12.22/4.91 YES 13.82/5.40 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 13.82/5.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.82/5.40 13.82/5.40 13.82/5.40 H-Termination with start terms of the given HASKELL could be proven: 13.82/5.40 13.82/5.40 (0) HASKELL 13.82/5.40 (1) BR [EQUIVALENT, 0 ms] 13.82/5.40 (2) HASKELL 13.82/5.40 (3) COR [EQUIVALENT, 17 ms] 13.82/5.40 (4) HASKELL 13.82/5.40 (5) Narrow [SOUND, 0 ms] 13.82/5.40 (6) AND 13.82/5.40 (7) QDP 13.82/5.40 (8) TransformationProof [EQUIVALENT, 0 ms] 13.82/5.40 (9) QDP 13.82/5.40 (10) UsableRulesProof [EQUIVALENT, 0 ms] 13.82/5.40 (11) QDP 13.82/5.40 (12) QReductionProof [EQUIVALENT, 0 ms] 13.82/5.40 (13) QDP 13.82/5.40 (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (15) YES 13.82/5.40 (16) QDP 13.82/5.40 (17) TransformationProof [EQUIVALENT, 0 ms] 13.82/5.40 (18) QDP 13.82/5.40 (19) UsableRulesProof [EQUIVALENT, 0 ms] 13.82/5.40 (20) QDP 13.82/5.40 (21) QReductionProof [EQUIVALENT, 0 ms] 13.82/5.40 (22) QDP 13.82/5.40 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (24) YES 13.82/5.40 (25) QDP 13.82/5.40 (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (27) YES 13.82/5.40 (28) QDP 13.82/5.40 (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (30) YES 13.82/5.40 (31) QDP 13.82/5.40 (32) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (33) YES 13.82/5.40 (34) QDP 13.82/5.40 (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (36) YES 13.82/5.40 (37) QDP 13.82/5.40 (38) QDPSizeChangeProof [EQUIVALENT, 0 ms] 13.82/5.40 (39) YES 13.82/5.40 13.82/5.40 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (0) 13.82/5.40 Obligation: 13.82/5.40 mainModule Main 13.82/5.40 module Maybe where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 module List where { 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 isPrefixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isPrefixOf [] _ = True; 13.82/5.40 isPrefixOf _ [] = False; 13.82/5.40 isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; 13.82/5.40 13.82/5.40 isSuffixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isSuffixOf x y = reverse x `isPrefixOf` reverse y; 13.82/5.40 13.82/5.40 } 13.82/5.40 module Main where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (1) BR (EQUIVALENT) 13.82/5.40 Replaced joker patterns by fresh variables and removed binding patterns. 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (2) 13.82/5.40 Obligation: 13.82/5.40 mainModule Main 13.82/5.40 module Maybe where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 module List where { 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 isPrefixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isPrefixOf [] xw = True; 13.82/5.40 isPrefixOf xx [] = False; 13.82/5.40 isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; 13.82/5.40 13.82/5.40 isSuffixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isSuffixOf x y = reverse x `isPrefixOf` reverse y; 13.82/5.40 13.82/5.40 } 13.82/5.40 module Main where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (3) COR (EQUIVALENT) 13.82/5.40 Cond Reductions: 13.82/5.40 The following Function with conditions 13.82/5.40 "undefined |Falseundefined; 13.82/5.40 " 13.82/5.40 is transformed to 13.82/5.40 "undefined = undefined1; 13.82/5.40 " 13.82/5.40 "undefined0 True = undefined; 13.82/5.40 " 13.82/5.40 "undefined1 = undefined0 False; 13.82/5.40 " 13.82/5.40 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (4) 13.82/5.40 Obligation: 13.82/5.40 mainModule Main 13.82/5.40 module Maybe where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 module List where { 13.82/5.40 import qualified Main; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 isPrefixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isPrefixOf [] xw = True; 13.82/5.40 isPrefixOf xx [] = False; 13.82/5.40 isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; 13.82/5.40 13.82/5.40 isSuffixOf :: Eq a => [a] -> [a] -> Bool; 13.82/5.40 isSuffixOf x y = reverse x `isPrefixOf` reverse y; 13.82/5.40 13.82/5.40 } 13.82/5.40 module Main where { 13.82/5.40 import qualified List; 13.82/5.40 import qualified Maybe; 13.82/5.40 import qualified Prelude; 13.82/5.40 } 13.82/5.40 13.82/5.40 ---------------------------------------- 13.82/5.40 13.82/5.40 (5) Narrow (SOUND) 13.82/5.40 Haskell To QDPs 13.82/5.40 13.82/5.40 digraph dp_graph { 13.82/5.40 node [outthreshold=100, inthreshold=100];1[label="List.isSuffixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 13.82/5.40 3[label="List.isSuffixOf xy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 13.82/5.40 4[label="List.isSuffixOf xy3 xy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 13.82/5.40 5[label="List.isPrefixOf (reverse xy3) (reverse xy4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 13.82/5.40 6[label="List.isPrefixOf (foldl (flip (:)) [] xy3) (reverse xy4)",fontsize=16,color="burlywood",shape="box"];1251[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];6 -> 1251[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1251 -> 7[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1252[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 1252[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1252 -> 8[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 7[label="List.isPrefixOf (foldl (flip (:)) [] (xy30 : xy31)) (reverse xy4)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 13.82/5.40 8[label="List.isPrefixOf (foldl (flip (:)) [] []) (reverse xy4)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 13.82/5.40 9 -> 350[label="",style="dashed", color="red", weight=0]; 13.82/5.40 9[label="List.isPrefixOf (foldl (flip (:)) (flip (:) [] xy30) xy31) (reverse xy4)",fontsize=16,color="magenta"];9 -> 351[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 9 -> 352[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 9 -> 353[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 9 -> 354[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 10[label="List.isPrefixOf [] (reverse xy4)",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 13.82/5.40 351[label="xy30",fontsize=16,color="green",shape="box"];352[label="xy31",fontsize=16,color="green",shape="box"];353[label="xy4",fontsize=16,color="green",shape="box"];354[label="[]",fontsize=16,color="green",shape="box"];350[label="List.isPrefixOf (foldl (flip (:)) (flip (:) xy33 xy34) xy35) (reverse xy36)",fontsize=16,color="burlywood",shape="triangle"];1253[label="xy35/xy350 : xy351",fontsize=10,color="white",style="solid",shape="box"];350 -> 1253[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1253 -> 387[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1254[label="xy35/[]",fontsize=10,color="white",style="solid",shape="box"];350 -> 1254[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1254 -> 388[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 13[label="True",fontsize=16,color="green",shape="box"];387[label="List.isPrefixOf (foldl (flip (:)) (flip (:) xy33 xy34) (xy350 : xy351)) (reverse xy36)",fontsize=16,color="black",shape="box"];387 -> 389[label="",style="solid", color="black", weight=3]; 13.82/5.40 388[label="List.isPrefixOf (foldl (flip (:)) (flip (:) xy33 xy34) []) (reverse xy36)",fontsize=16,color="black",shape="box"];388 -> 390[label="",style="solid", color="black", weight=3]; 13.82/5.40 389 -> 350[label="",style="dashed", color="red", weight=0]; 13.82/5.40 389[label="List.isPrefixOf (foldl (flip (:)) (flip (:) (flip (:) xy33 xy34) xy350) xy351) (reverse xy36)",fontsize=16,color="magenta"];389 -> 391[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 389 -> 392[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 389 -> 393[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 390[label="List.isPrefixOf (flip (:) xy33 xy34) (reverse xy36)",fontsize=16,color="black",shape="box"];390 -> 394[label="",style="solid", color="black", weight=3]; 13.82/5.40 391[label="xy350",fontsize=16,color="green",shape="box"];392[label="xy351",fontsize=16,color="green",shape="box"];393[label="flip (:) xy33 xy34",fontsize=16,color="black",shape="triangle"];393 -> 395[label="",style="solid", color="black", weight=3]; 13.82/5.40 394[label="List.isPrefixOf ((:) xy34 xy33) (reverse xy36)",fontsize=16,color="black",shape="box"];394 -> 396[label="",style="solid", color="black", weight=3]; 13.82/5.40 395[label="(:) xy34 xy33",fontsize=16,color="green",shape="box"];396 -> 401[label="",style="dashed", color="red", weight=0]; 13.82/5.40 396[label="List.isPrefixOf ((:) xy34 xy33) (foldl (flip (:)) [] xy36)",fontsize=16,color="magenta"];396 -> 402[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 396 -> 403[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 402[label="xy36",fontsize=16,color="green",shape="box"];403[label="[]",fontsize=16,color="green",shape="box"];401[label="List.isPrefixOf ((:) xy34 xy33) (foldl (flip (:)) xy37 xy361)",fontsize=16,color="burlywood",shape="triangle"];1255[label="xy361/xy3610 : xy3611",fontsize=10,color="white",style="solid",shape="box"];401 -> 1255[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1255 -> 405[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1256[label="xy361/[]",fontsize=10,color="white",style="solid",shape="box"];401 -> 1256[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1256 -> 406[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 405[label="List.isPrefixOf ((:) xy34 xy33) (foldl (flip (:)) xy37 (xy3610 : xy3611))",fontsize=16,color="black",shape="box"];405 -> 407[label="",style="solid", color="black", weight=3]; 13.82/5.40 406[label="List.isPrefixOf ((:) xy34 xy33) (foldl (flip (:)) xy37 [])",fontsize=16,color="black",shape="box"];406 -> 408[label="",style="solid", color="black", weight=3]; 13.82/5.40 407 -> 401[label="",style="dashed", color="red", weight=0]; 13.82/5.40 407[label="List.isPrefixOf ((:) xy34 xy33) (foldl (flip (:)) (flip (:) xy37 xy3610) xy3611)",fontsize=16,color="magenta"];407 -> 409[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 407 -> 410[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 408[label="List.isPrefixOf ((:) xy34 xy33) xy37",fontsize=16,color="burlywood",shape="box"];1257[label="xy37/xy370 : xy371",fontsize=10,color="white",style="solid",shape="box"];408 -> 1257[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1257 -> 411[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1258[label="xy37/[]",fontsize=10,color="white",style="solid",shape="box"];408 -> 1258[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1258 -> 412[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 409[label="xy3611",fontsize=16,color="green",shape="box"];410 -> 393[label="",style="dashed", color="red", weight=0]; 13.82/5.40 410[label="flip (:) xy37 xy3610",fontsize=16,color="magenta"];410 -> 413[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 410 -> 414[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 411[label="List.isPrefixOf ((:) xy34 xy33) (xy370 : xy371)",fontsize=16,color="black",shape="box"];411 -> 415[label="",style="solid", color="black", weight=3]; 13.82/5.40 412[label="List.isPrefixOf ((:) xy34 xy33) []",fontsize=16,color="black",shape="box"];412 -> 416[label="",style="solid", color="black", weight=3]; 13.82/5.40 413[label="xy3610",fontsize=16,color="green",shape="box"];414[label="xy37",fontsize=16,color="green",shape="box"];415 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 415[label="xy34 == xy370 && List.isPrefixOf xy33 xy371",fontsize=16,color="magenta"];415 -> 566[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 415 -> 567[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 416[label="False",fontsize=16,color="green",shape="box"];566[label="List.isPrefixOf xy33 xy371",fontsize=16,color="burlywood",shape="triangle"];1259[label="xy33/xy330 : xy331",fontsize=10,color="white",style="solid",shape="box"];566 -> 1259[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1259 -> 570[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1260[label="xy33/[]",fontsize=10,color="white",style="solid",shape="box"];566 -> 1260[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1260 -> 571[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 567[label="xy34 == xy370",fontsize=16,color="blue",shape="box"];1261[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1261[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1261 -> 572[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1262[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1262[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1262 -> 573[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1263[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1263[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1263 -> 574[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1264[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1264[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1264 -> 575[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1265[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1265[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1265 -> 576[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1266[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1266[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1266 -> 577[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1267[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1267[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1267 -> 578[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1268[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1268[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1268 -> 579[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1269[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1269[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1269 -> 580[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1270[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1270[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1270 -> 581[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1271[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1271[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1271 -> 582[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1272[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1272[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1272 -> 583[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1273[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1273[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1273 -> 584[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1274[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];567 -> 1274[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1274 -> 585[label="",style="solid", color="blue", weight=3]; 13.82/5.40 565[label="xy56 && xy57",fontsize=16,color="burlywood",shape="triangle"];1275[label="xy56/False",fontsize=10,color="white",style="solid",shape="box"];565 -> 1275[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1275 -> 586[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1276[label="xy56/True",fontsize=10,color="white",style="solid",shape="box"];565 -> 1276[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1276 -> 587[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 570[label="List.isPrefixOf (xy330 : xy331) xy371",fontsize=16,color="burlywood",shape="box"];1277[label="xy371/xy3710 : xy3711",fontsize=10,color="white",style="solid",shape="box"];570 -> 1277[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1277 -> 588[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1278[label="xy371/[]",fontsize=10,color="white",style="solid",shape="box"];570 -> 1278[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1278 -> 589[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 571[label="List.isPrefixOf [] xy371",fontsize=16,color="black",shape="box"];571 -> 590[label="",style="solid", color="black", weight=3]; 13.82/5.40 572[label="xy34 == xy370",fontsize=16,color="black",shape="triangle"];572 -> 591[label="",style="solid", color="black", weight=3]; 13.82/5.40 573[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1279[label="xy34/(xy340,xy341)",fontsize=10,color="white",style="solid",shape="box"];573 -> 1279[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1279 -> 592[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 574[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1280[label="xy34/Integer xy340",fontsize=10,color="white",style="solid",shape="box"];574 -> 1280[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1280 -> 593[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 575[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1281[label="xy34/(xy340,xy341,xy342)",fontsize=10,color="white",style="solid",shape="box"];575 -> 1281[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1281 -> 594[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 576[label="xy34 == xy370",fontsize=16,color="black",shape="triangle"];576 -> 595[label="",style="solid", color="black", weight=3]; 13.82/5.40 577[label="xy34 == xy370",fontsize=16,color="black",shape="triangle"];577 -> 596[label="",style="solid", color="black", weight=3]; 13.82/5.40 578[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1282[label="xy34/()",fontsize=10,color="white",style="solid",shape="box"];578 -> 1282[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1282 -> 597[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 579[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1283[label="xy34/Nothing",fontsize=10,color="white",style="solid",shape="box"];579 -> 1283[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1283 -> 598[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1284[label="xy34/Just xy340",fontsize=10,color="white",style="solid",shape="box"];579 -> 1284[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1284 -> 599[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 580[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1285[label="xy34/LT",fontsize=10,color="white",style="solid",shape="box"];580 -> 1285[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1285 -> 600[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1286[label="xy34/EQ",fontsize=10,color="white",style="solid",shape="box"];580 -> 1286[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1286 -> 601[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1287[label="xy34/GT",fontsize=10,color="white",style="solid",shape="box"];580 -> 1287[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1287 -> 602[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 581[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1288[label="xy34/xy340 :% xy341",fontsize=10,color="white",style="solid",shape="box"];581 -> 1288[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1288 -> 603[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 582[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1289[label="xy34/xy340 : xy341",fontsize=10,color="white",style="solid",shape="box"];582 -> 1289[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1289 -> 604[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1290[label="xy34/[]",fontsize=10,color="white",style="solid",shape="box"];582 -> 1290[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1290 -> 605[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 583[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1291[label="xy34/Left xy340",fontsize=10,color="white",style="solid",shape="box"];583 -> 1291[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1291 -> 606[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1292[label="xy34/Right xy340",fontsize=10,color="white",style="solid",shape="box"];583 -> 1292[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1292 -> 607[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 584[label="xy34 == xy370",fontsize=16,color="burlywood",shape="triangle"];1293[label="xy34/False",fontsize=10,color="white",style="solid",shape="box"];584 -> 1293[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1293 -> 608[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1294[label="xy34/True",fontsize=10,color="white",style="solid",shape="box"];584 -> 1294[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1294 -> 609[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 585[label="xy34 == xy370",fontsize=16,color="black",shape="triangle"];585 -> 610[label="",style="solid", color="black", weight=3]; 13.82/5.40 586[label="False && xy57",fontsize=16,color="black",shape="box"];586 -> 611[label="",style="solid", color="black", weight=3]; 13.82/5.40 587[label="True && xy57",fontsize=16,color="black",shape="box"];587 -> 612[label="",style="solid", color="black", weight=3]; 13.82/5.40 588[label="List.isPrefixOf (xy330 : xy331) (xy3710 : xy3711)",fontsize=16,color="black",shape="box"];588 -> 613[label="",style="solid", color="black", weight=3]; 13.82/5.40 589[label="List.isPrefixOf (xy330 : xy331) []",fontsize=16,color="black",shape="box"];589 -> 614[label="",style="solid", color="black", weight=3]; 13.82/5.40 590[label="True",fontsize=16,color="green",shape="box"];591[label="primEqChar xy34 xy370",fontsize=16,color="burlywood",shape="box"];1295[label="xy34/Char xy340",fontsize=10,color="white",style="solid",shape="box"];591 -> 1295[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1295 -> 615[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 592[label="(xy340,xy341) == xy370",fontsize=16,color="burlywood",shape="box"];1296[label="xy370/(xy3700,xy3701)",fontsize=10,color="white",style="solid",shape="box"];592 -> 1296[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1296 -> 616[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 593[label="Integer xy340 == xy370",fontsize=16,color="burlywood",shape="box"];1297[label="xy370/Integer xy3700",fontsize=10,color="white",style="solid",shape="box"];593 -> 1297[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1297 -> 617[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 594[label="(xy340,xy341,xy342) == xy370",fontsize=16,color="burlywood",shape="box"];1298[label="xy370/(xy3700,xy3701,xy3702)",fontsize=10,color="white",style="solid",shape="box"];594 -> 1298[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1298 -> 618[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 595[label="primEqFloat xy34 xy370",fontsize=16,color="burlywood",shape="box"];1299[label="xy34/Float xy340 xy341",fontsize=10,color="white",style="solid",shape="box"];595 -> 1299[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1299 -> 619[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 596[label="primEqDouble xy34 xy370",fontsize=16,color="burlywood",shape="box"];1300[label="xy34/Double xy340 xy341",fontsize=10,color="white",style="solid",shape="box"];596 -> 1300[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1300 -> 620[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 597[label="() == xy370",fontsize=16,color="burlywood",shape="box"];1301[label="xy370/()",fontsize=10,color="white",style="solid",shape="box"];597 -> 1301[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1301 -> 621[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 598[label="Nothing == xy370",fontsize=16,color="burlywood",shape="box"];1302[label="xy370/Nothing",fontsize=10,color="white",style="solid",shape="box"];598 -> 1302[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1302 -> 622[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1303[label="xy370/Just xy3700",fontsize=10,color="white",style="solid",shape="box"];598 -> 1303[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1303 -> 623[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 599[label="Just xy340 == xy370",fontsize=16,color="burlywood",shape="box"];1304[label="xy370/Nothing",fontsize=10,color="white",style="solid",shape="box"];599 -> 1304[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1304 -> 624[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1305[label="xy370/Just xy3700",fontsize=10,color="white",style="solid",shape="box"];599 -> 1305[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1305 -> 625[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 600[label="LT == xy370",fontsize=16,color="burlywood",shape="box"];1306[label="xy370/LT",fontsize=10,color="white",style="solid",shape="box"];600 -> 1306[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1306 -> 626[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1307[label="xy370/EQ",fontsize=10,color="white",style="solid",shape="box"];600 -> 1307[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1307 -> 627[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1308[label="xy370/GT",fontsize=10,color="white",style="solid",shape="box"];600 -> 1308[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1308 -> 628[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 601[label="EQ == xy370",fontsize=16,color="burlywood",shape="box"];1309[label="xy370/LT",fontsize=10,color="white",style="solid",shape="box"];601 -> 1309[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1309 -> 629[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1310[label="xy370/EQ",fontsize=10,color="white",style="solid",shape="box"];601 -> 1310[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1310 -> 630[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1311[label="xy370/GT",fontsize=10,color="white",style="solid",shape="box"];601 -> 1311[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1311 -> 631[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 602[label="GT == xy370",fontsize=16,color="burlywood",shape="box"];1312[label="xy370/LT",fontsize=10,color="white",style="solid",shape="box"];602 -> 1312[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1312 -> 632[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1313[label="xy370/EQ",fontsize=10,color="white",style="solid",shape="box"];602 -> 1313[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1313 -> 633[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1314[label="xy370/GT",fontsize=10,color="white",style="solid",shape="box"];602 -> 1314[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1314 -> 634[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 603[label="xy340 :% xy341 == xy370",fontsize=16,color="burlywood",shape="box"];1315[label="xy370/xy3700 :% xy3701",fontsize=10,color="white",style="solid",shape="box"];603 -> 1315[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1315 -> 635[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 604[label="xy340 : xy341 == xy370",fontsize=16,color="burlywood",shape="box"];1316[label="xy370/xy3700 : xy3701",fontsize=10,color="white",style="solid",shape="box"];604 -> 1316[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1316 -> 636[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1317[label="xy370/[]",fontsize=10,color="white",style="solid",shape="box"];604 -> 1317[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1317 -> 637[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 605[label="[] == xy370",fontsize=16,color="burlywood",shape="box"];1318[label="xy370/xy3700 : xy3701",fontsize=10,color="white",style="solid",shape="box"];605 -> 1318[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1318 -> 638[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1319[label="xy370/[]",fontsize=10,color="white",style="solid",shape="box"];605 -> 1319[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1319 -> 639[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 606[label="Left xy340 == xy370",fontsize=16,color="burlywood",shape="box"];1320[label="xy370/Left xy3700",fontsize=10,color="white",style="solid",shape="box"];606 -> 1320[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1320 -> 640[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1321[label="xy370/Right xy3700",fontsize=10,color="white",style="solid",shape="box"];606 -> 1321[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1321 -> 641[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 607[label="Right xy340 == xy370",fontsize=16,color="burlywood",shape="box"];1322[label="xy370/Left xy3700",fontsize=10,color="white",style="solid",shape="box"];607 -> 1322[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1322 -> 642[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1323[label="xy370/Right xy3700",fontsize=10,color="white",style="solid",shape="box"];607 -> 1323[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1323 -> 643[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 608[label="False == xy370",fontsize=16,color="burlywood",shape="box"];1324[label="xy370/False",fontsize=10,color="white",style="solid",shape="box"];608 -> 1324[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1324 -> 644[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1325[label="xy370/True",fontsize=10,color="white",style="solid",shape="box"];608 -> 1325[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1325 -> 645[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 609[label="True == xy370",fontsize=16,color="burlywood",shape="box"];1326[label="xy370/False",fontsize=10,color="white",style="solid",shape="box"];609 -> 1326[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1326 -> 646[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1327[label="xy370/True",fontsize=10,color="white",style="solid",shape="box"];609 -> 1327[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1327 -> 647[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 610[label="primEqInt xy34 xy370",fontsize=16,color="burlywood",shape="triangle"];1328[label="xy34/Pos xy340",fontsize=10,color="white",style="solid",shape="box"];610 -> 1328[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1328 -> 648[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1329[label="xy34/Neg xy340",fontsize=10,color="white",style="solid",shape="box"];610 -> 1329[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1329 -> 649[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 611[label="False",fontsize=16,color="green",shape="box"];612[label="xy57",fontsize=16,color="green",shape="box"];613 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 613[label="xy330 == xy3710 && List.isPrefixOf xy331 xy3711",fontsize=16,color="magenta"];613 -> 650[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 613 -> 651[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 614[label="False",fontsize=16,color="green",shape="box"];615[label="primEqChar (Char xy340) xy370",fontsize=16,color="burlywood",shape="box"];1330[label="xy370/Char xy3700",fontsize=10,color="white",style="solid",shape="box"];615 -> 1330[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1330 -> 652[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 616[label="(xy340,xy341) == (xy3700,xy3701)",fontsize=16,color="black",shape="box"];616 -> 653[label="",style="solid", color="black", weight=3]; 13.82/5.40 617[label="Integer xy340 == Integer xy3700",fontsize=16,color="black",shape="box"];617 -> 654[label="",style="solid", color="black", weight=3]; 13.82/5.40 618[label="(xy340,xy341,xy342) == (xy3700,xy3701,xy3702)",fontsize=16,color="black",shape="box"];618 -> 655[label="",style="solid", color="black", weight=3]; 13.82/5.40 619[label="primEqFloat (Float xy340 xy341) xy370",fontsize=16,color="burlywood",shape="box"];1331[label="xy370/Float xy3700 xy3701",fontsize=10,color="white",style="solid",shape="box"];619 -> 1331[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1331 -> 656[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 620[label="primEqDouble (Double xy340 xy341) xy370",fontsize=16,color="burlywood",shape="box"];1332[label="xy370/Double xy3700 xy3701",fontsize=10,color="white",style="solid",shape="box"];620 -> 1332[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1332 -> 657[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 621[label="() == ()",fontsize=16,color="black",shape="box"];621 -> 658[label="",style="solid", color="black", weight=3]; 13.82/5.40 622[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];622 -> 659[label="",style="solid", color="black", weight=3]; 13.82/5.40 623[label="Nothing == Just xy3700",fontsize=16,color="black",shape="box"];623 -> 660[label="",style="solid", color="black", weight=3]; 13.82/5.40 624[label="Just xy340 == Nothing",fontsize=16,color="black",shape="box"];624 -> 661[label="",style="solid", color="black", weight=3]; 13.82/5.40 625[label="Just xy340 == Just xy3700",fontsize=16,color="black",shape="box"];625 -> 662[label="",style="solid", color="black", weight=3]; 13.82/5.40 626[label="LT == LT",fontsize=16,color="black",shape="box"];626 -> 663[label="",style="solid", color="black", weight=3]; 13.82/5.40 627[label="LT == EQ",fontsize=16,color="black",shape="box"];627 -> 664[label="",style="solid", color="black", weight=3]; 13.82/5.40 628[label="LT == GT",fontsize=16,color="black",shape="box"];628 -> 665[label="",style="solid", color="black", weight=3]; 13.82/5.40 629[label="EQ == LT",fontsize=16,color="black",shape="box"];629 -> 666[label="",style="solid", color="black", weight=3]; 13.82/5.40 630[label="EQ == EQ",fontsize=16,color="black",shape="box"];630 -> 667[label="",style="solid", color="black", weight=3]; 13.82/5.40 631[label="EQ == GT",fontsize=16,color="black",shape="box"];631 -> 668[label="",style="solid", color="black", weight=3]; 13.82/5.40 632[label="GT == LT",fontsize=16,color="black",shape="box"];632 -> 669[label="",style="solid", color="black", weight=3]; 13.82/5.40 633[label="GT == EQ",fontsize=16,color="black",shape="box"];633 -> 670[label="",style="solid", color="black", weight=3]; 13.82/5.40 634[label="GT == GT",fontsize=16,color="black",shape="box"];634 -> 671[label="",style="solid", color="black", weight=3]; 13.82/5.40 635[label="xy340 :% xy341 == xy3700 :% xy3701",fontsize=16,color="black",shape="box"];635 -> 672[label="",style="solid", color="black", weight=3]; 13.82/5.40 636[label="xy340 : xy341 == xy3700 : xy3701",fontsize=16,color="black",shape="box"];636 -> 673[label="",style="solid", color="black", weight=3]; 13.82/5.40 637[label="xy340 : xy341 == []",fontsize=16,color="black",shape="box"];637 -> 674[label="",style="solid", color="black", weight=3]; 13.82/5.40 638[label="[] == xy3700 : xy3701",fontsize=16,color="black",shape="box"];638 -> 675[label="",style="solid", color="black", weight=3]; 13.82/5.40 639[label="[] == []",fontsize=16,color="black",shape="box"];639 -> 676[label="",style="solid", color="black", weight=3]; 13.82/5.40 640[label="Left xy340 == Left xy3700",fontsize=16,color="black",shape="box"];640 -> 677[label="",style="solid", color="black", weight=3]; 13.82/5.40 641[label="Left xy340 == Right xy3700",fontsize=16,color="black",shape="box"];641 -> 678[label="",style="solid", color="black", weight=3]; 13.82/5.40 642[label="Right xy340 == Left xy3700",fontsize=16,color="black",shape="box"];642 -> 679[label="",style="solid", color="black", weight=3]; 13.82/5.40 643[label="Right xy340 == Right xy3700",fontsize=16,color="black",shape="box"];643 -> 680[label="",style="solid", color="black", weight=3]; 13.82/5.40 644[label="False == False",fontsize=16,color="black",shape="box"];644 -> 681[label="",style="solid", color="black", weight=3]; 13.82/5.40 645[label="False == True",fontsize=16,color="black",shape="box"];645 -> 682[label="",style="solid", color="black", weight=3]; 13.82/5.40 646[label="True == False",fontsize=16,color="black",shape="box"];646 -> 683[label="",style="solid", color="black", weight=3]; 13.82/5.40 647[label="True == True",fontsize=16,color="black",shape="box"];647 -> 684[label="",style="solid", color="black", weight=3]; 13.82/5.40 648[label="primEqInt (Pos xy340) xy370",fontsize=16,color="burlywood",shape="box"];1333[label="xy340/Succ xy3400",fontsize=10,color="white",style="solid",shape="box"];648 -> 1333[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1333 -> 685[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1334[label="xy340/Zero",fontsize=10,color="white",style="solid",shape="box"];648 -> 1334[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1334 -> 686[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 649[label="primEqInt (Neg xy340) xy370",fontsize=16,color="burlywood",shape="box"];1335[label="xy340/Succ xy3400",fontsize=10,color="white",style="solid",shape="box"];649 -> 1335[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1335 -> 687[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1336[label="xy340/Zero",fontsize=10,color="white",style="solid",shape="box"];649 -> 1336[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1336 -> 688[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 650 -> 566[label="",style="dashed", color="red", weight=0]; 13.82/5.40 650[label="List.isPrefixOf xy331 xy3711",fontsize=16,color="magenta"];650 -> 689[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 650 -> 690[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 651[label="xy330 == xy3710",fontsize=16,color="blue",shape="box"];1337[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1337[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1337 -> 691[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1338[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1338[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1338 -> 692[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1339[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1339[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1339 -> 693[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1340[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1340[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1340 -> 694[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1341[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1341[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1341 -> 695[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1342[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1342[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1342 -> 696[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1343[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1343[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1343 -> 697[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1344[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1344[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1344 -> 698[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1345[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1345[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1345 -> 699[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1346[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1346[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1346 -> 700[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1347[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1347[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1347 -> 701[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1348[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1348[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1348 -> 702[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1349[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1349[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1349 -> 703[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1350[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];651 -> 1350[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1350 -> 704[label="",style="solid", color="blue", weight=3]; 13.82/5.40 652[label="primEqChar (Char xy340) (Char xy3700)",fontsize=16,color="black",shape="box"];652 -> 705[label="",style="solid", color="black", weight=3]; 13.82/5.40 653 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 653[label="xy340 == xy3700 && xy341 == xy3701",fontsize=16,color="magenta"];653 -> 706[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 653 -> 707[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 654 -> 610[label="",style="dashed", color="red", weight=0]; 13.82/5.40 654[label="primEqInt xy340 xy3700",fontsize=16,color="magenta"];654 -> 708[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 654 -> 709[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 655 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 655[label="xy340 == xy3700 && xy341 == xy3701 && xy342 == xy3702",fontsize=16,color="magenta"];655 -> 710[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 655 -> 711[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 656[label="primEqFloat (Float xy340 xy341) (Float xy3700 xy3701)",fontsize=16,color="black",shape="box"];656 -> 712[label="",style="solid", color="black", weight=3]; 13.82/5.40 657[label="primEqDouble (Double xy340 xy341) (Double xy3700 xy3701)",fontsize=16,color="black",shape="box"];657 -> 713[label="",style="solid", color="black", weight=3]; 13.82/5.40 658[label="True",fontsize=16,color="green",shape="box"];659[label="True",fontsize=16,color="green",shape="box"];660[label="False",fontsize=16,color="green",shape="box"];661[label="False",fontsize=16,color="green",shape="box"];662[label="xy340 == xy3700",fontsize=16,color="blue",shape="box"];1351[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1351[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1351 -> 714[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1352[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1352[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1352 -> 715[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1353[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1353[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1353 -> 716[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1354[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1354[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1354 -> 717[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1355[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1355[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1355 -> 718[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1356[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1356[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1356 -> 719[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1357[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1357[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1357 -> 720[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1358[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1358[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1358 -> 721[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1359[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1359[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1359 -> 722[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1360[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1360[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1360 -> 723[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1361[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1361[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1361 -> 724[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1362[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1362[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1362 -> 725[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1363[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1363[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1363 -> 726[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1364[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];662 -> 1364[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1364 -> 727[label="",style="solid", color="blue", weight=3]; 13.82/5.40 663[label="True",fontsize=16,color="green",shape="box"];664[label="False",fontsize=16,color="green",shape="box"];665[label="False",fontsize=16,color="green",shape="box"];666[label="False",fontsize=16,color="green",shape="box"];667[label="True",fontsize=16,color="green",shape="box"];668[label="False",fontsize=16,color="green",shape="box"];669[label="False",fontsize=16,color="green",shape="box"];670[label="False",fontsize=16,color="green",shape="box"];671[label="True",fontsize=16,color="green",shape="box"];672 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 672[label="xy340 == xy3700 && xy341 == xy3701",fontsize=16,color="magenta"];672 -> 728[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 672 -> 729[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 673 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 673[label="xy340 == xy3700 && xy341 == xy3701",fontsize=16,color="magenta"];673 -> 730[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 673 -> 731[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 674[label="False",fontsize=16,color="green",shape="box"];675[label="False",fontsize=16,color="green",shape="box"];676[label="True",fontsize=16,color="green",shape="box"];677[label="xy340 == xy3700",fontsize=16,color="blue",shape="box"];1365[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1365[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1365 -> 732[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1366[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1366[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1366 -> 733[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1367[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1367[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1367 -> 734[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1368[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1368[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1368 -> 735[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1369[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1369[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1369 -> 736[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1370[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1370[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1370 -> 737[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1371[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1371[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1371 -> 738[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1372[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1372[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1372 -> 739[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1373[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1373[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1373 -> 740[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1374[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1374[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1374 -> 741[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1375[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1375[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1375 -> 742[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1376[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1376[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1376 -> 743[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1377[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1377[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1377 -> 744[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1378[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];677 -> 1378[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1378 -> 745[label="",style="solid", color="blue", weight=3]; 13.82/5.40 678[label="False",fontsize=16,color="green",shape="box"];679[label="False",fontsize=16,color="green",shape="box"];680[label="xy340 == xy3700",fontsize=16,color="blue",shape="box"];1379[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1379[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1379 -> 746[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1380[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1380[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1380 -> 747[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1381[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1381[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1381 -> 748[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1382[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1382[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1382 -> 749[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1383[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1383[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1383 -> 750[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1384[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1384[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1384 -> 751[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1385[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1385[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1385 -> 752[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1386[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1386[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1386 -> 753[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1387[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1387[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1387 -> 754[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1388[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1388[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1388 -> 755[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1389[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1389[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1389 -> 756[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1390[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1390[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1390 -> 757[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1391[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1391[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1391 -> 758[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1392[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];680 -> 1392[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1392 -> 759[label="",style="solid", color="blue", weight=3]; 13.82/5.40 681[label="True",fontsize=16,color="green",shape="box"];682[label="False",fontsize=16,color="green",shape="box"];683[label="False",fontsize=16,color="green",shape="box"];684[label="True",fontsize=16,color="green",shape="box"];685[label="primEqInt (Pos (Succ xy3400)) xy370",fontsize=16,color="burlywood",shape="box"];1393[label="xy370/Pos xy3700",fontsize=10,color="white",style="solid",shape="box"];685 -> 1393[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1393 -> 760[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1394[label="xy370/Neg xy3700",fontsize=10,color="white",style="solid",shape="box"];685 -> 1394[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1394 -> 761[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 686[label="primEqInt (Pos Zero) xy370",fontsize=16,color="burlywood",shape="box"];1395[label="xy370/Pos xy3700",fontsize=10,color="white",style="solid",shape="box"];686 -> 1395[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1395 -> 762[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1396[label="xy370/Neg xy3700",fontsize=10,color="white",style="solid",shape="box"];686 -> 1396[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1396 -> 763[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 687[label="primEqInt (Neg (Succ xy3400)) xy370",fontsize=16,color="burlywood",shape="box"];1397[label="xy370/Pos xy3700",fontsize=10,color="white",style="solid",shape="box"];687 -> 1397[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1397 -> 764[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1398[label="xy370/Neg xy3700",fontsize=10,color="white",style="solid",shape="box"];687 -> 1398[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1398 -> 765[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 688[label="primEqInt (Neg Zero) xy370",fontsize=16,color="burlywood",shape="box"];1399[label="xy370/Pos xy3700",fontsize=10,color="white",style="solid",shape="box"];688 -> 1399[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1399 -> 766[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1400[label="xy370/Neg xy3700",fontsize=10,color="white",style="solid",shape="box"];688 -> 1400[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1400 -> 767[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 689[label="xy3711",fontsize=16,color="green",shape="box"];690[label="xy331",fontsize=16,color="green",shape="box"];691 -> 572[label="",style="dashed", color="red", weight=0]; 13.82/5.40 691[label="xy330 == xy3710",fontsize=16,color="magenta"];691 -> 768[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 691 -> 769[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 692 -> 573[label="",style="dashed", color="red", weight=0]; 13.82/5.40 692[label="xy330 == xy3710",fontsize=16,color="magenta"];692 -> 770[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 692 -> 771[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 693 -> 574[label="",style="dashed", color="red", weight=0]; 13.82/5.40 693[label="xy330 == xy3710",fontsize=16,color="magenta"];693 -> 772[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 693 -> 773[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 694 -> 575[label="",style="dashed", color="red", weight=0]; 13.82/5.40 694[label="xy330 == xy3710",fontsize=16,color="magenta"];694 -> 774[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 694 -> 775[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 695 -> 576[label="",style="dashed", color="red", weight=0]; 13.82/5.40 695[label="xy330 == xy3710",fontsize=16,color="magenta"];695 -> 776[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 695 -> 777[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 696 -> 577[label="",style="dashed", color="red", weight=0]; 13.82/5.40 696[label="xy330 == xy3710",fontsize=16,color="magenta"];696 -> 778[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 696 -> 779[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 697 -> 578[label="",style="dashed", color="red", weight=0]; 13.82/5.40 697[label="xy330 == xy3710",fontsize=16,color="magenta"];697 -> 780[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 697 -> 781[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 698 -> 579[label="",style="dashed", color="red", weight=0]; 13.82/5.40 698[label="xy330 == xy3710",fontsize=16,color="magenta"];698 -> 782[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 698 -> 783[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 699 -> 580[label="",style="dashed", color="red", weight=0]; 13.82/5.40 699[label="xy330 == xy3710",fontsize=16,color="magenta"];699 -> 784[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 699 -> 785[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 700 -> 581[label="",style="dashed", color="red", weight=0]; 13.82/5.40 700[label="xy330 == xy3710",fontsize=16,color="magenta"];700 -> 786[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 700 -> 787[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 701 -> 582[label="",style="dashed", color="red", weight=0]; 13.82/5.40 701[label="xy330 == xy3710",fontsize=16,color="magenta"];701 -> 788[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 701 -> 789[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 702 -> 583[label="",style="dashed", color="red", weight=0]; 13.82/5.40 702[label="xy330 == xy3710",fontsize=16,color="magenta"];702 -> 790[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 702 -> 791[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 703 -> 584[label="",style="dashed", color="red", weight=0]; 13.82/5.40 703[label="xy330 == xy3710",fontsize=16,color="magenta"];703 -> 792[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 703 -> 793[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 704 -> 585[label="",style="dashed", color="red", weight=0]; 13.82/5.40 704[label="xy330 == xy3710",fontsize=16,color="magenta"];704 -> 794[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 704 -> 795[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 705[label="primEqNat xy340 xy3700",fontsize=16,color="burlywood",shape="triangle"];1401[label="xy340/Succ xy3400",fontsize=10,color="white",style="solid",shape="box"];705 -> 1401[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1401 -> 796[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1402[label="xy340/Zero",fontsize=10,color="white",style="solid",shape="box"];705 -> 1402[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1402 -> 797[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 706[label="xy341 == xy3701",fontsize=16,color="blue",shape="box"];1403[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1403[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1403 -> 798[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1404[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1404[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1404 -> 799[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1405[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1405[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1405 -> 800[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1406[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1406[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1406 -> 801[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1407[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1407[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1407 -> 802[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1408[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1408[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1408 -> 803[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1409[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1409[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1409 -> 804[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1410[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1410[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1410 -> 805[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1411[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1411[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1411 -> 806[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1412[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1412[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1412 -> 807[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1413[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1413[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1413 -> 808[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1414[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1414[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1414 -> 809[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1415[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1415[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1415 -> 810[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1416[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];706 -> 1416[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1416 -> 811[label="",style="solid", color="blue", weight=3]; 13.82/5.40 707[label="xy340 == xy3700",fontsize=16,color="blue",shape="box"];1417[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1417[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1417 -> 812[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1418[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1418[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1418 -> 813[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1419[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1419[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1419 -> 814[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1420[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1420[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1420 -> 815[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1421[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1421[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1421 -> 816[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1422[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1422[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1422 -> 817[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1423[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1423[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1423 -> 818[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1424[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1424[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1424 -> 819[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1425[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1425[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1425 -> 820[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1426[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1426[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1426 -> 821[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1427[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1427[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1427 -> 822[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1428[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1428[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1428 -> 823[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1429[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1429[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1429 -> 824[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1430[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];707 -> 1430[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1430 -> 825[label="",style="solid", color="blue", weight=3]; 13.82/5.40 708[label="xy340",fontsize=16,color="green",shape="box"];709[label="xy3700",fontsize=16,color="green",shape="box"];710 -> 565[label="",style="dashed", color="red", weight=0]; 13.82/5.40 710[label="xy341 == xy3701 && xy342 == xy3702",fontsize=16,color="magenta"];710 -> 826[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 710 -> 827[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 711[label="xy340 == xy3700",fontsize=16,color="blue",shape="box"];1431[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1431[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1431 -> 828[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1432[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1432[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1432 -> 829[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1433[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1433[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1433 -> 830[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1434[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1434[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1434 -> 831[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1435[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1435[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1435 -> 832[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1436[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1436[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1436 -> 833[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1437[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1437[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1437 -> 834[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1438[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1438[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1438 -> 835[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1439[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1439[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1439 -> 836[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1440[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1440[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1440 -> 837[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1441[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1441[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1441 -> 838[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1442[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1442[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1442 -> 839[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1443[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1443[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1443 -> 840[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1444[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];711 -> 1444[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1444 -> 841[label="",style="solid", color="blue", weight=3]; 13.82/5.40 712 -> 585[label="",style="dashed", color="red", weight=0]; 13.82/5.40 712[label="xy340 * xy3701 == xy341 * xy3700",fontsize=16,color="magenta"];712 -> 842[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 712 -> 843[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 713 -> 585[label="",style="dashed", color="red", weight=0]; 13.82/5.40 713[label="xy340 * xy3701 == xy341 * xy3700",fontsize=16,color="magenta"];713 -> 844[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 713 -> 845[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 714 -> 572[label="",style="dashed", color="red", weight=0]; 13.82/5.40 714[label="xy340 == xy3700",fontsize=16,color="magenta"];714 -> 846[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 714 -> 847[label="",style="dashed", color="magenta", weight=3]; 13.82/5.40 715 -> 573[label="",style="dashed", color="red", weight=0]; 13.82/5.40 715[label="xy340 == xy3700",fontsize=16,color="magenta"];715 -> 848[label="",style="dashed", color="magenta", weight=3]; 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13.82/5.40 766[label="primEqInt (Neg Zero) (Pos xy3700)",fontsize=16,color="burlywood",shape="box"];1471[label="xy3700/Succ xy37000",fontsize=10,color="white",style="solid",shape="box"];766 -> 1471[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1471 -> 960[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1472[label="xy3700/Zero",fontsize=10,color="white",style="solid",shape="box"];766 -> 1472[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1472 -> 961[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 767[label="primEqInt (Neg Zero) (Neg xy3700)",fontsize=16,color="burlywood",shape="box"];1473[label="xy3700/Succ xy37000",fontsize=10,color="white",style="solid",shape="box"];767 -> 1473[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1473 -> 962[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 1474[label="xy3700/Zero",fontsize=10,color="white",style="solid",shape="box"];767 -> 1474[label="",style="solid", color="burlywood", weight=9]; 13.82/5.40 1474 -> 963[label="",style="solid", color="burlywood", weight=3]; 13.82/5.40 768[label="xy330",fontsize=16,color="green",shape="box"];769[label="xy3710",fontsize=16,color="green",shape="box"];770[label="xy330",fontsize=16,color="green",shape="box"];771[label="xy3710",fontsize=16,color="green",shape="box"];772[label="xy330",fontsize=16,color="green",shape="box"];773[label="xy3710",fontsize=16,color="green",shape="box"];774[label="xy330",fontsize=16,color="green",shape="box"];775[label="xy3710",fontsize=16,color="green",shape="box"];776[label="xy330",fontsize=16,color="green",shape="box"];777[label="xy3710",fontsize=16,color="green",shape="box"];778[label="xy330",fontsize=16,color="green",shape="box"];779[label="xy3710",fontsize=16,color="green",shape="box"];780[label="xy330",fontsize=16,color="green",shape="box"];781[label="xy3710",fontsize=16,color="green",shape="box"];782[label="xy330",fontsize=16,color="green",shape="box"];783[label="xy3710",fontsize=16,color="green",shape="box"];784[label="xy330",fontsize=16,color="green",shape="box"];785[label="xy3710",fontsize=16,color="green",shape="box"];786[label="xy330",fontsize=16,color="green",shape="box"];787[label="xy3710",fontsize=16,color="green",shape="box"];788[label="xy330",fontsize=16,color="green",shape="box"];789[label="xy3710",fontsize=16,color="green",shape="box"];790[label="xy330",fontsize=16,color="green",shape="box"];791[label="xy3710",fontsize=16,color="green",shape="box"];792[label="xy330",fontsize=16,color="green",shape="box"];793[label="xy3710",fontsize=16,color="green",shape="box"];794[label="xy330",fontsize=16,color="green",shape="box"];795[label="xy3710",fontsize=16,color="green",shape="box"];796[label="primEqNat (Succ xy3400) xy3700",fontsize=16,color="burlywood",shape="box"];1475[label="xy3700/Succ xy37000",fontsize=10,color="white",style="solid",shape="box"];796 -> 1475[label="",style="solid", color="burlywood", weight=9]; 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13.82/5.40 827[label="xy341 == xy3701",fontsize=16,color="blue",shape="box"];1493[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];827 -> 1493[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1493 -> 1038[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1494[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];827 -> 1494[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1494 -> 1039[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1495[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];827 -> 1495[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1495 -> 1040[label="",style="solid", color="blue", weight=3]; 13.82/5.40 1496[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];827 -> 1496[label="",style="solid", color="blue", weight=9]; 13.82/5.40 1496 -> 1041[label="",style="solid", color="blue", weight=3]; 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14.14/5.41 951[label="primEqInt (Pos (Succ xy3400)) (Pos Zero)",fontsize=16,color="black",shape="box"];951 -> 1124[label="",style="solid", color="black", weight=3]; 14.14/5.41 952[label="False",fontsize=16,color="green",shape="box"];953[label="primEqInt (Pos Zero) (Pos (Succ xy37000))",fontsize=16,color="black",shape="box"];953 -> 1125[label="",style="solid", color="black", weight=3]; 14.14/5.41 954[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];954 -> 1126[label="",style="solid", color="black", weight=3]; 14.14/5.41 955[label="primEqInt (Pos Zero) (Neg (Succ xy37000))",fontsize=16,color="black",shape="box"];955 -> 1127[label="",style="solid", color="black", weight=3]; 14.14/5.41 956[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];956 -> 1128[label="",style="solid", color="black", weight=3]; 14.14/5.41 957[label="False",fontsize=16,color="green",shape="box"];958[label="primEqInt (Neg (Succ xy3400)) (Neg (Succ xy37000))",fontsize=16,color="black",shape="box"];958 -> 1129[label="",style="solid", color="black", weight=3]; 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14.14/5.41 1507 -> 1195[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1508[label="xy340/Neg xy3400",fontsize=10,color="white",style="solid",shape="box"];1080 -> 1508[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1508 -> 1196[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1081[label="xy3700",fontsize=16,color="green",shape="box"];1082[label="xy341",fontsize=16,color="green",shape="box"];1083[label="xy3701",fontsize=16,color="green",shape="box"];1084[label="xy340",fontsize=16,color="green",shape="box"];1085[label="xy3700",fontsize=16,color="green",shape="box"];1086[label="xy341",fontsize=16,color="green",shape="box"];1087[label="xy341",fontsize=16,color="green",shape="box"];1088[label="xy3701",fontsize=16,color="green",shape="box"];1089[label="xy341",fontsize=16,color="green",shape="box"];1090[label="xy3701",fontsize=16,color="green",shape="box"];1091[label="xy340",fontsize=16,color="green",shape="box"];1092[label="xy3700",fontsize=16,color="green",shape="box"];1093[label="xy340",fontsize=16,color="green",shape="box"];1094[label="xy3700",fontsize=16,color="green",shape="box"];1095[label="xy340",fontsize=16,color="green",shape="box"];1096[label="xy3700",fontsize=16,color="green",shape="box"];1097[label="xy340",fontsize=16,color="green",shape="box"];1098[label="xy3700",fontsize=16,color="green",shape="box"];1099[label="xy340",fontsize=16,color="green",shape="box"];1100[label="xy3700",fontsize=16,color="green",shape="box"];1101[label="xy340",fontsize=16,color="green",shape="box"];1102[label="xy3700",fontsize=16,color="green",shape="box"];1103[label="xy340",fontsize=16,color="green",shape="box"];1104[label="xy3700",fontsize=16,color="green",shape="box"];1105[label="xy340",fontsize=16,color="green",shape="box"];1106[label="xy3700",fontsize=16,color="green",shape="box"];1107[label="xy340",fontsize=16,color="green",shape="box"];1108[label="xy3700",fontsize=16,color="green",shape="box"];1109[label="xy340",fontsize=16,color="green",shape="box"];1110[label="xy3700",fontsize=16,color="green",shape="box"];1111[label="xy340",fontsize=16,color="green",shape="box"];1112[label="xy3700",fontsize=16,color="green",shape="box"];1113[label="xy340",fontsize=16,color="green",shape="box"];1114[label="xy3700",fontsize=16,color="green",shape="box"];1115[label="xy340",fontsize=16,color="green",shape="box"];1116[label="xy3700",fontsize=16,color="green",shape="box"];1117[label="xy340",fontsize=16,color="green",shape="box"];1118[label="xy3700",fontsize=16,color="green",shape="box"];1119[label="xy340",fontsize=16,color="green",shape="box"];1120[label="xy3700",fontsize=16,color="green",shape="box"];1121[label="xy340",fontsize=16,color="green",shape="box"];1122[label="xy3700",fontsize=16,color="green",shape="box"];1123 -> 705[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1123[label="primEqNat xy3400 xy37000",fontsize=16,color="magenta"];1123 -> 1197[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1123 -> 1198[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1124[label="False",fontsize=16,color="green",shape="box"];1125[label="False",fontsize=16,color="green",shape="box"];1126[label="True",fontsize=16,color="green",shape="box"];1127[label="False",fontsize=16,color="green",shape="box"];1128[label="True",fontsize=16,color="green",shape="box"];1129 -> 705[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1129[label="primEqNat xy3400 xy37000",fontsize=16,color="magenta"];1129 -> 1199[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1129 -> 1200[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1130[label="False",fontsize=16,color="green",shape="box"];1131[label="False",fontsize=16,color="green",shape="box"];1132[label="True",fontsize=16,color="green",shape="box"];1133[label="False",fontsize=16,color="green",shape="box"];1134[label="True",fontsize=16,color="green",shape="box"];1135 -> 705[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1135[label="primEqNat xy3400 xy37000",fontsize=16,color="magenta"];1135 -> 1201[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1135 -> 1202[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1136[label="False",fontsize=16,color="green",shape="box"];1137[label="False",fontsize=16,color="green",shape="box"];1138[label="True",fontsize=16,color="green",shape="box"];1139[label="xy342",fontsize=16,color="green",shape="box"];1140[label="xy3702",fontsize=16,color="green",shape="box"];1141[label="xy342",fontsize=16,color="green",shape="box"];1142[label="xy3702",fontsize=16,color="green",shape="box"];1143[label="xy342",fontsize=16,color="green",shape="box"];1144[label="xy3702",fontsize=16,color="green",shape="box"];1145[label="xy342",fontsize=16,color="green",shape="box"];1146[label="xy3702",fontsize=16,color="green",shape="box"];1147[label="xy342",fontsize=16,color="green",shape="box"];1148[label="xy3702",fontsize=16,color="green",shape="box"];1149[label="xy342",fontsize=16,color="green",shape="box"];1150[label="xy3702",fontsize=16,color="green",shape="box"];1151[label="xy342",fontsize=16,color="green",shape="box"];1152[label="xy3702",fontsize=16,color="green",shape="box"];1153[label="xy342",fontsize=16,color="green",shape="box"];1154[label="xy3702",fontsize=16,color="green",shape="box"];1155[label="xy342",fontsize=16,color="green",shape="box"];1156[label="xy3702",fontsize=16,color="green",shape="box"];1157[label="xy342",fontsize=16,color="green",shape="box"];1158[label="xy3702",fontsize=16,color="green",shape="box"];1159[label="xy342",fontsize=16,color="green",shape="box"];1160[label="xy3702",fontsize=16,color="green",shape="box"];1161[label="xy342",fontsize=16,color="green",shape="box"];1162[label="xy3702",fontsize=16,color="green",shape="box"];1163[label="xy342",fontsize=16,color="green",shape="box"];1164[label="xy3702",fontsize=16,color="green",shape="box"];1165[label="xy342",fontsize=16,color="green",shape="box"];1166[label="xy3702",fontsize=16,color="green",shape="box"];1167[label="xy341",fontsize=16,color="green",shape="box"];1168[label="xy3701",fontsize=16,color="green",shape="box"];1169[label="xy341",fontsize=16,color="green",shape="box"];1170[label="xy3701",fontsize=16,color="green",shape="box"];1171[label="xy341",fontsize=16,color="green",shape="box"];1172[label="xy3701",fontsize=16,color="green",shape="box"];1173[label="xy341",fontsize=16,color="green",shape="box"];1174[label="xy3701",fontsize=16,color="green",shape="box"];1175[label="xy341",fontsize=16,color="green",shape="box"];1176[label="xy3701",fontsize=16,color="green",shape="box"];1177[label="xy341",fontsize=16,color="green",shape="box"];1178[label="xy3701",fontsize=16,color="green",shape="box"];1179[label="xy341",fontsize=16,color="green",shape="box"];1180[label="xy3701",fontsize=16,color="green",shape="box"];1181[label="xy341",fontsize=16,color="green",shape="box"];1182[label="xy3701",fontsize=16,color="green",shape="box"];1183[label="xy341",fontsize=16,color="green",shape="box"];1184[label="xy3701",fontsize=16,color="green",shape="box"];1185[label="xy341",fontsize=16,color="green",shape="box"];1186[label="xy3701",fontsize=16,color="green",shape="box"];1187[label="xy341",fontsize=16,color="green",shape="box"];1188[label="xy3701",fontsize=16,color="green",shape="box"];1189[label="xy341",fontsize=16,color="green",shape="box"];1190[label="xy3701",fontsize=16,color="green",shape="box"];1191[label="xy341",fontsize=16,color="green",shape="box"];1192[label="xy3701",fontsize=16,color="green",shape="box"];1193[label="xy341",fontsize=16,color="green",shape="box"];1194[label="xy3701",fontsize=16,color="green",shape="box"];1195[label="primMulInt (Pos xy3400) xy3701",fontsize=16,color="burlywood",shape="box"];1509[label="xy3701/Pos xy37010",fontsize=10,color="white",style="solid",shape="box"];1195 -> 1509[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1509 -> 1203[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1510[label="xy3701/Neg xy37010",fontsize=10,color="white",style="solid",shape="box"];1195 -> 1510[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1510 -> 1204[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1196[label="primMulInt (Neg xy3400) xy3701",fontsize=16,color="burlywood",shape="box"];1511[label="xy3701/Pos xy37010",fontsize=10,color="white",style="solid",shape="box"];1196 -> 1511[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1511 -> 1205[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1512[label="xy3701/Neg xy37010",fontsize=10,color="white",style="solid",shape="box"];1196 -> 1512[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1512 -> 1206[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1197[label="xy3400",fontsize=16,color="green",shape="box"];1198[label="xy37000",fontsize=16,color="green",shape="box"];1199[label="xy3400",fontsize=16,color="green",shape="box"];1200[label="xy37000",fontsize=16,color="green",shape="box"];1201[label="xy3400",fontsize=16,color="green",shape="box"];1202[label="xy37000",fontsize=16,color="green",shape="box"];1203[label="primMulInt (Pos xy3400) (Pos xy37010)",fontsize=16,color="black",shape="box"];1203 -> 1207[label="",style="solid", color="black", weight=3]; 14.14/5.41 1204[label="primMulInt (Pos xy3400) (Neg xy37010)",fontsize=16,color="black",shape="box"];1204 -> 1208[label="",style="solid", color="black", weight=3]; 14.14/5.41 1205[label="primMulInt (Neg xy3400) (Pos xy37010)",fontsize=16,color="black",shape="box"];1205 -> 1209[label="",style="solid", color="black", weight=3]; 14.14/5.41 1206[label="primMulInt (Neg xy3400) (Neg xy37010)",fontsize=16,color="black",shape="box"];1206 -> 1210[label="",style="solid", color="black", weight=3]; 14.14/5.41 1207[label="Pos (primMulNat xy3400 xy37010)",fontsize=16,color="green",shape="box"];1207 -> 1211[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1208[label="Neg (primMulNat xy3400 xy37010)",fontsize=16,color="green",shape="box"];1208 -> 1212[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1209[label="Neg (primMulNat xy3400 xy37010)",fontsize=16,color="green",shape="box"];1209 -> 1213[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1210[label="Pos (primMulNat xy3400 xy37010)",fontsize=16,color="green",shape="box"];1210 -> 1214[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1211[label="primMulNat xy3400 xy37010",fontsize=16,color="burlywood",shape="triangle"];1513[label="xy3400/Succ xy34000",fontsize=10,color="white",style="solid",shape="box"];1211 -> 1513[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1513 -> 1215[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1514[label="xy3400/Zero",fontsize=10,color="white",style="solid",shape="box"];1211 -> 1514[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1514 -> 1216[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1212 -> 1211[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1212[label="primMulNat xy3400 xy37010",fontsize=16,color="magenta"];1212 -> 1217[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1213 -> 1211[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1213[label="primMulNat xy3400 xy37010",fontsize=16,color="magenta"];1213 -> 1218[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1214 -> 1211[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1214[label="primMulNat xy3400 xy37010",fontsize=16,color="magenta"];1214 -> 1219[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1214 -> 1220[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1215[label="primMulNat (Succ xy34000) xy37010",fontsize=16,color="burlywood",shape="box"];1515[label="xy37010/Succ xy370100",fontsize=10,color="white",style="solid",shape="box"];1215 -> 1515[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1515 -> 1221[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1516[label="xy37010/Zero",fontsize=10,color="white",style="solid",shape="box"];1215 -> 1516[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1516 -> 1222[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1216[label="primMulNat Zero xy37010",fontsize=16,color="burlywood",shape="box"];1517[label="xy37010/Succ xy370100",fontsize=10,color="white",style="solid",shape="box"];1216 -> 1517[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1517 -> 1223[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1518[label="xy37010/Zero",fontsize=10,color="white",style="solid",shape="box"];1216 -> 1518[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1518 -> 1224[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1217[label="xy37010",fontsize=16,color="green",shape="box"];1218[label="xy3400",fontsize=16,color="green",shape="box"];1219[label="xy3400",fontsize=16,color="green",shape="box"];1220[label="xy37010",fontsize=16,color="green",shape="box"];1221[label="primMulNat (Succ xy34000) (Succ xy370100)",fontsize=16,color="black",shape="box"];1221 -> 1225[label="",style="solid", color="black", weight=3]; 14.14/5.41 1222[label="primMulNat (Succ xy34000) Zero",fontsize=16,color="black",shape="box"];1222 -> 1226[label="",style="solid", color="black", weight=3]; 14.14/5.41 1223[label="primMulNat Zero (Succ xy370100)",fontsize=16,color="black",shape="box"];1223 -> 1227[label="",style="solid", color="black", weight=3]; 14.14/5.41 1224[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1224 -> 1228[label="",style="solid", color="black", weight=3]; 14.14/5.41 1225 -> 1229[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1225[label="primPlusNat (primMulNat xy34000 (Succ xy370100)) (Succ xy370100)",fontsize=16,color="magenta"];1225 -> 1230[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1226[label="Zero",fontsize=16,color="green",shape="box"];1227[label="Zero",fontsize=16,color="green",shape="box"];1228[label="Zero",fontsize=16,color="green",shape="box"];1230 -> 1211[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1230[label="primMulNat xy34000 (Succ xy370100)",fontsize=16,color="magenta"];1230 -> 1231[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1230 -> 1232[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1229[label="primPlusNat xy58 (Succ xy370100)",fontsize=16,color="burlywood",shape="triangle"];1519[label="xy58/Succ xy580",fontsize=10,color="white",style="solid",shape="box"];1229 -> 1519[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1519 -> 1233[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1520[label="xy58/Zero",fontsize=10,color="white",style="solid",shape="box"];1229 -> 1520[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1520 -> 1234[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1231[label="xy34000",fontsize=16,color="green",shape="box"];1232[label="Succ xy370100",fontsize=16,color="green",shape="box"];1233[label="primPlusNat (Succ xy580) (Succ xy370100)",fontsize=16,color="black",shape="box"];1233 -> 1235[label="",style="solid", color="black", weight=3]; 14.14/5.41 1234[label="primPlusNat Zero (Succ xy370100)",fontsize=16,color="black",shape="box"];1234 -> 1236[label="",style="solid", color="black", weight=3]; 14.14/5.41 1235[label="Succ (Succ (primPlusNat xy580 xy370100))",fontsize=16,color="green",shape="box"];1235 -> 1237[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1236[label="Succ xy370100",fontsize=16,color="green",shape="box"];1237[label="primPlusNat xy580 xy370100",fontsize=16,color="burlywood",shape="triangle"];1521[label="xy580/Succ xy5800",fontsize=10,color="white",style="solid",shape="box"];1237 -> 1521[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1521 -> 1238[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1522[label="xy580/Zero",fontsize=10,color="white",style="solid",shape="box"];1237 -> 1522[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1522 -> 1239[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1238[label="primPlusNat (Succ xy5800) xy370100",fontsize=16,color="burlywood",shape="box"];1523[label="xy370100/Succ xy3701000",fontsize=10,color="white",style="solid",shape="box"];1238 -> 1523[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1523 -> 1240[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1524[label="xy370100/Zero",fontsize=10,color="white",style="solid",shape="box"];1238 -> 1524[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1524 -> 1241[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1239[label="primPlusNat Zero xy370100",fontsize=16,color="burlywood",shape="box"];1525[label="xy370100/Succ xy3701000",fontsize=10,color="white",style="solid",shape="box"];1239 -> 1525[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1525 -> 1242[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1526[label="xy370100/Zero",fontsize=10,color="white",style="solid",shape="box"];1239 -> 1526[label="",style="solid", color="burlywood", weight=9]; 14.14/5.41 1526 -> 1243[label="",style="solid", color="burlywood", weight=3]; 14.14/5.41 1240[label="primPlusNat (Succ xy5800) (Succ xy3701000)",fontsize=16,color="black",shape="box"];1240 -> 1244[label="",style="solid", color="black", weight=3]; 14.14/5.41 1241[label="primPlusNat (Succ xy5800) Zero",fontsize=16,color="black",shape="box"];1241 -> 1245[label="",style="solid", color="black", weight=3]; 14.14/5.41 1242[label="primPlusNat Zero (Succ xy3701000)",fontsize=16,color="black",shape="box"];1242 -> 1246[label="",style="solid", color="black", weight=3]; 14.14/5.41 1243[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1243 -> 1247[label="",style="solid", color="black", weight=3]; 14.14/5.41 1244[label="Succ (Succ (primPlusNat xy5800 xy3701000))",fontsize=16,color="green",shape="box"];1244 -> 1248[label="",style="dashed", color="green", weight=3]; 14.14/5.41 1245[label="Succ xy5800",fontsize=16,color="green",shape="box"];1246[label="Succ xy3701000",fontsize=16,color="green",shape="box"];1247[label="Zero",fontsize=16,color="green",shape="box"];1248 -> 1237[label="",style="dashed", color="red", weight=0]; 14.14/5.41 1248[label="primPlusNat xy5800 xy3701000",fontsize=16,color="magenta"];1248 -> 1249[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1248 -> 1250[label="",style="dashed", color="magenta", weight=3]; 14.14/5.41 1249[label="xy5800",fontsize=16,color="green",shape="box"];1250[label="xy3701000",fontsize=16,color="green",shape="box"];} 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (6) 14.14/5.41 Complex Obligation (AND) 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (7) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(new_flip(xy33, xy34, ba), xy350, xy351, xy36, ba) 14.14/5.41 14.14/5.41 The TRS R consists of the following rules: 14.14/5.41 14.14/5.41 new_flip(xy33, xy34, ba) -> :(xy34, xy33) 14.14/5.41 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (8) TransformationProof (EQUIVALENT) 14.14/5.41 By rewriting [LPAR04] the rule new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(new_flip(xy33, xy34, ba), xy350, xy351, xy36, ba) at position [0] we obtained the following new rules [LPAR04]: 14.14/5.41 14.14/5.41 (new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba),new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba)) 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (9) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba) 14.14/5.41 14.14/5.41 The TRS R consists of the following rules: 14.14/5.41 14.14/5.41 new_flip(xy33, xy34, ba) -> :(xy34, xy33) 14.14/5.41 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (10) UsableRulesProof (EQUIVALENT) 14.14/5.41 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (11) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (12) QReductionProof (EQUIVALENT) 14.14/5.41 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (13) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (14) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_isPrefixOf1(xy33, xy34, :(xy350, xy351), xy36, ba) -> new_isPrefixOf1(:(xy34, xy33), xy350, xy351, xy36, ba) 14.14/5.41 The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (15) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (16) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, new_flip(xy37, xy3610, ba), xy3611, ba) 14.14/5.41 14.14/5.41 The TRS R consists of the following rules: 14.14/5.41 14.14/5.41 new_flip(xy33, xy34, ba) -> :(xy34, xy33) 14.14/5.41 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (17) TransformationProof (EQUIVALENT) 14.14/5.41 By rewriting [LPAR04] the rule new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, new_flip(xy37, xy3610, ba), xy3611, ba) at position [2] we obtained the following new rules [LPAR04]: 14.14/5.41 14.14/5.41 (new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba),new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba)) 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (18) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba) 14.14/5.41 14.14/5.41 The TRS R consists of the following rules: 14.14/5.41 14.14/5.41 new_flip(xy33, xy34, ba) -> :(xy34, xy33) 14.14/5.41 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (19) UsableRulesProof (EQUIVALENT) 14.14/5.41 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (20) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 The set Q consists of the following terms: 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (21) QReductionProof (EQUIVALENT) 14.14/5.41 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 14.14/5.41 14.14/5.41 new_flip(x0, x1, x2) 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (22) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (23) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_isPrefixOf0(xy34, xy33, xy37, :(xy3610, xy3611), ba) -> new_isPrefixOf0(xy34, xy33, :(xy3610, xy37), xy3611, ba) 14.14/5.41 The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (24) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (25) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_esEs3(Left(xy340), Left(xy3700), app(app(ty_Either, bch), bda), bcb) -> new_esEs3(xy340, xy3700, bch, bda) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(ty_Maybe, ha), dg, fc) -> new_esEs1(xy340, xy3700, ha) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), baf) -> new_esEs2(xy341, xy3701, baf) 14.14/5.41 new_esEs3(Right(xy340), Right(xy3700), bdb, app(ty_[], bea)) -> new_esEs2(xy340, xy3700, bea) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(ty_Either, gb), gc), fc) -> new_esEs3(xy341, xy3701, gb, gc) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(app(ty_@3, fd), ff), fg), fc) -> new_esEs0(xy341, xy3701, fd, ff, fg) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy340, xy3700, cc, cd) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(ty_Maybe, ee)) -> new_esEs1(xy342, xy3702, ee) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(app(ty_@3, bd), be), bf)) -> new_esEs0(xy341, xy3701, bd, be, bf) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(ty_@2, bag), bah)) -> new_esEs(xy340, xy3700, bag, bah) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(ty_Maybe, fh), fc) -> new_esEs1(xy341, xy3701, fh) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs0(xy340, xy3700, bba, bbb, bbc) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(ty_Either, dd), de), ce) -> new_esEs3(xy340, xy3700, dd, de) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(ty_@2, gd), ge), dg, fc) -> new_esEs(xy340, xy3700, gd, ge) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(ty_Either, eg), eh)) -> new_esEs3(xy342, xy3702, eg, eh) 14.14/5.41 new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(ty_Either, beb), bec)) -> new_esEs3(xy340, xy3700, beb, bec) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs0(xy342, xy3702, eb, ec, ed) 14.14/5.41 new_esEs1(Just(xy340), Just(xy3700), app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(xy340, xy3700, hg, hh, baa) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy341, xy3701, bb, bc) 14.14/5.41 new_esEs3(Left(xy340), Left(xy3700), app(app(app(ty_@3, bcc), bcd), bce), bcb) -> new_esEs0(xy340, xy3700, bcc, bcd, bce) 14.14/5.41 new_esEs3(Left(xy340), Left(xy3700), app(app(ty_@2, bbh), bca), bcb) -> new_esEs(xy340, xy3700, bbh, bca) 14.14/5.41 new_esEs3(Right(xy340), Right(xy3700), bdb, app(ty_Maybe, bdh)) -> new_esEs1(xy340, xy3700, bdh) 14.14/5.41 new_esEs1(Just(xy340), Just(xy3700), app(app(ty_@2, he), hf)) -> new_esEs(xy340, xy3700, he, hf) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(ty_Either, ca), cb)) -> new_esEs3(xy341, xy3701, ca, cb) 14.14/5.41 new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(app(ty_@3, bde), bdf), bdg)) -> new_esEs0(xy340, xy3700, bde, bdf, bdg) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(ty_Maybe, bg)) -> new_esEs1(xy341, xy3701, bg) 14.14/5.41 new_esEs1(Just(xy340), Just(xy3700), app(ty_[], bac)) -> new_esEs2(xy340, xy3700, bac) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(ty_@2, fa), fb), fc) -> new_esEs(xy341, xy3701, fa, fb) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(ty_[], bbe)) -> new_esEs2(xy340, xy3700, bbe) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(ty_Maybe, db), ce) -> new_esEs1(xy340, xy3700, db) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(ty_[], ef)) -> new_esEs2(xy342, xy3702, ef) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(ty_Either, bbf), bbg)) -> new_esEs3(xy340, xy3700, bbf, bbg) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(ty_@2, dh), ea)) -> new_esEs(xy342, xy3702, dh, ea) 14.14/5.41 new_esEs3(Left(xy340), Left(xy3700), app(ty_Maybe, bcf), bcb) -> new_esEs1(xy340, xy3700, bcf) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(app(ty_@3, cf), cg), da), ce) -> new_esEs0(xy340, xy3700, cf, cg, da) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(ty_[], ga), fc) -> new_esEs2(xy341, xy3701, ga) 14.14/5.41 new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(ty_@2, bdc), bdd)) -> new_esEs(xy340, xy3700, bdc, bdd) 14.14/5.41 new_esEs1(Just(xy340), Just(xy3700), app(ty_Maybe, bab)) -> new_esEs1(xy340, xy3700, bab) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(ty_[], hb), dg, fc) -> new_esEs2(xy340, xy3700, hb) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(ty_[], bh)) -> new_esEs2(xy341, xy3701, bh) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(app(ty_@3, gf), gg), gh), dg, fc) -> new_esEs0(xy340, xy3700, gf, gg, gh) 14.14/5.41 new_esEs1(Just(xy340), Just(xy3700), app(app(ty_Either, bad), bae)) -> new_esEs3(xy340, xy3700, bad, bae) 14.14/5.41 new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(ty_Either, hc), hd), dg, fc) -> new_esEs3(xy340, xy3700, hc, hd) 14.14/5.41 new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(ty_Maybe, bbd)) -> new_esEs1(xy340, xy3700, bbd) 14.14/5.41 new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(ty_[], dc), ce) -> new_esEs2(xy340, xy3700, dc) 14.14/5.41 new_esEs3(Left(xy340), Left(xy3700), app(ty_[], bcg), bcb) -> new_esEs2(xy340, xy3700, bcg) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (26) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_esEs1(Just(xy340), Just(xy3700), app(app(ty_Either, bad), bae)) -> new_esEs3(xy340, xy3700, bad, bae) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs1(Just(xy340), Just(xy3700), app(app(app(ty_@3, hg), hh), baa)) -> new_esEs0(xy340, xy3700, hg, hh, baa) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(ty_Either, bbf), bbg)) -> new_esEs3(xy340, xy3700, bbf, bbg) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs1(Just(xy340), Just(xy3700), app(ty_[], bac)) -> new_esEs2(xy340, xy3700, bac) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(app(ty_@3, bba), bbb), bbc)) -> new_esEs0(xy340, xy3700, bba, bbb, bbc) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs1(Just(xy340), Just(xy3700), app(app(ty_@2, he), hf)) -> new_esEs(xy340, xy3700, he, hf) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs1(Just(xy340), Just(xy3700), app(ty_Maybe, bab)) -> new_esEs1(xy340, xy3700, bab) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(app(ty_@2, bag), bah)) -> new_esEs(xy340, xy3700, bag, bah) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(ty_Maybe, bbd)) -> new_esEs1(xy340, xy3700, bbd) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Left(xy340), Left(xy3700), app(app(ty_Either, bch), bda), bcb) -> new_esEs3(xy340, xy3700, bch, bda) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(ty_Either, beb), bec)) -> new_esEs3(xy340, xy3700, beb, bec) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Left(xy340), Left(xy3700), app(app(app(ty_@3, bcc), bcd), bce), bcb) -> new_esEs0(xy340, xy3700, bcc, bcd, bce) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(app(ty_@3, bde), bdf), bdg)) -> new_esEs0(xy340, xy3700, bde, bdf, bdg) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Right(xy340), Right(xy3700), bdb, app(ty_[], bea)) -> new_esEs2(xy340, xy3700, bea) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Left(xy340), Left(xy3700), app(ty_[], bcg), bcb) -> new_esEs2(xy340, xy3700, bcg) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Left(xy340), Left(xy3700), app(app(ty_@2, bbh), bca), bcb) -> new_esEs(xy340, xy3700, bbh, bca) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Right(xy340), Right(xy3700), bdb, app(app(ty_@2, bdc), bdd)) -> new_esEs(xy340, xy3700, bdc, bdd) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Right(xy340), Right(xy3700), bdb, app(ty_Maybe, bdh)) -> new_esEs1(xy340, xy3700, bdh) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs3(Left(xy340), Left(xy3700), app(ty_Maybe, bcf), bcb) -> new_esEs1(xy340, xy3700, bcf) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(ty_Either, gb), gc), fc) -> new_esEs3(xy341, xy3701, gb, gc) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(ty_Either, eg), eh)) -> new_esEs3(xy342, xy3702, eg, eh) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(ty_Either, hc), hd), dg, fc) -> new_esEs3(xy340, xy3700, hc, hd) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(ty_Either, dd), de), ce) -> new_esEs3(xy340, xy3700, dd, de) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(ty_Either, ca), cb)) -> new_esEs3(xy341, xy3701, ca, cb) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(app(ty_@3, fd), ff), fg), fc) -> new_esEs0(xy341, xy3701, fd, ff, fg) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(app(ty_@3, eb), ec), ed)) -> new_esEs0(xy342, xy3702, eb, ec, ed) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(app(ty_@3, gf), gg), gh), dg, fc) -> new_esEs0(xy340, xy3700, gf, gg, gh) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(app(ty_@3, bd), be), bf)) -> new_esEs0(xy341, xy3701, bd, be, bf) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(app(ty_@3, cf), cg), da), ce) -> new_esEs0(xy340, xy3700, cf, cg, da) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), baf) -> new_esEs2(xy341, xy3701, baf) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs2(:(xy340, xy341), :(xy3700, xy3701), app(ty_[], bbe)) -> new_esEs2(xy340, xy3700, bbe) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(ty_[], ef)) -> new_esEs2(xy342, xy3702, ef) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(ty_[], ga), fc) -> new_esEs2(xy341, xy3701, ga) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(ty_[], hb), dg, fc) -> new_esEs2(xy340, xy3700, hb) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(ty_[], bh)) -> new_esEs2(xy341, xy3701, bh) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(ty_[], dc), ce) -> new_esEs2(xy340, xy3700, dc) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(app(ty_@2, gd), ge), dg, fc) -> new_esEs(xy340, xy3700, gd, ge) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(app(ty_@2, fa), fb), fc) -> new_esEs(xy341, xy3701, fa, fb) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(app(ty_@2, dh), ea)) -> new_esEs(xy342, xy3702, dh, ea) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), app(ty_Maybe, ha), dg, fc) -> new_esEs1(xy340, xy3700, ha) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, dg, app(ty_Maybe, ee)) -> new_esEs1(xy342, xy3702, ee) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 5 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs0(@3(xy340, xy341, xy342), @3(xy3700, xy3701, xy3702), df, app(ty_Maybe, fh), fc) -> new_esEs1(xy341, xy3701, fh) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(app(ty_@2, cc), cd), ce) -> new_esEs(xy340, xy3700, cc, cd) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(app(ty_@2, bb), bc)) -> new_esEs(xy341, xy3701, bb, bc) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), ba, app(ty_Maybe, bg)) -> new_esEs1(xy341, xy3701, bg) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 4 > 3 14.14/5.41 14.14/5.41 14.14/5.41 *new_esEs(@2(xy340, xy341), @2(xy3700, xy3701), app(ty_Maybe, db), ce) -> new_esEs1(xy340, xy3700, db) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (27) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (28) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_isPrefixOf(:(xy330, xy331), :(xy3710, xy3711), ba) -> new_isPrefixOf(xy331, xy3711, ba) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (29) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_isPrefixOf(:(xy330, xy331), :(xy3710, xy3711), ba) -> new_isPrefixOf(xy331, xy3711, ba) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (30) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (31) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_primMulNat(Succ(xy34000), Succ(xy370100)) -> new_primMulNat(xy34000, Succ(xy370100)) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (32) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_primMulNat(Succ(xy34000), Succ(xy370100)) -> new_primMulNat(xy34000, Succ(xy370100)) 14.14/5.41 The graph contains the following edges 1 > 1, 2 >= 2 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (33) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (34) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_primPlusNat(Succ(xy5800), Succ(xy3701000)) -> new_primPlusNat(xy5800, xy3701000) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (35) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_primPlusNat(Succ(xy5800), Succ(xy3701000)) -> new_primPlusNat(xy5800, xy3701000) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (36) 14.14/5.41 YES 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (37) 14.14/5.41 Obligation: 14.14/5.41 Q DP problem: 14.14/5.41 The TRS P consists of the following rules: 14.14/5.41 14.14/5.41 new_primEqNat(Succ(xy3400), Succ(xy37000)) -> new_primEqNat(xy3400, xy37000) 14.14/5.41 14.14/5.41 R is empty. 14.14/5.41 Q is empty. 14.14/5.41 We have to consider all minimal (P,Q,R)-chains. 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (38) QDPSizeChangeProof (EQUIVALENT) 14.14/5.41 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. 14.14/5.41 14.14/5.41 From the DPs we obtained the following set of size-change graphs: 14.14/5.41 *new_primEqNat(Succ(xy3400), Succ(xy37000)) -> new_primEqNat(xy3400, xy37000) 14.14/5.41 The graph contains the following edges 1 > 1, 2 > 2 14.14/5.41 14.14/5.41 14.14/5.41 ---------------------------------------- 14.14/5.41 14.14/5.41 (39) 14.14/5.41 YES 14.14/5.45 EOF