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_esEs21(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_span2Ys3([], ba) -> [] new_esEs21(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs21(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs14(:(vuu3000, vuu3001), [], fh) -> False new_esEs14([], :(vuu31000, vuu31001), fh) -> False new_esEs25(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_groupByZs1(Nothing, :(Just(vuu3100), vuu311), ba) -> :(Just(vuu3100), vuu311) new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, beh), bfa), bfb)) -> new_esEs8(vuu3000, vuu31000, beh, bfa, bfb) new_esEs23(vuu3002, vuu31002, app(ty_Ratio, bch)) -> new_esEs12(vuu3002, vuu31002, bch) new_esEs8(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), hc, hd, he) -> new_asAs(new_esEs25(vuu3000, vuu31000, hc), new_asAs(new_esEs24(vuu3001, vuu31001, hd), new_esEs23(vuu3002, vuu31002, he))) new_esEs23(vuu3002, vuu31002, ty_Bool) -> new_esEs13(vuu3002, vuu31002) new_span2Zs01(vuu3110, vuu3111, False, ba) -> :(vuu3110, vuu3111) new_esEs20(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Ratio, eh)) -> new_esEs12(vuu3000, vuu31000, eh) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs21(vuu3001, vuu31001, app(app(ty_Either, cc), cd)) -> new_esEs15(vuu3001, vuu31001, cc, cd) new_esEs21(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs9(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3002, vuu31002, app(ty_Maybe, bcg)) -> new_esEs4(vuu3002, vuu31002, bcg) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Integer) -> new_esEs7(vuu3002, vuu31002) new_esEs23(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_Either, fb), fc)) -> new_esEs15(vuu3000, vuu31000, fb, fc) new_primPlusNat0(Succ(vuu5300), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu5300, vuu31001000))) new_esEs20(vuu3000, vuu31000, app(ty_[], gf)) -> new_esEs14(vuu3000, vuu31000, gf) new_esEs26(vuu300, vuu3100, app(app(ty_@2, bc), bd)) -> new_esEs16(vuu300, vuu3100, bc, bd) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(app(ty_@2, bcb), bcc)) -> new_esEs16(vuu3000, vuu31000, bcb, bcc) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs19(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs10(@0, @0) -> True new_esEs6(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs20(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Bool, hg) -> new_esEs13(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_Ratio, ca)) -> new_esEs12(vuu3001, vuu31001, ca) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(app(ty_@3, bcd), bce), bcf)) -> new_esEs8(vuu3002, vuu31002, bcd, bce, bcf) new_esEs21(vuu3001, vuu31001, app(app(ty_@2, ce), cf)) -> new_esEs16(vuu3001, vuu31001, ce, cf) new_span2Ys2(vuu9, [], bb) -> [] new_esEs25(vuu3000, vuu31000, app(ty_[], bfe)) -> new_esEs14(vuu3000, vuu31000, bfe) new_esEs25(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Zero) -> Zero new_primMulNat0(Zero, Succ(vuu3100100)) -> Zero new_groupByZs10(vuu18, vuu19, vuu20, False, eb) -> :(Just(vuu19), vuu20) new_sr(Pos(vuu30000), Pos(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_groupByZs1(Nothing, :(Nothing, vuu311), ba) -> new_span2Zs3(vuu311, ba) new_esEs15(Right(vuu3000), Right(vuu31000), hf, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bef), beg)) -> new_esEs16(vuu3001, vuu31001, bef, beg) new_esEs22(vuu3000, vuu31000, app(ty_[], de)) -> new_esEs14(vuu3000, vuu31000, de) new_esEs25(vuu3000, vuu31000, app(ty_Maybe, bfc)) -> new_esEs4(vuu3000, vuu31000, bfc) new_primPlusNat1(Succ(vuu530), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu530, vuu3100100))) new_esEs20(vuu3000, vuu31000, app(app(app(ty_@3, ga), gb), gc)) -> new_esEs8(vuu3000, vuu31000, ga, gb, gc) new_span2Zs03(vuu18, vuu200, vuu201, vuu52, vuu51, eb) -> vuu51 new_primPlusNat0(Succ(vuu5300), Zero) -> Succ(vuu5300) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_span2Ys01(vuu9, vuu110, vuu111, True, bb) -> new_span2Ys03(vuu9, vuu110, vuu111, new_span2Ys2(vuu9, vuu111, bb), new_span2Zs2(vuu9, vuu111, bb), bb) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_@2, fd), ff)) -> new_esEs16(vuu3000, vuu31000, fd, ff) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bc, bd) -> new_asAs(new_esEs22(vuu3000, vuu31000, bc), new_esEs21(vuu3001, vuu31001, bd)) new_span2Zs04(vuu18, vuu200, vuu201, True, eb) -> new_span2Zs03(vuu18, vuu200, vuu201, new_span2Ys2(vuu18, vuu201, eb), new_span2Zs2(vuu18, vuu201, eb), eb) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(app(ty_Either, bbh), bca)) -> new_esEs15(vuu3000, vuu31000, bbh, bca) new_esEs4(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs26(vuu300, vuu3100, ty_Bool) -> new_esEs13(vuu300, vuu3100) new_esEs20(vuu3000, vuu31000, app(ty_Maybe, gd)) -> new_esEs4(vuu3000, vuu31000, gd) new_esEs21(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_groupByZs1(vuu30, [], ba) -> [] new_esEs26(vuu300, vuu3100, ty_Double) -> new_esEs9(vuu300, vuu3100) new_span2Ys01(vuu9, vuu110, vuu111, False, bb) -> [] new_esEs13(True, True) -> True new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs5(vuu3000, vuu31000) new_span2Zs3(:(vuu3110, vuu3111), ba) -> new_span2Zs01(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) new_esEs26(vuu300, vuu3100, app(ty_Ratio, fg)) -> new_esEs12(vuu300, vuu3100, fg) new_span2Ys02(vuu3110, vuu3111, False, ba) -> [] new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_[], bae), hg) -> new_esEs14(vuu3000, vuu31000, bae) new_groupByZs1(Just(vuu300), :(Nothing, vuu311), ba) -> :(Nothing, vuu311) new_esEs25(vuu3000, vuu31000, app(ty_Ratio, bfd)) -> new_esEs12(vuu3000, vuu31000, bfd) new_esEs26(vuu300, vuu3100, app(ty_Maybe, ec)) -> new_esEs4(vuu300, vuu3100, ec) new_esEs25(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_primEqNat0(Zero, Zero) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs18(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs20(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(ty_Ratio, ge)) -> new_esEs12(vuu3000, vuu31000, ge) new_esEs21(vuu3001, vuu31001, app(ty_Maybe, bh)) -> new_esEs4(vuu3001, vuu31001, bh) new_esEs20(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs26(vuu300, vuu3100, app(ty_[], fh)) -> new_esEs14(vuu300, vuu3100, fh) new_esEs20(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_[], cb)) -> new_esEs14(vuu3001, vuu31001, cb) new_asAs(False, vuu40) -> False new_esEs25(vuu3000, vuu31000, app(app(ty_@2, bfh), bga)) -> new_esEs16(vuu3000, vuu31000, bfh, bga) new_esEs18(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(ty_[], bbg)) -> new_esEs14(vuu3000, vuu31000, bbg) new_esEs20(vuu3000, vuu31000, app(app(ty_@2, ha), hb)) -> new_esEs16(vuu3000, vuu31000, ha, hb) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs8(vuu3001, vuu31001, bdf, bdg, bdh) new_span2Zs2(vuu18, :(vuu200, vuu201), eb) -> new_span2Zs04(vuu18, vuu200, vuu201, new_esEs4(Just(vuu18), vuu200, eb), eb) new_esEs15(Right(vuu3000), Right(vuu31000), hf, app(ty_Maybe, bbe)) -> new_esEs4(vuu3000, vuu31000, bbe) new_span2Zs01(vuu3110, vuu3111, True, ba) -> new_span2Zs02(vuu3110, vuu3111, new_span2Ys3(vuu3111, ba), new_span2Zs3(vuu3111, ba), ba) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Maybe, eg)) -> new_esEs4(vuu3000, vuu31000, eg) new_esEs23(vuu3002, vuu31002, app(app(ty_Either, bdb), bdc)) -> new_esEs15(vuu3002, vuu31002, bdb, bdc) new_esEs21(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_[], fa)) -> new_esEs14(vuu3000, vuu31000, fa) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_esEs7(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) new_span2Ys03(vuu9, vuu110, vuu111, vuu50, vuu49, bb) -> :(vuu110, vuu50) The set Q consists of the following terms: new_esEs4(Just(x0), Just(x1), ty_Double) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs17(Char(x0), Char(x1)) new_esEs23(x0, x1, ty_Int) new_span2Zs01(x0, x1, False, x2) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_span2Ys02(x0, x1, True, x2) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs21(x0, x1, ty_Ordering) new_esEs15(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs21(x0, x1, ty_Double) new_esEs26(x0, x1, ty_Ordering) new_span2Ys01(x0, x1, x2, True, x3) new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Double) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Double) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs15(Right(x0), Right(x1), x2, ty_Double) new_primMulNat0(Zero, Zero) new_span2Ys04(x0, x1, x2, x3, x4) new_esEs4(Nothing, Nothing, x0) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(Right(x0), Right(x1), x2, ty_Float) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_span2Zs2(x0, :(x1, x2), x3) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Char) new_span2Zs3(:(x0, x1), x2) new_groupByZs1(x0, [], x1) new_esEs14(:(x0, x1), :(x2, x3), x4) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs24(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs15(Left(x0), Left(x1), ty_Int, x2) new_groupByZs1(Nothing, :(Nothing, x0), x1) new_primPlusNat0(Succ(x0), Zero) new_primPlusNat0(Zero, Succ(x0)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Zero, Succ(x0)) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Integer) new_span2Ys03(x0, x1, x2, x3, x4, x5) new_esEs15(Left(x0), Right(x1), x2, x3) new_esEs15(Right(x0), Left(x1), x2, x3) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs15(Left(x0), Left(x1), ty_Char, x2) new_esEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs25(x0, x1, ty_Bool) new_esEs20(x0, x1, ty_Float) new_primPlusNat0(Zero, Zero) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs26(x0, x1, ty_Float) new_esEs21(x0, x1, ty_Float) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs4(Just(x0), Just(x1), ty_Char) new_esEs15(Left(x0), Left(x1), ty_Ordering, x2) new_esEs24(x0, x1, ty_Integer) new_esEs21(x0, x1, ty_Char) new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Ordering) new_esEs15(Left(x0), Left(x1), ty_Bool, x2) new_esEs22(x0, x1, ty_Bool) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs12(:%(x0, x1), :%(x2, x3), x4) new_esEs15(Right(x0), Right(x1), x2, ty_Char) new_span2Ys2(x0, :(x1, x2), x3) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs4(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs13(True, True) new_esEs26(x0, x1, ty_Int) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_Char) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_esEs23(x0, x1, ty_Double) new_esEs21(x0, x1, ty_Int) new_span2Zs04(x0, x1, x2, False, x3) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Float) new_esEs22(x0, x1, ty_Integer) new_esEs15(Left(x0), Left(x1), ty_Integer, x2) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs7(Integer(x0), Integer(x1)) new_esEs14([], [], x0) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs11(EQ, EQ) new_esEs25(x0, x1, ty_Integer) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_primMulNat0(Succ(x0), Zero) new_esEs15(Right(x0), Right(x1), x2, ty_Int) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_@0) new_esEs26(x0, x1, ty_Bool) new_esEs19(x0, x1, ty_Int) new_esEs4(Just(x0), Just(x1), ty_Float) new_esEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs24(x0, x1, ty_Bool) new_esEs15(Right(x0), Right(x1), x2, ty_@0) new_span2Ys01(x0, x1, x2, False, x3) new_span2Zs01(x0, x1, True, x2) new_span2Ys02(x0, x1, False, x2) new_esEs21(x0, x1, ty_Bool) new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_@0) new_esEs21(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Integer) new_esEs4(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_Char) new_asAs(True, x0) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs14(:(x0, x1), [], x2) new_primMulNat0(Zero, Succ(x0)) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_Int) new_esEs4(Nothing, Just(x0), x1) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(ty_[], x2)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs15(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs4(Just(x0), Just(x1), app(ty_[], x2)) new_span2Ys2(x0, [], x1) new_esEs23(x0, x1, ty_Bool) new_esEs20(x0, x1, ty_@0) new_span2Zs04(x0, x1, x2, True, x3) new_esEs15(Right(x0), Right(x1), x2, ty_Bool) new_esEs4(Just(x0), Nothing, x1) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs9(Double(x0, x1), Double(x2, x3)) new_esEs18(x0, x1, ty_Int) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs6(x0, x1) new_span2Zs03(x0, x1, x2, x3, x4, x5) new_esEs24(x0, x1, ty_@0) new_esEs22(x0, x1, ty_Char) new_esEs14([], :(x0, x1), x2) new_esEs11(GT, GT) new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), ty_Double, x2) new_esEs4(Just(x0), Just(x1), ty_Bool) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs26(x0, x1, ty_Integer) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs21(x0, x1, ty_Integer) new_groupByZs10(x0, x1, x2, True, x3) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs13(False, True) new_esEs13(True, False) new_esEs15(Right(x0), Right(x1), x2, ty_Integer) new_groupByZs10(x0, x1, x2, False, x3) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs15(Left(x0), Left(x1), ty_Float, x2) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs25(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Double) new_primPlusNat1(Zero, x0) new_esEs15(Left(x0), Left(x1), ty_@0, x2) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_groupByZs1(Just(x0), :(Just(x1), x2), x3) new_esEs20(x0, x1, ty_Int) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_primPlusNat1(Succ(x0), x1) new_esEs11(LT, LT) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, ty_@0) new_span2Zs2(x0, [], x1) new_esEs19(x0, x1, ty_Integer) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs20(x0, x1, ty_Char) new_esEs20(x0, x1, ty_Double) new_esEs18(x0, x1, ty_Integer) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqNat0(Succ(x0), Zero) new_esEs10(@0, @0) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_span2Ys3(:(x0, x1), x2) new_span2Ys3([], x0) new_esEs4(Just(x0), Just(x1), ty_Integer) new_esEs4(Just(x0), Just(x1), ty_Ordering) new_span2Zs3([], x0) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, ty_Float) new_esEs5(Float(x0, x1), Float(x2, x3)) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_groupByZs1(Nothing, :(Just(x0), x1), x2) new_esEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_asAs(False, x0) new_primEqNat0(Succ(x0), Succ(x1)) new_groupByZs1(Just(x0), :(Nothing, x1), x2) new_span2Zs02(x0, x1, x2, x3, x4) new_esEs15(Right(x0), Right(x1), x2, ty_Ordering) new_esEs25(x0, x1, ty_Float) new_esEs20(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Ordering) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) QDPSizeChangeProof (EQUIVALENT) We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. Order:Polynomial interpretation [POLO]: POL(:(x_1, x_2)) = 1 + x_2 POL(:%(x_1, x_2)) = 0 POL(@0) = 0 POL(@2(x_1, x_2)) = 0 POL(@3(x_1, x_2, x_3)) = 0 POL(Char(x_1)) = 0 POL(Double(x_1, x_2)) = 0 POL(EQ) = 0 POL(False) = 1 POL(Float(x_1, x_2)) = 0 POL(GT) = 0 POL(Integer(x_1)) = 0 POL(Just(x_1)) = 0 POL(LT) = 0 POL(Left(x_1)) = 0 POL(Neg(x_1)) = 0 POL(Nothing) = 1 POL(Pos(x_1)) = 0 POL(Right(x_1)) = 0 POL(Succ(x_1)) = 0 POL(True) = 1 POL(Zero) = 0 POL([]) = 1 POL(app(x_1, x_2)) = 1 + x_2 POL(new_asAs(x_1, x_2)) = 1 + x_2 POL(new_esEs10(x_1, x_2)) = 1 POL(new_esEs11(x_1, x_2)) = 1 POL(new_esEs12(x_1, x_2, x_3)) = 1 POL(new_esEs13(x_1, x_2)) = 1 POL(new_esEs14(x_1, x_2, x_3)) = 1 POL(new_esEs15(x_1, x_2, x_3, x_4)) = 1 POL(new_esEs16(x_1, x_2, x_3, x_4)) = 0 POL(new_esEs17(x_1, x_2)) = 1 POL(new_esEs18(x_1, x_2, x_3)) = x_3 POL(new_esEs19(x_1, x_2, x_3)) = 1 + x_3 POL(new_esEs20(x_1, x_2, x_3)) = 1 POL(new_esEs21(x_1, x_2, x_3)) = 1 + x_1 + x_2 POL(new_esEs22(x_1, x_2, x_3)) = 1 + x_1 + x_3 POL(new_esEs23(x_1, x_2, x_3)) = 1 POL(new_esEs24(x_1, x_2, x_3)) = 0 POL(new_esEs25(x_1, x_2, x_3)) = 1 POL(new_esEs26(x_1, x_2, x_3)) = 1 + x_3 POL(new_esEs4(x_1, x_2, x_3)) = 1 POL(new_esEs5(x_1, x_2)) = 1 POL(new_esEs6(x_1, x_2)) = 0 POL(new_esEs7(x_1, x_2)) = 1 POL(new_esEs8(x_1, x_2, x_3, x_4, x_5)) = 1 POL(new_esEs9(x_1, x_2)) = 0 POL(new_groupByZs1(x_1, x_2, x_3)) = x_2 POL(new_groupByZs10(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_primEqInt(x_1, x_2)) = 0 POL(new_primEqNat0(x_1, x_2)) = 0 POL(new_primMulNat0(x_1, x_2)) = 0 POL(new_primPlusNat0(x_1, x_2)) = 0 POL(new_primPlusNat1(x_1, x_2)) = 0 POL(new_span2Ys01(x_1, x_2, x_3, x_4, x_5)) = 1 + x_1 + x_3 + x_5 POL(new_span2Ys02(x_1, x_2, x_3, x_4)) = 1 + x_2 POL(new_span2Ys03(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_4 POL(new_span2Ys04(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_span2Ys2(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(new_span2Ys3(x_1, x_2)) = x_1 POL(new_span2Zs01(x_1, x_2, x_3, x_4)) = x_2 + x_3 POL(new_span2Zs02(x_1, x_2, x_3, x_4, x_5)) = x_4 POL(new_span2Zs03(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_5 POL(new_span2Zs04(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_span2Zs2(x_1, x_2, x_3)) = x_2 POL(new_span2Zs3(x_1, x_2)) = x_1 POL(new_sr(x_1, x_2)) = 0 POL(ty_@0) = 0 POL(ty_@2) = 0 POL(ty_@3) = 0 POL(ty_Bool) = 1 POL(ty_Char) = 1 POL(ty_Double) = 1 POL(ty_Either) = 0 POL(ty_Float) = 1 POL(ty_Int) = 0 POL(ty_Integer) = 1 POL(ty_Maybe) = 0 POL(ty_Ordering) = 1 POL(ty_Ratio) = 0 POL(ty_[]) = 0 From the DPs we obtained the following set of size-change graphs: *new_groupBy(:(vuu30, vuu31), ba) -> new_groupBy(new_groupByZs1(vuu30, vuu31, ba), ba) (allowed arguments on rhs = {1, 2}) The graph contains the following edges 1 > 1, 2 >= 2 We oriented the following set of usable rules [AAECC05,FROCOS05]. new_span2Zs3([], ba) -> [] new_span2Zs3(:(vuu3110, vuu3111), ba) -> new_span2Zs01(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) new_span2Zs2(vuu18, [], eb) -> [] new_span2Zs2(vuu18, :(vuu200, vuu201), eb) -> new_span2Zs04(vuu18, vuu200, vuu201, new_esEs4(Just(vuu18), vuu200, eb), eb) new_span2Zs04(vuu18, vuu200, vuu201, True, eb) -> new_span2Zs03(vuu18, vuu200, vuu201, new_span2Ys2(vuu18, vuu201, eb), new_span2Zs2(vuu18, vuu201, eb), eb) new_span2Zs04(vuu18, vuu200, vuu201, False, eb) -> :(vuu200, vuu201) new_span2Zs03(vuu18, vuu200, vuu201, vuu52, vuu51, eb) -> vuu51 new_span2Zs02(vuu3110, vuu3111, vuu48, vuu47, ba) -> vuu47 new_span2Zs01(vuu3110, vuu3111, True, ba) -> new_span2Zs02(vuu3110, vuu3111, new_span2Ys3(vuu3111, ba), new_span2Zs3(vuu3111, ba), ba) new_span2Zs01(vuu3110, vuu3111, False, ba) -> :(vuu3110, vuu3111) new_span2Ys3([], ba) -> [] new_span2Ys3(:(vuu3110, vuu3111), ba) -> new_span2Ys02(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) new_span2Ys2(vuu9, [], bb) -> [] new_span2Ys2(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys01(vuu9, vuu110, vuu111, new_esEs4(Just(vuu9), vuu110, bb), bb) new_span2Ys04(vuu3110, vuu3111, vuu46, vuu45, ba) -> :(vuu3110, vuu46) new_span2Ys03(vuu9, vuu110, vuu111, vuu50, vuu49, bb) -> :(vuu110, vuu50) new_span2Ys02(vuu3110, vuu3111, True, ba) -> new_span2Ys04(vuu3110, vuu3111, new_span2Ys3(vuu3111, ba), new_span2Zs3(vuu3111, ba), ba) new_span2Ys02(vuu3110, vuu3111, False, ba) -> [] new_span2Ys01(vuu9, vuu110, vuu111, True, bb) -> new_span2Ys03(vuu9, vuu110, vuu111, new_span2Ys2(vuu9, vuu111, bb), new_span2Zs2(vuu9, vuu111, bb), bb) new_span2Ys01(vuu9, vuu110, vuu111, False, bb) -> [] new_groupByZs10(vuu18, vuu19, vuu20, True, eb) -> new_span2Zs2(vuu18, vuu20, eb) new_groupByZs10(vuu18, vuu19, vuu20, False, eb) -> :(Just(vuu19), vuu20) new_groupByZs1(vuu30, [], ba) -> [] new_groupByZs1(Nothing, :(Nothing, vuu311), ba) -> new_span2Zs3(vuu311, ba) new_groupByZs1(Nothing, :(Just(vuu3100), vuu311), ba) -> :(Just(vuu3100), vuu311) new_groupByZs1(Just(vuu300), :(Nothing, vuu311), ba) -> :(Nothing, vuu311) new_groupByZs1(Just(vuu300), :(Just(vuu3100), vuu311), ba) -> new_groupByZs10(vuu300, vuu3100, vuu311, new_esEs26(vuu300, vuu3100, ba), ba) new_esEs4(Nothing, Nothing, ec) -> True new_esEs4(Nothing, Just(vuu31000), ec) -> False ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bad), bae), hg) -> new_esEs3(vuu3000, vuu31000, bad, bae) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(ty_[], bg)) -> new_esEs1(vuu3002, vuu31002, bg) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(ty_@2, cb), cc)) -> new_esEs3(vuu3002, vuu31002, cb, cc) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(app(ty_@3, bc), bd), be)) -> new_esEs(vuu3002, vuu31002, bc, bd, be) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_@2, ef), eg), bb, cg) -> new_esEs3(vuu3000, vuu31000, ef, eg) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_Maybe, bdf), bde) -> new_esEs0(vuu3000, vuu31000, bdf) new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_Either, bbd), bbe)) -> new_esEs2(vuu3000, vuu31000, bbd, bbe) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_[], ec), bb, cg) -> new_esEs1(vuu3000, vuu31000, ec) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(ty_Either, bcf), bcg)) -> new_esEs2(vuu3001, vuu31001, bcf, bcg) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_Maybe, gf)) -> new_esEs0(vuu3000, vuu31000, gf) new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_[], baa), hg) -> new_esEs1(vuu3000, vuu31000, baa) new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(app(ty_@3, bag), bah), bba)) -> new_esEs(vuu3000, vuu31000, bag, bah, bba) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(ty_Maybe, bcd)) -> new_esEs0(vuu3001, vuu31001, bcd) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(ty_[], db), cg) -> new_esEs1(vuu3001, vuu31001, db) new_esEs0(Just(vuu3000), Just(vuu31000), app(app(ty_Either, ff), fg)) -> new_esEs2(vuu3000, vuu31000, ff, fg) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(app(ty_@3, gc), gd), ge)) -> new_esEs(vuu3000, vuu31000, gc, gd, ge) new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hh), hg) -> new_esEs0(vuu3000, vuu31000, hh) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_Maybe, eb), bb, cg) -> new_esEs0(vuu3000, vuu31000, eb) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_Either, gh), ha)) -> new_esEs2(vuu3000, vuu31000, gh, ha) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_Either, bdh), bea), bde) -> new_esEs2(vuu3000, vuu31000, bdh, bea) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(ty_Maybe, da), cg) -> new_esEs0(vuu3001, vuu31001, da) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(app(ty_@3, bca), bcb), bcc)) -> new_esEs(vuu3001, vuu31001, bca, bcb, bcc) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(ty_@2, bch), bda)) -> new_esEs3(vuu3001, vuu31001, bch, bda) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(app(ty_@3, cd), ce), cf), cg) -> new_esEs(vuu3001, vuu31001, cd, ce, cf) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(ty_Maybe, bf)) -> new_esEs0(vuu3002, vuu31002, bf) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(ty_Either, bh), ca)) -> new_esEs2(vuu3002, vuu31002, bh, ca) new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_Either, bab), bac), hg) -> new_esEs2(vuu3000, vuu31000, bab, bac) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(ty_[], bce)) -> new_esEs1(vuu3001, vuu31001, bce) new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_[], bbc)) -> new_esEs1(vuu3000, vuu31000, bbc) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(app(ty_@3, bdb), bdc), bdd), bde) -> new_esEs(vuu3000, vuu31000, bdb, bdc, bdd) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_@2, beb), bec), bde) -> new_esEs3(vuu3000, vuu31000, beb, bec) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(ty_Either, dc), dd), cg) -> new_esEs2(vuu3001, vuu31001, dc, dd) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), gb) -> new_esEs1(vuu3001, vuu31001, gb) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(app(ty_@3, dg), dh), ea), bb, cg) -> new_esEs(vuu3000, vuu31000, dg, dh, ea) new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_@2, bbf), bbg)) -> new_esEs3(vuu3000, vuu31000, bbf, bbg) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_[], gg)) -> new_esEs1(vuu3000, vuu31000, gg) new_esEs2(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hd), he), hf), hg) -> new_esEs(vuu3000, vuu31000, hd, he, hf) new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_@2, hb), hc)) -> new_esEs3(vuu3000, vuu31000, hb, hc) new_esEs0(Just(vuu3000), Just(vuu31000), app(app(ty_@2, fh), ga)) -> new_esEs3(vuu3000, vuu31000, fh, ga) new_esEs0(Just(vuu3000), Just(vuu31000), app(ty_Maybe, fc)) -> new_esEs0(vuu3000, vuu31000, fc) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_Either, ed), ee), bb, cg) -> new_esEs2(vuu3000, vuu31000, ed, ee) new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_Maybe, bbb)) -> new_esEs0(vuu3000, vuu31000, bbb) new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(ty_@2, de), df), cg) -> new_esEs3(vuu3001, vuu31001, de, df) new_esEs0(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, eh), fa), fb)) -> new_esEs(vuu3000, vuu31000, eh, fa, fb) new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_[], bdg), bde) -> new_esEs1(vuu3000, vuu31000, bdg) new_esEs0(Just(vuu3000), Just(vuu31000), app(ty_[], fd)) -> new_esEs1(vuu3000, vuu31000, fd) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) 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_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_Either, gh), ha)) -> new_esEs2(vuu3000, vuu31000, gh, ha) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(app(ty_@3, gc), gd), ge)) -> new_esEs(vuu3000, vuu31000, gc, gd, ge) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(Just(vuu3000), Just(vuu31000), app(app(ty_Either, ff), fg)) -> new_esEs2(vuu3000, vuu31000, ff, fg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_@2, hb), hc)) -> new_esEs3(vuu3000, vuu31000, hb, hc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, eh), fa), fb)) -> new_esEs(vuu3000, vuu31000, eh, fa, fb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(Just(vuu3000), Just(vuu31000), app(app(ty_@2, fh), ga)) -> new_esEs3(vuu3000, vuu31000, fh, ga) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_Maybe, gf)) -> new_esEs0(vuu3000, vuu31000, gf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(Just(vuu3000), Just(vuu31000), app(ty_[], fd)) -> new_esEs1(vuu3000, vuu31000, fd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(Just(vuu3000), Just(vuu31000), app(ty_Maybe, fc)) -> new_esEs0(vuu3000, vuu31000, fc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(ty_Either, bcf), bcg)) -> new_esEs2(vuu3001, vuu31001, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_Either, bdh), bea), bde) -> new_esEs2(vuu3000, vuu31000, bdh, bea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(app(ty_@3, bca), bcb), bcc)) -> new_esEs(vuu3001, vuu31001, bca, bcb, bcc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(app(ty_@3, bdb), bdc), bdd), bde) -> new_esEs(vuu3000, vuu31000, bdb, bdc, bdd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(app(ty_@2, bch), bda)) -> new_esEs3(vuu3001, vuu31001, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_@2, beb), bec), bde) -> new_esEs3(vuu3000, vuu31000, beb, bec) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(ty_[], bce)) -> new_esEs1(vuu3001, vuu31001, bce) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_[], bdg), bde) -> new_esEs1(vuu3000, vuu31000, bdg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_Maybe, bdf), bde) -> new_esEs0(vuu3000, vuu31000, bdf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bbh, app(ty_Maybe, bcd)) -> new_esEs0(vuu3001, vuu31001, bcd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(ty_Either, bh), ca)) -> new_esEs2(vuu3002, vuu31002, bh, ca) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(ty_Either, dc), dd), cg) -> new_esEs2(vuu3001, vuu31001, dc, dd) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_Either, ed), ee), bb, cg) -> new_esEs2(vuu3000, vuu31000, ed, ee) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_Either, bbd), bbe)) -> new_esEs2(vuu3000, vuu31000, bbd, bbe) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_Either, bab), bac), hg) -> new_esEs2(vuu3000, vuu31000, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), gb) -> new_esEs1(vuu3001, vuu31001, gb) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs1(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_[], gg)) -> new_esEs1(vuu3000, vuu31000, gg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(app(ty_@3, bc), bd), be)) -> new_esEs(vuu3002, vuu31002, bc, bd, be) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(app(ty_@3, cd), ce), cf), cg) -> new_esEs(vuu3001, vuu31001, cd, ce, cf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(app(ty_@3, dg), dh), ea), bb, cg) -> new_esEs(vuu3000, vuu31000, dg, dh, ea) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(app(ty_@3, bag), bah), bba)) -> new_esEs(vuu3000, vuu31000, bag, bah, bba) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs2(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hd), he), hf), hg) -> new_esEs(vuu3000, vuu31000, hd, he, hf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(app(ty_@2, cb), cc)) -> new_esEs3(vuu3002, vuu31002, cb, cc) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_@2, ef), eg), bb, cg) -> new_esEs3(vuu3000, vuu31000, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(app(ty_@2, de), df), cg) -> new_esEs3(vuu3001, vuu31001, de, df) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(ty_[], bg)) -> new_esEs1(vuu3002, vuu31002, bg) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_[], ec), bb, cg) -> new_esEs1(vuu3000, vuu31000, ec) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(ty_[], db), cg) -> new_esEs1(vuu3001, vuu31001, db) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_Maybe, eb), bb, cg) -> new_esEs0(vuu3000, vuu31000, eb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, app(ty_Maybe, da), cg) -> new_esEs0(vuu3001, vuu31001, da) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), ba, bb, app(ty_Maybe, bf)) -> new_esEs0(vuu3002, vuu31002, bf) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs2(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bad), bae), hg) -> new_esEs3(vuu3000, vuu31000, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(app(ty_@2, bbf), bbg)) -> new_esEs3(vuu3000, vuu31000, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_[], baa), hg) -> new_esEs1(vuu3000, vuu31000, baa) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_[], bbc)) -> new_esEs1(vuu3000, vuu31000, bbc) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hh), hg) -> new_esEs0(vuu3000, vuu31000, hh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(Right(vuu3000), Right(vuu31000), baf, app(ty_Maybe, bbb)) -> new_esEs0(vuu3000, vuu31000, bbb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 ---------------------------------------- (16) YES ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_span2Ys0(vuu9, vuu110, vuu111, True, bb) -> new_span2Zs(vuu9, vuu111, bb) new_span2Ys(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys0(vuu9, vuu110, vuu111, new_esEs4(Just(vuu9), vuu110, bb), bb) new_span2Zs0(vuu18, vuu200, vuu201, True, ba) -> new_span2Ys(vuu18, vuu201, ba) new_span2Zs(vuu18, :(vuu200, vuu201), ba) -> new_span2Zs0(vuu18, vuu200, vuu201, new_esEs4(Just(vuu18), vuu200, ba), ba) new_span2Ys0(vuu9, vuu110, vuu111, True, bb) -> new_span2Ys(vuu9, vuu111, bb) new_span2Zs0(vuu18, vuu200, vuu201, True, ba) -> new_span2Zs(vuu18, vuu201, ba) The TRS R consists of the following rules: new_esEs15(Left(vuu3000), Left(vuu31000), ty_Double, hb) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Int) -> new_esEs6(vuu3002, vuu31002) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bac), bad), hb) -> new_esEs16(vuu3000, vuu31000, bac, bad) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(Left(vuu3000), Right(vuu31000), bae, hb) -> False new_esEs15(Right(vuu3000), Left(vuu31000), bae, hb) -> False new_esEs23(vuu3002, vuu31002, ty_Char) -> new_esEs17(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_Maybe, bdh)) -> new_esEs4(vuu3001, vuu31001, bdh) new_esEs22(vuu3000, vuu31000, app(app(ty_Either, gf), gg)) -> new_esEs15(vuu3000, vuu31000, gf, gg) new_esEs12(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), cf) -> new_asAs(new_esEs19(vuu3000, vuu31000, cf), new_esEs18(vuu3001, vuu31001, cf)) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs14(:(vuu3000, vuu3001), :(vuu31000, vuu31001), cg) -> new_asAs(new_esEs20(vuu3000, vuu31000, cg), new_esEs14(vuu3001, vuu31001, cg)) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hf), hb) -> new_esEs4(vuu3000, vuu31000, hf) new_esEs13(False, False) -> True new_esEs22(vuu3000, vuu31000, app(ty_Ratio, gd)) -> new_esEs12(vuu3000, vuu31000, gd) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs15(Left(vuu3000), Left(vuu31000), ty_@0, hb) -> new_esEs10(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(ty_Ratio, bbb)) -> new_esEs12(vuu3000, vuu31000, bbb) new_esEs25(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_asAs(True, vuu40) -> vuu40 new_esEs23(vuu3002, vuu31002, ty_Double) -> new_esEs9(vuu3002, vuu31002) new_esEs21(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, bec), bed)) -> new_esEs15(vuu3001, vuu31001, bec, bed) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs8(vuu3000, vuu31000, baf, bag, bah) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) -> False new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, bea)) -> new_esEs12(vuu3001, vuu31001, bea) new_esEs19(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs5(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, gc)) -> new_esEs4(vuu3000, vuu31000, gc) new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Ratio, hg), hb) -> new_esEs12(vuu3000, vuu31000, hg) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Float, hb) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs17(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Ordering, hb) -> new_esEs11(vuu3000, vuu31000) new_esEs14([], [], cg) -> True new_esEs20(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(vuu3002, vuu31002, ty_@0) -> new_esEs10(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_[], beb)) -> new_esEs14(vuu3001, vuu31001, beb) new_esEs25(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(app(app(ty_@3, ee), ef), eg)) -> new_esEs8(vuu3001, vuu31001, ee, ef, eg) new_esEs20(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(ty_@2, bdc), bdd)) -> new_esEs16(vuu3002, vuu31002, bdc, bdd) new_esEs4(Nothing, Nothing, bc) -> True new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(Left(vuu3000), Left(vuu31000), ty_Integer, hb) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_Either, baa), bab), hb) -> new_esEs15(vuu3000, vuu31000, baa, bab) new_esEs4(Nothing, Just(vuu31000), bc) -> False new_esEs4(Just(vuu3000), Nothing, bc) -> False new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(ty_[], bch)) -> new_esEs14(vuu3002, vuu31002, bch) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, gh), ha)) -> new_esEs16(vuu3000, vuu31000, gh, ha) new_esEs25(vuu3000, vuu31000, app(app(ty_Either, bfe), bff)) -> new_esEs15(vuu3000, vuu31000, bfe, bff) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, fh), ga), gb)) -> new_esEs8(vuu3000, vuu31000, fh, ga, gb) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Int, hb) -> new_esEs6(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(app(ty_Either, dg), dh)) -> new_esEs15(vuu3000, vuu31000, dg, dh) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Char, hb) -> new_esEs17(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bd), be), bf)) -> new_esEs8(vuu3000, vuu31000, bd, be, bf) new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hc), hd), he), hb) -> new_esEs8(vuu3000, vuu31000, hc, hd, he) new_esEs11(EQ, EQ) -> True new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs23(vuu3002, vuu31002, ty_Float) -> new_esEs5(vuu3002, vuu31002) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_esEs21(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs21(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs14(:(vuu3000, vuu3001), [], cg) -> False new_esEs14([], :(vuu31000, vuu31001), cg) -> False new_esEs25(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, beg), beh), bfa)) -> new_esEs8(vuu3000, vuu31000, beg, beh, bfa) new_esEs23(vuu3002, vuu31002, app(ty_Ratio, bcg)) -> new_esEs12(vuu3002, vuu31002, bcg) new_esEs8(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), bbh, bca, bcb) -> new_asAs(new_esEs25(vuu3000, vuu31000, bbh), new_asAs(new_esEs24(vuu3001, vuu31001, bca), new_esEs23(vuu3002, vuu31002, bcb))) new_esEs23(vuu3002, vuu31002, ty_Bool) -> new_esEs13(vuu3002, vuu31002) new_esEs20(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bh)) -> new_esEs12(vuu3000, vuu31000, bh) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs21(vuu3001, vuu31001, app(app(ty_Either, fc), fd)) -> new_esEs15(vuu3001, vuu31001, fc, fd) new_esEs21(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs9(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3002, vuu31002, app(ty_Maybe, bcf)) -> new_esEs4(vuu3002, vuu31002, bcf) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Integer) -> new_esEs7(vuu3002, vuu31002) new_esEs23(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_Either, cb), cc)) -> new_esEs15(vuu3000, vuu31000, cb, cc) new_primPlusNat0(Succ(vuu5300), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu5300, vuu31001000))) new_esEs20(vuu3000, vuu31000, app(ty_[], df)) -> new_esEs14(vuu3000, vuu31000, df) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(app(ty_@2, bbf), bbg)) -> new_esEs16(vuu3000, vuu31000, bbf, bbg) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs19(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs10(@0, @0) -> True new_esEs6(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs20(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Bool, hb) -> new_esEs13(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_Ratio, fa)) -> new_esEs12(vuu3001, vuu31001, fa) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs8(vuu3002, vuu31002, bcc, bcd, bce) new_esEs21(vuu3001, vuu31001, app(app(ty_@2, ff), fg)) -> new_esEs16(vuu3001, vuu31001, ff, fg) new_esEs25(vuu3000, vuu31000, app(ty_[], bfd)) -> new_esEs14(vuu3000, vuu31000, bfd) new_esEs25(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Zero) -> Zero new_primMulNat0(Zero, Succ(vuu3100100)) -> Zero new_sr(Pos(vuu30000), Pos(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bae, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bee), bef)) -> new_esEs16(vuu3001, vuu31001, bee, bef) new_esEs22(vuu3000, vuu31000, app(ty_[], ge)) -> new_esEs14(vuu3000, vuu31000, ge) new_esEs25(vuu3000, vuu31000, app(ty_Maybe, bfb)) -> new_esEs4(vuu3000, vuu31000, bfb) new_primPlusNat1(Succ(vuu530), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu530, vuu3100100))) new_esEs20(vuu3000, vuu31000, app(app(app(ty_@3, da), db), dc)) -> new_esEs8(vuu3000, vuu31000, da, db, dc) new_primPlusNat0(Succ(vuu5300), Zero) -> Succ(vuu5300) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_@2, cd), ce)) -> new_esEs16(vuu3000, vuu31000, cd, ce) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), ec, ed) -> new_asAs(new_esEs22(vuu3000, vuu31000, ec), new_esEs21(vuu3001, vuu31001, ed)) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(app(ty_Either, bbd), bbe)) -> new_esEs15(vuu3000, vuu31000, bbd, bbe) new_esEs4(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(ty_Maybe, dd)) -> new_esEs4(vuu3000, vuu31000, dd) new_esEs21(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_esEs13(True, True) -> True new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_[], hh), hb) -> new_esEs14(vuu3000, vuu31000, hh) new_esEs25(vuu3000, vuu31000, app(ty_Ratio, bfc)) -> new_esEs12(vuu3000, vuu31000, bfc) new_esEs25(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_primEqNat0(Zero, Zero) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs18(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs20(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(ty_Ratio, de)) -> new_esEs12(vuu3000, vuu31000, de) new_esEs21(vuu3001, vuu31001, app(ty_Maybe, eh)) -> new_esEs4(vuu3001, vuu31001, eh) new_esEs20(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_[], fb)) -> new_esEs14(vuu3001, vuu31001, fb) new_asAs(False, vuu40) -> False new_esEs25(vuu3000, vuu31000, app(app(ty_@2, bfg), bfh)) -> new_esEs16(vuu3000, vuu31000, bfg, bfh) new_esEs18(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(ty_[], bbc)) -> new_esEs14(vuu3000, vuu31000, bbc) new_esEs20(vuu3000, vuu31000, app(app(ty_@2, ea), eb)) -> new_esEs16(vuu3000, vuu31000, ea, eb) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bde), bdf), bdg)) -> new_esEs8(vuu3001, vuu31001, bde, bdf, bdg) new_esEs15(Right(vuu3000), Right(vuu31000), bae, app(ty_Maybe, bba)) -> new_esEs4(vuu3000, vuu31000, bba) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bg)) -> new_esEs4(vuu3000, vuu31000, bg) new_esEs23(vuu3002, vuu31002, app(app(ty_Either, bda), bdb)) -> new_esEs15(vuu3002, vuu31002, bda, bdb) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_[], ca)) -> new_esEs14(vuu3000, vuu31000, ca) new_esEs21(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_esEs7(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) The set Q consists of the following terms: new_esEs4(Just(x0), Just(x1), ty_Double) new_esEs17(Char(x0), Char(x1)) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Int) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs21(x0, x1, ty_Ordering) new_esEs4(Nothing, Just(x0), x1) new_esEs21(x0, x1, ty_Double) new_esEs24(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs23(x0, x1, ty_Char) new_esEs4(Just(x0), Nothing, x1) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs24(x0, x1, ty_Ordering) new_esEs15(Right(x0), Right(x1), x2, ty_@0) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_primPlusNat0(Succ(x0), Zero) new_primPlusNat0(Zero, Succ(x0)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs16(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs14([], [], x0) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_primEqNat0(Zero, Succ(x0)) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs15(Right(x0), Right(x1), x2, ty_Int) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Integer) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs4(Just(x0), Just(x1), app(ty_[], x2)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs25(x0, x1, ty_Bool) new_esEs15(Right(x0), Right(x1), x2, ty_Char) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs20(x0, x1, ty_Float) new_primPlusNat0(Zero, Zero) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs21(x0, x1, ty_Float) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs4(Just(x0), Just(x1), ty_Char) new_esEs12(:%(x0, x1), :%(x2, x3), x4) new_esEs24(x0, x1, ty_Integer) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs21(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Ordering) new_esEs22(x0, x1, ty_Bool) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs15(Right(x0), Right(x1), x2, ty_Float) new_esEs4(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs13(True, True) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Char) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_esEs23(x0, x1, ty_Double) new_esEs21(x0, x1, ty_Int) new_esEs15(Left(x0), Left(x1), ty_Integer, x2) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs23(x0, x1, ty_Float) new_esEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs22(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs7(Integer(x0), Integer(x1)) new_esEs11(EQ, EQ) new_esEs14(:(x0, x1), :(x2, x3), x4) new_esEs25(x0, x1, ty_Integer) new_esEs15(Left(x0), Left(x1), ty_Ordering, x2) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_@0) new_esEs19(x0, x1, ty_Int) new_esEs4(Just(x0), Just(x1), ty_Float) new_esEs24(x0, x1, ty_Bool) new_esEs14(:(x0, x1), [], x2) new_esEs21(x0, x1, ty_Bool) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs21(x0, x1, ty_@0) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Integer) new_esEs4(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_Char) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_asAs(True, x0) new_primMulNat0(Zero, Succ(x0)) new_esEs25(x0, x1, ty_Int) new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs15(Left(x0), Right(x1), x2, x3) new_esEs15(Right(x0), Left(x1), x2, x3) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs4(Nothing, Nothing, x0) new_esEs23(x0, x1, ty_Bool) new_esEs20(x0, x1, ty_@0) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs9(Double(x0, x1), Double(x2, x3)) new_esEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs18(x0, x1, ty_Int) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs15(Right(x0), Right(x1), x2, ty_Double) new_esEs6(x0, x1) new_esEs24(x0, x1, ty_@0) new_esEs22(x0, x1, ty_Char) new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs11(GT, GT) new_esEs4(Just(x0), Just(x1), ty_Bool) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs13(False, True) new_esEs13(True, False) new_esEs15(Right(x0), Right(x1), x2, ty_Ordering) new_esEs25(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Double) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Zero, x0) new_esEs15(Right(x0), Right(x1), x2, ty_Bool) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(x0, x1, ty_Int) new_esEs15(Left(x0), Left(x1), ty_Bool, x2) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), x1) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs11(LT, LT) new_esEs22(x0, x1, ty_@0) new_esEs19(x0, x1, ty_Integer) new_esEs15(Left(x0), Left(x1), ty_Float, x2) new_esEs15(Left(x0), Left(x1), ty_Char, x2) new_esEs20(x0, x1, ty_Char) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_Double) new_esEs18(x0, x1, ty_Integer) new_primEqNat0(Succ(x0), Zero) new_esEs15(Right(x0), Right(x1), x2, ty_Integer) new_esEs10(@0, @0) new_esEs15(Left(x0), Left(x1), ty_@0, x2) new_esEs15(Left(x0), Left(x1), ty_Double, x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs4(Just(x0), Just(x1), ty_Integer) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs4(Just(x0), Just(x1), ty_Ordering) new_esEs15(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs22(x0, x1, ty_Float) new_esEs5(Float(x0, x1), Float(x2, x3)) new_asAs(False, x0) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs15(Left(x0), Left(x1), ty_Int, x2) new_esEs25(x0, x1, ty_Float) new_esEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs20(x0, x1, ty_Bool) new_esEs23(x0, x1, ty_Ordering) new_esEs14([], :(x0, x1), x2) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) 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_span2Zs(vuu18, :(vuu200, vuu201), ba) -> new_span2Zs0(vuu18, vuu200, vuu201, new_esEs4(Just(vuu18), vuu200, ba), ba) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 >= 5 *new_span2Ys(vuu9, :(vuu110, vuu111), bb) -> new_span2Ys0(vuu9, vuu110, vuu111, new_esEs4(Just(vuu9), vuu110, bb), bb) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 3 >= 5 *new_span2Ys0(vuu9, vuu110, vuu111, True, bb) -> new_span2Ys(vuu9, vuu111, bb) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Ys0(vuu9, vuu110, vuu111, True, bb) -> new_span2Zs(vuu9, vuu111, bb) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Zs0(vuu18, vuu200, vuu201, True, ba) -> new_span2Ys(vuu18, vuu201, ba) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 *new_span2Zs0(vuu18, vuu200, vuu201, True, ba) -> new_span2Zs(vuu18, vuu201, ba) The graph contains the following edges 1 >= 1, 3 >= 2, 5 >= 3 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMulNat(Succ(vuu300000), Succ(vuu3100100)) -> new_primMulNat(vuu300000, Succ(vuu3100100)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) 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(vuu300000), Succ(vuu3100100)) -> new_primMulNat(vuu300000, Succ(vuu3100100)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_span2Ys00(vuu3110, vuu3111, True, ba) -> new_span2Ys1(vuu3111, ba) new_span2Ys00(vuu3110, vuu3111, True, ba) -> new_span2Zs1(vuu3111, ba) new_span2Zs00(vuu3110, vuu3111, True, ba) -> new_span2Ys1(vuu3111, ba) new_span2Zs1(:(vuu3110, vuu3111), ba) -> new_span2Zs00(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) new_span2Zs00(vuu3110, vuu3111, True, ba) -> new_span2Zs1(vuu3111, ba) new_span2Ys1(:(vuu3110, vuu3111), ba) -> new_span2Ys00(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) The TRS R consists of the following rules: new_esEs15(Left(vuu3000), Left(vuu31000), ty_Double, ha) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Int) -> new_esEs6(vuu3002, vuu31002) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_@2, bab), bac), ha) -> new_esEs16(vuu3000, vuu31000, bab, bac) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(Left(vuu3000), Right(vuu31000), bad, ha) -> False new_esEs15(Right(vuu3000), Left(vuu31000), bad, ha) -> False new_esEs23(vuu3002, vuu31002, ty_Char) -> new_esEs17(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_Maybe, bdg)) -> new_esEs4(vuu3001, vuu31001, bdg) new_esEs22(vuu3000, vuu31000, app(app(ty_Either, ge), gf)) -> new_esEs15(vuu3000, vuu31000, ge, gf) new_esEs12(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), ce) -> new_asAs(new_esEs19(vuu3000, vuu31000, ce), new_esEs18(vuu3001, vuu31001, ce)) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs14(:(vuu3000, vuu3001), :(vuu31000, vuu31001), cf) -> new_asAs(new_esEs20(vuu3000, vuu31000, cf), new_esEs14(vuu3001, vuu31001, cf)) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Maybe, he), ha) -> new_esEs4(vuu3000, vuu31000, he) new_esEs13(False, False) -> True new_esEs22(vuu3000, vuu31000, app(ty_Ratio, gc)) -> new_esEs12(vuu3000, vuu31000, gc) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs15(Left(vuu3000), Left(vuu31000), ty_@0, ha) -> new_esEs10(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(ty_Ratio, bba)) -> new_esEs12(vuu3000, vuu31000, bba) new_esEs25(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_asAs(True, vuu40) -> vuu40 new_esEs23(vuu3002, vuu31002, ty_Double) -> new_esEs9(vuu3002, vuu31002) new_esEs21(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, beb), bec)) -> new_esEs15(vuu3001, vuu31001, beb, bec) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(app(app(ty_@3, bae), baf), bag)) -> new_esEs8(vuu3000, vuu31000, bae, baf, bag) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) -> False new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs10(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, bdh)) -> new_esEs12(vuu3001, vuu31001, bdh) new_esEs19(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs5(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, gb)) -> new_esEs4(vuu3000, vuu31000, gb) new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_Ratio, hf), ha) -> new_esEs12(vuu3000, vuu31000, hf) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Float, ha) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs17(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Ordering, ha) -> new_esEs11(vuu3000, vuu31000) new_esEs14([], [], cf) -> True new_esEs20(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_primMulNat0(Zero, Zero) -> Zero new_esEs23(vuu3002, vuu31002, ty_@0) -> new_esEs10(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(ty_[], bea)) -> new_esEs14(vuu3001, vuu31001, bea) new_esEs25(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs8(vuu3001, vuu31001, ed, ee, ef) new_esEs20(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(ty_@2, bdb), bdc)) -> new_esEs16(vuu3002, vuu31002, bdb, bdc) new_esEs4(Nothing, Nothing, bb) -> True new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(Left(vuu3000), Left(vuu31000), ty_Integer, ha) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), app(app(ty_Either, hh), baa), ha) -> new_esEs15(vuu3000, vuu31000, hh, baa) new_esEs4(Nothing, Just(vuu31000), bb) -> False new_esEs4(Just(vuu3000), Nothing, bb) -> False new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(ty_[], bcg)) -> new_esEs14(vuu3002, vuu31002, bcg) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, gg), gh)) -> new_esEs16(vuu3000, vuu31000, gg, gh) new_esEs25(vuu3000, vuu31000, app(app(ty_Either, bfd), bfe)) -> new_esEs15(vuu3000, vuu31000, bfd, bfe) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, fg), fh), ga)) -> new_esEs8(vuu3000, vuu31000, fg, fh, ga) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Int, ha) -> new_esEs6(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(app(ty_Either, df), dg)) -> new_esEs15(vuu3000, vuu31000, df, dg) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Char, ha) -> new_esEs17(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bc), bd), be)) -> new_esEs8(vuu3000, vuu31000, bc, bd, be) new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs13(False, True) -> False new_esEs13(True, False) -> False new_esEs15(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, hb), hc), hd), ha) -> new_esEs8(vuu3000, vuu31000, hb, hc, hd) new_esEs11(EQ, EQ) -> True new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs23(vuu3002, vuu31002, ty_Float) -> new_esEs5(vuu3002, vuu31002) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_esEs21(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs21(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs14(:(vuu3000, vuu3001), [], cf) -> False new_esEs14([], :(vuu31000, vuu31001), cf) -> False new_esEs25(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, app(app(app(ty_@3, bef), beg), beh)) -> new_esEs8(vuu3000, vuu31000, bef, beg, beh) new_esEs23(vuu3002, vuu31002, app(ty_Ratio, bcf)) -> new_esEs12(vuu3002, vuu31002, bcf) new_esEs8(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), bbg, bbh, bca) -> new_asAs(new_esEs25(vuu3000, vuu31000, bbg), new_asAs(new_esEs24(vuu3001, vuu31001, bbh), new_esEs23(vuu3002, vuu31002, bca))) new_esEs23(vuu3002, vuu31002, ty_Bool) -> new_esEs13(vuu3002, vuu31002) new_esEs20(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bg)) -> new_esEs12(vuu3000, vuu31000, bg) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs21(vuu3001, vuu31001, app(app(ty_Either, fb), fc)) -> new_esEs15(vuu3001, vuu31001, fb, fc) new_esEs21(vuu3001, vuu31001, ty_Bool) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs9(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs6(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3002, vuu31002, app(ty_Maybe, bce)) -> new_esEs4(vuu3002, vuu31002, bce) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, ty_Integer) -> new_esEs7(vuu3002, vuu31002) new_esEs23(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_Either, ca), cb)) -> new_esEs15(vuu3000, vuu31000, ca, cb) new_primPlusNat0(Succ(vuu5300), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu5300, vuu31001000))) new_esEs20(vuu3000, vuu31000, app(ty_[], de)) -> new_esEs14(vuu3000, vuu31000, de) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(app(ty_@2, bbe), bbf)) -> new_esEs16(vuu3000, vuu31000, bbe, bbf) new_esEs4(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs19(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs10(@0, @0) -> True new_esEs6(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs20(vuu3000, vuu31000, ty_Char) -> new_esEs17(vuu3000, vuu31000) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs15(Left(vuu3000), Left(vuu31000), ty_Bool, ha) -> new_esEs13(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, ty_Int) -> new_esEs6(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_Ratio, eh)) -> new_esEs12(vuu3001, vuu31001, eh) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs23(vuu3002, vuu31002, app(app(app(ty_@3, bcb), bcc), bcd)) -> new_esEs8(vuu3002, vuu31002, bcb, bcc, bcd) new_esEs21(vuu3001, vuu31001, app(app(ty_@2, fd), ff)) -> new_esEs16(vuu3001, vuu31001, fd, ff) new_esEs25(vuu3000, vuu31000, app(ty_[], bfc)) -> new_esEs14(vuu3000, vuu31000, bfc) new_esEs25(vuu3000, vuu31000, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Zero) -> Zero new_primMulNat0(Zero, Succ(vuu3100100)) -> Zero new_sr(Pos(vuu30000), Pos(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Integer) -> new_esEs7(vuu3000, vuu31000) new_esEs15(Right(vuu3000), Right(vuu31000), bad, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bed), bee)) -> new_esEs16(vuu3001, vuu31001, bed, bee) new_esEs22(vuu3000, vuu31000, app(ty_[], gd)) -> new_esEs14(vuu3000, vuu31000, gd) new_esEs25(vuu3000, vuu31000, app(ty_Maybe, bfa)) -> new_esEs4(vuu3000, vuu31000, bfa) new_primPlusNat1(Succ(vuu530), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu530, vuu3100100))) new_esEs20(vuu3000, vuu31000, app(app(app(ty_@3, cg), da), db)) -> new_esEs8(vuu3000, vuu31000, cg, da, db) new_primPlusNat0(Succ(vuu5300), Zero) -> Succ(vuu5300) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs4(Just(vuu3000), Just(vuu31000), app(app(ty_@2, cc), cd)) -> new_esEs16(vuu3000, vuu31000, cc, cd) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), eb, ec) -> new_asAs(new_esEs22(vuu3000, vuu31000, eb), new_esEs21(vuu3001, vuu31001, ec)) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(app(ty_Either, bbc), bbd)) -> new_esEs15(vuu3000, vuu31000, bbc, bbd) new_esEs4(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(ty_Maybe, dc)) -> new_esEs4(vuu3000, vuu31000, dc) new_esEs21(vuu3001, vuu31001, ty_Float) -> new_esEs5(vuu3001, vuu31001) new_esEs13(True, True) -> True new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs15(Left(vuu3000), Left(vuu31000), app(ty_[], hg), ha) -> new_esEs14(vuu3000, vuu31000, hg) new_esEs25(vuu3000, vuu31000, app(ty_Ratio, bfb)) -> new_esEs12(vuu3000, vuu31000, bfb) new_esEs25(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_primEqNat0(Zero, Zero) -> True new_esEs4(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs9(vuu3000, vuu31000) new_esEs18(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs20(vuu3000, vuu31000, ty_Float) -> new_esEs5(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, app(ty_Ratio, dd)) -> new_esEs12(vuu3000, vuu31000, dd) new_esEs21(vuu3001, vuu31001, app(ty_Maybe, eg)) -> new_esEs4(vuu3001, vuu31001, eg) new_esEs20(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs25(vuu3000, vuu31000, ty_Bool) -> new_esEs13(vuu3000, vuu31000) new_esEs20(vuu3000, vuu31000, ty_@0) -> new_esEs10(vuu3000, vuu31000) new_esEs21(vuu3001, vuu31001, app(ty_[], fa)) -> new_esEs14(vuu3001, vuu31001, fa) new_asAs(False, vuu40) -> False new_esEs25(vuu3000, vuu31000, app(app(ty_@2, bff), bfg)) -> new_esEs16(vuu3000, vuu31000, bff, bfg) new_esEs18(vuu3001, vuu31001, ty_Integer) -> new_esEs7(vuu3001, vuu31001) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(ty_[], bbb)) -> new_esEs14(vuu3000, vuu31000, bbb) new_esEs20(vuu3000, vuu31000, app(app(ty_@2, dh), ea)) -> new_esEs16(vuu3000, vuu31000, dh, ea) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs6(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs8(vuu3001, vuu31001, bdd, bde, bdf) new_esEs15(Right(vuu3000), Right(vuu31000), bad, app(ty_Maybe, bah)) -> new_esEs4(vuu3000, vuu31000, bah) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bf)) -> new_esEs4(vuu3000, vuu31000, bf) new_esEs23(vuu3002, vuu31002, app(app(ty_Either, bch), bda)) -> new_esEs15(vuu3002, vuu31002, bch, bda) new_esEs4(Just(vuu3000), Just(vuu31000), app(ty_[], bh)) -> new_esEs14(vuu3000, vuu31000, bh) new_esEs21(vuu3001, vuu31001, ty_Double) -> new_esEs9(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs17(vuu3001, vuu31001) new_esEs7(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) The set Q consists of the following terms: new_esEs4(Just(x0), Just(x1), ty_Double) new_esEs17(Char(x0), Char(x1)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, ty_Int) new_esEs4(Nothing, Nothing, x0) new_esEs21(x0, x1, ty_Ordering) new_esEs21(x0, x1, ty_Double) new_esEs24(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs15(Right(x0), Right(x1), x2, ty_Integer) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs23(x0, x1, ty_Char) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, ty_Ordering) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12(:%(x0, x1), :%(x2, x3), x4) new_primPlusNat0(Succ(x0), Zero) new_primPlusNat0(Zero, Succ(x0)) new_esEs14(:(x0, x1), [], x2) new_esEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs20(x0, x1, app(app(ty_@2, x2), x3)) new_primEqNat0(Zero, Succ(x0)) new_esEs22(x0, x1, ty_Double) new_esEs20(x0, x1, ty_Ordering) new_esEs20(x0, x1, ty_Integer) new_esEs24(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs20(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs25(x0, x1, ty_Bool) new_esEs20(x0, x1, ty_Float) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat0(Zero, Zero) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs14([], [], x0) new_esEs21(x0, x1, ty_Float) new_esEs15(Left(x0), Left(x1), ty_Bool, x2) new_esEs4(Just(x0), Just(x1), ty_Char) new_esEs21(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Integer) new_esEs15(Right(x0), Right(x1), x2, ty_Double) new_esEs15(Right(x0), Right(x1), x2, ty_Bool) new_esEs21(x0, x1, ty_Char) new_esEs21(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Int) new_esEs25(x0, x1, ty_Ordering) new_esEs15(Left(x0), Left(x1), ty_Float, x2) new_esEs22(x0, x1, ty_Bool) new_esEs14([], :(x0, x1), x2) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs4(Just(x0), Just(x1), ty_Int) new_sr(Pos(x0), Pos(x1)) new_esEs13(True, True) new_esEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs24(x0, x1, ty_Char) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_esEs23(x0, x1, ty_Double) new_esEs21(x0, x1, ty_Int) new_esEs15(Left(x0), Left(x1), ty_Double, x2) new_esEs15(Left(x0), Left(x1), ty_Int, x2) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs23(x0, x1, ty_Float) new_esEs20(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Integer) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs7(Integer(x0), Integer(x1)) new_esEs21(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs11(EQ, EQ) new_esEs25(x0, x1, ty_Integer) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_primMulNat0(Succ(x0), Zero) new_esEs20(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, ty_@0) new_esEs19(x0, x1, ty_Int) new_esEs4(Just(x0), Just(x1), ty_Float) new_esEs24(x0, x1, ty_Bool) new_esEs20(x0, x1, app(ty_Maybe, x2)) new_esEs15(Left(x0), Left(x1), ty_@0, x2) new_esEs21(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4(Just(x0), Nothing, x1) new_esEs21(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs15(Right(x0), Right(x1), x2, ty_Char) new_esEs21(x0, x1, ty_Bool) new_esEs14(:(x0, x1), :(x2, x3), x4) new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs21(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Integer) new_esEs4(Just(x0), Just(x1), ty_@0) new_esEs25(x0, x1, ty_Char) new_asAs(True, x0) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2)) new_primMulNat0(Zero, Succ(x0)) new_esEs15(Left(x0), Right(x1), x2, x3) new_esEs15(Right(x0), Left(x1), x2, x3) new_esEs25(x0, x1, ty_Int) new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs15(Left(x0), Left(x1), ty_Char, x2) new_esEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs4(Nothing, Just(x0), x1) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs15(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs23(x0, x1, ty_Bool) new_esEs20(x0, x1, ty_@0) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs9(Double(x0, x1), Double(x2, x3)) new_esEs18(x0, x1, ty_Int) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_esEs15(Right(x0), Right(x1), x2, ty_Ordering) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs6(x0, x1) new_esEs24(x0, x1, ty_@0) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, ty_Char) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs11(GT, GT) new_esEs4(Just(x0), Just(x1), ty_Bool) new_esEs15(Right(x0), Right(x1), x2, ty_Int) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs21(x0, x1, ty_Integer) new_primEqNat0(Zero, Zero) new_esEs13(False, False) new_esEs15(Right(x0), Right(x1), x2, ty_Float) new_esEs13(False, True) new_esEs13(True, False) new_esEs15(Right(x0), Right(x1), x2, ty_@0) new_esEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Double) new_primPlusNat1(Zero, x0) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs22(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs20(x0, x1, ty_Int) new_esEs16(@2(x0, x1), @2(x2, x3), x4, x5) new_primPlusNat1(Succ(x0), x1) new_esEs11(LT, LT) new_esEs22(x0, x1, ty_@0) new_esEs19(x0, x1, ty_Integer) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs20(x0, x1, ty_Char) new_esEs4(Just(x0), Just(x1), app(ty_[], x2)) new_esEs20(x0, x1, ty_Double) new_esEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs18(x0, x1, ty_Integer) new_esEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_primEqNat0(Succ(x0), Zero) new_esEs10(@0, @0) new_esEs15(Left(x0), Left(x1), ty_Integer, x2) new_esEs4(Just(x0), Just(x1), ty_Integer) new_esEs4(Just(x0), Just(x1), ty_Ordering) new_esEs22(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs5(Float(x0, x1), Float(x2, x3)) new_asAs(False, x0) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs15(Left(x0), Left(x1), ty_Ordering, x2) new_esEs25(x0, x1, ty_Float) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs20(x0, x1, ty_Bool) new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs23(x0, x1, ty_Ordering) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) 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_span2Ys1(:(vuu3110, vuu3111), ba) -> new_span2Ys00(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) The graph contains the following edges 1 > 1, 1 > 2, 2 >= 4 *new_span2Zs1(:(vuu3110, vuu3111), ba) -> new_span2Zs00(vuu3110, vuu3111, new_esEs4(Nothing, vuu3110, ba), ba) The graph contains the following edges 1 > 1, 1 > 2, 2 >= 4 *new_span2Zs00(vuu3110, vuu3111, True, ba) -> new_span2Zs1(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Zs00(vuu3110, vuu3111, True, ba) -> new_span2Ys1(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Ys00(vuu3110, vuu3111, True, ba) -> new_span2Zs1(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Ys00(vuu3110, vuu3111, True, ba) -> new_span2Ys1(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 ---------------------------------------- (25) YES ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuu5300), Succ(vuu31001000)) -> new_primPlusNat(vuu5300, vuu31001000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) 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(vuu5300), Succ(vuu31001000)) -> new_primPlusNat(vuu5300, vuu31001000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (28) YES ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEqNat(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat(vuu30000, vuu310000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) 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(vuu30000), Succ(vuu310000)) -> new_primEqNat(vuu30000, vuu310000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (31) YES