/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 4 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) AND (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 3 ms] (13) YES (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 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, 462 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@(vz : wu)" is replaced by the following term "vz : wu" ---------------------------------------- (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 (vz : wu)|p vz(vz : ys,zs)|otherwise([],vz : wu) where { vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,zs) = zs; } ; " is transformed to "span p [] = span3 p []; span p (vz : wu) = span2 p (vz : wu); " "span2 p (vz : wu) = span1 p vz wu (p vz) where { span0 p vz wu True = ([],vz : wu); ; span1 p vz wu True = (vz : ys,zs); span1 p vz wu False = span0 p vz wu otherwise; ; vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,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 vz wu (p vz) where { span0 p vz wu True = ([],vz : wu); ; span1 p vz wu True = (vz : ys,zs); span1 p vz wu False = span0 p vz wu otherwise; ; vu43 = span p wu; ; ys = ys0 vu43; ; ys0 (ys,ww) = ys; ; zs = zs0 vu43; ; zs0 (wv,zs) = zs; } " are unpacked to the following functions on top level "span2Span1 zv zw p vz wu True = (vz : span2Ys zv zw,span2Zs zv zw); span2Span1 zv zw p vz wu False = span2Span0 zv zw p vz wu otherwise; " "span2Zs0 zv zw (wv,zs) = zs; " "span2Ys zv zw = span2Ys0 zv zw (span2Vu43 zv zw); " "span2Zs zv zw = span2Zs0 zv zw (span2Vu43 zv zw); " "span2Vu43 zv zw = span zv zw; " "span2Span0 zv zw p vz wu True = ([],vz : wu); " "span2Ys0 zv zw (ys,ww) = ys; " 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"];976[label="vuu3/vuu30 : vuu31",fontsize=10,color="white",style="solid",shape="box"];4 -> 976[label="",style="solid", color="burlywood", weight=9]; 976 -> 5[label="",style="solid", color="burlywood", weight=3]; 977[label="vuu3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 977[label="",style="solid", color="burlywood", weight=9]; 977 -> 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"];978[label="vuu31/vuu310 : vuu311",fontsize=10,color="white",style="solid",shape="box"];13 -> 978[label="",style="solid", color="burlywood", weight=9]; 978 -> 15[label="",style="solid", color="burlywood", weight=3]; 979[label="vuu31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 979[label="",style="solid", color="burlywood", weight=9]; 979 -> 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981[label="",style="solid", color="burlywood", weight=9]; 981 -> 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"];982[label="vuu30/vuu300 : vuu301",fontsize=10,color="white",style="solid",shape="box"];22 -> 982[label="",style="solid", color="burlywood", weight=9]; 982 -> 26[label="",style="solid", color="burlywood", weight=3]; 983[label="vuu30/[]",fontsize=10,color="white",style="solid",shape="box"];22 -> 983[label="",style="solid", color="burlywood", weight=9]; 983 -> 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 (==) (vuu300 : vuu301) (vuu310 : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) vuu310 vuu311 ((==) vuu300 : vuu301 vuu310))",fontsize=16,color="burlywood",shape="box"];984[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];26 -> 984[label="",style="solid", color="burlywood", weight=9]; 984 -> 31[label="",style="solid", color="burlywood", weight=3]; 985[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];26 -> 985[label="",style="solid", color="burlywood", weight=9]; 985 -> 32[label="",style="solid", color="burlywood", weight=3]; 27[label="List.groupByYs1 (==) [] (vuu310 : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) vuu310 vuu311 ((==) [] vuu310))",fontsize=16,color="burlywood",shape="box"];986[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];27 -> 986[label="",style="solid", color="burlywood", weight=9]; 986 -> 33[label="",style="solid", color="burlywood", weight=3]; 987[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];27 -> 987[label="",style="solid", color="burlywood", weight=9]; 987 -> 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"];988[label="vuu30/vuu300 : vuu301",fontsize=10,color="white",style="solid",shape="box"];29 -> 988[label="",style="solid", color="burlywood", weight=9]; 988 -> 35[label="",style="solid", color="burlywood", weight=3]; 989[label="vuu30/[]",fontsize=10,color="white",style="solid",shape="box"];29 -> 989[label="",style="solid", color="burlywood", weight=9]; 989 -> 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 (==) (vuu300 : vuu301) ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) (vuu3100 : vuu3101) vuu311 ((==) vuu300 : vuu301 vuu3100 : vuu3101))",fontsize=16,color="black",shape="box"];31 -> 38[label="",style="solid", color="black", weight=3]; 32[label="List.groupByYs1 (==) (vuu300 : vuu301) ([] : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) [] vuu311 ((==) vuu300 : vuu301 []))",fontsize=16,color="black",shape="box"];32 -> 39[label="",style="solid", color="black", weight=3]; 33[label="List.groupByYs1 (==) [] ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) (vuu3100 : vuu3101) vuu311 ((==) [] vuu3100 : vuu3101))",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3]; 34[label="List.groupByYs1 (==) [] ([] : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) [] vuu311 ((==) [] []))",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3]; 35[label="List.groupByZs1 (==) (vuu300 : vuu301) (vuu310 : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) vuu310 vuu311 ((==) vuu300 : vuu301 vuu310))",fontsize=16,color="burlywood",shape="box"];990[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];35 -> 990[label="",style="solid", color="burlywood", weight=9]; 990 -> 42[label="",style="solid", color="burlywood", weight=3]; 991[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];35 -> 991[label="",style="solid", color="burlywood", weight=9]; 991 -> 43[label="",style="solid", color="burlywood", weight=3]; 36[label="List.groupByZs1 (==) [] (vuu310 : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) vuu310 vuu311 ((==) [] vuu310))",fontsize=16,color="burlywood",shape="box"];992[label="vuu310/vuu3100 : vuu3101",fontsize=10,color="white",style="solid",shape="box"];36 -> 992[label="",style="solid", color="burlywood", weight=9]; 992 -> 44[label="",style="solid", color="burlywood", weight=3]; 993[label="vuu310/[]",fontsize=10,color="white",style="solid",shape="box"];36 -> 993[label="",style="solid", color="burlywood", weight=9]; 993 -> 45[label="",style="solid", color="burlywood", weight=3]; 37[label="[]",fontsize=16,color="green",shape="box"];38 -> 194[label="",style="dashed", color="red", weight=0]; 38[label="List.groupByYs1 (==) (vuu300 : vuu301) ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) (vuu3100 : vuu3101) vuu311 (vuu300 == vuu3100 && vuu301 == vuu3101))",fontsize=16,color="magenta"];38 -> 195[label="",style="dashed", color="magenta", weight=3]; 38 -> 196[label="",style="dashed", color="magenta", weight=3]; 38 -> 197[label="",style="dashed", color="magenta", weight=3]; 38 -> 198[label="",style="dashed", color="magenta", weight=3]; 38 -> 199[label="",style="dashed", color="magenta", weight=3]; 38 -> 200[label="",style="dashed", color="magenta", weight=3]; 39[label="List.groupByYs1 (==) (vuu300 : vuu301) ([] : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) [] vuu311 False)",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3]; 40[label="List.groupByYs1 (==) [] ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) (vuu3100 : vuu3101) vuu311 False)",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3]; 41[label="List.groupByYs1 (==) [] ([] : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) [] vuu311 True)",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3]; 42[label="List.groupByZs1 (==) (vuu300 : vuu301) ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) (vuu3100 : vuu3101) vuu311 ((==) vuu300 : vuu301 vuu3100 : vuu3101))",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3]; 43[label="List.groupByZs1 (==) (vuu300 : vuu301) ([] : vuu311) (span2Span1 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) [] vuu311 ((==) vuu300 : vuu301 []))",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3]; 44[label="List.groupByZs1 (==) [] ((vuu3100 : vuu3101) : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) (vuu3100 : vuu3101) vuu311 ((==) [] vuu3100 : vuu3101))",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3]; 45[label="List.groupByZs1 (==) [] ([] : vuu311) (span2Span1 ((==) []) vuu311 ((==) []) [] vuu311 ((==) [] []))",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3]; 195[label="vuu3101",fontsize=16,color="green",shape="box"];196 -> 210[label="",style="dashed", color="red", weight=0]; 196[label="vuu300 == vuu3100 && vuu301 == vuu3101",fontsize=16,color="magenta"];196 -> 211[label="",style="dashed", color="magenta", weight=3]; 196 -> 212[label="",style="dashed", color="magenta", weight=3]; 197[label="vuu3100",fontsize=16,color="green",shape="box"];198[label="vuu300",fontsize=16,color="green",shape="box"];199[label="vuu301",fontsize=16,color="green",shape="box"];200[label="vuu311",fontsize=16,color="green",shape="box"];194[label="List.groupByYs1 (==) (vuu11 : vuu12) ((vuu13 : vuu14) : vuu15) (span2Span1 ((==) vuu11 : vuu12) vuu15 ((==) vuu11 : vuu12) (vuu13 : vuu14) vuu15 vuu31)",fontsize=16,color="burlywood",shape="triangle"];994[label="vuu31/False",fontsize=10,color="white",style="solid",shape="box"];194 -> 994[label="",style="solid", color="burlywood", weight=9]; 994 -> 206[label="",style="solid", color="burlywood", weight=3]; 995[label="vuu31/True",fontsize=10,color="white",style="solid",shape="box"];194 -> 995[label="",style="solid", color="burlywood", weight=9]; 995 -> 207[label="",style="solid", color="burlywood", weight=3]; 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218[label="",style="solid", color="blue", weight=3]; 1000[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 1000[label="",style="solid", color="blue", weight=9]; 1000 -> 219[label="",style="solid", color="blue", weight=3]; 1001[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 1001[label="",style="solid", color="blue", weight=9]; 1001 -> 220[label="",style="solid", color="blue", weight=3]; 1002[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 1002[label="",style="solid", color="blue", weight=9]; 1002 -> 221[label="",style="solid", color="blue", weight=3]; 1003[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 1003[label="",style="solid", color="blue", weight=9]; 1003 -> 222[label="",style="solid", color="blue", weight=3]; 1004[label="== :: Int -> Int -> 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weight=9]; 1008 -> 227[label="",style="solid", color="blue", weight=3]; 1009[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];211 -> 1009[label="",style="solid", color="blue", weight=9]; 1009 -> 228[label="",style="solid", color="blue", weight=3]; 212 -> 62[label="",style="dashed", color="red", weight=0]; 212[label="vuu301 == vuu3101",fontsize=16,color="magenta"];212 -> 229[label="",style="dashed", color="magenta", weight=3]; 212 -> 230[label="",style="dashed", color="magenta", weight=3]; 210[label="vuu36 && vuu37",fontsize=16,color="burlywood",shape="triangle"];1010[label="vuu36/False",fontsize=10,color="white",style="solid",shape="box"];210 -> 1010[label="",style="solid", color="burlywood", weight=9]; 1010 -> 231[label="",style="solid", color="burlywood", weight=3]; 1011[label="vuu36/True",fontsize=10,color="white",style="solid",shape="box"];210 -> 1011[label="",style="solid", color="burlywood", weight=9]; 1011 -> 232[label="",style="solid", color="burlywood", weight=3]; 206[label="List.groupByYs1 (==) (vuu11 : vuu12) ((vuu13 : vuu14) : vuu15) (span2Span1 ((==) vuu11 : vuu12) vuu15 ((==) vuu11 : vuu12) (vuu13 : vuu14) vuu15 False)",fontsize=16,color="black",shape="box"];206 -> 233[label="",style="solid", color="black", weight=3]; 207[label="List.groupByYs1 (==) (vuu11 : vuu12) ((vuu13 : vuu14) : vuu15) (span2Span1 ((==) vuu11 : vuu12) vuu15 ((==) vuu11 : vuu12) (vuu13 : vuu14) vuu15 True)",fontsize=16,color="black",shape="box"];207 -> 234[label="",style="solid", color="black", weight=3]; 76[label="List.groupByYs1 (==) (vuu300 : vuu301) ([] : vuu311) (span2Span0 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) [] vuu311 True)",fontsize=16,color="black",shape="box"];76 -> 111[label="",style="solid", color="black", weight=3]; 77[label="List.groupByYs1 (==) [] ((vuu3100 : vuu3101) : vuu311) (span2Span0 ((==) []) vuu311 ((==) []) (vuu3100 : vuu3101) vuu311 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1013[label="",style="solid", color="blue", weight=9]; 1013 -> 140[label="",style="solid", color="blue", weight=3]; 1014[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1014[label="",style="solid", color="blue", weight=9]; 1014 -> 141[label="",style="solid", color="blue", weight=3]; 1015[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1015[label="",style="solid", color="blue", weight=9]; 1015 -> 142[label="",style="solid", color="blue", weight=3]; 1016[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1016[label="",style="solid", color="blue", weight=9]; 1016 -> 143[label="",style="solid", color="blue", weight=3]; 1017[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1017[label="",style="solid", color="blue", weight=9]; 1017 -> 144[label="",style="solid", color="blue", weight=3]; 1018[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1018[label="",style="solid", color="blue", weight=9]; 1018 -> 145[label="",style="solid", color="blue", weight=3]; 1019[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1019[label="",style="solid", color="blue", weight=9]; 1019 -> 146[label="",style="solid", color="blue", weight=3]; 1020[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1020[label="",style="solid", color="blue", weight=9]; 1020 -> 147[label="",style="solid", color="blue", weight=3]; 1021[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1021[label="",style="solid", color="blue", weight=9]; 1021 -> 148[label="",style="solid", color="blue", weight=3]; 1022[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1022[label="",style="solid", color="blue", weight=9]; 1022 -> 149[label="",style="solid", color="blue", weight=3]; 1023[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1023[label="",style="solid", color="blue", weight=9]; 1023 -> 150[label="",style="solid", color="blue", weight=3]; 1024[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1024[label="",style="solid", color="blue", weight=9]; 1024 -> 151[label="",style="solid", color="blue", weight=3]; 1025[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];132 -> 1025[label="",style="solid", color="blue", weight=9]; 1025 -> 152[label="",style="solid", color="blue", weight=3]; 133[label="vuu311",fontsize=16,color="green",shape="box"];134[label="vuu3100",fontsize=16,color="green",shape="box"];135[label="vuu301",fontsize=16,color="green",shape="box"];128[label="List.groupByZs1 (==) (vuu24 : 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137[label="vuu301",fontsize=16,color="green",shape="box"];138[label="vuu3101",fontsize=16,color="green",shape="box"];139[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1030[label="vuu300/()",fontsize=10,color="white",style="solid",shape="box"];139 -> 1030[label="",style="solid", color="burlywood", weight=9]; 1030 -> 238[label="",style="solid", color="burlywood", weight=3]; 140[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];140 -> 239[label="",style="solid", color="black", weight=3]; 141 -> 62[label="",style="dashed", color="red", weight=0]; 141[label="vuu300 == vuu3100",fontsize=16,color="magenta"];142[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1031[label="vuu300/Integer vuu3000",fontsize=10,color="white",style="solid",shape="box"];142 -> 1031[label="",style="solid", color="burlywood", weight=9]; 1031 -> 240[label="",style="solid", color="burlywood", weight=3]; 143[label="vuu300 == 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145[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];145 -> 245[label="",style="solid", color="black", weight=3]; 146[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1036[label="vuu300/vuu3000 :% vuu3001",fontsize=10,color="white",style="solid",shape="box"];146 -> 1036[label="",style="solid", color="burlywood", weight=9]; 1036 -> 246[label="",style="solid", color="burlywood", weight=3]; 147[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];147 -> 247[label="",style="solid", color="black", weight=3]; 148[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1037[label="vuu300/Left vuu3000",fontsize=10,color="white",style="solid",shape="box"];148 -> 1037[label="",style="solid", color="burlywood", weight=9]; 1037 -> 248[label="",style="solid", color="burlywood", weight=3]; 1038[label="vuu300/Right vuu3000",fontsize=10,color="white",style="solid",shape="box"];148 -> 1038[label="",style="solid", color="burlywood", weight=9]; 1038 -> 249[label="",style="solid", color="burlywood", weight=3]; 149[label="vuu300 == vuu3100",fontsize=16,color="black",shape="triangle"];149 -> 250[label="",style="solid", color="black", weight=3]; 150[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1039[label="vuu300/False",fontsize=10,color="white",style="solid",shape="box"];150 -> 1039[label="",style="solid", color="burlywood", weight=9]; 1039 -> 251[label="",style="solid", color="burlywood", weight=3]; 1040[label="vuu300/True",fontsize=10,color="white",style="solid",shape="box"];150 -> 1040[label="",style="solid", color="burlywood", weight=9]; 1040 -> 252[label="",style="solid", color="burlywood", weight=3]; 151[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1041[label="vuu300/(vuu3000,vuu3001)",fontsize=10,color="white",style="solid",shape="box"];151 -> 1041[label="",style="solid", color="burlywood", weight=9]; 1041 -> 253[label="",style="solid", color="burlywood", weight=3]; 152[label="vuu300 == vuu3100",fontsize=16,color="burlywood",shape="triangle"];1042[label="vuu300/Nothing",fontsize=10,color="white",style="solid",shape="box"];152 -> 1042[label="",style="solid", color="burlywood", weight=9]; 1042 -> 254[label="",style="solid", color="burlywood", weight=3]; 1043[label="vuu300/Just vuu3000",fontsize=10,color="white",style="solid",shape="box"];152 -> 1043[label="",style="solid", color="burlywood", weight=9]; 1043 -> 255[label="",style="solid", color="burlywood", weight=3]; 153[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 (False && vuu30))",fontsize=16,color="black",shape="box"];153 -> 256[label="",style="solid", color="black", weight=3]; 154[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 (True && vuu30))",fontsize=16,color="black",shape="box"];154 -> 257[label="",style="solid", color="black", weight=3]; 155[label="List.groupByZs1 (==) (vuu300 : vuu301) ([] : vuu311) (span2Span0 ((==) vuu300 : vuu301) vuu311 ((==) vuu300 : vuu301) [] vuu311 True)",fontsize=16,color="black",shape="box"];155 -> 258[label="",style="solid", color="black", weight=3]; 156[label="List.groupByZs1 (==) [] ((vuu3100 : vuu3101) : vuu311) (span2Span0 ((==) []) vuu311 ((==) []) (vuu3100 : vuu3101) vuu311 True)",fontsize=16,color="black",shape="box"];156 -> 259[label="",style="solid", color="black", weight=3]; 157[label="span2Zs ((==) []) vuu311",fontsize=16,color="black",shape="triangle"];157 -> 260[label="",style="solid", color="black", weight=3]; 91[label="vuu3000 : vuu3001 == vuu3100",fontsize=16,color="burlywood",shape="box"];1044[label="vuu3100/vuu31000 : vuu31001",fontsize=10,color="white",style="solid",shape="box"];91 -> 1044[label="",style="solid", color="burlywood", weight=9]; 1044 -> 160[label="",style="solid", color="burlywood", weight=3]; 1045[label="vuu3100/[]",fontsize=10,color="white",style="solid",shape="box"];91 -> 1045[label="",style="solid", color="burlywood", weight=9]; 1045 -> 161[label="",style="solid", color="burlywood", weight=3]; 92[label="[] == vuu3100",fontsize=16,color="burlywood",shape="box"];1046[label="vuu3100/vuu31000 : vuu31001",fontsize=10,color="white",style="solid",shape="box"];92 -> 1046[label="",style="solid", color="burlywood", weight=9]; 1046 -> 162[label="",style="solid", color="burlywood", weight=3]; 1047[label="vuu3100/[]",fontsize=10,color="white",style="solid",shape="box"];92 -> 1047[label="",style="solid", color="burlywood", weight=9]; 1047 -> 163[label="",style="solid", color="burlywood", weight=3]; 265[label="False",fontsize=16,color="green",shape="box"];266[label="vuu37",fontsize=16,color="green",shape="box"];267[label="List.groupByYs1 (==) (vuu11 : vuu12) ((vuu13 : vuu14) : vuu15) (span2Span0 ((==) vuu11 : vuu12) vuu15 ((==) vuu11 : vuu12) (vuu13 : vuu14) vuu15 True)",fontsize=16,color="black",shape="box"];267 -> 309[label="",style="solid", color="black", weight=3]; 268[label="(vuu13 : vuu14) : span2Ys ((==) vuu11 : vuu12) vuu15",fontsize=16,color="green",shape="box"];268 -> 310[label="",style="dashed", color="green", weight=3]; 235[label="[]",fontsize=16,color="green",shape="box"];236[label="[]",fontsize=16,color="green",shape="box"];237[label="span2Ys0 ((==) []) vuu311 (span2Vu43 ((==) []) vuu311)",fontsize=16,color="black",shape="box"];237 -> 269[label="",style="solid", color="black", weight=3]; 238[label="() == vuu3100",fontsize=16,color="burlywood",shape="box"];1048[label="vuu3100/()",fontsize=10,color="white",style="solid",shape="box"];238 -> 1048[label="",style="solid", color="burlywood", weight=9]; 1048 -> 270[label="",style="solid", color="burlywood", weight=3]; 239[label="primEqFloat vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];1049[label="vuu300/Float vuu3000 vuu3001",fontsize=10,color="white",style="solid",shape="box"];239 -> 1049[label="",style="solid", color="burlywood", weight=9]; 1049 -> 271[label="",style="solid", color="burlywood", weight=3]; 240[label="Integer vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];1050[label="vuu3100/Integer vuu31000",fontsize=10,color="white",style="solid",shape="box"];240 -> 1050[label="",style="solid", color="burlywood", weight=9]; 1050 -> 272[label="",style="solid", color="burlywood", weight=3]; 241[label="(vuu3000,vuu3001,vuu3002) == vuu3100",fontsize=16,color="burlywood",shape="box"];1051[label="vuu3100/(vuu31000,vuu31001,vuu31002)",fontsize=10,color="white",style="solid",shape="box"];241 -> 1051[label="",style="solid", color="burlywood", weight=9]; 1051 -> 273[label="",style="solid", color="burlywood", weight=3]; 242[label="LT == vuu3100",fontsize=16,color="burlywood",shape="box"];1052[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];242 -> 1052[label="",style="solid", color="burlywood", weight=9]; 1052 -> 274[label="",style="solid", color="burlywood", weight=3]; 1053[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];242 -> 1053[label="",style="solid", color="burlywood", weight=9]; 1053 -> 275[label="",style="solid", color="burlywood", weight=3]; 1054[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];242 -> 1054[label="",style="solid", color="burlywood", weight=9]; 1054 -> 276[label="",style="solid", color="burlywood", weight=3]; 243[label="EQ == vuu3100",fontsize=16,color="burlywood",shape="box"];1055[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];243 -> 1055[label="",style="solid", color="burlywood", weight=9]; 1055 -> 277[label="",style="solid", color="burlywood", weight=3]; 1056[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];243 -> 1056[label="",style="solid", color="burlywood", weight=9]; 1056 -> 278[label="",style="solid", color="burlywood", weight=3]; 1057[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];243 -> 1057[label="",style="solid", color="burlywood", weight=9]; 1057 -> 279[label="",style="solid", color="burlywood", weight=3]; 244[label="GT == vuu3100",fontsize=16,color="burlywood",shape="box"];1058[label="vuu3100/LT",fontsize=10,color="white",style="solid",shape="box"];244 -> 1058[label="",style="solid", color="burlywood", weight=9]; 1058 -> 280[label="",style="solid", color="burlywood", weight=3]; 1059[label="vuu3100/EQ",fontsize=10,color="white",style="solid",shape="box"];244 -> 1059[label="",style="solid", color="burlywood", weight=9]; 1059 -> 281[label="",style="solid", color="burlywood", weight=3]; 1060[label="vuu3100/GT",fontsize=10,color="white",style="solid",shape="box"];244 -> 1060[label="",style="solid", color="burlywood", weight=9]; 1060 -> 282[label="",style="solid", color="burlywood", weight=3]; 245[label="primEqDouble vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];1061[label="vuu300/Double vuu3000 vuu3001",fontsize=10,color="white",style="solid",shape="box"];245 -> 1061[label="",style="solid", color="burlywood", weight=9]; 1061 -> 283[label="",style="solid", color="burlywood", weight=3]; 246[label="vuu3000 :% vuu3001 == vuu3100",fontsize=16,color="burlywood",shape="box"];1062[label="vuu3100/vuu31000 :% vuu31001",fontsize=10,color="white",style="solid",shape="box"];246 -> 1062[label="",style="solid", color="burlywood", weight=9]; 1062 -> 284[label="",style="solid", color="burlywood", weight=3]; 247[label="primEqInt vuu300 vuu3100",fontsize=16,color="burlywood",shape="triangle"];1063[label="vuu300/Pos vuu3000",fontsize=10,color="white",style="solid",shape="box"];247 -> 1063[label="",style="solid", color="burlywood", weight=9]; 1063 -> 285[label="",style="solid", color="burlywood", weight=3]; 1064[label="vuu300/Neg vuu3000",fontsize=10,color="white",style="solid",shape="box"];247 -> 1064[label="",style="solid", color="burlywood", weight=9]; 1064 -> 286[label="",style="solid", color="burlywood", weight=3]; 248[label="Left vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];1065[label="vuu3100/Left vuu31000",fontsize=10,color="white",style="solid",shape="box"];248 -> 1065[label="",style="solid", color="burlywood", weight=9]; 1065 -> 287[label="",style="solid", color="burlywood", weight=3]; 1066[label="vuu3100/Right vuu31000",fontsize=10,color="white",style="solid",shape="box"];248 -> 1066[label="",style="solid", color="burlywood", weight=9]; 1066 -> 288[label="",style="solid", color="burlywood", weight=3]; 249[label="Right vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];1067[label="vuu3100/Left vuu31000",fontsize=10,color="white",style="solid",shape="box"];249 -> 1067[label="",style="solid", color="burlywood", weight=9]; 1067 -> 289[label="",style="solid", color="burlywood", weight=3]; 1068[label="vuu3100/Right vuu31000",fontsize=10,color="white",style="solid",shape="box"];249 -> 1068[label="",style="solid", color="burlywood", weight=9]; 1068 -> 290[label="",style="solid", color="burlywood", weight=3]; 250[label="primEqChar vuu300 vuu3100",fontsize=16,color="burlywood",shape="box"];1069[label="vuu300/Char vuu3000",fontsize=10,color="white",style="solid",shape="box"];250 -> 1069[label="",style="solid", color="burlywood", weight=9]; 1069 -> 291[label="",style="solid", color="burlywood", weight=3]; 251[label="False == vuu3100",fontsize=16,color="burlywood",shape="box"];1070[label="vuu3100/False",fontsize=10,color="white",style="solid",shape="box"];251 -> 1070[label="",style="solid", color="burlywood", weight=9]; 1070 -> 292[label="",style="solid", color="burlywood", weight=3]; 1071[label="vuu3100/True",fontsize=10,color="white",style="solid",shape="box"];251 -> 1071[label="",style="solid", color="burlywood", weight=9]; 1071 -> 293[label="",style="solid", color="burlywood", weight=3]; 252[label="True == vuu3100",fontsize=16,color="burlywood",shape="box"];1072[label="vuu3100/False",fontsize=10,color="white",style="solid",shape="box"];252 -> 1072[label="",style="solid", color="burlywood", weight=9]; 1072 -> 294[label="",style="solid", color="burlywood", weight=3]; 1073[label="vuu3100/True",fontsize=10,color="white",style="solid",shape="box"];252 -> 1073[label="",style="solid", color="burlywood", weight=9]; 1073 -> 295[label="",style="solid", color="burlywood", weight=3]; 253[label="(vuu3000,vuu3001) == vuu3100",fontsize=16,color="burlywood",shape="box"];1074[label="vuu3100/(vuu31000,vuu31001)",fontsize=10,color="white",style="solid",shape="box"];253 -> 1074[label="",style="solid", color="burlywood", weight=9]; 1074 -> 296[label="",style="solid", color="burlywood", weight=3]; 254[label="Nothing == vuu3100",fontsize=16,color="burlywood",shape="box"];1075[label="vuu3100/Nothing",fontsize=10,color="white",style="solid",shape="box"];254 -> 1075[label="",style="solid", color="burlywood", weight=9]; 1075 -> 297[label="",style="solid", color="burlywood", weight=3]; 1076[label="vuu3100/Just vuu31000",fontsize=10,color="white",style="solid",shape="box"];254 -> 1076[label="",style="solid", color="burlywood", weight=9]; 1076 -> 298[label="",style="solid", color="burlywood", weight=3]; 255[label="Just vuu3000 == vuu3100",fontsize=16,color="burlywood",shape="box"];1077[label="vuu3100/Nothing",fontsize=10,color="white",style="solid",shape="box"];255 -> 1077[label="",style="solid", color="burlywood", weight=9]; 1077 -> 299[label="",style="solid", color="burlywood", weight=3]; 1078[label="vuu3100/Just vuu31000",fontsize=10,color="white",style="solid",shape="box"];255 -> 1078[label="",style="solid", color="burlywood", weight=9]; 1078 -> 300[label="",style="solid", color="burlywood", weight=3]; 256[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 False)",fontsize=16,color="black",shape="box"];256 -> 301[label="",style="solid", color="black", weight=3]; 257[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 vuu30)",fontsize=16,color="burlywood",shape="box"];1079[label="vuu30/False",fontsize=10,color="white",style="solid",shape="box"];257 -> 1079[label="",style="solid", color="burlywood", weight=9]; 1079 -> 302[label="",style="solid", color="burlywood", weight=3]; 1080[label="vuu30/True",fontsize=10,color="white",style="solid",shape="box"];257 -> 1080[label="",style="solid", color="burlywood", weight=9]; 1080 -> 303[label="",style="solid", color="burlywood", weight=3]; 258[label="List.groupByZs1 (==) (vuu300 : vuu301) ([] : vuu311) ([],[] : vuu311)",fontsize=16,color="black",shape="box"];258 -> 304[label="",style="solid", color="black", weight=3]; 259[label="List.groupByZs1 (==) [] ((vuu3100 : vuu3101) : vuu311) ([],(vuu3100 : vuu3101) : vuu311)",fontsize=16,color="black",shape="box"];259 -> 305[label="",style="solid", color="black", weight=3]; 260[label="span2Zs0 ((==) []) vuu311 (span2Vu43 ((==) []) vuu311)",fontsize=16,color="black",shape="box"];260 -> 306[label="",style="solid", color="black", weight=3]; 160[label="vuu3000 : vuu3001 == vuu31000 : vuu31001",fontsize=16,color="black",shape="box"];160 -> 261[label="",style="solid", color="black", weight=3]; 161[label="vuu3000 : vuu3001 == []",fontsize=16,color="black",shape="box"];161 -> 262[label="",style="solid", color="black", weight=3]; 162[label="[] == vuu31000 : vuu31001",fontsize=16,color="black",shape="box"];162 -> 263[label="",style="solid", color="black", weight=3]; 163[label="[] == []",fontsize=16,color="black",shape="box"];163 -> 264[label="",style="solid", color="black", weight=3]; 309[label="List.groupByYs1 (==) (vuu11 : vuu12) ((vuu13 : vuu14) : vuu15) ([],(vuu13 : vuu14) : vuu15)",fontsize=16,color="black",shape="box"];309 -> 367[label="",style="solid", color="black", weight=3]; 310[label="span2Ys ((==) vuu11 : vuu12) vuu15",fontsize=16,color="black",shape="triangle"];310 -> 368[label="",style="solid", color="black", weight=3]; 269[label="span2Ys0 ((==) []) vuu311 (span ((==) []) vuu311)",fontsize=16,color="burlywood",shape="box"];1081[label="vuu311/vuu3110 : vuu3111",fontsize=10,color="white",style="solid",shape="box"];269 -> 1081[label="",style="solid", color="burlywood", weight=9]; 1081 -> 311[label="",style="solid", color="burlywood", weight=3]; 1082[label="vuu311/[]",fontsize=10,color="white",style="solid",shape="box"];269 -> 1082[label="",style="solid", color="burlywood", weight=9]; 1082 -> 312[label="",style="solid", color="burlywood", weight=3]; 270[label="() == ()",fontsize=16,color="black",shape="box"];270 -> 313[label="",style="solid", color="black", weight=3]; 271[label="primEqFloat (Float vuu3000 vuu3001) vuu3100",fontsize=16,color="burlywood",shape="box"];1083[label="vuu3100/Float vuu31000 vuu31001",fontsize=10,color="white",style="solid",shape="box"];271 -> 1083[label="",style="solid", color="burlywood", weight=9]; 1083 -> 314[label="",style="solid", color="burlywood", weight=3]; 272[label="Integer vuu3000 == Integer vuu31000",fontsize=16,color="black",shape="box"];272 -> 315[label="",style="solid", color="black", weight=3]; 273[label="(vuu3000,vuu3001,vuu3002) == (vuu31000,vuu31001,vuu31002)",fontsize=16,color="black",shape="box"];273 -> 316[label="",style="solid", color="black", weight=3]; 274[label="LT == LT",fontsize=16,color="black",shape="box"];274 -> 317[label="",style="solid", color="black", weight=3]; 275[label="LT == EQ",fontsize=16,color="black",shape="box"];275 -> 318[label="",style="solid", color="black", weight=3]; 276[label="LT == GT",fontsize=16,color="black",shape="box"];276 -> 319[label="",style="solid", color="black", weight=3]; 277[label="EQ == LT",fontsize=16,color="black",shape="box"];277 -> 320[label="",style="solid", color="black", weight=3]; 278[label="EQ == EQ",fontsize=16,color="black",shape="box"];278 -> 321[label="",style="solid", color="black", weight=3]; 279[label="EQ == GT",fontsize=16,color="black",shape="box"];279 -> 322[label="",style="solid", color="black", weight=3]; 280[label="GT == LT",fontsize=16,color="black",shape="box"];280 -> 323[label="",style="solid", color="black", weight=3]; 281[label="GT == EQ",fontsize=16,color="black",shape="box"];281 -> 324[label="",style="solid", color="black", weight=3]; 282[label="GT == GT",fontsize=16,color="black",shape="box"];282 -> 325[label="",style="solid", color="black", weight=3]; 283[label="primEqDouble (Double vuu3000 vuu3001) vuu3100",fontsize=16,color="burlywood",shape="box"];1084[label="vuu3100/Double vuu31000 vuu31001",fontsize=10,color="white",style="solid",shape="box"];283 -> 1084[label="",style="solid", color="burlywood", weight=9]; 1084 -> 326[label="",style="solid", color="burlywood", weight=3]; 284[label="vuu3000 :% vuu3001 == vuu31000 :% vuu31001",fontsize=16,color="black",shape="box"];284 -> 327[label="",style="solid", color="black", weight=3]; 285[label="primEqInt (Pos vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];1085[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];285 -> 1085[label="",style="solid", color="burlywood", weight=9]; 1085 -> 328[label="",style="solid", color="burlywood", weight=3]; 1086[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];285 -> 1086[label="",style="solid", color="burlywood", weight=9]; 1086 -> 329[label="",style="solid", color="burlywood", weight=3]; 286[label="primEqInt (Neg vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];1087[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];286 -> 1087[label="",style="solid", color="burlywood", weight=9]; 1087 -> 330[label="",style="solid", color="burlywood", weight=3]; 1088[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];286 -> 1088[label="",style="solid", color="burlywood", weight=9]; 1088 -> 331[label="",style="solid", color="burlywood", weight=3]; 287[label="Left vuu3000 == Left vuu31000",fontsize=16,color="black",shape="box"];287 -> 332[label="",style="solid", color="black", weight=3]; 288[label="Left vuu3000 == Right vuu31000",fontsize=16,color="black",shape="box"];288 -> 333[label="",style="solid", color="black", weight=3]; 289[label="Right vuu3000 == Left vuu31000",fontsize=16,color="black",shape="box"];289 -> 334[label="",style="solid", color="black", weight=3]; 290[label="Right vuu3000 == Right vuu31000",fontsize=16,color="black",shape="box"];290 -> 335[label="",style="solid", color="black", weight=3]; 291[label="primEqChar (Char vuu3000) vuu3100",fontsize=16,color="burlywood",shape="box"];1089[label="vuu3100/Char vuu31000",fontsize=10,color="white",style="solid",shape="box"];291 -> 1089[label="",style="solid", color="burlywood", weight=9]; 1089 -> 336[label="",style="solid", color="burlywood", weight=3]; 292[label="False == False",fontsize=16,color="black",shape="box"];292 -> 337[label="",style="solid", color="black", weight=3]; 293[label="False == True",fontsize=16,color="black",shape="box"];293 -> 338[label="",style="solid", color="black", weight=3]; 294[label="True == False",fontsize=16,color="black",shape="box"];294 -> 339[label="",style="solid", color="black", weight=3]; 295[label="True == True",fontsize=16,color="black",shape="box"];295 -> 340[label="",style="solid", color="black", weight=3]; 296[label="(vuu3000,vuu3001) == (vuu31000,vuu31001)",fontsize=16,color="black",shape="box"];296 -> 341[label="",style="solid", color="black", weight=3]; 297[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];297 -> 342[label="",style="solid", color="black", weight=3]; 298[label="Nothing == Just vuu31000",fontsize=16,color="black",shape="box"];298 -> 343[label="",style="solid", color="black", weight=3]; 299[label="Just vuu3000 == Nothing",fontsize=16,color="black",shape="box"];299 -> 344[label="",style="solid", color="black", weight=3]; 300[label="Just vuu3000 == Just vuu31000",fontsize=16,color="black",shape="box"];300 -> 345[label="",style="solid", color="black", weight=3]; 301[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span0 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 otherwise)",fontsize=16,color="black",shape="triangle"];301 -> 346[label="",style="solid", color="black", weight=3]; 302[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 False)",fontsize=16,color="black",shape="box"];302 -> 347[label="",style="solid", color="black", weight=3]; 303[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span1 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : vuu27) vuu28 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308[label="",style="dashed", color="magenta", weight=3]; 262[label="False",fontsize=16,color="green",shape="box"];263[label="False",fontsize=16,color="green",shape="box"];264[label="True",fontsize=16,color="green",shape="box"];367[label="[]",fontsize=16,color="green",shape="box"];368[label="span2Ys0 ((==) vuu11 : vuu12) vuu15 (span2Vu43 ((==) vuu11 : vuu12) vuu15)",fontsize=16,color="black",shape="box"];368 -> 435[label="",style="solid", color="black", weight=3]; 311[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (span ((==) []) (vuu3110 : vuu3111))",fontsize=16,color="black",shape="box"];311 -> 369[label="",style="solid", color="black", weight=3]; 312[label="span2Ys0 ((==) []) [] (span ((==) []) [])",fontsize=16,color="black",shape="box"];312 -> 370[label="",style="solid", color="black", weight=3]; 313[label="True",fontsize=16,color="green",shape="box"];314[label="primEqFloat (Float vuu3000 vuu3001) (Float vuu31000 vuu31001)",fontsize=16,color="black",shape="box"];314 -> 371[label="",style="solid", color="black", weight=3]; 315 -> 247[label="",style="dashed", color="red", weight=0]; 315[label="primEqInt vuu3000 vuu31000",fontsize=16,color="magenta"];315 -> 372[label="",style="dashed", color="magenta", weight=3]; 315 -> 373[label="",style="dashed", color="magenta", weight=3]; 316 -> 210[label="",style="dashed", color="red", weight=0]; 316[label="vuu3000 == vuu31000 && vuu3001 == vuu31001 && vuu3002 == vuu31002",fontsize=16,color="magenta"];316 -> 374[label="",style="dashed", color="magenta", weight=3]; 316 -> 375[label="",style="dashed", color="magenta", weight=3]; 317[label="True",fontsize=16,color="green",shape="box"];318[label="False",fontsize=16,color="green",shape="box"];319[label="False",fontsize=16,color="green",shape="box"];320[label="False",fontsize=16,color="green",shape="box"];321[label="True",fontsize=16,color="green",shape="box"];322[label="False",fontsize=16,color="green",shape="box"];323[label="False",fontsize=16,color="green",shape="box"];324[label="False",fontsize=16,color="green",shape="box"];325[label="True",fontsize=16,color="green",shape="box"];326[label="primEqDouble (Double vuu3000 vuu3001) (Double vuu31000 vuu31001)",fontsize=16,color="black",shape="box"];326 -> 376[label="",style="solid", color="black", weight=3]; 327 -> 210[label="",style="dashed", color="red", weight=0]; 327[label="vuu3000 == vuu31000 && vuu3001 == vuu31001",fontsize=16,color="magenta"];327 -> 377[label="",style="dashed", color="magenta", weight=3]; 327 -> 378[label="",style="dashed", color="magenta", weight=3]; 328[label="primEqInt (Pos (Succ vuu30000)) vuu3100",fontsize=16,color="burlywood",shape="box"];1092[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];328 -> 1092[label="",style="solid", color="burlywood", weight=9]; 1092 -> 379[label="",style="solid", color="burlywood", weight=3]; 1093[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];328 -> 1093[label="",style="solid", color="burlywood", weight=9]; 1093 -> 380[label="",style="solid", color="burlywood", weight=3]; 329[label="primEqInt (Pos Zero) vuu3100",fontsize=16,color="burlywood",shape="box"];1094[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];329 -> 1094[label="",style="solid", color="burlywood", weight=9]; 1094 -> 381[label="",style="solid", color="burlywood", weight=3]; 1095[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];329 -> 1095[label="",style="solid", color="burlywood", weight=9]; 1095 -> 382[label="",style="solid", color="burlywood", weight=3]; 330[label="primEqInt (Neg (Succ vuu30000)) vuu3100",fontsize=16,color="burlywood",shape="box"];1096[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];330 -> 1096[label="",style="solid", color="burlywood", weight=9]; 1096 -> 383[label="",style="solid", color="burlywood", weight=3]; 1097[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];330 -> 1097[label="",style="solid", color="burlywood", weight=9]; 1097 -> 384[label="",style="solid", color="burlywood", weight=3]; 331[label="primEqInt (Neg Zero) vuu3100",fontsize=16,color="burlywood",shape="box"];1098[label="vuu3100/Pos vuu31000",fontsize=10,color="white",style="solid",shape="box"];331 -> 1098[label="",style="solid", color="burlywood", weight=9]; 1098 -> 385[label="",style="solid", color="burlywood", weight=3]; 1099[label="vuu3100/Neg vuu31000",fontsize=10,color="white",style="solid",shape="box"];331 -> 1099[label="",style="solid", color="burlywood", weight=9]; 1099 -> 386[label="",style="solid", color="burlywood", weight=3]; 332[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];1100[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1100[label="",style="solid", color="blue", weight=9]; 1100 -> 387[label="",style="solid", color="blue", weight=3]; 1101[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1101[label="",style="solid", color="blue", weight=9]; 1101 -> 388[label="",style="solid", color="blue", weight=3]; 1102[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1102[label="",style="solid", color="blue", weight=9]; 1102 -> 389[label="",style="solid", color="blue", weight=3]; 1103[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1103[label="",style="solid", color="blue", weight=9]; 1103 -> 390[label="",style="solid", color="blue", weight=3]; 1104[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1104[label="",style="solid", color="blue", weight=9]; 1104 -> 391[label="",style="solid", color="blue", weight=3]; 1105[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1105[label="",style="solid", color="blue", weight=9]; 1105 -> 392[label="",style="solid", color="blue", weight=3]; 1106[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1106[label="",style="solid", color="blue", weight=9]; 1106 -> 393[label="",style="solid", color="blue", weight=3]; 1107[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1107[label="",style="solid", color="blue", weight=9]; 1107 -> 394[label="",style="solid", color="blue", weight=3]; 1108[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1108[label="",style="solid", color="blue", weight=9]; 1108 -> 395[label="",style="solid", color="blue", weight=3]; 1109[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1109[label="",style="solid", color="blue", weight=9]; 1109 -> 396[label="",style="solid", color="blue", weight=3]; 1110[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1110[label="",style="solid", color="blue", weight=9]; 1110 -> 397[label="",style="solid", color="blue", weight=3]; 1111[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1111[label="",style="solid", color="blue", weight=9]; 1111 -> 398[label="",style="solid", color="blue", weight=3]; 1112[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1112[label="",style="solid", color="blue", weight=9]; 1112 -> 399[label="",style="solid", color="blue", weight=3]; 1113[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];332 -> 1113[label="",style="solid", color="blue", weight=9]; 1113 -> 400[label="",style="solid", color="blue", weight=3]; 333[label="False",fontsize=16,color="green",shape="box"];334[label="False",fontsize=16,color="green",shape="box"];335[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];1114[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1114[label="",style="solid", color="blue", weight=9]; 1114 -> 401[label="",style="solid", color="blue", weight=3]; 1115[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1115[label="",style="solid", color="blue", weight=9]; 1115 -> 402[label="",style="solid", color="blue", weight=3]; 1116[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1116[label="",style="solid", color="blue", weight=9]; 1116 -> 403[label="",style="solid", color="blue", weight=3]; 1117[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1117[label="",style="solid", color="blue", weight=9]; 1117 -> 404[label="",style="solid", color="blue", weight=3]; 1118[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1118[label="",style="solid", color="blue", weight=9]; 1118 -> 405[label="",style="solid", color="blue", weight=3]; 1119[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1119[label="",style="solid", color="blue", weight=9]; 1119 -> 406[label="",style="solid", color="blue", weight=3]; 1120[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1120[label="",style="solid", color="blue", weight=9]; 1120 -> 407[label="",style="solid", color="blue", weight=3]; 1121[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1121[label="",style="solid", color="blue", weight=9]; 1121 -> 408[label="",style="solid", color="blue", weight=3]; 1122[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1122[label="",style="solid", color="blue", weight=9]; 1122 -> 409[label="",style="solid", color="blue", weight=3]; 1123[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1123[label="",style="solid", color="blue", weight=9]; 1123 -> 410[label="",style="solid", color="blue", weight=3]; 1124[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1124[label="",style="solid", color="blue", weight=9]; 1124 -> 411[label="",style="solid", color="blue", weight=3]; 1125[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1125[label="",style="solid", color="blue", weight=9]; 1125 -> 412[label="",style="solid", color="blue", weight=3]; 1126[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1126[label="",style="solid", color="blue", weight=9]; 1126 -> 413[label="",style="solid", color="blue", weight=3]; 1127[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];335 -> 1127[label="",style="solid", color="blue", weight=9]; 1127 -> 414[label="",style="solid", color="blue", weight=3]; 336[label="primEqChar (Char vuu3000) (Char vuu31000)",fontsize=16,color="black",shape="box"];336 -> 415[label="",style="solid", color="black", weight=3]; 337[label="True",fontsize=16,color="green",shape="box"];338[label="False",fontsize=16,color="green",shape="box"];339[label="False",fontsize=16,color="green",shape="box"];340[label="True",fontsize=16,color="green",shape="box"];341 -> 210[label="",style="dashed", color="red", weight=0]; 341[label="vuu3000 == vuu31000 && vuu3001 == vuu31001",fontsize=16,color="magenta"];341 -> 416[label="",style="dashed", color="magenta", weight=3]; 341 -> 417[label="",style="dashed", color="magenta", weight=3]; 342[label="True",fontsize=16,color="green",shape="box"];343[label="False",fontsize=16,color="green",shape="box"];344[label="False",fontsize=16,color="green",shape="box"];345[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];1128[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1128[label="",style="solid", color="blue", weight=9]; 1128 -> 418[label="",style="solid", color="blue", weight=3]; 1129[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1129[label="",style="solid", color="blue", weight=9]; 1129 -> 419[label="",style="solid", color="blue", weight=3]; 1130[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1130[label="",style="solid", color="blue", weight=9]; 1130 -> 420[label="",style="solid", color="blue", weight=3]; 1131[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1131[label="",style="solid", color="blue", weight=9]; 1131 -> 421[label="",style="solid", color="blue", weight=3]; 1132[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1132[label="",style="solid", color="blue", weight=9]; 1132 -> 422[label="",style="solid", color="blue", weight=3]; 1133[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1133[label="",style="solid", color="blue", weight=9]; 1133 -> 423[label="",style="solid", color="blue", weight=3]; 1134[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1134[label="",style="solid", color="blue", weight=9]; 1134 -> 424[label="",style="solid", color="blue", weight=3]; 1135[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1135[label="",style="solid", color="blue", weight=9]; 1135 -> 425[label="",style="solid", color="blue", weight=3]; 1136[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1136[label="",style="solid", color="blue", weight=9]; 1136 -> 426[label="",style="solid", color="blue", weight=3]; 1137[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1137[label="",style="solid", color="blue", weight=9]; 1137 -> 427[label="",style="solid", color="blue", weight=3]; 1138[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1138[label="",style="solid", color="blue", weight=9]; 1138 -> 428[label="",style="solid", color="blue", weight=3]; 1139[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1139[label="",style="solid", color="blue", weight=9]; 1139 -> 429[label="",style="solid", color="blue", weight=3]; 1140[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1140[label="",style="solid", color="blue", weight=9]; 1140 -> 430[label="",style="solid", color="blue", weight=3]; 1141[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];345 -> 1141[label="",style="solid", color="blue", weight=9]; 1141 -> 431[label="",style="solid", color="blue", weight=3]; 346[label="List.groupByZs1 (==) (vuu24 : vuu25) ((vuu26 : vuu27) : vuu28) (span2Span0 ((==) vuu24 : vuu25) vuu28 ((==) vuu24 : vuu25) (vuu26 : 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437[label="",style="solid", color="black", weight=3]; 307[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];1142[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1142[label="",style="solid", color="blue", weight=9]; 1142 -> 351[label="",style="solid", color="blue", weight=3]; 1143[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1143[label="",style="solid", color="blue", weight=9]; 1143 -> 352[label="",style="solid", color="blue", weight=3]; 1144[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1144[label="",style="solid", color="blue", weight=9]; 1144 -> 353[label="",style="solid", color="blue", weight=3]; 1145[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1145[label="",style="solid", color="blue", weight=9]; 1145 -> 354[label="",style="solid", color="blue", weight=3]; 1146[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1146[label="",style="solid", color="blue", weight=9]; 1146 -> 355[label="",style="solid", color="blue", weight=3]; 1147[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1147[label="",style="solid", color="blue", weight=9]; 1147 -> 356[label="",style="solid", color="blue", weight=3]; 1148[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1148[label="",style="solid", color="blue", weight=9]; 1148 -> 357[label="",style="solid", color="blue", weight=3]; 1149[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1149[label="",style="solid", color="blue", weight=9]; 1149 -> 358[label="",style="solid", color="blue", weight=3]; 1150[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1150[label="",style="solid", color="blue", weight=9]; 1150 -> 359[label="",style="solid", color="blue", weight=3]; 1151[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1151[label="",style="solid", color="blue", weight=9]; 1151 -> 360[label="",style="solid", color="blue", weight=3]; 1152[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1152[label="",style="solid", color="blue", weight=9]; 1152 -> 361[label="",style="solid", color="blue", weight=3]; 1153[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1153[label="",style="solid", color="blue", weight=9]; 1153 -> 362[label="",style="solid", color="blue", weight=3]; 1154[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];307 -> 1154[label="",style="solid", color="blue", weight=9]; 1154 -> 363[label="",style="solid", color="blue", 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color="magenta", weight=3]; 411 -> 149[label="",style="dashed", color="red", weight=0]; 411[label="vuu3000 == vuu31000",fontsize=16,color="magenta"];411 -> 526[label="",style="dashed", color="magenta", weight=3]; 411 -> 527[label="",style="dashed", color="magenta", weight=3]; 412 -> 150[label="",style="dashed", color="red", weight=0]; 412[label="vuu3000 == vuu31000",fontsize=16,color="magenta"];412 -> 528[label="",style="dashed", color="magenta", weight=3]; 412 -> 529[label="",style="dashed", color="magenta", weight=3]; 413 -> 151[label="",style="dashed", color="red", weight=0]; 413[label="vuu3000 == vuu31000",fontsize=16,color="magenta"];413 -> 530[label="",style="dashed", color="magenta", weight=3]; 413 -> 531[label="",style="dashed", color="magenta", weight=3]; 414 -> 152[label="",style="dashed", color="red", weight=0]; 414[label="vuu3000 == vuu31000",fontsize=16,color="magenta"];414 -> 532[label="",style="dashed", color="magenta", weight=3]; 414 -> 533[label="",style="dashed", color="magenta", weight=3]; 415[label="primEqNat vuu3000 vuu31000",fontsize=16,color="burlywood",shape="triangle"];1188[label="vuu3000/Succ vuu30000",fontsize=10,color="white",style="solid",shape="box"];415 -> 1188[label="",style="solid", color="burlywood", weight=9]; 1188 -> 534[label="",style="solid", color="burlywood", weight=3]; 1189[label="vuu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];415 -> 1189[label="",style="solid", color="burlywood", weight=9]; 1189 -> 535[label="",style="solid", color="burlywood", weight=3]; 416[label="vuu3000 == vuu31000",fontsize=16,color="blue",shape="box"];1190[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1190[label="",style="solid", color="blue", weight=9]; 1190 -> 536[label="",style="solid", color="blue", weight=3]; 1191[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1191[label="",style="solid", color="blue", weight=9]; 1191 -> 537[label="",style="solid", color="blue", weight=3]; 1192[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1192[label="",style="solid", color="blue", weight=9]; 1192 -> 538[label="",style="solid", color="blue", weight=3]; 1193[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1193[label="",style="solid", color="blue", weight=9]; 1193 -> 539[label="",style="solid", color="blue", weight=3]; 1194[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1194[label="",style="solid", color="blue", weight=9]; 1194 -> 540[label="",style="solid", color="blue", weight=3]; 1195[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];416 -> 1195[label="",style="solid", color="blue", weight=9]; 1195 -> 541[label="",style="solid", color="blue", weight=3]; 1196[label="== :: Double -> Double -> 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color="blue", weight=9]; 1222 -> 669[label="",style="solid", color="blue", weight=3]; 1223[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];456 -> 1223[label="",style="solid", color="blue", weight=9]; 1223 -> 670[label="",style="solid", color="blue", weight=3]; 1224[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];456 -> 1224[label="",style="solid", color="blue", weight=9]; 1224 -> 671[label="",style="solid", color="blue", weight=3]; 1225[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];456 -> 1225[label="",style="solid", color="blue", weight=9]; 1225 -> 672[label="",style="solid", color="blue", weight=3]; 1226[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];456 -> 1226[label="",style="solid", color="blue", weight=9]; 1226 -> 673[label="",style="solid", color="blue", weight=3]; 1227[label="== :: (Either a b) -> 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1251[label="vuu39/True",fontsize=10,color="white",style="solid",shape="box"];629 -> 1251[label="",style="solid", color="burlywood", weight=9]; 1251 -> 786[label="",style="solid", color="burlywood", weight=3]; 633[label="[]",fontsize=16,color="green",shape="box"];634[label="primMulInt vuu3000 vuu31001",fontsize=16,color="burlywood",shape="box"];1252[label="vuu3000/Pos vuu30000",fontsize=10,color="white",style="solid",shape="box"];634 -> 1252[label="",style="solid", color="burlywood", weight=9]; 1252 -> 787[label="",style="solid", color="burlywood", weight=3]; 1253[label="vuu3000/Neg vuu30000",fontsize=10,color="white",style="solid",shape="box"];634 -> 1253[label="",style="solid", color="burlywood", weight=9]; 1253 -> 788[label="",style="solid", color="burlywood", weight=3]; 635[label="vuu3001",fontsize=16,color="green",shape="box"];636[label="vuu31000",fontsize=16,color="green",shape="box"];637[label="vuu3000",fontsize=16,color="green",shape="box"];638[label="vuu31000",fontsize=16,color="green",shape="box"];639[label="vuu3000",fontsize=16,color="green",shape="box"];640[label="vuu31000",fontsize=16,color="green",shape="box"];641[label="vuu3000",fontsize=16,color="green",shape="box"];642[label="vuu31000",fontsize=16,color="green",shape="box"];643[label="vuu3000",fontsize=16,color="green",shape="box"];644[label="vuu31000",fontsize=16,color="green",shape="box"];645[label="vuu3000",fontsize=16,color="green",shape="box"];646[label="vuu31000",fontsize=16,color="green",shape="box"];647[label="vuu3000",fontsize=16,color="green",shape="box"];648[label="vuu31000",fontsize=16,color="green",shape="box"];649[label="vuu3000",fontsize=16,color="green",shape="box"];650[label="vuu31000",fontsize=16,color="green",shape="box"];651[label="vuu3000",fontsize=16,color="green",shape="box"];652[label="vuu31000",fontsize=16,color="green",shape="box"];653[label="vuu3000",fontsize=16,color="green",shape="box"];654[label="vuu31000",fontsize=16,color="green",shape="box"];655[label="vuu3000",fontsize=16,color="green",shape="box"];656[label="vuu31000",fontsize=16,color="green",shape="box"];657[label="vuu3000",fontsize=16,color="green",shape="box"];658[label="vuu31000",fontsize=16,color="green",shape="box"];659[label="vuu3000",fontsize=16,color="green",shape="box"];660[label="vuu31000",fontsize=16,color="green",shape="box"];661[label="vuu3000",fontsize=16,color="green",shape="box"];662[label="vuu31000",fontsize=16,color="green",shape="box"];663[label="vuu3000",fontsize=16,color="green",shape="box"];664[label="vuu31000",fontsize=16,color="green",shape="box"];665 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62[label="",style="dashed", color="red", weight=0]; 681[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];681 -> 821[label="",style="dashed", color="magenta", weight=3]; 681 -> 822[label="",style="dashed", color="magenta", weight=3]; 682 -> 142[label="",style="dashed", color="red", weight=0]; 682[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];682 -> 823[label="",style="dashed", color="magenta", weight=3]; 682 -> 824[label="",style="dashed", color="magenta", weight=3]; 683 -> 143[label="",style="dashed", color="red", weight=0]; 683[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];683 -> 825[label="",style="dashed", color="magenta", weight=3]; 683 -> 826[label="",style="dashed", color="magenta", weight=3]; 684 -> 144[label="",style="dashed", color="red", weight=0]; 684[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];684 -> 827[label="",style="dashed", color="magenta", weight=3]; 684 -> 828[label="",style="dashed", color="magenta", weight=3]; 685 -> 145[label="",style="dashed", color="red", weight=0]; 685[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];685 -> 829[label="",style="dashed", color="magenta", weight=3]; 685 -> 830[label="",style="dashed", color="magenta", weight=3]; 686 -> 146[label="",style="dashed", color="red", weight=0]; 686[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];686 -> 831[label="",style="dashed", color="magenta", weight=3]; 686 -> 832[label="",style="dashed", color="magenta", weight=3]; 687 -> 147[label="",style="dashed", color="red", weight=0]; 687[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];687 -> 833[label="",style="dashed", color="magenta", weight=3]; 687 -> 834[label="",style="dashed", color="magenta", weight=3]; 688 -> 148[label="",style="dashed", color="red", weight=0]; 688[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];688 -> 835[label="",style="dashed", color="magenta", weight=3]; 688 -> 836[label="",style="dashed", color="magenta", weight=3]; 689 -> 149[label="",style="dashed", color="red", weight=0]; 689[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];689 -> 837[label="",style="dashed", color="magenta", weight=3]; 689 -> 838[label="",style="dashed", color="magenta", weight=3]; 690 -> 150[label="",style="dashed", color="red", weight=0]; 690[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];690 -> 839[label="",style="dashed", color="magenta", weight=3]; 690 -> 840[label="",style="dashed", color="magenta", weight=3]; 691 -> 151[label="",style="dashed", color="red", weight=0]; 691[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];691 -> 841[label="",style="dashed", color="magenta", weight=3]; 691 -> 842[label="",style="dashed", color="magenta", weight=3]; 692 -> 152[label="",style="dashed", color="red", weight=0]; 692[label="vuu3002 == vuu31002",fontsize=16,color="magenta"];692 -> 843[label="",style="dashed", color="magenta", weight=3]; 692 -> 844[label="",style="dashed", color="magenta", weight=3]; 693[label="vuu3000",fontsize=16,color="green",shape="box"];694[label="vuu31001",fontsize=16,color="green",shape="box"];695[label="vuu3001",fontsize=16,color="green",shape="box"];696[label="vuu31000",fontsize=16,color="green",shape="box"];697[label="vuu3000",fontsize=16,color="green",shape="box"];698[label="vuu31000",fontsize=16,color="green",shape="box"];699[label="vuu3000",fontsize=16,color="green",shape="box"];700[label="vuu31000",fontsize=16,color="green",shape="box"];701[label="vuu3001",fontsize=16,color="green",shape="box"];702[label="vuu31001",fontsize=16,color="green",shape="box"];703[label="vuu3001",fontsize=16,color="green",shape="box"];704[label="vuu31001",fontsize=16,color="green",shape="box"];705 -> 415[label="",style="dashed", color="red", weight=0]; 705[label="primEqNat vuu30000 vuu310000",fontsize=16,color="magenta"];705 -> 845[label="",style="dashed", color="magenta", weight=3]; 705 -> 846[label="",style="dashed", color="magenta", weight=3]; 706[label="False",fontsize=16,color="green",shape="box"];707[label="False",fontsize=16,color="green",shape="box"];708[label="True",fontsize=16,color="green",shape="box"];709[label="False",fontsize=16,color="green",shape="box"];710[label="True",fontsize=16,color="green",shape="box"];711 -> 415[label="",style="dashed", color="red", weight=0]; 711[label="primEqNat vuu30000 vuu310000",fontsize=16,color="magenta"];711 -> 847[label="",style="dashed", color="magenta", weight=3]; 711 -> 848[label="",style="dashed", color="magenta", weight=3]; 712[label="False",fontsize=16,color="green",shape="box"];713[label="False",fontsize=16,color="green",shape="box"];714[label="True",fontsize=16,color="green",shape="box"];715[label="False",fontsize=16,color="green",shape="box"];716[label="True",fontsize=16,color="green",shape="box"];717[label="primEqNat (Succ vuu30000) (Succ vuu310000)",fontsize=16,color="black",shape="box"];717 -> 849[label="",style="solid", color="black", weight=3]; 718[label="primEqNat 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721[label="vuu3000",fontsize=16,color="green",shape="box"];722[label="vuu31000",fontsize=16,color="green",shape="box"];723[label="vuu3000",fontsize=16,color="green",shape="box"];724[label="vuu31000",fontsize=16,color="green",shape="box"];725[label="vuu3000",fontsize=16,color="green",shape="box"];726[label="vuu31000",fontsize=16,color="green",shape="box"];727[label="vuu3000",fontsize=16,color="green",shape="box"];728[label="vuu31000",fontsize=16,color="green",shape="box"];729[label="vuu3000",fontsize=16,color="green",shape="box"];730[label="vuu31000",fontsize=16,color="green",shape="box"];731[label="vuu3000",fontsize=16,color="green",shape="box"];732[label="vuu31000",fontsize=16,color="green",shape="box"];733[label="vuu3000",fontsize=16,color="green",shape="box"];734[label="vuu31000",fontsize=16,color="green",shape="box"];735[label="vuu3000",fontsize=16,color="green",shape="box"];736[label="vuu31000",fontsize=16,color="green",shape="box"];737[label="vuu3000",fontsize=16,color="green",shape="box"];738[label="vuu31000",fontsize=16,color="green",shape="box"];739[label="vuu3000",fontsize=16,color="green",shape="box"];740[label="vuu31000",fontsize=16,color="green",shape="box"];741[label="vuu3000",fontsize=16,color="green",shape="box"];742[label="vuu31000",fontsize=16,color="green",shape="box"];743[label="vuu3000",fontsize=16,color="green",shape="box"];744[label="vuu31000",fontsize=16,color="green",shape="box"];745[label="vuu3000",fontsize=16,color="green",shape="box"];746[label="vuu31000",fontsize=16,color="green",shape="box"];747[label="vuu3000",fontsize=16,color="green",shape="box"];748[label="vuu31000",fontsize=16,color="green",shape="box"];749[label="vuu3001",fontsize=16,color="green",shape="box"];750[label="vuu31001",fontsize=16,color="green",shape="box"];751[label="vuu3001",fontsize=16,color="green",shape="box"];752[label="vuu31001",fontsize=16,color="green",shape="box"];753[label="vuu3001",fontsize=16,color="green",shape="box"];754[label="vuu31001",fontsize=16,color="green",shape="box"];755[label="vuu3001",fontsize=16,color="green",shape="box"];756[label="vuu31001",fontsize=16,color="green",shape="box"];757[label="vuu3001",fontsize=16,color="green",shape="box"];758[label="vuu31001",fontsize=16,color="green",shape="box"];759[label="vuu3001",fontsize=16,color="green",shape="box"];760[label="vuu31001",fontsize=16,color="green",shape="box"];761[label="vuu3001",fontsize=16,color="green",shape="box"];762[label="vuu31001",fontsize=16,color="green",shape="box"];763[label="vuu3001",fontsize=16,color="green",shape="box"];764[label="vuu31001",fontsize=16,color="green",shape="box"];765[label="vuu3001",fontsize=16,color="green",shape="box"];766[label="vuu31001",fontsize=16,color="green",shape="box"];767[label="vuu3001",fontsize=16,color="green",shape="box"];768[label="vuu31001",fontsize=16,color="green",shape="box"];769[label="vuu3001",fontsize=16,color="green",shape="box"];770[label="vuu31001",fontsize=16,color="green",shape="box"];771[label="vuu3001",fontsize=16,color="green",shape="box"];772[label="vuu31001",fontsize=16,color="green",shape="box"];773[label="vuu3001",fontsize=16,color="green",shape="box"];774[label="vuu31001",fontsize=16,color="green",shape="box"];775[label="vuu3001",fontsize=16,color="green",shape="box"];776[label="vuu31001",fontsize=16,color="green",shape="box"];777[label="span2Zs0 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780[label="[]",fontsize=16,color="green",shape="box"];781 -> 858[label="",style="dashed", color="red", weight=0]; 781[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span1 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 ((==) vuu11 : vuu12 vuu150))",fontsize=16,color="magenta"];781 -> 859[label="",style="dashed", color="magenta", weight=3]; 782[label="span2Ys0 ((==) vuu11 : vuu12) [] ([],[])",fontsize=16,color="black",shape="box"];782 -> 860[label="",style="solid", color="black", weight=3]; 783[label="[]",fontsize=16,color="green",shape="box"];784[label="vuu3110",fontsize=16,color="green",shape="box"];785[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (span2Span1 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 False)",fontsize=16,color="black",shape="box"];785 -> 861[label="",style="solid", color="black", weight=3]; 786[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (span2Span1 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];786 -> 862[label="",style="solid", color="black", weight=3]; 787[label="primMulInt (Pos vuu30000) vuu31001",fontsize=16,color="burlywood",shape="box"];1256[label="vuu31001/Pos vuu310010",fontsize=10,color="white",style="solid",shape="box"];787 -> 1256[label="",style="solid", color="burlywood", weight=9]; 1256 -> 863[label="",style="solid", color="burlywood", weight=3]; 1257[label="vuu31001/Neg vuu310010",fontsize=10,color="white",style="solid",shape="box"];787 -> 1257[label="",style="solid", color="burlywood", weight=9]; 1257 -> 864[label="",style="solid", color="burlywood", weight=3]; 788[label="primMulInt (Neg vuu30000) vuu31001",fontsize=16,color="burlywood",shape="box"];1258[label="vuu31001/Pos vuu310010",fontsize=10,color="white",style="solid",shape="box"];788 -> 1258[label="",style="solid", color="burlywood", weight=9]; 1258 -> 865[label="",style="solid", color="burlywood", weight=3]; 1259[label="vuu31001/Neg vuu310010",fontsize=10,color="white",style="solid",shape="box"];788 -> 1259[label="",style="solid", color="burlywood", weight=9]; 1259 -> 866[label="",style="solid", color="burlywood", weight=3]; 789[label="vuu3001",fontsize=16,color="green",shape="box"];790[label="vuu31001",fontsize=16,color="green",shape="box"];791[label="vuu3001",fontsize=16,color="green",shape="box"];792[label="vuu31001",fontsize=16,color="green",shape="box"];793[label="vuu3001",fontsize=16,color="green",shape="box"];794[label="vuu31001",fontsize=16,color="green",shape="box"];795[label="vuu3001",fontsize=16,color="green",shape="box"];796[label="vuu31001",fontsize=16,color="green",shape="box"];797[label="vuu3001",fontsize=16,color="green",shape="box"];798[label="vuu31001",fontsize=16,color="green",shape="box"];799[label="vuu3001",fontsize=16,color="green",shape="box"];800[label="vuu31001",fontsize=16,color="green",shape="box"];801[label="vuu3001",fontsize=16,color="green",shape="box"];802[label="vuu31001",fontsize=16,color="green",shape="box"];803[label="vuu3001",fontsize=16,color="green",shape="box"];804[label="vuu31001",fontsize=16,color="green",shape="box"];805[label="vuu3001",fontsize=16,color="green",shape="box"];806[label="vuu31001",fontsize=16,color="green",shape="box"];807[label="vuu3001",fontsize=16,color="green",shape="box"];808[label="vuu31001",fontsize=16,color="green",shape="box"];809[label="vuu3001",fontsize=16,color="green",shape="box"];810[label="vuu31001",fontsize=16,color="green",shape="box"];811[label="vuu3001",fontsize=16,color="green",shape="box"];812[label="vuu31001",fontsize=16,color="green",shape="box"];813[label="vuu3001",fontsize=16,color="green",shape="box"];814[label="vuu31001",fontsize=16,color="green",shape="box"];815[label="vuu3001",fontsize=16,color="green",shape="box"];816[label="vuu31001",fontsize=16,color="green",shape="box"];817[label="vuu3002",fontsize=16,color="green",shape="box"];818[label="vuu31002",fontsize=16,color="green",shape="box"];819[label="vuu3002",fontsize=16,color="green",shape="box"];820[label="vuu31002",fontsize=16,color="green",shape="box"];821[label="vuu3002",fontsize=16,color="green",shape="box"];822[label="vuu31002",fontsize=16,color="green",shape="box"];823[label="vuu3002",fontsize=16,color="green",shape="box"];824[label="vuu31002",fontsize=16,color="green",shape="box"];825[label="vuu3002",fontsize=16,color="green",shape="box"];826[label="vuu31002",fontsize=16,color="green",shape="box"];827[label="vuu3002",fontsize=16,color="green",shape="box"];828[label="vuu31002",fontsize=16,color="green",shape="box"];829[label="vuu3002",fontsize=16,color="green",shape="box"];830[label="vuu31002",fontsize=16,color="green",shape="box"];831[label="vuu3002",fontsize=16,color="green",shape="box"];832[label="vuu31002",fontsize=16,color="green",shape="box"];833[label="vuu3002",fontsize=16,color="green",shape="box"];834[label="vuu31002",fontsize=16,color="green",shape="box"];835[label="vuu3002",fontsize=16,color="green",shape="box"];836[label="vuu31002",fontsize=16,color="green",shape="box"];837[label="vuu3002",fontsize=16,color="green",shape="box"];838[label="vuu31002",fontsize=16,color="green",shape="box"];839[label="vuu3002",fontsize=16,color="green",shape="box"];840[label="vuu31002",fontsize=16,color="green",shape="box"];841[label="vuu3002",fontsize=16,color="green",shape="box"];842[label="vuu31002",fontsize=16,color="green",shape="box"];843[label="vuu3002",fontsize=16,color="green",shape="box"];844[label="vuu31002",fontsize=16,color="green",shape="box"];845[label="vuu310000",fontsize=16,color="green",shape="box"];846[label="vuu30000",fontsize=16,color="green",shape="box"];847[label="vuu310000",fontsize=16,color="green",shape="box"];848[label="vuu30000",fontsize=16,color="green",shape="box"];849 -> 415[label="",style="dashed", color="red", weight=0]; 849[label="primEqNat vuu30000 vuu310000",fontsize=16,color="magenta"];849 -> 867[label="",style="dashed", color="magenta", weight=3]; 849 -> 868[label="",style="dashed", color="magenta", weight=3]; 850[label="False",fontsize=16,color="green",shape="box"];851[label="False",fontsize=16,color="green",shape="box"];852[label="True",fontsize=16,color="green",shape="box"];853[label="span2Zs0 ((==) vuu24 : vuu25) vuu28 (span ((==) vuu24 : vuu25) vuu28)",fontsize=16,color="burlywood",shape="box"];1260[label="vuu28/vuu280 : vuu281",fontsize=10,color="white",style="solid",shape="box"];853 -> 1260[label="",style="solid", color="burlywood", weight=9]; 1260 -> 869[label="",style="solid", color="burlywood", weight=3]; 1261[label="vuu28/[]",fontsize=10,color="white",style="solid",shape="box"];853 -> 1261[label="",style="solid", color="burlywood", weight=9]; 1261 -> 870[label="",style="solid", color="burlywood", weight=3]; 854[label="[]",fontsize=16,color="green",shape="box"];855[label="vuu3110",fontsize=16,color="green",shape="box"];856[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (span2Span1 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 False)",fontsize=16,color="black",shape="box"];856 -> 871[label="",style="solid", color="black", weight=3]; 857[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (span2Span1 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];857 -> 872[label="",style="solid", color="black", weight=3]; 859 -> 62[label="",style="dashed", color="red", weight=0]; 859[label="(==) vuu11 : vuu12 vuu150",fontsize=16,color="magenta"];859 -> 873[label="",style="dashed", color="magenta", weight=3]; 859 -> 874[label="",style="dashed", color="magenta", weight=3]; 858[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span1 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 vuu41)",fontsize=16,color="burlywood",shape="triangle"];1262[label="vuu41/False",fontsize=10,color="white",style="solid",shape="box"];858 -> 1262[label="",style="solid", color="burlywood", weight=9]; 1262 -> 875[label="",style="solid", color="burlywood", weight=3]; 1263[label="vuu41/True",fontsize=10,color="white",style="solid",shape="box"];858 -> 1263[label="",style="solid", color="burlywood", weight=9]; 1263 -> 876[label="",style="solid", color="burlywood", weight=3]; 860[label="[]",fontsize=16,color="green",shape="box"];861[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (span2Span0 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 otherwise)",fontsize=16,color="black",shape="box"];861 -> 877[label="",style="solid", color="black", weight=3]; 862 -> 878[label="",style="dashed", color="red", weight=0]; 862[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (vuu3110 : span2Ys ((==) []) vuu3111,span2Zs ((==) []) vuu3111)",fontsize=16,color="magenta"];862 -> 879[label="",style="dashed", color="magenta", weight=3]; 862 -> 880[label="",style="dashed", color="magenta", weight=3]; 863[label="primMulInt (Pos vuu30000) (Pos vuu310010)",fontsize=16,color="black",shape="box"];863 -> 881[label="",style="solid", color="black", weight=3]; 864[label="primMulInt (Pos vuu30000) (Neg vuu310010)",fontsize=16,color="black",shape="box"];864 -> 882[label="",style="solid", color="black", weight=3]; 865[label="primMulInt (Neg vuu30000) (Pos vuu310010)",fontsize=16,color="black",shape="box"];865 -> 883[label="",style="solid", color="black", weight=3]; 866[label="primMulInt (Neg vuu30000) (Neg vuu310010)",fontsize=16,color="black",shape="box"];866 -> 884[label="",style="solid", color="black", weight=3]; 867[label="vuu310000",fontsize=16,color="green",shape="box"];868[label="vuu30000",fontsize=16,color="green",shape="box"];869[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span ((==) vuu24 : vuu25) (vuu280 : vuu281))",fontsize=16,color="black",shape="box"];869 -> 885[label="",style="solid", color="black", weight=3]; 870[label="span2Zs0 ((==) vuu24 : vuu25) [] (span ((==) vuu24 : vuu25) [])",fontsize=16,color="black",shape="box"];870 -> 886[label="",style="solid", color="black", weight=3]; 871[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (span2Span0 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 otherwise)",fontsize=16,color="black",shape="box"];871 -> 887[label="",style="solid", color="black", weight=3]; 872 -> 888[label="",style="dashed", color="red", weight=0]; 872[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (vuu3110 : span2Ys ((==) []) vuu3111,span2Zs ((==) []) vuu3111)",fontsize=16,color="magenta"];872 -> 889[label="",style="dashed", color="magenta", weight=3]; 872 -> 890[label="",style="dashed", color="magenta", weight=3]; 873[label="vuu11 : vuu12",fontsize=16,color="green",shape="box"];874[label="vuu150",fontsize=16,color="green",shape="box"];875[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span1 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 False)",fontsize=16,color="black",shape="box"];875 -> 891[label="",style="solid", color="black", weight=3]; 876[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span1 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 True)",fontsize=16,color="black",shape="box"];876 -> 892[label="",style="solid", color="black", weight=3]; 877[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (span2Span0 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];877 -> 893[label="",style="solid", color="black", weight=3]; 879 -> 113[label="",style="dashed", color="red", weight=0]; 879[label="span2Ys ((==) []) vuu3111",fontsize=16,color="magenta"];879 -> 894[label="",style="dashed", color="magenta", weight=3]; 880 -> 157[label="",style="dashed", color="red", weight=0]; 880[label="span2Zs ((==) []) vuu3111",fontsize=16,color="magenta"];880 -> 895[label="",style="dashed", color="magenta", weight=3]; 878[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) (vuu3110 : vuu43,vuu42)",fontsize=16,color="black",shape="triangle"];878 -> 896[label="",style="solid", color="black", weight=3]; 881[label="Pos (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];881 -> 897[label="",style="dashed", color="green", weight=3]; 882[label="Neg (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];882 -> 898[label="",style="dashed", color="green", weight=3]; 883[label="Neg (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];883 -> 899[label="",style="dashed", color="green", weight=3]; 884[label="Pos (primMulNat vuu30000 vuu310010)",fontsize=16,color="green",shape="box"];884 -> 900[label="",style="dashed", color="green", weight=3]; 885[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2 ((==) vuu24 : vuu25) (vuu280 : vuu281))",fontsize=16,color="black",shape="box"];885 -> 901[label="",style="solid", color="black", weight=3]; 886[label="span2Zs0 ((==) vuu24 : vuu25) [] (span3 ((==) vuu24 : vuu25) [])",fontsize=16,color="black",shape="box"];886 -> 902[label="",style="solid", color="black", weight=3]; 887[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (span2Span0 ((==) []) vuu3111 ((==) []) vuu3110 vuu3111 True)",fontsize=16,color="black",shape="box"];887 -> 903[label="",style="solid", color="black", weight=3]; 889 -> 157[label="",style="dashed", color="red", weight=0]; 889[label="span2Zs ((==) []) vuu3111",fontsize=16,color="magenta"];889 -> 904[label="",style="dashed", color="magenta", weight=3]; 890 -> 113[label="",style="dashed", color="red", weight=0]; 890[label="span2Ys ((==) []) vuu3111",fontsize=16,color="magenta"];890 -> 905[label="",style="dashed", color="magenta", weight=3]; 888[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) (vuu3110 : vuu45,vuu44)",fontsize=16,color="black",shape="triangle"];888 -> 906[label="",style="solid", color="black", weight=3]; 891[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span0 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 otherwise)",fontsize=16,color="black",shape="box"];891 -> 907[label="",style="solid", color="black", weight=3]; 892 -> 908[label="",style="dashed", color="red", weight=0]; 892[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (vuu150 : span2Ys ((==) vuu11 : vuu12) vuu151,span2Zs ((==) vuu11 : vuu12) vuu151)",fontsize=16,color="magenta"];892 -> 909[label="",style="dashed", color="magenta", weight=3]; 892 -> 910[label="",style="dashed", color="magenta", weight=3]; 893[label="span2Ys0 ((==) []) (vuu3110 : vuu3111) ([],vuu3110 : vuu3111)",fontsize=16,color="black",shape="box"];893 -> 911[label="",style="solid", color="black", weight=3]; 894[label="vuu3111",fontsize=16,color="green",shape="box"];895[label="vuu3111",fontsize=16,color="green",shape="box"];896[label="vuu3110 : vuu43",fontsize=16,color="green",shape="box"];897[label="primMulNat vuu30000 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vuu310010",fontsize=16,color="magenta"];900 -> 916[label="",style="dashed", color="magenta", weight=3]; 900 -> 917[label="",style="dashed", color="magenta", weight=3]; 901 -> 918[label="",style="dashed", color="red", weight=0]; 901[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span1 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 ((==) vuu24 : vuu25 vuu280))",fontsize=16,color="magenta"];901 -> 919[label="",style="dashed", color="magenta", weight=3]; 902[label="span2Zs0 ((==) vuu24 : vuu25) [] ([],[])",fontsize=16,color="black",shape="box"];902 -> 920[label="",style="solid", color="black", weight=3]; 903[label="span2Zs0 ((==) []) (vuu3110 : vuu3111) ([],vuu3110 : vuu3111)",fontsize=16,color="black",shape="box"];903 -> 921[label="",style="solid", color="black", weight=3]; 904[label="vuu3111",fontsize=16,color="green",shape="box"];905[label="vuu3111",fontsize=16,color="green",shape="box"];906[label="vuu44",fontsize=16,color="green",shape="box"];907[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (span2Span0 ((==) vuu11 : vuu12) vuu151 ((==) vuu11 : vuu12) vuu150 vuu151 True)",fontsize=16,color="black",shape="box"];907 -> 922[label="",style="solid", color="black", weight=3]; 909 -> 596[label="",style="dashed", color="red", weight=0]; 909[label="span2Zs ((==) vuu11 : vuu12) vuu151",fontsize=16,color="magenta"];909 -> 923[label="",style="dashed", color="magenta", weight=3]; 909 -> 924[label="",style="dashed", color="magenta", weight=3]; 909 -> 925[label="",style="dashed", color="magenta", weight=3]; 910 -> 310[label="",style="dashed", color="red", weight=0]; 910[label="span2Ys ((==) vuu11 : vuu12) vuu151",fontsize=16,color="magenta"];910 -> 926[label="",style="dashed", color="magenta", weight=3]; 908[label="span2Ys0 ((==) vuu11 : vuu12) (vuu150 : vuu151) (vuu150 : vuu47,vuu46)",fontsize=16,color="black",shape="triangle"];908 -> 927[label="",style="solid", color="black", weight=3]; 911[label="[]",fontsize=16,color="green",shape="box"];912[label="primMulNat (Succ vuu300000) vuu310010",fontsize=16,color="burlywood",shape="box"];1266[label="vuu310010/Succ vuu3100100",fontsize=10,color="white",style="solid",shape="box"];912 -> 1266[label="",style="solid", color="burlywood", weight=9]; 1266 -> 928[label="",style="solid", color="burlywood", weight=3]; 1267[label="vuu310010/Zero",fontsize=10,color="white",style="solid",shape="box"];912 -> 1267[label="",style="solid", color="burlywood", weight=9]; 1267 -> 929[label="",style="solid", color="burlywood", weight=3]; 913[label="primMulNat Zero vuu310010",fontsize=16,color="burlywood",shape="box"];1268[label="vuu310010/Succ vuu3100100",fontsize=10,color="white",style="solid",shape="box"];913 -> 1268[label="",style="solid", color="burlywood", weight=9]; 1268 -> 930[label="",style="solid", color="burlywood", weight=3]; 1269[label="vuu310010/Zero",fontsize=10,color="white",style="solid",shape="box"];913 -> 1269[label="",style="solid", color="burlywood", weight=9]; 1269 -> 931[label="",style="solid", color="burlywood", weight=3]; 914[label="vuu310010",fontsize=16,color="green",shape="box"];915[label="vuu30000",fontsize=16,color="green",shape="box"];916[label="vuu310010",fontsize=16,color="green",shape="box"];917[label="vuu30000",fontsize=16,color="green",shape="box"];919 -> 62[label="",style="dashed", color="red", weight=0]; 919[label="(==) vuu24 : vuu25 vuu280",fontsize=16,color="magenta"];919 -> 932[label="",style="dashed", color="magenta", weight=3]; 919 -> 933[label="",style="dashed", color="magenta", weight=3]; 918[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span1 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 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923[label="vuu11",fontsize=16,color="green",shape="box"];924[label="vuu151",fontsize=16,color="green",shape="box"];925[label="vuu12",fontsize=16,color="green",shape="box"];926[label="vuu151",fontsize=16,color="green",shape="box"];927[label="vuu150 : vuu47",fontsize=16,color="green",shape="box"];928[label="primMulNat (Succ vuu300000) (Succ vuu3100100)",fontsize=16,color="black",shape="box"];928 -> 937[label="",style="solid", color="black", weight=3]; 929[label="primMulNat (Succ vuu300000) Zero",fontsize=16,color="black",shape="box"];929 -> 938[label="",style="solid", color="black", weight=3]; 930[label="primMulNat Zero (Succ vuu3100100)",fontsize=16,color="black",shape="box"];930 -> 939[label="",style="solid", color="black", weight=3]; 931[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];931 -> 940[label="",style="solid", color="black", weight=3]; 932[label="vuu24 : vuu25",fontsize=16,color="green",shape="box"];933[label="vuu280",fontsize=16,color="green",shape="box"];934[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span1 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 False)",fontsize=16,color="black",shape="box"];934 -> 941[label="",style="solid", color="black", weight=3]; 935[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span1 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 True)",fontsize=16,color="black",shape="box"];935 -> 942[label="",style="solid", color="black", weight=3]; 936[label="[]",fontsize=16,color="green",shape="box"];937 -> 943[label="",style="dashed", color="red", weight=0]; 937[label="primPlusNat (primMulNat vuu300000 (Succ vuu3100100)) (Succ vuu3100100)",fontsize=16,color="magenta"];937 -> 944[label="",style="dashed", color="magenta", weight=3]; 938[label="Zero",fontsize=16,color="green",shape="box"];939[label="Zero",fontsize=16,color="green",shape="box"];940[label="Zero",fontsize=16,color="green",shape="box"];941[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span0 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 otherwise)",fontsize=16,color="black",shape="box"];941 -> 945[label="",style="solid", color="black", weight=3]; 942 -> 946[label="",style="dashed", color="red", weight=0]; 942[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (vuu280 : span2Ys ((==) vuu24 : vuu25) vuu281,span2Zs ((==) vuu24 : vuu25) vuu281)",fontsize=16,color="magenta"];942 -> 947[label="",style="dashed", color="magenta", weight=3]; 942 -> 948[label="",style="dashed", color="magenta", weight=3]; 944 -> 897[label="",style="dashed", color="red", weight=0]; 944[label="primMulNat vuu300000 (Succ vuu3100100)",fontsize=16,color="magenta"];944 -> 949[label="",style="dashed", color="magenta", weight=3]; 944 -> 950[label="",style="dashed", color="magenta", weight=3]; 943[label="primPlusNat vuu49 (Succ vuu3100100)",fontsize=16,color="burlywood",shape="triangle"];1272[label="vuu49/Succ vuu490",fontsize=10,color="white",style="solid",shape="box"];943 -> 1272[label="",style="solid", color="burlywood", weight=9]; 1272 -> 951[label="",style="solid", color="burlywood", weight=3]; 1273[label="vuu49/Zero",fontsize=10,color="white",style="solid",shape="box"];943 -> 1273[label="",style="solid", color="burlywood", weight=9]; 1273 -> 952[label="",style="solid", color="burlywood", weight=3]; 945[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (span2Span0 ((==) vuu24 : vuu25) vuu281 ((==) vuu24 : vuu25) vuu280 vuu281 True)",fontsize=16,color="black",shape="box"];945 -> 953[label="",style="solid", color="black", weight=3]; 947 -> 596[label="",style="dashed", color="red", weight=0]; 947[label="span2Zs ((==) vuu24 : vuu25) vuu281",fontsize=16,color="magenta"];947 -> 954[label="",style="dashed", color="magenta", weight=3]; 948 -> 310[label="",style="dashed", color="red", weight=0]; 948[label="span2Ys ((==) vuu24 : vuu25) vuu281",fontsize=16,color="magenta"];948 -> 955[label="",style="dashed", color="magenta", weight=3]; 948 -> 956[label="",style="dashed", color="magenta", weight=3]; 948 -> 957[label="",style="dashed", color="magenta", weight=3]; 946[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) (vuu280 : vuu51,vuu50)",fontsize=16,color="black",shape="triangle"];946 -> 958[label="",style="solid", color="black", weight=3]; 949[label="Succ vuu3100100",fontsize=16,color="green",shape="box"];950[label="vuu300000",fontsize=16,color="green",shape="box"];951[label="primPlusNat (Succ vuu490) (Succ vuu3100100)",fontsize=16,color="black",shape="box"];951 -> 959[label="",style="solid", color="black", weight=3]; 952[label="primPlusNat Zero (Succ vuu3100100)",fontsize=16,color="black",shape="box"];952 -> 960[label="",style="solid", color="black", weight=3]; 953[label="span2Zs0 ((==) vuu24 : vuu25) (vuu280 : vuu281) ([],vuu280 : vuu281)",fontsize=16,color="black",shape="box"];953 -> 961[label="",style="solid", color="black", weight=3]; 954[label="vuu281",fontsize=16,color="green",shape="box"];955[label="vuu24",fontsize=16,color="green",shape="box"];956[label="vuu25",fontsize=16,color="green",shape="box"];957[label="vuu281",fontsize=16,color="green",shape="box"];958[label="vuu50",fontsize=16,color="green",shape="box"];959[label="Succ (Succ (primPlusNat vuu490 vuu3100100))",fontsize=16,color="green",shape="box"];959 -> 962[label="",style="dashed", color="green", weight=3]; 960[label="Succ vuu3100100",fontsize=16,color="green",shape="box"];961[label="vuu280 : vuu281",fontsize=16,color="green",shape="box"];962[label="primPlusNat vuu490 vuu3100100",fontsize=16,color="burlywood",shape="triangle"];1274[label="vuu490/Succ vuu4900",fontsize=10,color="white",style="solid",shape="box"];962 -> 1274[label="",style="solid", color="burlywood", weight=9]; 1274 -> 963[label="",style="solid", color="burlywood", weight=3]; 1275[label="vuu490/Zero",fontsize=10,color="white",style="solid",shape="box"];962 -> 1275[label="",style="solid", color="burlywood", weight=9]; 1275 -> 964[label="",style="solid", color="burlywood", weight=3]; 963[label="primPlusNat (Succ vuu4900) vuu3100100",fontsize=16,color="burlywood",shape="box"];1276[label="vuu3100100/Succ vuu31001000",fontsize=10,color="white",style="solid",shape="box"];963 -> 1276[label="",style="solid", color="burlywood", weight=9]; 1276 -> 965[label="",style="solid", color="burlywood", weight=3]; 1277[label="vuu3100100/Zero",fontsize=10,color="white",style="solid",shape="box"];963 -> 1277[label="",style="solid", color="burlywood", weight=9]; 1277 -> 966[label="",style="solid", color="burlywood", weight=3]; 964[label="primPlusNat Zero vuu3100100",fontsize=16,color="burlywood",shape="box"];1278[label="vuu3100100/Succ vuu31001000",fontsize=10,color="white",style="solid",shape="box"];964 -> 1278[label="",style="solid", color="burlywood", weight=9]; 1278 -> 967[label="",style="solid", color="burlywood", weight=3]; 1279[label="vuu3100100/Zero",fontsize=10,color="white",style="solid",shape="box"];964 -> 1279[label="",style="solid", color="burlywood", weight=9]; 1279 -> 968[label="",style="solid", color="burlywood", weight=3]; 965[label="primPlusNat (Succ vuu4900) (Succ vuu31001000)",fontsize=16,color="black",shape="box"];965 -> 969[label="",style="solid", color="black", weight=3]; 966[label="primPlusNat (Succ vuu4900) Zero",fontsize=16,color="black",shape="box"];966 -> 970[label="",style="solid", color="black", weight=3]; 967[label="primPlusNat Zero (Succ vuu31001000)",fontsize=16,color="black",shape="box"];967 -> 971[label="",style="solid", color="black", weight=3]; 968[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];968 -> 972[label="",style="solid", color="black", weight=3]; 969[label="Succ (Succ (primPlusNat vuu4900 vuu31001000))",fontsize=16,color="green",shape="box"];969 -> 973[label="",style="dashed", color="green", weight=3]; 970[label="Succ vuu4900",fontsize=16,color="green",shape="box"];971[label="Succ vuu31001000",fontsize=16,color="green",shape="box"];972[label="Zero",fontsize=16,color="green",shape="box"];973 -> 962[label="",style="dashed", color="red", weight=0]; 973[label="primPlusNat vuu4900 vuu31001000",fontsize=16,color="magenta"];973 -> 974[label="",style="dashed", color="magenta", weight=3]; 973 -> 975[label="",style="dashed", color="magenta", weight=3]; 974[label="vuu31001000",fontsize=16,color="green",shape="box"];975[label="vuu4900",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs3(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bdg), bdh)) -> new_esEs1(vuu3000, vuu31000, bdg, bdh) new_esEs1(Left(vuu3000), Left(vuu31000), app(app(ty_Either, gh), ha), gd) -> new_esEs1(vuu3000, vuu31000, gh, ha) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_@2, bg), bh)) -> new_esEs2(vuu3000, vuu31000, bg, bh) new_esEs1(Right(vuu3000), Right(vuu31000), he, app(ty_Maybe, baf)) -> new_esEs3(vuu3000, vuu31000, baf) new_esEs3(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(vuu3000, vuu31000, bdd, bde, bdf) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(app(ty_@3, ea), eb), ec), ce) -> new_esEs0(vuu3001, vuu31001, ea, eb, ec) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(ty_Maybe, eh), ce) -> new_esEs3(vuu3001, vuu31001, eh) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(ty_Maybe, bdb)) -> new_esEs3(vuu3001, vuu31001, bdb) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(ty_@2, bch), bda)) -> new_esEs2(vuu3001, vuu31001, bch, bda) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(ty_[], bcb)) -> new_esEs(vuu3001, vuu31001, bcb) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), cb) -> new_esEs(vuu3001, vuu31001, cb) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(ty_Maybe, gb)) -> new_esEs3(vuu3002, vuu31002, gb) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_Maybe, bbh), bah) -> new_esEs3(vuu3000, vuu31000, bbh) new_esEs3(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bec)) -> new_esEs3(vuu3000, vuu31000, bec) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_Either, db), dc), cd, ce) -> new_esEs1(vuu3000, vuu31000, db, dc) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(ty_@2, fh), ga)) -> new_esEs2(vuu3002, vuu31002, fh, ga) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_[], ba)) -> new_esEs(vuu3000, vuu31000, ba) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_Maybe, df), cd, ce) -> new_esEs3(vuu3000, vuu31000, df) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(ty_@2, ef), eg), ce) -> new_esEs2(vuu3001, vuu31001, ef, eg) new_esEs1(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hd), gd) -> new_esEs3(vuu3000, vuu31000, hd) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_@2, bbf), bbg), bah) -> new_esEs2(vuu3000, vuu31000, bbf, bbg) new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(ty_@2, bad), bae)) -> new_esEs2(vuu3000, vuu31000, bad, bae) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(vuu3000, vuu31000, bb, bc, bd) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(app(ty_@3, fb), fc), fd)) -> new_esEs0(vuu3002, vuu31002, fb, fc, fd) new_esEs1(Left(vuu3000), Left(vuu31000), app(ty_[], gc), gd) -> new_esEs(vuu3000, vuu31000, gc) new_esEs1(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ge), gf), gg), gd) -> new_esEs0(vuu3000, vuu31000, ge, gf, gg) new_esEs3(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bea), beb)) -> new_esEs2(vuu3000, vuu31000, bea, beb) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_Either, be), bf)) -> new_esEs1(vuu3000, vuu31000, be, bf) new_esEs3(Just(vuu3000), Just(vuu31000), app(ty_[], bdc)) -> new_esEs(vuu3000, vuu31000, bdc) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_[], cc), cd, ce) -> new_esEs(vuu3000, vuu31000, cc) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(ty_[], dh), ce) -> new_esEs(vuu3001, vuu31001, dh) new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_Maybe, ca)) -> new_esEs3(vuu3000, vuu31000, ca) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(ty_[], fa)) -> new_esEs(vuu3002, vuu31002, fa) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(ty_Either, ed), ee), ce) -> new_esEs1(vuu3001, vuu31001, ed, ee) new_esEs1(Left(vuu3000), Left(vuu31000), app(app(ty_@2, hb), hc), gd) -> new_esEs2(vuu3000, vuu31000, hb, hc) new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(vuu3000, vuu31000, hg, hh, baa) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_[], bag), bah) -> new_esEs(vuu3000, vuu31000, bag) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_@2, dd), de), cd, ce) -> new_esEs2(vuu3000, vuu31000, dd, de) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(app(ty_@3, bba), bbb), bbc), bah) -> new_esEs0(vuu3000, vuu31000, bba, bbb, bbc) new_esEs1(Right(vuu3000), Right(vuu31000), he, app(ty_[], hf)) -> new_esEs(vuu3000, vuu31000, hf) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_Either, bbd), bbe), bah) -> new_esEs1(vuu3000, vuu31000, bbd, bbe) new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(ty_Either, bab), bac)) -> new_esEs1(vuu3000, vuu31000, bab, bac) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(ty_Either, bcf), bcg)) -> new_esEs1(vuu3001, vuu31001, bcf, bcg) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(app(ty_@3, cf), cg), da), cd, ce) -> new_esEs0(vuu3000, vuu31000, cf, cg, da) new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(ty_Either, ff), fg)) -> new_esEs1(vuu3002, vuu31002, ff, fg) new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(vuu3001, vuu31001, bcc, bcd, bce) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_esEs3(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bec)) -> new_esEs3(vuu3000, vuu31000, bec) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs3(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bdg), bdh)) -> new_esEs1(vuu3000, vuu31000, bdg, bdh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Just(vuu3000), Just(vuu31000), app(ty_[], bdc)) -> new_esEs(vuu3000, vuu31000, bdc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_Maybe, ca)) -> new_esEs3(vuu3000, vuu31000, ca) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_Either, be), bf)) -> new_esEs1(vuu3000, vuu31000, be, bf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs3(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bdd), bde), bdf)) -> new_esEs0(vuu3000, vuu31000, bdd, bde, bdf) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs3(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bea), beb)) -> new_esEs2(vuu3000, vuu31000, bea, beb) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(app(ty_@3, bb), bc), bd)) -> new_esEs0(vuu3000, vuu31000, bb, bc, bd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(app(ty_@2, bg), bh)) -> new_esEs2(vuu3000, vuu31000, bg, bh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(Right(vuu3000), Right(vuu31000), he, app(ty_Maybe, baf)) -> new_esEs3(vuu3000, vuu31000, baf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(Left(vuu3000), Left(vuu31000), app(ty_Maybe, hd), gd) -> new_esEs3(vuu3000, vuu31000, hd) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(Left(vuu3000), Left(vuu31000), app(app(ty_Either, gh), ha), gd) -> new_esEs1(vuu3000, vuu31000, gh, ha) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(ty_Either, bab), bac)) -> new_esEs1(vuu3000, vuu31000, bab, bac) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(Left(vuu3000), Left(vuu31000), app(ty_[], gc), gd) -> new_esEs(vuu3000, vuu31000, gc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs1(Right(vuu3000), Right(vuu31000), he, app(ty_[], hf)) -> new_esEs(vuu3000, vuu31000, hf) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs1(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ge), gf), gg), gd) -> new_esEs0(vuu3000, vuu31000, ge, gf, gg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(vuu3000, vuu31000, hg, hh, baa) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs1(Right(vuu3000), Right(vuu31000), he, app(app(ty_@2, bad), bae)) -> new_esEs2(vuu3000, vuu31000, bad, bae) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs1(Left(vuu3000), Left(vuu31000), app(app(ty_@2, hb), hc), gd) -> new_esEs2(vuu3000, vuu31000, hb, hc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(ty_Maybe, bdb)) -> new_esEs3(vuu3001, vuu31001, bdb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_Maybe, bbh), bah) -> new_esEs3(vuu3000, vuu31000, bbh) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(ty_Maybe, eh), ce) -> new_esEs3(vuu3001, vuu31001, eh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(ty_Maybe, gb)) -> new_esEs3(vuu3002, vuu31002, gb) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_Maybe, df), cd, ce) -> new_esEs3(vuu3000, vuu31000, df) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_Either, bbd), bbe), bah) -> new_esEs1(vuu3000, vuu31000, bbd, bbe) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(ty_Either, bcf), bcg)) -> new_esEs1(vuu3001, vuu31001, bcf, bcg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_Either, db), dc), cd, ce) -> new_esEs1(vuu3000, vuu31000, db, dc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(ty_Either, ed), ee), ce) -> new_esEs1(vuu3001, vuu31001, ed, ee) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(ty_Either, ff), fg)) -> new_esEs1(vuu3002, vuu31002, ff, fg) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(ty_[], bcb)) -> new_esEs(vuu3001, vuu31001, bcb) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(ty_[], bag), bah) -> new_esEs(vuu3000, vuu31000, bag) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(app(ty_@3, bba), bbb), bbc), bah) -> new_esEs0(vuu3000, vuu31000, bba, bbb, bbc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs0(vuu3001, vuu31001, bcc, bcd, bce) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bca, app(app(ty_@2, bch), bda)) -> new_esEs2(vuu3001, vuu31001, bch, bda) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs2(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), app(app(ty_@2, bbf), bbg), bah) -> new_esEs2(vuu3000, vuu31000, bbf, bbg) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(ty_[], cc), cd, ce) -> new_esEs(vuu3000, vuu31000, cc) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(ty_[], dh), ce) -> new_esEs(vuu3001, vuu31001, dh) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(ty_[], fa)) -> new_esEs(vuu3002, vuu31002, fa) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), cb) -> new_esEs(vuu3001, vuu31001, cb) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 *new_esEs(:(vuu3000, vuu3001), :(vuu31000, vuu31001), app(ty_[], ba)) -> new_esEs(vuu3000, vuu31000, ba) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(app(ty_@3, ea), eb), ec), ce) -> new_esEs0(vuu3001, vuu31001, ea, eb, ec) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(app(ty_@3, fb), fc), fd)) -> new_esEs0(vuu3002, vuu31002, fb, fc, fd) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(app(ty_@3, cf), cg), da), cd, ce) -> new_esEs0(vuu3000, vuu31000, cf, cg, da) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, cd, app(app(ty_@2, fh), ga)) -> new_esEs2(vuu3002, vuu31002, fh, ga) The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), dg, app(app(ty_@2, ef), eg), ce) -> new_esEs2(vuu3001, vuu31001, ef, eg) The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 *new_esEs0(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), app(app(ty_@2, dd), de), cd, ce) -> new_esEs2(vuu3000, vuu31000, dd, de) The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_span2Zs00(vuu24, vuu25, vuu280, vuu281, True, bb) -> new_span2Zs1(vuu24, vuu25, vuu281, bb) new_span2Zs1(vuu24, vuu25, :(vuu280, vuu281), bb) -> new_span2Zs00(vuu24, vuu25, vuu280, vuu281, new_esEs4(:(vuu24, vuu25), vuu280, bb), bb) new_span2Zs00(vuu24, vuu25, vuu280, vuu281, True, bb) -> new_span2Ys1(vuu24, vuu25, vuu281, bb) new_span2Ys1(vuu11, vuu12, :(vuu150, vuu151), ba) -> new_span2Ys00(vuu11, vuu12, vuu150, vuu151, new_esEs4(:(vuu11, vuu12), vuu150, ba), ba) new_span2Ys00(vuu11, vuu12, vuu150, vuu151, True, ba) -> new_span2Zs1(vuu11, vuu12, vuu151, ba) new_span2Ys00(vuu11, vuu12, vuu150, vuu151, True, ba) -> new_span2Ys1(vuu11, vuu12, vuu151, ba) The TRS R consists of the following rules: new_esEs24(vuu3001, vuu31001, app(ty_Maybe, bef)) -> new_esEs21(vuu3001, vuu31001, bef) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(vuu3000, vuu31000, app(app(ty_Either, fa), fb)) -> new_esEs19(vuu3000, vuu31000, fa, fb) new_esEs25(vuu3002, vuu31002, ty_@0) -> new_esEs5(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(vuu3000, vuu31000, app(app(app(ty_@3, bg), bh), ca)) -> new_esEs18(vuu3000, vuu31000, bg, bh, ca) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_Either, ge), gf), fg) -> new_esEs19(vuu3000, vuu31000, ge, gf) new_esEs23(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, app(ty_Maybe, eb)) -> new_esEs21(vuu3001, vuu31001, eb) new_esEs4(:(vuu3000, vuu3001), :(vuu31000, vuu31001), ec) -> new_asAs(new_esEs22(vuu3000, vuu31000, ec), new_esEs4(vuu3001, vuu31001, ec)) new_esEs23(vuu3000, vuu31000, app(app(app(ty_@3, bcd), bce), bcf)) -> new_esEs18(vuu3000, vuu31000, bcd, bce, bcf) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs20(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, app(ty_[], da)) -> new_esEs4(vuu3001, vuu31001, da) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs22(vuu3000, vuu31000, app(ty_[], ed)) -> new_esEs4(vuu3000, vuu31000, ed) new_asAs(True, vuu37) -> vuu37 new_esEs16(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, ff)) -> new_esEs21(vuu3000, vuu31000, ff) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Integer) -> new_esEs9(vuu3000, vuu31000) 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_esEs15(vuu3000, vuu31000, app(ty_Ratio, cb)) -> new_esEs6(vuu3000, vuu31000, cb) new_esEs15(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bbe), bbf)) -> new_esEs14(vuu3000, vuu31000, bbe, bbf) new_esEs15(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs18(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), bbh, bca, bcb) -> new_asAs(new_esEs23(vuu3000, vuu31000, bbh), new_asAs(new_esEs24(vuu3001, vuu31001, bca), new_esEs25(vuu3002, vuu31002, bcb))) new_esEs16(vuu3001, vuu31001, app(app(ty_Either, df), dg)) -> new_esEs19(vuu3001, vuu31001, df, dg) new_esEs15(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_[], bde)) -> new_esEs4(vuu3001, vuu31001, bde) new_esEs12(False, True) -> False new_esEs12(True, False) -> False new_primMulNat0(Zero, Zero) -> Zero new_esEs12(True, True) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Maybe, ha), fg) -> new_esEs21(vuu3000, vuu31000, ha) new_esEs15(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, app(app(ty_@2, dh), ea)) -> new_esEs14(vuu3001, vuu31001, dh, ea) new_esEs21(Nothing, Just(vuu31000), bae) -> False new_esEs21(Just(vuu3000), Nothing, bae) -> False new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs21(Nothing, Nothing, bae) -> True new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs9(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Double, fg) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(ty_Maybe, bad)) -> new_esEs21(vuu3000, vuu31000, bad) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bbg)) -> new_esEs21(vuu3000, vuu31000, bbg) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, ty_Double) -> new_esEs13(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, ty_Char) -> new_esEs20(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, beb), bec)) -> new_esEs19(vuu3001, vuu31001, beb, bec) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs13(vuu3000, vuu31000) new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(app(ty_@2, bab), bac)) -> new_esEs14(vuu3000, vuu31000, bab, bac) new_esEs16(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Ratio, gd), fg) -> new_esEs6(vuu3000, vuu31000, gd) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Float, fg) -> new_esEs17(vuu3000, vuu31000) new_esEs11(EQ, EQ) -> True new_esEs17(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Float) -> new_esEs17(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(ty_Ratio, hg)) -> new_esEs6(vuu3000, vuu31000, hg) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_esEs19(Left(vuu3000), Left(vuu31000), ty_@0, fg) -> new_esEs5(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bbb)) -> new_esEs6(vuu3000, vuu31000, bbb) new_esEs15(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, ee), ef), eg)) -> new_esEs18(vuu3000, vuu31000, ee, ef, eg) new_esEs25(vuu3002, vuu31002, app(ty_Ratio, bfc)) -> new_esEs6(vuu3002, vuu31002, bfc) new_esEs16(vuu3001, vuu31001, app(app(app(ty_@3, db), dc), dd)) -> new_esEs18(vuu3001, vuu31001, db, dc, dd) new_esEs16(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(app(ty_@2, ce), cf)) -> new_esEs14(vuu3000, vuu31000, ce, cf) new_esEs25(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(app(ty_Either, hh), baa)) -> new_esEs19(vuu3000, vuu31000, hh, baa) new_esEs15(vuu3000, vuu31000, app(app(ty_Either, cc), cd)) -> new_esEs19(vuu3000, vuu31000, cc, cd) new_esEs12(False, False) -> True new_esEs15(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_[], bf)) -> new_esEs4(vuu3000, vuu31000, bf) new_esEs23(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs23(vuu3000, vuu31000, app(ty_[], bcc)) -> new_esEs4(vuu3000, vuu31000, bcc) new_esEs25(vuu3002, vuu31002, app(ty_Maybe, bfh)) -> new_esEs21(vuu3002, vuu31002, bfh) new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_esEs23(vuu3000, vuu31000, app(app(ty_Either, bch), bda)) -> new_esEs19(vuu3000, vuu31000, bch, bda) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Ordering, fg) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs14(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bd, be) -> new_asAs(new_esEs15(vuu3000, vuu31000, bd), new_esEs16(vuu3001, vuu31001, be)) new_esEs16(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_primPlusNat0(Succ(vuu4900), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu4900, vuu31001000))) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_esEs8(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs18(vuu3001, vuu31001, bdf, bdg, bdh) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Char, fg) -> new_esEs20(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_Maybe, cg)) -> new_esEs21(vuu3000, vuu31000, cg) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, fc), fd)) -> new_esEs14(vuu3000, vuu31000, fc, fd) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Bool, fg) -> new_esEs12(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, bea)) -> new_esEs6(vuu3001, vuu31001, bea) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_@2, gg), gh), fg) -> new_esEs14(vuu3000, vuu31000, gg, gh) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_esEs25(vuu3002, vuu31002, app(app(ty_@2, bff), bfg)) -> new_esEs14(vuu3002, vuu31002, bff, bfg) new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, app(app(ty_Either, bfd), bfe)) -> new_esEs19(vuu3002, vuu31002, bfd, bfe) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs10(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bbc), bbd)) -> new_esEs19(vuu3000, vuu31000, bbc, bbd) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), hb, ty_Bool) -> new_esEs12(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_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs6(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bc) -> new_asAs(new_esEs7(vuu3000, vuu31000, bc), new_esEs8(vuu3001, vuu31001, bc)) new_primPlusNat1(Succ(vuu490), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu490, vuu3100100))) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs13(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Int) -> new_esEs10(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(app(app(ty_@3, hd), he), hf)) -> new_esEs18(vuu3000, vuu31000, hd, he, hf) new_primPlusNat0(Succ(vuu4900), Zero) -> Succ(vuu4900) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bed), bee)) -> new_esEs14(vuu3001, vuu31001, bed, bee) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ga), gb), gc), fg) -> new_esEs18(vuu3000, vuu31000, ga, gb, gc) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs23(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs8(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Ratio, eh)) -> new_esEs6(vuu3000, vuu31000, eh) new_esEs4(:(vuu3000, vuu3001), [], ec) -> False new_esEs4([], :(vuu31000, vuu31001), ec) -> False new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Int, fg) -> new_esEs10(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs23(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(app(ty_@2, bdb), bdc)) -> new_esEs14(vuu3000, vuu31000, bdb, bdc) new_esEs23(vuu3000, vuu31000, app(ty_Ratio, bcg)) -> new_esEs6(vuu3000, vuu31000, bcg) new_esEs25(vuu3002, vuu31002, ty_Bool) -> new_esEs12(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, app(ty_[], beg)) -> new_esEs4(vuu3002, vuu31002, beg) new_esEs16(vuu3001, vuu31001, app(ty_Ratio, de)) -> new_esEs6(vuu3001, vuu31001, de) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_[], baf)) -> new_esEs4(vuu3000, vuu31000, baf) new_esEs23(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_primEqNat0(Zero, Zero) -> True new_esEs4([], [], ec) -> True new_esEs21(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), hb, app(ty_[], hc)) -> new_esEs4(vuu3000, vuu31000, hc) new_asAs(False, vuu37) -> False new_esEs25(vuu3002, vuu31002, ty_Integer) -> new_esEs9(vuu3002, vuu31002) new_esEs19(Left(vuu3000), Right(vuu31000), hb, fg) -> False new_esEs19(Right(vuu3000), Left(vuu31000), hb, fg) -> False new_esEs21(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bag), bah), bba)) -> new_esEs18(vuu3000, vuu31000, bag, bah, bba) new_esEs25(vuu3002, vuu31002, app(app(app(ty_@3, beh), bfa), bfb)) -> new_esEs18(vuu3002, vuu31002, beh, bfa, bfb) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Integer, fg) -> new_esEs9(vuu3000, vuu31000) new_esEs7(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(ty_Maybe, bdd)) -> new_esEs21(vuu3000, vuu31000, bdd) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs5(@0, @0) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_[], fh), fg) -> new_esEs4(vuu3000, vuu31000, fh) new_esEs7(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) The set Q consists of the following terms: new_esEs21(Just(x0), Just(x1), ty_Char) new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs15(x0, x1, ty_@0) new_esEs25(x0, x1, ty_Ordering) new_asAs(False, x0) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(Right(x0), Right(x1), x2, ty_Bool) new_esEs8(x0, x1, ty_Integer) new_esEs24(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs16(x0, x1, app(app(ty_@2, x2), x3)) new_esEs9(Integer(x0), Integer(x1)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_esEs25(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs19(Right(x0), Right(x1), x2, ty_@0) new_esEs21(Just(x0), Just(x1), ty_Int) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs24(x0, x1, ty_Ordering) new_esEs16(x0, x1, ty_@0) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs15(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(Left(x0), Left(x1), ty_Float, x2) new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5) new_esEs19(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_primPlusNat0(Zero, Succ(x0)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs4([], [], x0) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Integer) new_primEqNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Integer) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs22(x0, x1, ty_Double) new_esEs21(Nothing, Nothing, x0) new_esEs24(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs19(Right(x0), Right(x1), x2, ty_Integer) new_esEs19(Left(x0), Left(x1), ty_Integer, x2) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs15(x0, x1, ty_Integer) new_esEs15(x0, x1, app(ty_Ratio, x2)) new_primPlusNat0(Zero, Zero) new_esEs12(False, True) new_esEs12(True, False) new_esEs23(x0, x1, ty_Ordering) new_esEs21(Just(x0), Just(x1), ty_Double) new_esEs21(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs24(x0, x1, ty_Integer) new_esEs21(Just(x0), Just(x1), ty_@0) new_esEs19(Right(x0), Right(x1), x2, ty_Char) new_esEs21(Just(x0), Just(x1), ty_Float) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs12(False, False) new_esEs24(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), ty_Bool) new_esEs23(x0, x1, ty_Float) new_esEs22(x0, x1, ty_Bool) new_esEs19(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs19(Left(x0), Left(x1), ty_Ordering, x2) new_esEs19(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_sr(Pos(x0), Pos(x1)) new_esEs24(x0, x1, ty_Char) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs16(x0, x1, ty_Double) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs19(Right(x0), Right(x1), x2, ty_Int) new_esEs22(x0, x1, ty_Integer) new_esEs16(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs19(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs16(x0, x1, ty_Bool) new_esEs11(EQ, EQ) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs16(x0, x1, app(ty_Maybe, x2)) new_primMulNat0(Succ(x0), Zero) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs21(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs24(x0, x1, ty_Bool) new_esEs19(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs19(Right(x0), Right(x1), x2, ty_Float) new_esEs19(Right(x0), Right(x1), x2, ty_Double) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs13(Double(x0, x1), Double(x2, x3)) new_esEs15(x0, x1, ty_Double) new_esEs21(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs8(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), x1) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs20(Char(x0), Char(x1)) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs23(x0, x1, ty_Char) new_esEs16(x0, x1, ty_Ordering) new_esEs15(x0, x1, ty_Ordering) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_primMulNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Int) new_esEs15(x0, x1, app(app(ty_Either, x2), x3)) new_esEs15(x0, x1, app(ty_Maybe, x2)) new_esEs19(Right(x0), Right(x1), x2, ty_Ordering) new_esEs4([], :(x0, x1), x2) new_esEs19(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs7(x0, x1, ty_Int) new_esEs25(x0, x1, ty_@0) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs19(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(x0, x1, ty_Float) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs19(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs19(Left(x0), Left(x1), ty_@0, x2) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs15(x0, x1, app(ty_[], x2)) new_esEs21(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs21(Nothing, Just(x0), x1) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs10(x0, x1) new_esEs23(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs21(Just(x0), Nothing, x1) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs4(:(x0, x1), [], x2) new_esEs23(x0, x1, ty_@0) new_esEs17(Float(x0, x1), Float(x2, x3)) new_asAs(True, x0) new_esEs15(x0, x1, ty_Float) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(Just(x0), Just(x1), ty_Integer) new_esEs5(@0, @0) new_esEs24(x0, x1, ty_@0) new_esEs22(x0, x1, ty_Char) new_esEs11(GT, GT) new_esEs25(x0, x1, ty_Integer) new_esEs19(Left(x0), Right(x1), x2, x3) new_esEs19(Right(x0), Left(x1), x2, x3) new_esEs21(Just(x0), Just(x1), app(ty_[], x2)) new_primEqNat0(Zero, Zero) new_esEs23(x0, x1, ty_Bool) new_esEs12(True, True) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs15(x0, x1, ty_Char) new_primPlusNat1(Zero, x0) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs16(x0, x1, app(ty_[], x2)) new_esEs21(Just(x0), Just(x1), ty_Ordering) new_esEs19(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs16(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_esEs16(x0, x1, app(app(ty_Either, x2), x3)) new_esEs11(LT, LT) new_esEs19(Left(x0), Left(x1), ty_Int, x2) new_esEs22(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Double) new_esEs15(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_esEs19(Left(x0), Left(x1), ty_Double, x2) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs25(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs4(:(x0, x1), :(x2, x3), x4) new_esEs25(x0, x1, ty_Double) new_esEs19(Left(x0), Left(x1), ty_Char, x2) new_esEs19(Left(x0), Left(x1), ty_Bool, x2) new_esEs7(x0, x1, ty_Integer) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs15(x0, x1, ty_Bool) new_esEs25(x0, x1, ty_Bool) new_esEs22(x0, x1, ty_Float) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_primEqNat0(Succ(x0), Succ(x1)) 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_span2Zs1(vuu24, vuu25, :(vuu280, vuu281), bb) -> new_span2Zs00(vuu24, vuu25, vuu280, vuu281, new_esEs4(:(vuu24, vuu25), vuu280, bb), bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 4 >= 6 *new_span2Zs00(vuu24, vuu25, vuu280, vuu281, True, bb) -> new_span2Zs1(vuu24, vuu25, vuu281, bb) The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 6 >= 4 *new_span2Zs00(vuu24, vuu25, vuu280, vuu281, True, bb) -> new_span2Ys1(vuu24, vuu25, vuu281, bb) The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 6 >= 4 *new_span2Ys00(vuu11, vuu12, vuu150, vuu151, True, ba) -> new_span2Zs1(vuu11, vuu12, vuu151, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 6 >= 4 *new_span2Ys1(vuu11, vuu12, :(vuu150, vuu151), ba) -> new_span2Ys00(vuu11, vuu12, vuu150, vuu151, new_esEs4(:(vuu11, vuu12), vuu150, ba), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 4 >= 6 *new_span2Ys00(vuu11, vuu12, vuu150, vuu151, True, ba) -> new_span2Ys1(vuu11, vuu12, vuu151, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 3, 6 >= 4 ---------------------------------------- (16) YES ---------------------------------------- (17) 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. ---------------------------------------- (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_primMulNat(Succ(vuu300000), Succ(vuu3100100)) -> new_primMulNat(vuu300000, Succ(vuu3100100)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_span2Ys(:(vuu3110, vuu3111), ba) -> new_span2Ys0(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) new_span2Ys0(vuu3110, vuu3111, True, ba) -> new_span2Zs(vuu3111, ba) new_span2Zs0(vuu3110, vuu3111, True, ba) -> new_span2Ys(vuu3111, ba) new_span2Ys0(vuu3110, vuu3111, True, ba) -> new_span2Ys(vuu3111, ba) new_span2Zs0(vuu3110, vuu3111, True, ba) -> new_span2Zs(vuu3111, ba) new_span2Zs(:(vuu3110, vuu3111), ba) -> new_span2Zs0(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) The TRS R consists of the following rules: new_esEs24(vuu3001, vuu31001, app(ty_Maybe, bee)) -> new_esEs21(vuu3001, vuu31001, bee) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_primPlusNat0(Zero, Zero) -> Zero new_esEs22(vuu3000, vuu31000, app(app(ty_Either, eh), fa)) -> new_esEs19(vuu3000, vuu31000, eh, fa) new_esEs25(vuu3002, vuu31002, ty_@0) -> new_esEs5(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(vuu3000, vuu31000, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs18(vuu3000, vuu31000, bf, bg, bh) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_Either, gd), ge), ff) -> new_esEs19(vuu3000, vuu31000, gd, ge) new_esEs23(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, app(ty_Maybe, ea)) -> new_esEs21(vuu3001, vuu31001, ea) new_esEs4(:(vuu3000, vuu3001), :(vuu31000, vuu31001), eb) -> new_asAs(new_esEs22(vuu3000, vuu31000, eb), new_esEs4(vuu3001, vuu31001, eb)) new_esEs23(vuu3000, vuu31000, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs18(vuu3000, vuu31000, bcc, bcd, bce) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs20(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, app(ty_[], cg)) -> new_esEs4(vuu3001, vuu31001, cg) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs22(vuu3000, vuu31000, app(ty_[], ec)) -> new_esEs4(vuu3000, vuu31000, ec) new_asAs(True, vuu37) -> vuu37 new_esEs16(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, fd)) -> new_esEs21(vuu3000, vuu31000, fd) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Integer) -> new_esEs9(vuu3000, vuu31000) 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_esEs15(vuu3000, vuu31000, app(ty_Ratio, ca)) -> new_esEs6(vuu3000, vuu31000, ca) new_esEs15(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bbd), bbe)) -> new_esEs14(vuu3000, vuu31000, bbd, bbe) new_esEs15(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs18(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), bbg, bbh, bca) -> new_asAs(new_esEs23(vuu3000, vuu31000, bbg), new_asAs(new_esEs24(vuu3001, vuu31001, bbh), new_esEs25(vuu3002, vuu31002, bca))) new_esEs16(vuu3001, vuu31001, app(app(ty_Either, de), df)) -> new_esEs19(vuu3001, vuu31001, de, df) new_esEs15(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_[], bdd)) -> new_esEs4(vuu3001, vuu31001, bdd) new_esEs12(False, True) -> False new_esEs12(True, False) -> False new_primMulNat0(Zero, Zero) -> Zero new_esEs12(True, True) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Maybe, gh), ff) -> new_esEs21(vuu3000, vuu31000, gh) new_esEs15(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, app(app(ty_@2, dg), dh)) -> new_esEs14(vuu3001, vuu31001, dg, dh) new_esEs21(Nothing, Just(vuu31000), bad) -> False new_esEs21(Just(vuu3000), Nothing, bad) -> False new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs21(Nothing, Nothing, bad) -> True new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs9(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Double, ff) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(ty_Maybe, bac)) -> new_esEs21(vuu3000, vuu31000, bac) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bbf)) -> new_esEs21(vuu3000, vuu31000, bbf) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, ty_Double) -> new_esEs13(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, ty_Char) -> new_esEs20(vuu3002, vuu31002) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, bea), beb)) -> new_esEs19(vuu3001, vuu31001, bea, beb) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs13(vuu3000, vuu31000) new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(app(ty_@2, baa), bab)) -> new_esEs14(vuu3000, vuu31000, baa, bab) new_esEs16(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Ratio, gc), ff) -> new_esEs6(vuu3000, vuu31000, gc) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Float, ff) -> new_esEs17(vuu3000, vuu31000) new_esEs11(EQ, EQ) -> True new_esEs17(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Float) -> new_esEs17(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(ty_Ratio, hf)) -> new_esEs6(vuu3000, vuu31000, hf) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_esEs19(Left(vuu3000), Left(vuu31000), ty_@0, ff) -> new_esEs5(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bba)) -> new_esEs6(vuu3000, vuu31000, bba) new_esEs15(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, ed), ee), ef)) -> new_esEs18(vuu3000, vuu31000, ed, ee, ef) new_esEs25(vuu3002, vuu31002, app(ty_Ratio, bfb)) -> new_esEs6(vuu3002, vuu31002, bfb) new_esEs16(vuu3001, vuu31001, app(app(app(ty_@3, da), db), dc)) -> new_esEs18(vuu3001, vuu31001, da, db, dc) new_esEs16(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(app(ty_@2, cd), ce)) -> new_esEs14(vuu3000, vuu31000, cd, ce) new_esEs25(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(app(ty_Either, hg), hh)) -> new_esEs19(vuu3000, vuu31000, hg, hh) new_esEs15(vuu3000, vuu31000, app(app(ty_Either, cb), cc)) -> new_esEs19(vuu3000, vuu31000, cb, cc) new_esEs12(False, False) -> True new_esEs15(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_[], be)) -> new_esEs4(vuu3000, vuu31000, be) new_esEs23(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs23(vuu3000, vuu31000, app(ty_[], bcb)) -> new_esEs4(vuu3000, vuu31000, bcb) new_esEs25(vuu3002, vuu31002, app(ty_Maybe, bfg)) -> new_esEs21(vuu3002, vuu31002, bfg) new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_esEs23(vuu3000, vuu31000, app(app(ty_Either, bcg), bch)) -> new_esEs19(vuu3000, vuu31000, bcg, bch) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Ordering, ff) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs14(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bc, bd) -> new_asAs(new_esEs15(vuu3000, vuu31000, bc), new_esEs16(vuu3001, vuu31001, bd)) new_esEs16(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_primPlusNat0(Succ(vuu4900), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu4900, vuu31001000))) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_esEs8(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bde), bdf), bdg)) -> new_esEs18(vuu3001, vuu31001, bde, bdf, bdg) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Char, ff) -> new_esEs20(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_Maybe, cf)) -> new_esEs21(vuu3000, vuu31000, cf) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, fb), fc)) -> new_esEs14(vuu3000, vuu31000, fb, fc) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Bool, ff) -> new_esEs12(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, bdh)) -> new_esEs6(vuu3001, vuu31001, bdh) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_@2, gf), gg), ff) -> new_esEs14(vuu3000, vuu31000, gf, gg) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_esEs25(vuu3002, vuu31002, app(app(ty_@2, bfe), bff)) -> new_esEs14(vuu3002, vuu31002, bfe, bff) new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, app(app(ty_Either, bfc), bfd)) -> new_esEs19(vuu3002, vuu31002, bfc, bfd) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs10(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bbb), bbc)) -> new_esEs19(vuu3000, vuu31000, bbb, bbc) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), ha, ty_Bool) -> new_esEs12(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_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs6(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bb) -> new_asAs(new_esEs7(vuu3000, vuu31000, bb), new_esEs8(vuu3001, vuu31001, bb)) new_primPlusNat1(Succ(vuu490), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu490, vuu3100100))) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs13(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Int) -> new_esEs10(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(app(app(ty_@3, hc), hd), he)) -> new_esEs18(vuu3000, vuu31000, hc, hd, he) new_primPlusNat0(Succ(vuu4900), Zero) -> Succ(vuu4900) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bec), bed)) -> new_esEs14(vuu3001, vuu31001, bec, bed) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, fh), ga), gb), ff) -> new_esEs18(vuu3000, vuu31000, fh, ga, gb) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs23(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs8(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Ratio, eg)) -> new_esEs6(vuu3000, vuu31000, eg) new_esEs4(:(vuu3000, vuu3001), [], eb) -> False new_esEs4([], :(vuu31000, vuu31001), eb) -> False new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Int, ff) -> new_esEs10(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs23(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(app(ty_@2, bda), bdb)) -> new_esEs14(vuu3000, vuu31000, bda, bdb) new_esEs23(vuu3000, vuu31000, app(ty_Ratio, bcf)) -> new_esEs6(vuu3000, vuu31000, bcf) new_esEs25(vuu3002, vuu31002, ty_Bool) -> new_esEs12(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs25(vuu3002, vuu31002, app(ty_[], bef)) -> new_esEs4(vuu3002, vuu31002, bef) new_esEs16(vuu3001, vuu31001, app(ty_Ratio, dd)) -> new_esEs6(vuu3001, vuu31001, dd) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_[], bae)) -> new_esEs4(vuu3000, vuu31000, bae) new_esEs23(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_primEqNat0(Zero, Zero) -> True new_esEs4([], [], eb) -> True new_esEs21(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), ha, app(ty_[], hb)) -> new_esEs4(vuu3000, vuu31000, hb) new_asAs(False, vuu37) -> False new_esEs25(vuu3002, vuu31002, ty_Integer) -> new_esEs9(vuu3002, vuu31002) new_esEs19(Left(vuu3000), Right(vuu31000), ha, ff) -> False new_esEs19(Right(vuu3000), Left(vuu31000), ha, ff) -> False new_esEs21(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, baf), bag), bah)) -> new_esEs18(vuu3000, vuu31000, baf, bag, bah) new_esEs25(vuu3002, vuu31002, app(app(app(ty_@3, beg), beh), bfa)) -> new_esEs18(vuu3002, vuu31002, beg, beh, bfa) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Integer, ff) -> new_esEs9(vuu3000, vuu31000) new_esEs7(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(ty_Maybe, bdc)) -> new_esEs21(vuu3000, vuu31000, bdc) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs5(@0, @0) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_[], fg), ff) -> new_esEs4(vuu3000, vuu31000, fg) new_esEs7(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) The set Q consists of the following terms: new_esEs21(Just(x0), Just(x1), ty_Char) new_esEs4(:(x0, x1), [], x2) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_esEs15(x0, x1, ty_@0) new_esEs19(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_esEs21(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs25(x0, x1, ty_Ordering) new_asAs(False, x0) new_esEs8(x0, x1, ty_Integer) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs21(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs9(Integer(x0), Integer(x1)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_esEs25(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, ty_Float) new_esEs21(Just(x0), Just(x1), ty_Int) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs24(x0, x1, ty_Ordering) new_esEs16(x0, x1, ty_@0) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs21(Just(x0), Nothing, x1) new_primPlusNat0(Zero, Succ(x0)) new_esEs4([], :(x0, x1), x2) new_esEs23(x0, x1, ty_Integer) new_primEqNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Integer) new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs22(x0, x1, ty_Double) new_esEs21(Nothing, Just(x0), x1) new_esEs24(x0, x1, ty_Float) new_esEs25(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs16(x0, x1, app(ty_Maybe, x2)) new_esEs15(x0, x1, ty_Integer) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_primPlusNat0(Zero, Zero) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_esEs12(False, True) new_esEs12(True, False) new_esEs19(Left(x0), Right(x1), x2, x3) new_esEs19(Right(x0), Left(x1), x2, x3) new_esEs16(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, ty_Ordering) new_esEs19(Right(x0), Right(x1), x2, ty_Integer) new_esEs21(Just(x0), Just(x1), ty_Double) new_esEs24(x0, x1, ty_Integer) new_esEs21(Just(x0), Just(x1), ty_@0) new_esEs19(Left(x0), Left(x1), ty_Float, x2) new_esEs21(Just(x0), Just(x1), ty_Float) new_esEs12(False, False) new_esEs24(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), ty_Bool) new_esEs23(x0, x1, ty_Float) new_esEs19(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs22(x0, x1, ty_Bool) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(Left(x0), Left(x1), ty_@0, x2) new_esEs15(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, app(ty_[], x2)) new_sr(Pos(x0), Pos(x1)) new_esEs24(x0, x1, ty_Char) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_esEs19(Left(x0), Left(x1), ty_Bool, x2) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs19(Right(x0), Right(x1), x2, ty_Ordering) new_esEs16(x0, x1, ty_Double) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs19(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs22(x0, x1, ty_Integer) new_esEs16(x0, x1, ty_Char) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs19(Left(x0), Left(x1), ty_Int, x2) new_esEs19(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs16(x0, x1, ty_Bool) new_esEs11(EQ, EQ) new_esEs19(Left(x0), Left(x1), ty_Char, x2) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs16(x0, x1, app(app(ty_@2, x2), x3)) new_primMulNat0(Succ(x0), Zero) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_esEs19(Left(x0), Left(x1), ty_Double, x2) new_esEs24(x0, x1, ty_Bool) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs15(x0, x1, app(app(ty_Either, x2), x3)) new_esEs13(Double(x0, x1), Double(x2, x3)) new_esEs15(x0, x1, ty_Double) new_esEs8(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), x1) new_esEs20(Char(x0), Char(x1)) new_esEs19(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_esEs4(:(x0, x1), :(x2, x3), x4) new_esEs23(x0, x1, ty_Char) new_esEs19(Right(x0), Right(x1), x2, ty_@0) new_esEs16(x0, x1, ty_Ordering) new_esEs15(x0, x1, ty_Ordering) new_primMulNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), app(ty_Maybe, x2)) new_esEs19(Right(x0), Right(x1), x2, ty_Bool) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs25(x0, x1, ty_@0) new_esEs21(Nothing, Nothing, x0) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_esEs19(Left(x0), Left(x1), ty_Integer, x2) new_esEs16(x0, x1, ty_Float) new_esEs19(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs10(x0, x1) new_esEs23(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs19(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs23(x0, x1, ty_@0) new_esEs17(Float(x0, x1), Float(x2, x3)) new_asAs(True, x0) new_esEs15(x0, x1, ty_Float) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(Just(x0), Just(x1), ty_Integer) new_esEs5(@0, @0) new_esEs24(x0, x1, ty_@0) new_esEs22(x0, x1, ty_Char) new_esEs11(GT, GT) new_esEs25(x0, x1, ty_Integer) new_esEs21(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_primEqNat0(Zero, Zero) new_esEs23(x0, x1, ty_Bool) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs19(Left(x0), Left(x1), ty_Ordering, x2) new_esEs12(True, True) new_esEs19(Right(x0), Right(x1), x2, ty_Int) new_esEs19(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs15(x0, x1, ty_Char) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_primPlusNat1(Zero, x0) new_esEs15(x0, x1, app(ty_[], x2)) new_esEs21(Just(x0), Just(x1), ty_Ordering) 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_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs11(LT, LT) new_esEs22(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Double) new_esEs16(x0, x1, app(ty_Ratio, x2)) new_esEs15(x0, x1, ty_Int) new_esEs4([], [], x0) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_esEs19(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_Char) new_primEqNat0(Succ(x0), Zero) new_esEs19(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs25(x0, x1, ty_Double) new_esEs19(Right(x0), Right(x1), x2, ty_Double) new_esEs7(x0, x1, ty_Integer) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs19(Right(x0), Right(x1), x2, ty_Char) new_esEs15(x0, x1, ty_Bool) new_esEs25(x0, x1, ty_Bool) new_esEs21(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs15(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Float) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs21(Just(x0), Just(x1), app(ty_[], x2)) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs15(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(x0, x1, app(app(ty_Either, x2), x3)) 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_span2Ys0(vuu3110, vuu3111, True, ba) -> new_span2Ys(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Ys0(vuu3110, vuu3111, True, ba) -> new_span2Zs(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Zs0(vuu3110, vuu3111, True, ba) -> new_span2Ys(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 *new_span2Zs(:(vuu3110, vuu3111), ba) -> new_span2Zs0(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) The graph contains the following edges 1 > 1, 1 > 2, 2 >= 4 *new_span2Ys(:(vuu3110, vuu3111), ba) -> new_span2Ys0(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) The graph contains the following edges 1 > 1, 1 > 2, 2 >= 4 *new_span2Zs0(vuu3110, vuu3111, True, ba) -> new_span2Zs(vuu3111, ba) The graph contains the following edges 2 >= 1, 4 >= 2 ---------------------------------------- (22) YES ---------------------------------------- (23) 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_esEs24(vuu3001, vuu31001, app(ty_Maybe, bca)) -> new_esEs21(vuu3001, vuu31001, bca) new_primEqInt(Pos(Zero), Pos(Zero)) -> True new_primPlusNat0(Zero, Zero) -> Zero new_esEs25(vuu3002, vuu31002, ty_@0) -> new_esEs5(vuu3002, vuu31002) new_esEs22(vuu3000, vuu31000, app(app(ty_Either, beb), bec)) -> new_esEs19(vuu3000, vuu31000, beb, bec) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs11(LT, EQ) -> False new_esEs11(EQ, LT) -> False new_esEs15(vuu3000, vuu31000, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs18(vuu3000, vuu31000, bf, bg, bh) new_esEs26(vuu300, vuu3100, ty_Ordering) -> new_esEs11(vuu300, vuu3100) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_Either, fa), fb), ec) -> new_esEs19(vuu3000, vuu31000, fa, fb) new_esEs23(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs26(vuu300, vuu3100, ty_Double) -> new_esEs13(vuu300, vuu3100) new_esEs16(vuu3001, vuu31001, app(ty_Maybe, ea)) -> new_esEs21(vuu3001, vuu31001, ea) new_esEs4(:(vuu3000, vuu3001), :(vuu31000, vuu31001), bdd) -> new_asAs(new_esEs22(vuu3000, vuu31000, bdd), new_esEs4(vuu3001, vuu31001, bdd)) new_esEs23(vuu3000, vuu31000, app(app(app(ty_@3, hg), hh), baa)) -> new_esEs18(vuu3000, vuu31000, hg, hh, baa) new_groupByZs1([], :(:(vuu3100, vuu3101), vuu311), ba) -> :(:(vuu3100, vuu3101), vuu311) new_esEs11(LT, GT) -> False new_esEs11(GT, LT) -> False new_esEs20(Char(vuu3000), Char(vuu31000)) -> new_primEqNat0(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, app(ty_[], cg)) -> new_esEs4(vuu3001, vuu31001, cg) new_esEs22(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_primMulNat0(Succ(vuu300000), Succ(vuu3100100)) -> new_primPlusNat1(new_primMulNat0(vuu300000, Succ(vuu3100100)), vuu3100100) new_esEs22(vuu3000, vuu31000, app(ty_[], bde)) -> new_esEs4(vuu3000, vuu31000, bde) new_asAs(True, vuu37) -> vuu37 new_esEs16(vuu3001, vuu31001, ty_Ordering) -> new_esEs11(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, app(ty_Maybe, bef)) -> new_esEs21(vuu3000, vuu31000, bef) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_span2Zs02(vuu24, vuu25, vuu280, vuu281, True, hb) -> new_span2Zs04(vuu24, vuu25, vuu280, vuu281, new_span2Ys3(vuu24, vuu25, vuu281, hb), new_span2Zs3(vuu24, vuu25, vuu281, hb), hb) new_esEs22(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_groupByZs12(vuu24, vuu25, vuu26, vuu27, vuu28, vuu38, hb) -> new_span2Zs3(vuu24, vuu25, vuu28, hb) new_primEqInt(Pos(Succ(vuu30000)), Pos(Zero)) -> False new_primEqInt(Pos(Zero), Pos(Succ(vuu310000))) -> False new_esEs15(vuu3000, vuu31000, app(ty_Ratio, ca)) -> new_esEs6(vuu3000, vuu31000, ca) new_esEs26(vuu300, vuu3100, ty_Char) -> new_esEs20(vuu300, vuu3100) new_esEs15(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs26(vuu300, vuu3100, ty_Bool) -> new_esEs12(vuu300, vuu3100) new_esEs24(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, False, vuu30, hb) -> new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) new_primEqNat0(Succ(vuu30000), Succ(vuu310000)) -> new_primEqNat0(vuu30000, vuu310000) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_@2, bfg), bfh)) -> new_esEs14(vuu3000, vuu31000, bfg, bfh) new_esEs15(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs18(@3(vuu3000, vuu3001, vuu3002), @3(vuu31000, vuu31001, vuu31002), hc, hd, he) -> new_asAs(new_esEs23(vuu3000, vuu31000, hc), new_asAs(new_esEs24(vuu3001, vuu31001, hd), new_esEs25(vuu3002, vuu31002, he))) new_esEs16(vuu3001, vuu31001, app(app(ty_Either, de), df)) -> new_esEs19(vuu3001, vuu31001, de, df) new_groupByZs1(:(vuu300, vuu301), :(:(vuu3100, vuu3101), vuu311), ba) -> new_groupByZs10(vuu300, vuu301, vuu3100, vuu3101, vuu311, new_esEs26(vuu300, vuu3100, ba), new_esEs4(vuu301, vuu3101, ba), ba) new_esEs15(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Float) -> new_esEs17(vuu3001, vuu31001) new_esEs24(vuu3001, vuu31001, app(ty_[], bah)) -> new_esEs4(vuu3001, vuu31001, bah) new_esEs12(False, True) -> False new_esEs12(True, False) -> False new_primMulNat0(Zero, Zero) -> Zero new_esEs12(True, True) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Maybe, ff), ec) -> new_esEs21(vuu3000, vuu31000, ff) new_esEs15(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), ty_@0) -> new_esEs5(vuu3000, vuu31000) new_span2Zs2(:(vuu3110, vuu3111), ba) -> new_span2Zs01(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) new_esEs23(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, app(app(ty_@2, dg), dh)) -> new_esEs14(vuu3001, vuu31001, dg, dh) new_esEs21(Nothing, Just(vuu31000), beg) -> False new_esEs21(Just(vuu3000), Nothing, beg) -> False new_esEs11(EQ, GT) -> False new_esEs11(GT, EQ) -> False new_esEs15(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs21(Nothing, Nothing, beg) -> True new_primEqNat0(Succ(vuu30000), Zero) -> False new_primEqNat0(Zero, Succ(vuu310000)) -> False new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs9(Integer(vuu3000), Integer(vuu31000)) -> new_primEqInt(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Double, ec) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(ty_Maybe, ha)) -> new_esEs21(vuu3000, vuu31000, ha) new_esEs26(vuu300, vuu3100, ty_Float) -> new_esEs17(vuu300, vuu3100) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Maybe, bga)) -> new_esEs21(vuu3000, vuu31000, bga) new_esEs25(vuu3002, vuu31002, ty_Double) -> new_esEs13(vuu3002, vuu31002) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs26(vuu300, vuu3100, app(app(ty_@2, bc), bd)) -> new_esEs14(vuu300, vuu3100, bc, bd) new_esEs25(vuu3002, vuu31002, ty_Char) -> new_esEs20(vuu3002, vuu31002) new_esEs26(vuu300, vuu3100, app(ty_Maybe, beg)) -> new_esEs21(vuu300, vuu3100, beg) new_groupByZs1(:(vuu300, vuu301), :([], vuu311), ba) -> :([], vuu311) new_esEs24(vuu3001, vuu31001, app(app(ty_Either, bbe), bbf)) -> new_esEs19(vuu3001, vuu31001, bbe, bbf) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Double) -> new_esEs13(vuu3000, vuu31000) new_span2Ys3(vuu11, vuu12, [], eb) -> [] new_primEqInt(Neg(Succ(vuu30000)), Neg(Zero)) -> False new_primEqInt(Neg(Zero), Neg(Succ(vuu310000))) -> False new_esEs11(GT, GT) -> True new_span2Zs01(vuu3110, vuu3111, True, ba) -> new_span2Zs03(vuu3110, vuu3111, new_span2Ys2(vuu3111, ba), new_span2Zs2(vuu3111, ba), ba) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(app(ty_@2, gg), gh)) -> new_esEs14(vuu3000, vuu31000, gg, gh) new_esEs16(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Pos(Succ(vuu30000)), Pos(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs22(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_Ratio, eh), ec) -> new_esEs6(vuu3000, vuu31000, eh) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Float, ec) -> new_esEs17(vuu3000, vuu31000) new_esEs11(EQ, EQ) -> True new_esEs17(Float(vuu3000, vuu3001), Float(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Float) -> new_esEs17(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(ty_Ratio, gd)) -> new_esEs6(vuu3000, vuu31000, gd) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_sr(Pos(vuu30000), Neg(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_sr(Neg(vuu30000), Pos(vuu310010)) -> Neg(new_primMulNat0(vuu30000, vuu310010)) new_primEqInt(Pos(Succ(vuu30000)), Neg(vuu31000)) -> False new_primEqInt(Neg(Succ(vuu30000)), Pos(vuu31000)) -> False new_esEs19(Left(vuu3000), Left(vuu31000), ty_@0, ec) -> new_esEs5(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_Ratio, bfd)) -> new_esEs6(vuu3000, vuu31000, bfd) new_esEs15(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs22(vuu3000, vuu31000, app(app(app(ty_@3, bdf), bdg), bdh)) -> new_esEs18(vuu3000, vuu31000, bdf, bdg, bdh) new_esEs25(vuu3002, vuu31002, app(ty_Ratio, bcf)) -> new_esEs6(vuu3002, vuu31002, bcf) new_esEs16(vuu3001, vuu31001, app(app(app(ty_@3, da), db), dc)) -> new_esEs18(vuu3001, vuu31001, da, db, dc) new_span2Zs02(vuu24, vuu25, vuu280, vuu281, False, hb) -> :(vuu280, vuu281) new_esEs16(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(app(ty_@2, cd), ce)) -> new_esEs14(vuu3000, vuu31000, cd, ce) new_esEs25(vuu3002, vuu31002, ty_Ordering) -> new_esEs11(vuu3002, vuu31002) new_span2Ys04(vuu11, vuu12, vuu150, vuu151, False, eb) -> [] new_span2Ys3(vuu11, vuu12, :(vuu150, vuu151), eb) -> new_span2Ys04(vuu11, vuu12, vuu150, vuu151, new_esEs4(:(vuu11, vuu12), vuu150, eb), eb) new_span2Ys03(vuu3110, vuu3111, vuu43, vuu42, ba) -> :(vuu3110, vuu43) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(app(ty_Either, ge), gf)) -> new_esEs19(vuu3000, vuu31000, ge, gf) new_esEs26(vuu300, vuu3100, ty_@0) -> new_esEs5(vuu300, vuu3100) new_span2Zs01(vuu3110, vuu3111, False, ba) -> :(vuu3110, vuu3111) new_span2Zs04(vuu24, vuu25, vuu280, vuu281, vuu51, vuu50, hb) -> vuu50 new_esEs15(vuu3000, vuu31000, app(app(ty_Either, cb), cc)) -> new_esEs19(vuu3000, vuu31000, cb, cc) new_esEs12(False, False) -> True new_span2Zs03(vuu3110, vuu3111, vuu45, vuu44, ba) -> vuu44 new_span2Ys2([], ba) -> [] new_esEs26(vuu300, vuu3100, app(ty_Ratio, bb)) -> new_esEs6(vuu300, vuu3100, bb) new_esEs15(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_[], be)) -> new_esEs4(vuu3000, vuu31000, be) new_esEs23(vuu3000, vuu31000, ty_Float) -> new_esEs17(vuu3000, vuu31000) new_span2Zs3(vuu24, vuu25, :(vuu280, vuu281), hb) -> new_span2Zs02(vuu24, vuu25, vuu280, vuu281, new_esEs4(:(vuu24, vuu25), vuu280, hb), hb) new_sr(Neg(vuu30000), Neg(vuu310010)) -> Pos(new_primMulNat0(vuu30000, vuu310010)) new_esEs23(vuu3000, vuu31000, app(ty_[], hf)) -> new_esEs4(vuu3000, vuu31000, hf) new_esEs25(vuu3002, vuu31002, app(ty_Maybe, bdc)) -> new_esEs21(vuu3002, vuu31002, bdc) new_esEs24(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, True, False, hb) -> new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) new_esEs23(vuu3000, vuu31000, app(app(ty_Either, bac), bad)) -> new_esEs19(vuu3000, vuu31000, bac, bad) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Ordering, ec) -> new_esEs11(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Succ(vuu310000))) -> False new_primEqInt(Neg(Zero), Pos(Succ(vuu310000))) -> False new_esEs23(vuu3000, vuu31000, ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs14(@2(vuu3000, vuu3001), @2(vuu31000, vuu31001), bc, bd) -> new_asAs(new_esEs15(vuu3000, vuu31000, bc), new_esEs16(vuu3001, vuu31001, bd)) new_esEs16(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_primPlusNat0(Succ(vuu4900), Succ(vuu31001000)) -> Succ(Succ(new_primPlusNat0(vuu4900, vuu31001000))) new_esEs22(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, ty_@0) -> new_esEs5(vuu3001, vuu31001) new_span2Ys04(vuu11, vuu12, vuu150, vuu151, True, eb) -> new_span2Ys01(vuu11, vuu12, vuu150, vuu151, new_span2Ys3(vuu11, vuu12, vuu151, eb), new_span2Zs3(vuu11, vuu12, vuu151, eb), eb) new_esEs8(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_primEqInt(Neg(Succ(vuu30000)), Neg(Succ(vuu310000))) -> new_primEqNat0(vuu30000, vuu310000) new_esEs24(vuu3001, vuu31001, app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs18(vuu3001, vuu31001, bba, bbb, bbc) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Char, ec) -> new_esEs20(vuu3000, vuu31000) new_esEs15(vuu3000, vuu31000, app(ty_Maybe, cf)) -> new_esEs21(vuu3000, vuu31000, cf) new_esEs22(vuu3000, vuu31000, app(app(ty_@2, bed), bee)) -> new_esEs14(vuu3000, vuu31000, bed, bee) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Bool, ec) -> new_esEs12(vuu3000, vuu31000) new_esEs24(vuu3001, vuu31001, app(ty_Ratio, bbd)) -> new_esEs6(vuu3001, vuu31001, bbd) new_span2Ys2(:(vuu3110, vuu3111), ba) -> new_span2Ys02(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(ty_@2, fc), fd), ec) -> new_esEs14(vuu3000, vuu31000, fc, fd) new_esEs24(vuu3001, vuu31001, ty_Int) -> new_esEs10(vuu3001, vuu31001) new_esEs25(vuu3002, vuu31002, app(app(ty_@2, bda), bdb)) -> new_esEs14(vuu3002, vuu31002, bda, bdb) new_esEs25(vuu3002, vuu31002, app(app(ty_Either, bcg), bch)) -> new_esEs19(vuu3002, vuu31002, bcg, bch) new_esEs22(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs10(vuu300, vuu3100) -> new_primEqInt(vuu300, vuu3100) new_esEs21(Just(vuu3000), Just(vuu31000), app(app(ty_Either, bfe), bff)) -> new_esEs19(vuu3000, vuu31000, bfe, bff) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, ty_Bool) -> new_esEs12(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_esEs24(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs6(:%(vuu3000, vuu3001), :%(vuu31000, vuu31001), bb) -> new_asAs(new_esEs7(vuu3000, vuu31000, bb), new_esEs8(vuu3001, vuu31001, bb)) new_primPlusNat1(Succ(vuu490), vuu3100100) -> Succ(Succ(new_primPlusNat0(vuu490, vuu3100100))) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Ordering) -> new_esEs11(vuu3000, vuu31000) new_esEs13(Double(vuu3000, vuu3001), Double(vuu31000, vuu31001)) -> new_esEs10(new_sr(vuu3000, vuu31001), new_sr(vuu3001, vuu31000)) new_esEs25(vuu3002, vuu31002, ty_Int) -> new_esEs10(vuu3002, vuu31002) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(app(app(ty_@3, ga), gb), gc)) -> new_esEs18(vuu3000, vuu31000, ga, gb, gc) new_primPlusNat0(Succ(vuu4900), Zero) -> Succ(vuu4900) new_primPlusNat0(Zero, Succ(vuu31001000)) -> Succ(vuu31001000) new_esEs24(vuu3001, vuu31001, app(app(ty_@2, bbg), bbh)) -> new_esEs14(vuu3001, vuu31001, bbg, bbh) new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) -> :(:(vuu26, vuu27), vuu28) new_esEs19(Left(vuu3000), Left(vuu31000), app(app(app(ty_@3, ee), ef), eg), ec) -> new_esEs18(vuu3000, vuu31000, ee, ef, eg) new_primEqInt(Neg(Zero), Neg(Zero)) -> True new_esEs11(LT, LT) -> True new_esEs23(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs26(vuu300, vuu3100, app(app(ty_Either, fg), ec)) -> new_esEs19(vuu300, vuu3100, fg, ec) new_esEs26(vuu300, vuu3100, app(app(app(ty_@3, hc), hd), he)) -> new_esEs18(vuu300, vuu3100, hc, hd, he) new_esEs15(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_primPlusNat1(Zero, vuu3100100) -> Succ(vuu3100100) new_esEs16(vuu3001, vuu31001, ty_Char) -> new_esEs20(vuu3001, vuu31001) new_esEs22(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs8(vuu3001, vuu31001, ty_Integer) -> new_esEs9(vuu3001, vuu31001) new_esEs16(vuu3001, vuu31001, ty_Double) -> new_esEs13(vuu3001, vuu31001) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, True, True, hb) -> new_groupByZs12(vuu24, vuu25, vuu26, vuu27, vuu28, new_span2Ys3(vuu24, vuu25, vuu28, hb), hb) new_esEs22(vuu3000, vuu31000, app(ty_Ratio, bea)) -> new_esEs6(vuu3000, vuu31000, bea) new_esEs4(:(vuu3000, vuu3001), [], bdd) -> False new_esEs4([], :(vuu31000, vuu31001), bdd) -> False new_esEs24(vuu3001, vuu31001, ty_Bool) -> new_esEs12(vuu3001, vuu31001) new_groupByZs1(vuu30, [], ba) -> [] new_esEs26(vuu300, vuu3100, ty_Int) -> new_esEs10(vuu300, vuu3100) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Int, ec) -> new_esEs10(vuu3000, vuu31000) new_primEqInt(Pos(Zero), Neg(Zero)) -> True new_primEqInt(Neg(Zero), Pos(Zero)) -> True new_esEs23(vuu3000, vuu31000, ty_Double) -> new_esEs13(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(app(ty_@2, bae), baf)) -> new_esEs14(vuu3000, vuu31000, bae, baf) new_span2Ys02(vuu3110, vuu3111, False, ba) -> [] new_esEs26(vuu300, vuu3100, app(ty_[], bdd)) -> new_esEs4(vuu300, vuu3100, bdd) new_esEs26(vuu300, vuu3100, ty_Integer) -> new_esEs9(vuu300, vuu3100) new_esEs23(vuu3000, vuu31000, app(ty_Ratio, bab)) -> new_esEs6(vuu3000, vuu31000, bab) new_esEs25(vuu3002, vuu31002, ty_Bool) -> new_esEs12(vuu3002, vuu31002) new_esEs25(vuu3002, vuu31002, app(ty_[], bcb)) -> new_esEs4(vuu3002, vuu31002, bcb) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Bool) -> new_esEs12(vuu3000, vuu31000) new_esEs16(vuu3001, vuu31001, app(ty_Ratio, dd)) -> new_esEs6(vuu3001, vuu31001, dd) new_esEs23(vuu3000, vuu31000, ty_@0) -> new_esEs5(vuu3000, vuu31000) new_esEs21(Just(vuu3000), Just(vuu31000), app(ty_[], beh)) -> new_esEs4(vuu3000, vuu31000, beh) new_primEqNat0(Zero, Zero) -> True new_span2Ys02(vuu3110, vuu3111, True, ba) -> new_span2Ys03(vuu3110, vuu3111, new_span2Ys2(vuu3111, ba), new_span2Zs2(vuu3111, ba), ba) new_esEs4([], [], bdd) -> True new_span2Zs3(vuu24, vuu25, [], hb) -> [] new_groupByZs1([], :([], vuu311), ba) -> new_span2Zs2(vuu311, ba) new_esEs21(Just(vuu3000), Just(vuu31000), ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_esEs19(Right(vuu3000), Right(vuu31000), fg, app(ty_[], fh)) -> new_esEs4(vuu3000, vuu31000, fh) new_asAs(False, vuu37) -> False new_span2Ys01(vuu11, vuu12, vuu150, vuu151, vuu47, vuu46, eb) -> :(vuu150, vuu47) new_esEs25(vuu3002, vuu31002, ty_Integer) -> new_esEs9(vuu3002, vuu31002) new_esEs19(Left(vuu3000), Right(vuu31000), fg, ec) -> False new_esEs19(Right(vuu3000), Left(vuu31000), fg, ec) -> False new_esEs21(Just(vuu3000), Just(vuu31000), app(app(app(ty_@3, bfa), bfb), bfc)) -> new_esEs18(vuu3000, vuu31000, bfa, bfb, bfc) new_esEs25(vuu3002, vuu31002, app(app(app(ty_@3, bcc), bcd), bce)) -> new_esEs18(vuu3002, vuu31002, bcc, bcd, bce) new_esEs19(Left(vuu3000), Left(vuu31000), ty_Integer, ec) -> new_esEs9(vuu3000, vuu31000) new_esEs7(vuu3000, vuu31000, ty_Int) -> new_esEs10(vuu3000, vuu31000) new_esEs23(vuu3000, vuu31000, app(ty_Maybe, bag)) -> new_esEs21(vuu3000, vuu31000, bag) new_esEs22(vuu3000, vuu31000, ty_Char) -> new_esEs20(vuu3000, vuu31000) new_esEs5(@0, @0) -> True new_esEs19(Left(vuu3000), Left(vuu31000), app(ty_[], ed), ec) -> new_esEs4(vuu3000, vuu31000, ed) new_esEs7(vuu3000, vuu31000, ty_Integer) -> new_esEs9(vuu3000, vuu31000) new_span2Zs2([], ba) -> [] The set Q consists of the following terms: new_esEs21(Just(x0), Just(x1), ty_Char) new_span2Zs01(x0, x1, False, x2) new_esEs15(x0, x1, ty_@0) new_groupByZs11(x0, x1, x2, x3, x4, x5) new_span2Ys02(x0, x1, True, x2) new_groupByZs10(x0, x1, x2, x3, x4, True, False, x5) new_esEs4([], :(x0, x1), x2) new_esEs26(x0, x1, app(app(ty_@2, x2), x3)) new_esEs25(x0, x1, app(ty_Maybe, x2)) new_esEs24(x0, x1, app(ty_Maybe, x2)) new_esEs19(Right(x0), Right(x1), x2, ty_Int) new_esEs25(x0, x1, ty_Ordering) new_esEs24(x0, x1, app(ty_Ratio, x2)) new_asAs(False, x0) new_esEs25(x0, x1, app(ty_Ratio, x2)) new_esEs26(x0, x1, ty_Ordering) new_esEs8(x0, x1, ty_Integer) new_esEs26(x0, x1, ty_Double) new_esEs24(x0, x1, ty_Double) new_primMulNat0(Zero, Zero) new_esEs9(Integer(x0), Integer(x1)) new_primEqInt(Neg(Zero), Neg(Succ(x0))) new_span2Ys3(x0, x1, [], x2) new_esEs25(x0, x1, ty_Int) new_esEs19(Right(x0), Right(x1), x2, ty_Ordering) new_esEs25(x0, x1, app(ty_[], x2)) new_esEs21(Just(x0), Just(x1), ty_Int) new_esEs19(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5)) new_groupByZs1(x0, [], x1) new_esEs19(Left(x0), Left(x1), app(ty_Ratio, x2), x3) new_primEqInt(Pos(Zero), Pos(Succ(x0))) new_esEs19(Right(x0), Right(x1), x2, ty_Char) new_esEs24(x0, x1, ty_Ordering) new_esEs16(x0, x1, ty_@0) new_esEs19(Left(x0), Left(x1), ty_Char, x2) new_primEqInt(Pos(Zero), Pos(Zero)) new_esEs19(Right(x0), Right(x1), x2, ty_Double) new_primPlusNat0(Zero, Succ(x0)) new_esEs19(Left(x0), Left(x1), ty_@0, x2) new_esEs23(x0, x1, ty_Integer) new_primEqNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Integer) new_esEs16(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs22(x0, x1, ty_Double) new_esEs24(x0, x1, ty_Float) new_esEs19(Left(x0), Left(x1), app(ty_Maybe, x2), x3) new_esEs25(x0, x1, ty_Float) new_sr(Neg(x0), Neg(x1)) new_span2Ys2([], x0) new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5) new_groupByZs1(:(x0, x1), :([], x2), x3) new_primEqInt(Neg(Zero), Neg(Zero)) new_esEs19(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4) new_esEs24(x0, x1, app(ty_[], x2)) new_esEs16(x0, x1, app(ty_Maybe, x2)) new_esEs15(x0, x1, ty_Integer) new_primPlusNat0(Zero, Zero) new_esEs21(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, ty_Float) new_esEs12(False, True) new_esEs12(True, False) new_esEs16(x0, x1, app(ty_[], x2)) new_esEs23(x0, x1, ty_Ordering) new_esEs19(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4) new_esEs21(Just(x0), Just(x1), ty_Double) new_esEs21(Just(x0), Just(x1), app(ty_Ratio, x2)) new_esEs24(x0, x1, ty_Integer) new_esEs21(Just(x0), Just(x1), ty_@0) new_esEs21(Nothing, Nothing, x0) new_esEs19(Left(x0), Left(x1), ty_Int, x2) new_groupByZs10(x0, x1, x2, x3, x4, False, x5, x6) new_esEs21(Just(x0), Just(x1), ty_Float) new_esEs22(x0, x1, app(app(ty_Either, x2), x3)) new_esEs12(False, False) new_esEs26(x0, x1, ty_Char) new_esEs24(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), ty_Bool) new_esEs23(x0, x1, ty_Float) new_esEs22(x0, x1, ty_Bool) new_esEs15(x0, x1, app(ty_Maybe, x2)) new_span2Zs04(x0, x1, x2, x3, x4, x5, x6) new_esEs22(x0, x1, app(ty_Ratio, x2)) new_sr(Pos(x0), Pos(x1)) new_esEs24(x0, x1, app(app(ty_@2, x2), x3)) new_groupByZs1(:(x0, x1), :(:(x2, x3), x4), x5) new_esEs24(x0, x1, ty_Char) new_esEs26(x0, x1, ty_Int) new_esEs22(x0, x1, ty_Ordering) new_esEs11(EQ, GT) new_esEs11(GT, EQ) new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs21(Just(x0), Just(x1), app(app(ty_@2, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Zero)) new_esEs16(x0, x1, ty_Double) new_primEqInt(Pos(Zero), Neg(Zero)) new_primEqInt(Neg(Zero), Pos(Zero)) new_esEs19(Left(x0), Left(x1), ty_Float, x2) new_esEs22(x0, x1, ty_Integer) new_esEs16(x0, x1, ty_Char) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4)) new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_span2Ys04(x0, x1, x2, x3, False, x4) new_primEqInt(Pos(Zero), Neg(Succ(x0))) new_primEqInt(Neg(Zero), Pos(Succ(x0))) new_esEs4(:(x0, x1), [], x2) new_esEs19(Right(x0), Right(x1), x2, ty_Float) new_esEs16(x0, x1, ty_Bool) new_esEs11(EQ, EQ) new_primEqInt(Pos(Succ(x0)), Neg(x1)) new_primEqInt(Neg(Succ(x0)), Pos(x1)) new_esEs16(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(ty_Either, x2), x3)) new_span2Zs02(x0, x1, x2, x3, False, x4) new_primMulNat0(Succ(x0), Zero) new_span2Zs2(:(x0, x1), x2) new_esEs23(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, ty_Bool) new_esEs24(x0, x1, ty_Bool) new_groupByZs1([], :(:(x0, x1), x2), x3) new_esEs6(:%(x0, x1), :%(x2, x3), x4) new_esEs15(x0, x1, app(app(ty_Either, x2), x3)) new_span2Zs01(x0, x1, True, x2) new_esEs21(Just(x0), Just(x1), app(ty_[], x2)) new_groupByZs10(x0, x1, x2, x3, x4, True, True, x5) new_span2Ys02(x0, x1, False, x2) new_esEs13(Double(x0, x1), Double(x2, x3)) new_esEs22(x0, x1, app(app(ty_@2, x2), x3)) new_esEs15(x0, x1, ty_Double) new_esEs26(x0, x1, ty_@0) new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_span2Zs2([], x0) new_esEs8(x0, x1, ty_Int) new_primPlusNat1(Succ(x0), x1) new_esEs20(Char(x0), Char(x1)) new_esEs19(Right(x0), Right(x1), x2, ty_Integer) new_esEs23(x0, x1, ty_Char) new_esEs16(x0, x1, ty_Ordering) new_span2Ys03(x0, x1, x2, x3, x4) new_span2Ys2(:(x0, x1), x2) new_esEs22(x0, x1, app(ty_[], x2)) new_esEs15(x0, x1, ty_Ordering) new_primMulNat0(Zero, Succ(x0)) new_esEs16(x0, x1, ty_Int) new_esEs21(Just(x0), Just(x1), app(app(ty_Either, x2), x3)) new_esEs19(Right(x0), Right(x1), x2, ty_Bool) new_esEs19(Left(x0), Right(x1), x2, x3) new_esEs19(Right(x0), Left(x1), x2, x3) new_esEs19(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5) new_esEs25(x0, x1, app(app(ty_@2, x2), x3)) new_esEs19(Left(x0), Left(x1), ty_Double, x2) new_esEs7(x0, x1, ty_Int) new_esEs23(x0, x1, app(ty_[], x2)) new_esEs25(x0, x1, ty_@0) new_esEs19(Right(x0), Right(x1), x2, ty_@0) new_esEs24(x0, x1, app(app(ty_Either, x2), x3)) new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1))) new_span2Zs3(x0, x1, :(x2, x3), x4) new_esEs16(x0, x1, ty_Float) new_esEs11(LT, GT) new_esEs11(GT, LT) new_esEs25(x0, x1, app(app(ty_Either, x2), x3)) new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8) new_span2Ys04(x0, x1, x2, x3, True, x4) new_esEs10(x0, x1) new_esEs23(x0, x1, ty_Int) new_primPlusNat0(Succ(x0), Zero) new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1))) new_esEs19(Right(x0), Right(x1), x2, app(ty_Ratio, x3)) new_esEs23(x0, x1, ty_@0) new_esEs17(Float(x0, x1), Float(x2, x3)) new_asAs(True, x0) new_esEs15(x0, x1, ty_Float) new_esEs11(LT, EQ) new_esEs11(EQ, LT) new_primMulNat0(Succ(x0), Succ(x1)) new_esEs21(Just(x0), Just(x1), ty_Integer) new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs26(x0, x1, app(app(ty_Either, x2), x3)) new_esEs5(@0, @0) new_esEs24(x0, x1, ty_@0) new_esEs22(x0, x1, ty_Char) new_esEs11(GT, GT) new_esEs25(x0, x1, ty_Integer) new_esEs4(:(x0, x1), :(x2, x3), x4) new_esEs19(Right(x0), Right(x1), x2, app(ty_[], x3)) new_esEs22(x0, x1, app(ty_Maybe, x2)) new_esEs26(x0, x1, ty_Integer) new_esEs26(x0, x1, app(ty_Maybe, x2)) new_esEs21(Just(x0), Just(x1), app(ty_Maybe, x2)) new_span2Zs03(x0, x1, x2, x3, x4) new_primEqNat0(Zero, Zero) new_esEs21(Just(x0), Nothing, x1) new_esEs23(x0, x1, ty_Bool) new_esEs12(True, True) new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_span2Zs02(x0, x1, x2, x3, True, x4) new_esEs15(x0, x1, ty_Char) new_esEs21(Nothing, Just(x0), x1) new_primPlusNat1(Zero, x0) new_esEs15(x0, x1, app(ty_[], x2)) new_esEs21(Just(x0), Just(x1), ty_Ordering) new_esEs19(Left(x0), Left(x1), ty_Integer, x2) new_esEs19(Left(x0), Left(x1), ty_Ordering, x2) new_sr(Pos(x0), Neg(x1)) new_sr(Neg(x0), Pos(x1)) new_esEs19(Left(x0), Left(x1), app(ty_[], x2), x3) new_esEs22(x0, x1, ty_Int) new_primEqInt(Neg(Succ(x0)), Neg(Zero)) new_span2Ys01(x0, x1, x2, x3, x4, x5, x6) new_groupByZs1([], :([], x0), x1) new_esEs19(Left(x0), Left(x1), ty_Bool, x2) new_esEs11(LT, LT) new_esEs22(x0, x1, ty_@0) new_esEs23(x0, x1, ty_Double) new_esEs16(x0, x1, app(ty_Ratio, x2)) new_esEs15(x0, x1, ty_Int) new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_esEs25(x0, x1, ty_Char) new_span2Ys3(x0, x1, :(x2, x3), x4) new_primEqNat0(Succ(x0), Zero) new_esEs19(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4)) new_esEs26(x0, x1, app(ty_Ratio, x2)) new_groupByZs12(x0, x1, x2, x3, x4, x5, x6) new_esEs25(x0, x1, ty_Double) new_esEs23(x0, x1, app(ty_Ratio, x2)) new_esEs7(x0, x1, ty_Integer) new_esEs19(Right(x0), Right(x1), x2, app(ty_Maybe, x3)) new_span2Zs3(x0, x1, [], x2) new_esEs15(x0, x1, ty_Bool) new_esEs25(x0, x1, ty_Bool) new_esEs15(x0, x1, app(ty_Ratio, x2)) new_esEs22(x0, x1, ty_Float) new_esEs4([], [], x0) new_primEqNat0(Succ(x0), Succ(x1)) new_esEs26(x0, x1, app(ty_[], x2)) new_esEs15(x0, x1, app(app(ty_@2, x2), x3)) new_esEs23(x0, x1, app(app(ty_@2, x2), x3)) new_esEs16(x0, x1, app(app(ty_Either, x2), x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) 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)) = 1 + x_1 + x_2 POL(@0) = 1 POL(@2(x_1, x_2)) = 1 + x_1 + x_2 POL(@3(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(Char(x_1)) = 1 POL(Double(x_1, x_2)) = 1 + x_1 + x_2 POL(EQ) = 1 POL(False) = 1 POL(Float(x_1, x_2)) = 1 + x_1 + x_2 POL(GT) = 1 POL(Integer(x_1)) = 1 + x_1 POL(Just(x_1)) = 1 + x_1 POL(LT) = 1 POL(Left(x_1)) = 1 + x_1 POL(Neg(x_1)) = 1 + x_1 POL(Nothing) = 0 POL(Pos(x_1)) = x_1 POL(Right(x_1)) = 1 + x_1 POL(Succ(x_1)) = 1 POL(True) = 1 POL(Zero) = 1 POL([]) = 0 POL(app(x_1, x_2)) = x_1 + x_2 POL(new_asAs(x_1, x_2)) = 1 + x_2 POL(new_esEs10(x_1, x_2)) = x_1 + x_2 POL(new_esEs11(x_1, x_2)) = x_1 + x_2 POL(new_esEs12(x_1, x_2)) = 1 + x_1 POL(new_esEs13(x_1, x_2)) = x_1 + x_2 POL(new_esEs14(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_4 POL(new_esEs15(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(new_esEs16(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs17(x_1, x_2)) = x_1 + x_2 POL(new_esEs18(x_1, x_2, x_3, x_4, x_5)) = x_1 + x_2 + x_4 + x_5 POL(new_esEs19(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(new_esEs20(x_1, x_2)) = 1 + x_2 POL(new_esEs21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs22(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs23(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs24(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(new_esEs25(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(new_esEs26(x_1, x_2, x_3)) = 0 POL(new_esEs4(x_1, x_2, x_3)) = x_1 + x_2 POL(new_esEs5(x_1, x_2)) = 1 + x_1 POL(new_esEs6(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(new_esEs7(x_1, x_2, x_3)) = x_1 + x_2 POL(new_esEs8(x_1, x_2, x_3)) = 0 POL(new_esEs9(x_1, x_2)) = x_1 + x_2 POL(new_groupByZs1(x_1, x_2, x_3)) = x_2 POL(new_groupByZs10(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8)) = 1 + x_5 POL(new_groupByZs11(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_5 POL(new_groupByZs12(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = 1 + x_5 POL(new_primEqInt(x_1, x_2)) = x_1 POL(new_primEqNat0(x_1, x_2)) = 1 POL(new_primMulNat0(x_1, x_2)) = 1 POL(new_primPlusNat0(x_1, x_2)) = 1 POL(new_primPlusNat1(x_1, x_2)) = 1 POL(new_span2Ys01(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = 1 + x_5 POL(new_span2Ys02(x_1, x_2, x_3, x_4)) = 1 + x_2 + x_4 POL(new_span2Ys03(x_1, x_2, x_3, x_4, x_5)) = 1 + x_3 POL(new_span2Ys04(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_1 + x_4 + x_6 POL(new_span2Ys2(x_1, x_2)) = x_1 + x_2 POL(new_span2Ys3(x_1, x_2, x_3, x_4)) = x_1 + x_3 + x_4 POL(new_span2Zs01(x_1, x_2, x_3, x_4)) = 1 + x_2 POL(new_span2Zs02(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_4 POL(new_span2Zs03(x_1, x_2, x_3, x_4, x_5)) = x_4 POL(new_span2Zs04(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = 1 + x_6 POL(new_span2Zs2(x_1, x_2)) = x_1 POL(new_span2Zs3(x_1, x_2, x_3, x_4)) = x_3 POL(new_sr(x_1, x_2)) = 1 + x_1 + x_2 POL(ty_@0) = 1 POL(ty_@2) = 1 POL(ty_@3) = 0 POL(ty_Bool) = 1 POL(ty_Char) = 1 POL(ty_Double) = 0 POL(ty_Either) = 1 POL(ty_Float) = 1 POL(ty_Int) = 0 POL(ty_Integer) = 0 POL(ty_Maybe) = 1 POL(ty_Ordering) = 0 POL(ty_Ratio) = 1 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(vuu24, vuu25, [], hb) -> [] new_span2Zs3(vuu24, vuu25, :(vuu280, vuu281), hb) -> new_span2Zs02(vuu24, vuu25, vuu280, vuu281, new_esEs4(:(vuu24, vuu25), vuu280, hb), hb) new_span2Zs2([], ba) -> [] new_span2Zs2(:(vuu3110, vuu3111), ba) -> new_span2Zs01(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) new_span2Zs04(vuu24, vuu25, vuu280, vuu281, vuu51, vuu50, hb) -> vuu50 new_span2Zs03(vuu3110, vuu3111, vuu45, vuu44, ba) -> vuu44 new_span2Zs02(vuu24, vuu25, vuu280, vuu281, True, hb) -> new_span2Zs04(vuu24, vuu25, vuu280, vuu281, new_span2Ys3(vuu24, vuu25, vuu281, hb), new_span2Zs3(vuu24, vuu25, vuu281, hb), hb) new_span2Zs02(vuu24, vuu25, vuu280, vuu281, False, hb) -> :(vuu280, vuu281) new_span2Zs01(vuu3110, vuu3111, True, ba) -> new_span2Zs03(vuu3110, vuu3111, new_span2Ys2(vuu3111, ba), new_span2Zs2(vuu3111, ba), ba) new_span2Zs01(vuu3110, vuu3111, False, ba) -> :(vuu3110, vuu3111) new_span2Ys3(vuu11, vuu12, [], eb) -> [] new_span2Ys3(vuu11, vuu12, :(vuu150, vuu151), eb) -> new_span2Ys04(vuu11, vuu12, vuu150, vuu151, new_esEs4(:(vuu11, vuu12), vuu150, eb), eb) new_span2Ys2([], ba) -> [] new_span2Ys2(:(vuu3110, vuu3111), ba) -> new_span2Ys02(vuu3110, vuu3111, new_esEs4([], vuu3110, ba), ba) new_span2Ys04(vuu11, vuu12, vuu150, vuu151, True, eb) -> new_span2Ys01(vuu11, vuu12, vuu150, vuu151, new_span2Ys3(vuu11, vuu12, vuu151, eb), new_span2Zs3(vuu11, vuu12, vuu151, eb), eb) new_span2Ys04(vuu11, vuu12, vuu150, vuu151, False, eb) -> [] new_span2Ys03(vuu3110, vuu3111, vuu43, vuu42, ba) -> :(vuu3110, vuu43) new_span2Ys02(vuu3110, vuu3111, True, ba) -> new_span2Ys03(vuu3110, vuu3111, new_span2Ys2(vuu3111, ba), new_span2Zs2(vuu3111, ba), ba) new_span2Ys02(vuu3110, vuu3111, False, ba) -> [] new_span2Ys01(vuu11, vuu12, vuu150, vuu151, vuu47, vuu46, eb) -> :(vuu150, vuu47) new_groupByZs12(vuu24, vuu25, vuu26, vuu27, vuu28, vuu38, hb) -> new_span2Zs3(vuu24, vuu25, vuu28, hb) new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) -> :(:(vuu26, vuu27), vuu28) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, True, True, hb) -> new_groupByZs12(vuu24, vuu25, vuu26, vuu27, vuu28, new_span2Ys3(vuu24, vuu25, vuu28, hb), hb) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, True, False, hb) -> new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) new_groupByZs10(vuu24, vuu25, vuu26, vuu27, vuu28, False, vuu30, hb) -> new_groupByZs11(vuu24, vuu25, vuu26, vuu27, vuu28, hb) new_groupByZs1(vuu30, [], ba) -> [] new_groupByZs1([], :([], vuu311), ba) -> new_span2Zs2(vuu311, ba) new_groupByZs1([], :(:(vuu3100, vuu3101), vuu311), ba) -> :(:(vuu3100, vuu3101), vuu311) new_groupByZs1(:(vuu300, vuu301), :([], vuu311), ba) -> :([], vuu311) new_groupByZs1(:(vuu300, vuu301), :(:(vuu3100, vuu3101), vuu311), ba) -> new_groupByZs10(vuu300, vuu301, vuu3100, vuu3101, vuu311, new_esEs26(vuu300, vuu3100, ba), new_esEs4(vuu301, vuu3101, ba), ba) ---------------------------------------- (25) YES ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(vuu4900), Succ(vuu31001000)) -> new_primPlusNat(vuu4900, 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(vuu4900), Succ(vuu31001000)) -> new_primPlusNat(vuu4900, 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