11.38/4.67	YES
13.16/5.19	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
13.16/5.19	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.16/5.19	
13.16/5.19	
13.16/5.19	H-Termination with start terms of the given HASKELL could be proven:
13.16/5.19	
13.16/5.19	(0) HASKELL
13.16/5.19	(1) BR [EQUIVALENT, 0 ms]
13.16/5.19	(2) HASKELL
13.16/5.19	(3) COR [EQUIVALENT, 18 ms]
13.16/5.19	(4) HASKELL
13.16/5.19	(5) Narrow [SOUND, 0 ms]
13.16/5.19	(6) AND
13.16/5.19	    (7) QDP
13.16/5.19	        (8) TransformationProof [EQUIVALENT, 0 ms]
13.16/5.19	        (9) QDP
13.16/5.19	        (10) UsableRulesProof [EQUIVALENT, 0 ms]
13.16/5.19	        (11) QDP
13.16/5.19	        (12) QReductionProof [EQUIVALENT, 0 ms]
13.16/5.19	        (13) QDP
13.16/5.19	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.19	        (15) YES
13.16/5.19	    (16) QDP
13.16/5.19	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.19	        (18) YES
13.16/5.19	    (19) QDP
13.16/5.19	        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.19	        (21) YES
13.16/5.19	    (22) QDP
13.16/5.19	        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.19	        (24) YES
13.16/5.19	    (25) QDP
13.16/5.19	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.19	        (27) YES
13.16/5.19	    (28) QDP
13.16/5.19	        (29) TransformationProof [EQUIVALENT, 0 ms]
13.16/5.19	        (30) QDP
13.16/5.20	        (31) UsableRulesProof [EQUIVALENT, 0 ms]
13.16/5.20	        (32) QDP
13.16/5.20	        (33) QReductionProof [EQUIVALENT, 0 ms]
13.16/5.20	        (34) QDP
13.16/5.20	        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.16/5.20	        (36) YES
13.16/5.20	
13.16/5.20	
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(0)
13.16/5.20	Obligation:
13.16/5.20	mainModule Main 
13.16/5.20	module Maybe where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	module List where {
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isPrefixOf [] _ = True;
13.16/5.20	isPrefixOf _ [] = False;
13.16/5.20	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.16/5.20	
13.16/5.20	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.16/5.20	
13.16/5.20	}
13.16/5.20	module Main where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(1) BR (EQUIVALENT)
13.16/5.20	Replaced joker patterns by fresh variables and removed binding patterns.
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(2)
13.16/5.20	Obligation:
13.16/5.20	mainModule Main 
13.16/5.20	module Maybe where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	module List where {
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isPrefixOf [] wu = True;
13.16/5.20	isPrefixOf wv [] = False;
13.16/5.20	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.16/5.20	
13.16/5.20	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.16/5.20	
13.16/5.20	}
13.16/5.20	module Main where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(3) COR (EQUIVALENT)
13.16/5.20	Cond Reductions:
13.16/5.20	The following Function with conditions
13.16/5.20	"undefined |Falseundefined;
13.16/5.20	"
13.16/5.20	is transformed to
13.16/5.20	"undefined  = undefined1;
13.16/5.20	"
13.16/5.20	"undefined0 True = undefined;
13.16/5.20	"
13.16/5.20	"undefined1  = undefined0 False;
13.16/5.20	"
13.16/5.20	
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(4)
13.16/5.20	Obligation:
13.16/5.20	mainModule Main 
13.16/5.20	module Maybe where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	module List where {
13.16/5.20	import qualified Main;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isPrefixOf [] wu = True;
13.16/5.20	isPrefixOf wv [] = False;
13.16/5.20	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.16/5.20	
13.16/5.20	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.16/5.20	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.16/5.20	
13.16/5.20	}
13.16/5.20	module Main where {
13.16/5.20	import qualified List;
13.16/5.20	import qualified Maybe;
13.16/5.20	import qualified Prelude;
13.16/5.20	}
13.16/5.20	
13.16/5.20	----------------------------------------
13.16/5.20	
13.16/5.20	(5) Narrow (SOUND)
13.16/5.20	Haskell To QDPs
13.16/5.20	
13.16/5.20	digraph dp_graph {
13.16/5.20	node [outthreshold=100, inthreshold=100];1[label="List.isSuffixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.16/5.20	3[label="List.isSuffixOf ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.16/5.20	4[label="List.isSuffixOf ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
13.16/5.20	5[label="List.isPrefixOf (reverse ww3) (reverse ww4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
13.16/5.20	6[label="List.isPrefixOf (foldl (flip (:)) [] ww3) (reverse ww4)",fontsize=16,color="burlywood",shape="box"];497[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];6 -> 497[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	497 -> 7[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	498[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 498[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	498 -> 8[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	7[label="List.isPrefixOf (foldl (flip (:)) [] (ww30 : ww31)) (reverse ww4)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
13.16/5.20	8[label="List.isPrefixOf (foldl (flip (:)) [] []) (reverse ww4)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
13.16/5.20	9 -> 230[label="",style="dashed", color="red", weight=0];
13.16/5.20	9[label="List.isPrefixOf (foldl (flip (:)) (flip (:) [] ww30) ww31) (reverse ww4)",fontsize=16,color="magenta"];9 -> 231[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	9 -> 232[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	9 -> 233[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	9 -> 234[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	10[label="List.isPrefixOf [] (reverse ww4)",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
13.16/5.20	231[label="ww4",fontsize=16,color="green",shape="box"];232[label="ww30",fontsize=16,color="green",shape="box"];233[label="ww31",fontsize=16,color="green",shape="box"];234[label="[]",fontsize=16,color="green",shape="box"];230[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww14 ww15) ww16) (reverse ww17)",fontsize=16,color="burlywood",shape="triangle"];499[label="ww16/ww160 : ww161",fontsize=10,color="white",style="solid",shape="box"];230 -> 499[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	499 -> 267[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	500[label="ww16/[]",fontsize=10,color="white",style="solid",shape="box"];230 -> 500[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	500 -> 268[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	13[label="True",fontsize=16,color="green",shape="box"];267[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww14 ww15) (ww160 : ww161)) (reverse ww17)",fontsize=16,color="black",shape="box"];267 -> 269[label="",style="solid", color="black", weight=3];
13.16/5.20	268[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww14 ww15) []) (reverse ww17)",fontsize=16,color="black",shape="box"];268 -> 270[label="",style="solid", color="black", weight=3];
13.16/5.20	269 -> 230[label="",style="dashed", color="red", weight=0];
13.16/5.20	269[label="List.isPrefixOf (foldl (flip (:)) (flip (:) (flip (:) ww14 ww15) ww160) ww161) (reverse ww17)",fontsize=16,color="magenta"];269 -> 271[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	269 -> 272[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	269 -> 273[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	270[label="List.isPrefixOf (flip (:) ww14 ww15) (reverse ww17)",fontsize=16,color="black",shape="box"];270 -> 274[label="",style="solid", color="black", weight=3];
13.16/5.20	271[label="ww160",fontsize=16,color="green",shape="box"];272[label="ww161",fontsize=16,color="green",shape="box"];273[label="flip (:) ww14 ww15",fontsize=16,color="black",shape="triangle"];273 -> 275[label="",style="solid", color="black", weight=3];
13.16/5.20	274[label="List.isPrefixOf ((:) ww15 ww14) (reverse ww17)",fontsize=16,color="black",shape="box"];274 -> 276[label="",style="solid", color="black", weight=3];
13.16/5.20	275[label="(:) ww15 ww14",fontsize=16,color="green",shape="box"];276 -> 281[label="",style="dashed", color="red", weight=0];
13.16/5.20	276[label="List.isPrefixOf ((:) ww15 ww14) (foldl (flip (:)) [] ww17)",fontsize=16,color="magenta"];276 -> 282[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	276 -> 283[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	282[label="ww17",fontsize=16,color="green",shape="box"];283[label="[]",fontsize=16,color="green",shape="box"];281[label="List.isPrefixOf ((:) ww15 ww14) (foldl (flip (:)) ww18 ww171)",fontsize=16,color="burlywood",shape="triangle"];501[label="ww171/ww1710 : ww1711",fontsize=10,color="white",style="solid",shape="box"];281 -> 501[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	501 -> 285[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	502[label="ww171/[]",fontsize=10,color="white",style="solid",shape="box"];281 -> 502[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	502 -> 286[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	285[label="List.isPrefixOf ((:) ww15 ww14) (foldl (flip (:)) ww18 (ww1710 : ww1711))",fontsize=16,color="black",shape="box"];285 -> 287[label="",style="solid", color="black", weight=3];
13.16/5.20	286[label="List.isPrefixOf ((:) ww15 ww14) (foldl (flip (:)) ww18 [])",fontsize=16,color="black",shape="box"];286 -> 288[label="",style="solid", color="black", weight=3];
13.16/5.20	287 -> 281[label="",style="dashed", color="red", weight=0];
13.16/5.20	287[label="List.isPrefixOf ((:) ww15 ww14) (foldl (flip (:)) (flip (:) ww18 ww1710) ww1711)",fontsize=16,color="magenta"];287 -> 289[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	287 -> 290[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	288[label="List.isPrefixOf ((:) ww15 ww14) ww18",fontsize=16,color="burlywood",shape="box"];503[label="ww18/ww180 : ww181",fontsize=10,color="white",style="solid",shape="box"];288 -> 503[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	503 -> 291[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	504[label="ww18/[]",fontsize=10,color="white",style="solid",shape="box"];288 -> 504[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	504 -> 292[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	289[label="ww1711",fontsize=16,color="green",shape="box"];290 -> 273[label="",style="dashed", color="red", weight=0];
13.16/5.20	290[label="flip (:) ww18 ww1710",fontsize=16,color="magenta"];290 -> 293[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	290 -> 294[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	291[label="List.isPrefixOf ((:) ww15 ww14) (ww180 : ww181)",fontsize=16,color="black",shape="box"];291 -> 295[label="",style="solid", color="black", weight=3];
13.16/5.20	292[label="List.isPrefixOf ((:) ww15 ww14) []",fontsize=16,color="black",shape="box"];292 -> 296[label="",style="solid", color="black", weight=3];
13.16/5.20	293[label="ww1710",fontsize=16,color="green",shape="box"];294[label="ww18",fontsize=16,color="green",shape="box"];295 -> 297[label="",style="dashed", color="red", weight=0];
13.16/5.20	295[label="ww15 == ww180 && List.isPrefixOf ww14 ww181",fontsize=16,color="magenta"];295 -> 298[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	295 -> 299[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	295 -> 300[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	296[label="False",fontsize=16,color="green",shape="box"];298[label="ww181",fontsize=16,color="green",shape="box"];299[label="ww14",fontsize=16,color="green",shape="box"];300[label="ww15 == ww180",fontsize=16,color="blue",shape="box"];505[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 505[label="",style="solid", color="blue", weight=9];
13.16/5.20	505 -> 301[label="",style="solid", color="blue", weight=3];
13.16/5.20	506[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 506[label="",style="solid", color="blue", weight=9];
13.16/5.20	506 -> 302[label="",style="solid", color="blue", weight=3];
13.16/5.20	507[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 507[label="",style="solid", color="blue", weight=9];
13.16/5.20	507 -> 303[label="",style="solid", color="blue", weight=3];
13.16/5.20	508[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 508[label="",style="solid", color="blue", weight=9];
13.16/5.20	508 -> 304[label="",style="solid", color="blue", weight=3];
13.16/5.20	509[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 509[label="",style="solid", color="blue", weight=9];
13.16/5.20	509 -> 305[label="",style="solid", color="blue", weight=3];
13.16/5.20	510[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 510[label="",style="solid", color="blue", weight=9];
13.16/5.20	510 -> 306[label="",style="solid", color="blue", weight=3];
13.16/5.20	511[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 511[label="",style="solid", color="blue", weight=9];
13.16/5.20	511 -> 307[label="",style="solid", color="blue", weight=3];
13.16/5.20	512[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 512[label="",style="solid", color="blue", weight=9];
13.16/5.20	512 -> 308[label="",style="solid", color="blue", weight=3];
13.16/5.20	513[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 513[label="",style="solid", color="blue", weight=9];
13.16/5.20	513 -> 309[label="",style="solid", color="blue", weight=3];
13.16/5.20	514[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 514[label="",style="solid", color="blue", weight=9];
13.16/5.20	514 -> 310[label="",style="solid", color="blue", weight=3];
13.16/5.20	515[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 515[label="",style="solid", color="blue", weight=9];
13.16/5.20	515 -> 311[label="",style="solid", color="blue", weight=3];
13.16/5.20	516[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 516[label="",style="solid", color="blue", weight=9];
13.16/5.20	516 -> 312[label="",style="solid", color="blue", weight=3];
13.16/5.20	517[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 517[label="",style="solid", color="blue", weight=9];
13.16/5.20	517 -> 313[label="",style="solid", color="blue", weight=3];
13.16/5.20	518[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];300 -> 518[label="",style="solid", color="blue", weight=9];
13.16/5.20	518 -> 314[label="",style="solid", color="blue", weight=3];
13.16/5.20	297[label="ww23 && List.isPrefixOf ww24 ww25",fontsize=16,color="burlywood",shape="triangle"];519[label="ww23/False",fontsize=10,color="white",style="solid",shape="box"];297 -> 519[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	519 -> 315[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	520[label="ww23/True",fontsize=10,color="white",style="solid",shape="box"];297 -> 520[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	520 -> 316[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	301[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];301 -> 317[label="",style="solid", color="black", weight=3];
13.16/5.20	302[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];302 -> 318[label="",style="solid", color="black", weight=3];
13.16/5.20	303[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];303 -> 319[label="",style="solid", color="black", weight=3];
13.16/5.20	304[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];304 -> 320[label="",style="solid", color="black", weight=3];
13.16/5.20	305[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];305 -> 321[label="",style="solid", color="black", weight=3];
13.16/5.20	306[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];306 -> 322[label="",style="solid", color="black", weight=3];
13.16/5.20	307[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];307 -> 323[label="",style="solid", color="black", weight=3];
13.16/5.20	308[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];308 -> 324[label="",style="solid", color="black", weight=3];
13.16/5.20	309[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];309 -> 325[label="",style="solid", color="black", weight=3];
13.16/5.20	310[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];310 -> 326[label="",style="solid", color="black", weight=3];
13.16/5.20	311[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];311 -> 327[label="",style="solid", color="black", weight=3];
13.16/5.20	312[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];312 -> 328[label="",style="solid", color="black", weight=3];
13.16/5.20	313[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];313 -> 329[label="",style="solid", color="black", weight=3];
13.16/5.20	314[label="ww15 == ww180",fontsize=16,color="black",shape="triangle"];314 -> 330[label="",style="solid", color="black", weight=3];
13.16/5.20	315[label="False && List.isPrefixOf ww24 ww25",fontsize=16,color="black",shape="box"];315 -> 331[label="",style="solid", color="black", weight=3];
13.16/5.20	316[label="True && List.isPrefixOf ww24 ww25",fontsize=16,color="black",shape="box"];316 -> 332[label="",style="solid", color="black", weight=3];
13.16/5.20	317[label="error []",fontsize=16,color="red",shape="box"];318[label="primEqInt ww15 ww180",fontsize=16,color="burlywood",shape="box"];521[label="ww15/Pos ww150",fontsize=10,color="white",style="solid",shape="box"];318 -> 521[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	521 -> 333[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	522[label="ww15/Neg ww150",fontsize=10,color="white",style="solid",shape="box"];318 -> 522[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	522 -> 334[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	319[label="error []",fontsize=16,color="red",shape="box"];320[label="error []",fontsize=16,color="red",shape="box"];321[label="error []",fontsize=16,color="red",shape="box"];322[label="error []",fontsize=16,color="red",shape="box"];323[label="error []",fontsize=16,color="red",shape="box"];324[label="primEqFloat ww15 ww180",fontsize=16,color="burlywood",shape="box"];523[label="ww15/Float ww150 ww151",fontsize=10,color="white",style="solid",shape="box"];324 -> 523[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	523 -> 335[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	325[label="error []",fontsize=16,color="red",shape="box"];326[label="error []",fontsize=16,color="red",shape="box"];327[label="error []",fontsize=16,color="red",shape="box"];328[label="error []",fontsize=16,color="red",shape="box"];329[label="error []",fontsize=16,color="red",shape="box"];330[label="error []",fontsize=16,color="red",shape="box"];331[label="False",fontsize=16,color="green",shape="box"];332[label="List.isPrefixOf ww24 ww25",fontsize=16,color="burlywood",shape="box"];524[label="ww24/ww240 : ww241",fontsize=10,color="white",style="solid",shape="box"];332 -> 524[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	524 -> 336[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	525[label="ww24/[]",fontsize=10,color="white",style="solid",shape="box"];332 -> 525[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	525 -> 337[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	333[label="primEqInt (Pos ww150) ww180",fontsize=16,color="burlywood",shape="box"];526[label="ww150/Succ ww1500",fontsize=10,color="white",style="solid",shape="box"];333 -> 526[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	526 -> 338[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	527[label="ww150/Zero",fontsize=10,color="white",style="solid",shape="box"];333 -> 527[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	527 -> 339[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	334[label="primEqInt (Neg ww150) ww180",fontsize=16,color="burlywood",shape="box"];528[label="ww150/Succ ww1500",fontsize=10,color="white",style="solid",shape="box"];334 -> 528[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	528 -> 340[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	529[label="ww150/Zero",fontsize=10,color="white",style="solid",shape="box"];334 -> 529[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	529 -> 341[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	335[label="primEqFloat (Float ww150 ww151) ww180",fontsize=16,color="burlywood",shape="box"];530[label="ww180/Float ww1800 ww1801",fontsize=10,color="white",style="solid",shape="box"];335 -> 530[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	530 -> 342[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	336[label="List.isPrefixOf (ww240 : ww241) ww25",fontsize=16,color="burlywood",shape="box"];531[label="ww25/ww250 : ww251",fontsize=10,color="white",style="solid",shape="box"];336 -> 531[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	531 -> 343[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	532[label="ww25/[]",fontsize=10,color="white",style="solid",shape="box"];336 -> 532[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	532 -> 344[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	337[label="List.isPrefixOf [] ww25",fontsize=16,color="black",shape="box"];337 -> 345[label="",style="solid", color="black", weight=3];
13.16/5.20	338[label="primEqInt (Pos (Succ ww1500)) ww180",fontsize=16,color="burlywood",shape="box"];533[label="ww180/Pos ww1800",fontsize=10,color="white",style="solid",shape="box"];338 -> 533[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	533 -> 346[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	534[label="ww180/Neg ww1800",fontsize=10,color="white",style="solid",shape="box"];338 -> 534[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	534 -> 347[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	339[label="primEqInt (Pos Zero) ww180",fontsize=16,color="burlywood",shape="box"];535[label="ww180/Pos ww1800",fontsize=10,color="white",style="solid",shape="box"];339 -> 535[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	535 -> 348[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	536[label="ww180/Neg ww1800",fontsize=10,color="white",style="solid",shape="box"];339 -> 536[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	536 -> 349[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	340[label="primEqInt (Neg (Succ ww1500)) ww180",fontsize=16,color="burlywood",shape="box"];537[label="ww180/Pos ww1800",fontsize=10,color="white",style="solid",shape="box"];340 -> 537[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	537 -> 350[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	538[label="ww180/Neg ww1800",fontsize=10,color="white",style="solid",shape="box"];340 -> 538[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	538 -> 351[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	341[label="primEqInt (Neg Zero) ww180",fontsize=16,color="burlywood",shape="box"];539[label="ww180/Pos ww1800",fontsize=10,color="white",style="solid",shape="box"];341 -> 539[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	539 -> 352[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	540[label="ww180/Neg ww1800",fontsize=10,color="white",style="solid",shape="box"];341 -> 540[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	540 -> 353[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	342[label="primEqFloat (Float ww150 ww151) (Float ww1800 ww1801)",fontsize=16,color="black",shape="box"];342 -> 354[label="",style="solid", color="black", weight=3];
13.16/5.20	343[label="List.isPrefixOf (ww240 : ww241) (ww250 : ww251)",fontsize=16,color="black",shape="box"];343 -> 355[label="",style="solid", color="black", weight=3];
13.16/5.20	344[label="List.isPrefixOf (ww240 : ww241) []",fontsize=16,color="black",shape="box"];344 -> 356[label="",style="solid", color="black", weight=3];
13.16/5.20	345[label="True",fontsize=16,color="green",shape="box"];346[label="primEqInt (Pos (Succ ww1500)) (Pos ww1800)",fontsize=16,color="burlywood",shape="box"];541[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];346 -> 541[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	541 -> 357[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	542[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];346 -> 542[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	542 -> 358[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	347[label="primEqInt (Pos (Succ ww1500)) (Neg ww1800)",fontsize=16,color="black",shape="box"];347 -> 359[label="",style="solid", color="black", weight=3];
13.16/5.20	348[label="primEqInt (Pos Zero) (Pos ww1800)",fontsize=16,color="burlywood",shape="box"];543[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];348 -> 543[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	543 -> 360[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	544[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];348 -> 544[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	544 -> 361[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	349[label="primEqInt (Pos Zero) (Neg ww1800)",fontsize=16,color="burlywood",shape="box"];545[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];349 -> 545[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	545 -> 362[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	546[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];349 -> 546[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	546 -> 363[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	350[label="primEqInt (Neg (Succ ww1500)) (Pos ww1800)",fontsize=16,color="black",shape="box"];350 -> 364[label="",style="solid", color="black", weight=3];
13.16/5.20	351[label="primEqInt (Neg (Succ ww1500)) (Neg ww1800)",fontsize=16,color="burlywood",shape="box"];547[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];351 -> 547[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	547 -> 365[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	548[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];351 -> 548[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	548 -> 366[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	352[label="primEqInt (Neg Zero) (Pos ww1800)",fontsize=16,color="burlywood",shape="box"];549[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];352 -> 549[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	549 -> 367[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	550[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];352 -> 550[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	550 -> 368[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	353[label="primEqInt (Neg Zero) (Neg ww1800)",fontsize=16,color="burlywood",shape="box"];551[label="ww1800/Succ ww18000",fontsize=10,color="white",style="solid",shape="box"];353 -> 551[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	551 -> 369[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	552[label="ww1800/Zero",fontsize=10,color="white",style="solid",shape="box"];353 -> 552[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	552 -> 370[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	354 -> 302[label="",style="dashed", color="red", weight=0];
13.16/5.20	354[label="ww150 * ww1801 == ww151 * ww1800",fontsize=16,color="magenta"];354 -> 371[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	354 -> 372[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	355 -> 297[label="",style="dashed", color="red", weight=0];
13.16/5.20	355[label="ww240 == ww250 && List.isPrefixOf ww241 ww251",fontsize=16,color="magenta"];355 -> 373[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	355 -> 374[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	355 -> 375[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	356[label="False",fontsize=16,color="green",shape="box"];357[label="primEqInt (Pos (Succ ww1500)) (Pos (Succ ww18000))",fontsize=16,color="black",shape="box"];357 -> 376[label="",style="solid", color="black", weight=3];
13.16/5.20	358[label="primEqInt (Pos (Succ ww1500)) (Pos Zero)",fontsize=16,color="black",shape="box"];358 -> 377[label="",style="solid", color="black", weight=3];
13.16/5.20	359[label="False",fontsize=16,color="green",shape="box"];360[label="primEqInt (Pos Zero) (Pos (Succ ww18000))",fontsize=16,color="black",shape="box"];360 -> 378[label="",style="solid", color="black", weight=3];
13.16/5.20	361[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];361 -> 379[label="",style="solid", color="black", weight=3];
13.16/5.20	362[label="primEqInt (Pos Zero) (Neg (Succ ww18000))",fontsize=16,color="black",shape="box"];362 -> 380[label="",style="solid", color="black", weight=3];
13.16/5.20	363[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];363 -> 381[label="",style="solid", color="black", weight=3];
13.16/5.20	364[label="False",fontsize=16,color="green",shape="box"];365[label="primEqInt (Neg (Succ ww1500)) (Neg (Succ ww18000))",fontsize=16,color="black",shape="box"];365 -> 382[label="",style="solid", color="black", weight=3];
13.16/5.20	366[label="primEqInt (Neg (Succ ww1500)) (Neg Zero)",fontsize=16,color="black",shape="box"];366 -> 383[label="",style="solid", color="black", weight=3];
13.16/5.20	367[label="primEqInt (Neg Zero) (Pos (Succ ww18000))",fontsize=16,color="black",shape="box"];367 -> 384[label="",style="solid", color="black", weight=3];
13.16/5.20	368[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];368 -> 385[label="",style="solid", color="black", weight=3];
13.16/5.20	369[label="primEqInt (Neg Zero) (Neg (Succ ww18000))",fontsize=16,color="black",shape="box"];369 -> 386[label="",style="solid", color="black", weight=3];
13.16/5.20	370[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];370 -> 387[label="",style="solid", color="black", weight=3];
13.16/5.20	371[label="ww150 * ww1801",fontsize=16,color="black",shape="triangle"];371 -> 388[label="",style="solid", color="black", weight=3];
13.16/5.20	372 -> 371[label="",style="dashed", color="red", weight=0];
13.16/5.20	372[label="ww151 * ww1800",fontsize=16,color="magenta"];372 -> 389[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	372 -> 390[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	373[label="ww251",fontsize=16,color="green",shape="box"];374[label="ww241",fontsize=16,color="green",shape="box"];375[label="ww240 == ww250",fontsize=16,color="blue",shape="box"];553[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 553[label="",style="solid", color="blue", weight=9];
13.16/5.20	553 -> 391[label="",style="solid", color="blue", weight=3];
13.16/5.20	554[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 554[label="",style="solid", color="blue", weight=9];
13.16/5.20	554 -> 392[label="",style="solid", color="blue", weight=3];
13.16/5.20	555[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 555[label="",style="solid", color="blue", weight=9];
13.16/5.20	555 -> 393[label="",style="solid", color="blue", weight=3];
13.16/5.20	556[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 556[label="",style="solid", color="blue", weight=9];
13.16/5.20	556 -> 394[label="",style="solid", color="blue", weight=3];
13.16/5.20	557[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 557[label="",style="solid", color="blue", weight=9];
13.16/5.20	557 -> 395[label="",style="solid", color="blue", weight=3];
13.16/5.20	558[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 558[label="",style="solid", color="blue", weight=9];
13.16/5.20	558 -> 396[label="",style="solid", color="blue", weight=3];
13.16/5.20	559[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 559[label="",style="solid", color="blue", weight=9];
13.16/5.20	559 -> 397[label="",style="solid", color="blue", weight=3];
13.16/5.20	560[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 560[label="",style="solid", color="blue", weight=9];
13.16/5.20	560 -> 398[label="",style="solid", color="blue", weight=3];
13.16/5.20	561[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 561[label="",style="solid", color="blue", weight=9];
13.16/5.20	561 -> 399[label="",style="solid", color="blue", weight=3];
13.16/5.20	562[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 562[label="",style="solid", color="blue", weight=9];
13.16/5.20	562 -> 400[label="",style="solid", color="blue", weight=3];
13.16/5.20	563[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 563[label="",style="solid", color="blue", weight=9];
13.16/5.20	563 -> 401[label="",style="solid", color="blue", weight=3];
13.16/5.20	564[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 564[label="",style="solid", color="blue", weight=9];
13.16/5.20	564 -> 402[label="",style="solid", color="blue", weight=3];
13.16/5.20	565[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 565[label="",style="solid", color="blue", weight=9];
13.16/5.20	565 -> 403[label="",style="solid", color="blue", weight=3];
13.16/5.20	566[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 566[label="",style="solid", color="blue", weight=9];
13.16/5.20	566 -> 404[label="",style="solid", color="blue", weight=3];
13.16/5.20	376[label="primEqNat ww1500 ww18000",fontsize=16,color="burlywood",shape="triangle"];567[label="ww1500/Succ ww15000",fontsize=10,color="white",style="solid",shape="box"];376 -> 567[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	567 -> 405[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	568[label="ww1500/Zero",fontsize=10,color="white",style="solid",shape="box"];376 -> 568[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	568 -> 406[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	377[label="False",fontsize=16,color="green",shape="box"];378[label="False",fontsize=16,color="green",shape="box"];379[label="True",fontsize=16,color="green",shape="box"];380[label="False",fontsize=16,color="green",shape="box"];381[label="True",fontsize=16,color="green",shape="box"];382 -> 376[label="",style="dashed", color="red", weight=0];
13.16/5.20	382[label="primEqNat ww1500 ww18000",fontsize=16,color="magenta"];382 -> 407[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	382 -> 408[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	383[label="False",fontsize=16,color="green",shape="box"];384[label="False",fontsize=16,color="green",shape="box"];385[label="True",fontsize=16,color="green",shape="box"];386[label="False",fontsize=16,color="green",shape="box"];387[label="True",fontsize=16,color="green",shape="box"];388[label="primMulInt ww150 ww1801",fontsize=16,color="burlywood",shape="box"];569[label="ww150/Pos ww1500",fontsize=10,color="white",style="solid",shape="box"];388 -> 569[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	569 -> 409[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	570[label="ww150/Neg ww1500",fontsize=10,color="white",style="solid",shape="box"];388 -> 570[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	570 -> 410[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	389[label="ww151",fontsize=16,color="green",shape="box"];390[label="ww1800",fontsize=16,color="green",shape="box"];391 -> 301[label="",style="dashed", color="red", weight=0];
13.16/5.20	391[label="ww240 == ww250",fontsize=16,color="magenta"];391 -> 411[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	391 -> 412[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	392 -> 302[label="",style="dashed", color="red", weight=0];
13.16/5.20	392[label="ww240 == ww250",fontsize=16,color="magenta"];392 -> 413[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	392 -> 414[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	393 -> 303[label="",style="dashed", color="red", weight=0];
13.16/5.20	393[label="ww240 == ww250",fontsize=16,color="magenta"];393 -> 415[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	393 -> 416[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	394 -> 304[label="",style="dashed", color="red", weight=0];
13.16/5.20	394[label="ww240 == ww250",fontsize=16,color="magenta"];394 -> 417[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	394 -> 418[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	395 -> 305[label="",style="dashed", color="red", weight=0];
13.16/5.20	395[label="ww240 == ww250",fontsize=16,color="magenta"];395 -> 419[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	395 -> 420[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	396 -> 306[label="",style="dashed", color="red", weight=0];
13.16/5.20	396[label="ww240 == ww250",fontsize=16,color="magenta"];396 -> 421[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	396 -> 422[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	397 -> 307[label="",style="dashed", color="red", weight=0];
13.16/5.20	397[label="ww240 == ww250",fontsize=16,color="magenta"];397 -> 423[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	397 -> 424[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	398 -> 308[label="",style="dashed", color="red", weight=0];
13.16/5.20	398[label="ww240 == ww250",fontsize=16,color="magenta"];398 -> 425[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	398 -> 426[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	399 -> 309[label="",style="dashed", color="red", weight=0];
13.16/5.20	399[label="ww240 == ww250",fontsize=16,color="magenta"];399 -> 427[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	399 -> 428[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	400 -> 310[label="",style="dashed", color="red", weight=0];
13.16/5.20	400[label="ww240 == ww250",fontsize=16,color="magenta"];400 -> 429[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	400 -> 430[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	401 -> 311[label="",style="dashed", color="red", weight=0];
13.16/5.20	401[label="ww240 == ww250",fontsize=16,color="magenta"];401 -> 431[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	401 -> 432[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	402 -> 312[label="",style="dashed", color="red", weight=0];
13.16/5.20	402[label="ww240 == ww250",fontsize=16,color="magenta"];402 -> 433[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	402 -> 434[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	403 -> 313[label="",style="dashed", color="red", weight=0];
13.16/5.20	403[label="ww240 == ww250",fontsize=16,color="magenta"];403 -> 435[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	403 -> 436[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	404 -> 314[label="",style="dashed", color="red", weight=0];
13.16/5.20	404[label="ww240 == ww250",fontsize=16,color="magenta"];404 -> 437[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	404 -> 438[label="",style="dashed", color="magenta", weight=3];
13.16/5.20	405[label="primEqNat (Succ ww15000) ww18000",fontsize=16,color="burlywood",shape="box"];571[label="ww18000/Succ ww180000",fontsize=10,color="white",style="solid",shape="box"];405 -> 571[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	571 -> 439[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	572[label="ww18000/Zero",fontsize=10,color="white",style="solid",shape="box"];405 -> 572[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	572 -> 440[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	406[label="primEqNat Zero ww18000",fontsize=16,color="burlywood",shape="box"];573[label="ww18000/Succ ww180000",fontsize=10,color="white",style="solid",shape="box"];406 -> 573[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	573 -> 441[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	574[label="ww18000/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 574[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	574 -> 442[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	407[label="ww1500",fontsize=16,color="green",shape="box"];408[label="ww18000",fontsize=16,color="green",shape="box"];409[label="primMulInt (Pos ww1500) ww1801",fontsize=16,color="burlywood",shape="box"];575[label="ww1801/Pos ww18010",fontsize=10,color="white",style="solid",shape="box"];409 -> 575[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	575 -> 443[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	576[label="ww1801/Neg ww18010",fontsize=10,color="white",style="solid",shape="box"];409 -> 576[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	576 -> 444[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	410[label="primMulInt (Neg ww1500) ww1801",fontsize=16,color="burlywood",shape="box"];577[label="ww1801/Pos ww18010",fontsize=10,color="white",style="solid",shape="box"];410 -> 577[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	577 -> 445[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	578[label="ww1801/Neg ww18010",fontsize=10,color="white",style="solid",shape="box"];410 -> 578[label="",style="solid", color="burlywood", weight=9];
13.16/5.20	578 -> 446[label="",style="solid", color="burlywood", weight=3];
13.16/5.20	411[label="ww240",fontsize=16,color="green",shape="box"];412[label="ww250",fontsize=16,color="green",shape="box"];413[label="ww240",fontsize=16,color="green",shape="box"];414[label="ww250",fontsize=16,color="green",shape="box"];415[label="ww240",fontsize=16,color="green",shape="box"];416[label="ww250",fontsize=16,color="green",shape="box"];417[label="ww240",fontsize=16,color="green",shape="box"];418[label="ww250",fontsize=16,color="green",shape="box"];419[label="ww240",fontsize=16,color="green",shape="box"];420[label="ww250",fontsize=16,color="green",shape="box"];421[label="ww240",fontsize=16,color="green",shape="box"];422[label="ww250",fontsize=16,color="green",shape="box"];423[label="ww240",fontsize=16,color="green",shape="box"];424[label="ww250",fontsize=16,color="green",shape="box"];425[label="ww240",fontsize=16,color="green",shape="box"];426[label="ww250",fontsize=16,color="green",shape="box"];427[label="ww240",fontsize=16,color="green",shape="box"];428[label="ww250",fontsize=16,color="green",shape="box"];429[label="ww240",fontsize=16,color="green",shape="box"];430[label="ww250",fontsize=16,color="green",shape="box"];431[label="ww240",fontsize=16,color="green",shape="box"];432[label="ww250",fontsize=16,color="green",shape="box"];433[label="ww240",fontsize=16,color="green",shape="box"];434[label="ww250",fontsize=16,color="green",shape="box"];435[label="ww240",fontsize=16,color="green",shape="box"];436[label="ww250",fontsize=16,color="green",shape="box"];437[label="ww240",fontsize=16,color="green",shape="box"];438[label="ww250",fontsize=16,color="green",shape="box"];439[label="primEqNat (Succ ww15000) (Succ ww180000)",fontsize=16,color="black",shape="box"];439 -> 447[label="",style="solid", color="black", weight=3];
13.36/5.20	440[label="primEqNat (Succ ww15000) Zero",fontsize=16,color="black",shape="box"];440 -> 448[label="",style="solid", color="black", weight=3];
13.36/5.20	441[label="primEqNat Zero (Succ ww180000)",fontsize=16,color="black",shape="box"];441 -> 449[label="",style="solid", color="black", weight=3];
13.36/5.20	442[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];442 -> 450[label="",style="solid", color="black", weight=3];
13.36/5.20	443[label="primMulInt (Pos ww1500) (Pos ww18010)",fontsize=16,color="black",shape="box"];443 -> 451[label="",style="solid", color="black", weight=3];
13.36/5.20	444[label="primMulInt (Pos ww1500) (Neg ww18010)",fontsize=16,color="black",shape="box"];444 -> 452[label="",style="solid", color="black", weight=3];
13.36/5.20	445[label="primMulInt (Neg ww1500) (Pos ww18010)",fontsize=16,color="black",shape="box"];445 -> 453[label="",style="solid", color="black", weight=3];
13.36/5.20	446[label="primMulInt (Neg ww1500) (Neg ww18010)",fontsize=16,color="black",shape="box"];446 -> 454[label="",style="solid", color="black", weight=3];
13.36/5.20	447 -> 376[label="",style="dashed", color="red", weight=0];
13.36/5.20	447[label="primEqNat ww15000 ww180000",fontsize=16,color="magenta"];447 -> 455[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	447 -> 456[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	448[label="False",fontsize=16,color="green",shape="box"];449[label="False",fontsize=16,color="green",shape="box"];450[label="True",fontsize=16,color="green",shape="box"];451[label="Pos (primMulNat ww1500 ww18010)",fontsize=16,color="green",shape="box"];451 -> 457[label="",style="dashed", color="green", weight=3];
13.36/5.20	452[label="Neg (primMulNat ww1500 ww18010)",fontsize=16,color="green",shape="box"];452 -> 458[label="",style="dashed", color="green", weight=3];
13.36/5.20	453[label="Neg (primMulNat ww1500 ww18010)",fontsize=16,color="green",shape="box"];453 -> 459[label="",style="dashed", color="green", weight=3];
13.36/5.20	454[label="Pos (primMulNat ww1500 ww18010)",fontsize=16,color="green",shape="box"];454 -> 460[label="",style="dashed", color="green", weight=3];
13.36/5.20	455[label="ww15000",fontsize=16,color="green",shape="box"];456[label="ww180000",fontsize=16,color="green",shape="box"];457[label="primMulNat ww1500 ww18010",fontsize=16,color="burlywood",shape="triangle"];579[label="ww1500/Succ ww15000",fontsize=10,color="white",style="solid",shape="box"];457 -> 579[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	579 -> 461[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	580[label="ww1500/Zero",fontsize=10,color="white",style="solid",shape="box"];457 -> 580[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	580 -> 462[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	458 -> 457[label="",style="dashed", color="red", weight=0];
13.36/5.20	458[label="primMulNat ww1500 ww18010",fontsize=16,color="magenta"];458 -> 463[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	459 -> 457[label="",style="dashed", color="red", weight=0];
13.36/5.20	459[label="primMulNat ww1500 ww18010",fontsize=16,color="magenta"];459 -> 464[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	460 -> 457[label="",style="dashed", color="red", weight=0];
13.36/5.20	460[label="primMulNat ww1500 ww18010",fontsize=16,color="magenta"];460 -> 465[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	460 -> 466[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	461[label="primMulNat (Succ ww15000) ww18010",fontsize=16,color="burlywood",shape="box"];581[label="ww18010/Succ ww180100",fontsize=10,color="white",style="solid",shape="box"];461 -> 581[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	581 -> 467[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	582[label="ww18010/Zero",fontsize=10,color="white",style="solid",shape="box"];461 -> 582[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	582 -> 468[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	462[label="primMulNat Zero ww18010",fontsize=16,color="burlywood",shape="box"];583[label="ww18010/Succ ww180100",fontsize=10,color="white",style="solid",shape="box"];462 -> 583[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	583 -> 469[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	584[label="ww18010/Zero",fontsize=10,color="white",style="solid",shape="box"];462 -> 584[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	584 -> 470[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	463[label="ww18010",fontsize=16,color="green",shape="box"];464[label="ww1500",fontsize=16,color="green",shape="box"];465[label="ww1500",fontsize=16,color="green",shape="box"];466[label="ww18010",fontsize=16,color="green",shape="box"];467[label="primMulNat (Succ ww15000) (Succ ww180100)",fontsize=16,color="black",shape="box"];467 -> 471[label="",style="solid", color="black", weight=3];
13.36/5.20	468[label="primMulNat (Succ ww15000) Zero",fontsize=16,color="black",shape="box"];468 -> 472[label="",style="solid", color="black", weight=3];
13.36/5.20	469[label="primMulNat Zero (Succ ww180100)",fontsize=16,color="black",shape="box"];469 -> 473[label="",style="solid", color="black", weight=3];
13.36/5.20	470[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];470 -> 474[label="",style="solid", color="black", weight=3];
13.36/5.20	471 -> 475[label="",style="dashed", color="red", weight=0];
13.36/5.20	471[label="primPlusNat (primMulNat ww15000 (Succ ww180100)) (Succ ww180100)",fontsize=16,color="magenta"];471 -> 476[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	472[label="Zero",fontsize=16,color="green",shape="box"];473[label="Zero",fontsize=16,color="green",shape="box"];474[label="Zero",fontsize=16,color="green",shape="box"];476 -> 457[label="",style="dashed", color="red", weight=0];
13.36/5.20	476[label="primMulNat ww15000 (Succ ww180100)",fontsize=16,color="magenta"];476 -> 477[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	476 -> 478[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	475[label="primPlusNat ww26 (Succ ww180100)",fontsize=16,color="burlywood",shape="triangle"];585[label="ww26/Succ ww260",fontsize=10,color="white",style="solid",shape="box"];475 -> 585[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	585 -> 479[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	586[label="ww26/Zero",fontsize=10,color="white",style="solid",shape="box"];475 -> 586[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	586 -> 480[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	477[label="ww15000",fontsize=16,color="green",shape="box"];478[label="Succ ww180100",fontsize=16,color="green",shape="box"];479[label="primPlusNat (Succ ww260) (Succ ww180100)",fontsize=16,color="black",shape="box"];479 -> 481[label="",style="solid", color="black", weight=3];
13.36/5.20	480[label="primPlusNat Zero (Succ ww180100)",fontsize=16,color="black",shape="box"];480 -> 482[label="",style="solid", color="black", weight=3];
13.36/5.20	481[label="Succ (Succ (primPlusNat ww260 ww180100))",fontsize=16,color="green",shape="box"];481 -> 483[label="",style="dashed", color="green", weight=3];
13.36/5.20	482[label="Succ ww180100",fontsize=16,color="green",shape="box"];483[label="primPlusNat ww260 ww180100",fontsize=16,color="burlywood",shape="triangle"];587[label="ww260/Succ ww2600",fontsize=10,color="white",style="solid",shape="box"];483 -> 587[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	587 -> 484[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	588[label="ww260/Zero",fontsize=10,color="white",style="solid",shape="box"];483 -> 588[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	588 -> 485[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	484[label="primPlusNat (Succ ww2600) ww180100",fontsize=16,color="burlywood",shape="box"];589[label="ww180100/Succ ww1801000",fontsize=10,color="white",style="solid",shape="box"];484 -> 589[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	589 -> 486[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	590[label="ww180100/Zero",fontsize=10,color="white",style="solid",shape="box"];484 -> 590[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	590 -> 487[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	485[label="primPlusNat Zero ww180100",fontsize=16,color="burlywood",shape="box"];591[label="ww180100/Succ ww1801000",fontsize=10,color="white",style="solid",shape="box"];485 -> 591[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	591 -> 488[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	592[label="ww180100/Zero",fontsize=10,color="white",style="solid",shape="box"];485 -> 592[label="",style="solid", color="burlywood", weight=9];
13.36/5.20	592 -> 489[label="",style="solid", color="burlywood", weight=3];
13.36/5.20	486[label="primPlusNat (Succ ww2600) (Succ ww1801000)",fontsize=16,color="black",shape="box"];486 -> 490[label="",style="solid", color="black", weight=3];
13.36/5.20	487[label="primPlusNat (Succ ww2600) Zero",fontsize=16,color="black",shape="box"];487 -> 491[label="",style="solid", color="black", weight=3];
13.36/5.20	488[label="primPlusNat Zero (Succ ww1801000)",fontsize=16,color="black",shape="box"];488 -> 492[label="",style="solid", color="black", weight=3];
13.36/5.20	489[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];489 -> 493[label="",style="solid", color="black", weight=3];
13.36/5.20	490[label="Succ (Succ (primPlusNat ww2600 ww1801000))",fontsize=16,color="green",shape="box"];490 -> 494[label="",style="dashed", color="green", weight=3];
13.36/5.20	491[label="Succ ww2600",fontsize=16,color="green",shape="box"];492[label="Succ ww1801000",fontsize=16,color="green",shape="box"];493[label="Zero",fontsize=16,color="green",shape="box"];494 -> 483[label="",style="dashed", color="red", weight=0];
13.36/5.20	494[label="primPlusNat ww2600 ww1801000",fontsize=16,color="magenta"];494 -> 495[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	494 -> 496[label="",style="dashed", color="magenta", weight=3];
13.36/5.20	495[label="ww2600",fontsize=16,color="green",shape="box"];496[label="ww1801000",fontsize=16,color="green",shape="box"];}
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(6)
13.36/5.20	Complex Obligation (AND)
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(7)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, new_flip(ww18, ww1710, ba), ww1711, ba)
13.36/5.20	
13.36/5.20	The TRS R consists of the following rules:
13.36/5.20	
13.36/5.20	   new_flip(ww14, ww15, ba) -> :(ww15, ww14)
13.36/5.20	
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(8) TransformationProof (EQUIVALENT)
13.36/5.20	By rewriting [LPAR04] the rule new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, new_flip(ww18, ww1710, ba), ww1711, ba) at position [2] we obtained the following new rules [LPAR04]:
13.36/5.20	
13.36/5.20	   (new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba),new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba))
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(9)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba)
13.36/5.20	
13.36/5.20	The TRS R consists of the following rules:
13.36/5.20	
13.36/5.20	   new_flip(ww14, ww15, ba) -> :(ww15, ww14)
13.36/5.20	
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(10) UsableRulesProof (EQUIVALENT)
13.36/5.20	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.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(11)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(12) QReductionProof (EQUIVALENT)
13.36/5.20	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(13)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	Q is empty.
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(14) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_isPrefixOf(ww15, ww14, ww18, :(ww1710, ww1711), ba) -> new_isPrefixOf(ww15, ww14, :(ww1710, ww18), ww1711, ba)
13.36/5.20	The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(15)
13.36/5.20	YES
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(16)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_primMulNat(Succ(ww15000), Succ(ww180100)) -> new_primMulNat(ww15000, Succ(ww180100))
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	Q is empty.
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(17) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_primMulNat(Succ(ww15000), Succ(ww180100)) -> new_primMulNat(ww15000, Succ(ww180100))
13.36/5.20	The graph contains the following edges 1 > 1, 2 >= 2
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(18)
13.36/5.20	YES
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(19)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_asAs(True, :(ww240, ww241), :(ww250, ww251), ba) -> new_asAs(new_esEs(ww240, ww250, ba), ww241, ww251, ba)
13.36/5.20	
13.36/5.20	The TRS R consists of the following rules:
13.36/5.20	
13.36/5.20	   new_esEs(ww240, ww250, app(ty_Ratio, db)) -> new_esEs3(ww240, ww250, db)
13.36/5.20	   new_primPlusNat0(Succ(ww2600), Zero) -> Succ(ww2600)
13.36/5.20	   new_primPlusNat0(Zero, Succ(ww1801000)) -> Succ(ww1801000)
13.36/5.20	   new_esEs7(ww15, ww180, be, bf) -> error([])
13.36/5.20	   new_primMulNat0(Zero, Zero) -> Zero
13.36/5.20	   new_primPlusNat0(Zero, Zero) -> Zero
13.36/5.20	   new_esEs13(ww15, ww180) -> error([])
13.36/5.20	   new_esEs1(ww15, ww180) -> error([])
13.36/5.20	   new_primPlusNat1(Zero, ww180100) -> Succ(ww180100)
13.36/5.20	   new_esEs6(Pos(Zero), Neg(Succ(ww18000))) -> False
13.36/5.20	   new_esEs6(Neg(Zero), Pos(Succ(ww18000))) -> False
13.36/5.20	   new_esEs6(Neg(Zero), Neg(Zero)) -> True
13.36/5.20	   new_esEs10(ww15, ww180, bg, bh) -> error([])
13.36/5.20	   new_esEs9(ww15, ww180) -> error([])
13.36/5.20	   new_sr(Neg(ww1500), Neg(ww18010)) -> Pos(new_primMulNat0(ww1500, ww18010))
13.36/5.20	   new_esEs6(Pos(Succ(ww1500)), Neg(ww1800)) -> False
13.36/5.20	   new_esEs6(Neg(Succ(ww1500)), Pos(ww1800)) -> False
13.36/5.20	   new_esEs12(ww15, ww180) -> error([])
13.36/5.20	   new_esEs0(ww15, ww180, bb) -> error([])
13.36/5.20	   new_esEs(ww240, ww250, ty_@0) -> new_esEs8(ww240, ww250)
13.36/5.20	   new_esEs(ww240, ww250, ty_Double) -> new_esEs12(ww240, ww250)
13.36/5.20	   new_primEqNat0(Succ(ww15000), Zero) -> False
13.36/5.20	   new_primEqNat0(Zero, Succ(ww180000)) -> False
13.36/5.20	   new_esEs11(ww15, ww180, ca, cb, cc) -> error([])
13.36/5.20	   new_esEs(ww240, ww250, app(app(ty_Either, cd), ce)) -> new_esEs10(ww240, ww250, cd, ce)
13.36/5.20	   new_esEs(ww240, ww250, ty_Float) -> new_esEs5(ww240, ww250)
13.36/5.20	   new_esEs(ww240, ww250, app(app(ty_@2, dc), dd)) -> new_esEs7(ww240, ww250, dc, dd)
13.36/5.20	   new_esEs3(ww15, ww180, bc) -> error([])
13.36/5.20	   new_primPlusNat0(Succ(ww2600), Succ(ww1801000)) -> Succ(Succ(new_primPlusNat0(ww2600, ww1801000)))
13.36/5.20	   new_esEs8(ww15, ww180) -> error([])
13.36/5.20	   new_esEs(ww240, ww250, ty_Bool) -> new_esEs13(ww240, ww250)
13.36/5.20	   new_primMulNat0(Succ(ww15000), Succ(ww180100)) -> new_primPlusNat1(new_primMulNat0(ww15000, Succ(ww180100)), ww180100)
13.36/5.20	   new_primEqNat0(Zero, Zero) -> True
13.36/5.20	   new_esEs6(Pos(Succ(ww1500)), Pos(Succ(ww18000))) -> new_primEqNat0(ww1500, ww18000)
13.36/5.20	   new_esEs(ww240, ww250, ty_Ordering) -> new_esEs2(ww240, ww250)
13.36/5.20	   new_esEs(ww240, ww250, ty_Integer) -> new_esEs9(ww240, ww250)
13.36/5.20	   new_esEs6(Pos(Zero), Neg(Zero)) -> True
13.36/5.20	   new_esEs6(Neg(Zero), Pos(Zero)) -> True
13.36/5.20	   new_esEs4(ww15, ww180, bd) -> error([])
13.36/5.20	   new_esEs6(Neg(Succ(ww1500)), Neg(Zero)) -> False
13.36/5.20	   new_esEs6(Neg(Zero), Neg(Succ(ww18000))) -> False
13.36/5.20	   new_esEs(ww240, ww250, ty_Int) -> new_esEs6(ww240, ww250)
13.36/5.20	   new_esEs6(Neg(Succ(ww1500)), Neg(Succ(ww18000))) -> new_primEqNat0(ww1500, ww18000)
13.36/5.20	   new_esEs(ww240, ww250, app(app(app(ty_@3, cf), cg), da)) -> new_esEs11(ww240, ww250, cf, cg, da)
13.36/5.20	   new_sr(Pos(ww1500), Neg(ww18010)) -> Neg(new_primMulNat0(ww1500, ww18010))
13.36/5.20	   new_sr(Neg(ww1500), Pos(ww18010)) -> Neg(new_primMulNat0(ww1500, ww18010))
13.36/5.20	   new_esEs2(ww15, ww180) -> error([])
13.36/5.20	   new_esEs5(Float(ww150, ww151), Float(ww1800, ww1801)) -> new_esEs6(new_sr(ww150, ww1801), new_sr(ww151, ww1800))
13.36/5.20	   new_primMulNat0(Succ(ww15000), Zero) -> Zero
13.36/5.20	   new_primMulNat0(Zero, Succ(ww180100)) -> Zero
13.36/5.20	   new_primEqNat0(Succ(ww15000), Succ(ww180000)) -> new_primEqNat0(ww15000, ww180000)
13.36/5.20	   new_sr(Pos(ww1500), Pos(ww18010)) -> Pos(new_primMulNat0(ww1500, ww18010))
13.36/5.20	   new_esEs(ww240, ww250, ty_Char) -> new_esEs1(ww240, ww250)
13.36/5.20	   new_esEs6(Pos(Succ(ww1500)), Pos(Zero)) -> False
13.36/5.20	   new_esEs6(Pos(Zero), Pos(Succ(ww18000))) -> False
13.36/5.20	   new_esEs(ww240, ww250, app(ty_Maybe, df)) -> new_esEs4(ww240, ww250, df)
13.36/5.20	   new_esEs6(Pos(Zero), Pos(Zero)) -> True
13.36/5.20	   new_esEs(ww240, ww250, app(ty_[], de)) -> new_esEs0(ww240, ww250, de)
13.36/5.20	   new_primPlusNat1(Succ(ww260), ww180100) -> Succ(Succ(new_primPlusNat0(ww260, ww180100)))
13.36/5.20	
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_primMulNat0(Succ(x0), Zero)
13.36/5.20	   new_primEqNat0(Zero, Zero)
13.36/5.20	   new_esEs6(Pos(Zero), Pos(Zero))
13.36/5.20	   new_sr(Neg(x0), Neg(x1))
13.36/5.20	   new_esEs(x0, x1, ty_Integer)
13.36/5.20	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
13.36/5.20	   new_esEs6(Pos(Zero), Neg(Zero))
13.36/5.20	   new_esEs6(Neg(Zero), Pos(Zero))
13.36/5.20	   new_esEs(x0, x1, app(ty_Maybe, x2))
13.36/5.20	   new_esEs(x0, x1, ty_@0)
13.36/5.20	   new_esEs(x0, x1, ty_Int)
13.36/5.20	   new_esEs2(x0, x1)
13.36/5.20	   new_esEs6(Pos(Succ(x0)), Pos(Succ(x1)))
13.36/5.20	   new_esEs(x0, x1, app(ty_[], x2))
13.36/5.20	   new_primMulNat0(Zero, Zero)
13.36/5.20	   new_esEs6(Neg(Succ(x0)), Neg(Succ(x1)))
13.36/5.20	   new_primPlusNat0(Succ(x0), Succ(x1))
13.36/5.20	   new_primMulNat0(Succ(x0), Succ(x1))
13.36/5.20	   new_esEs1(x0, x1)
13.36/5.20	   new_esEs12(x0, x1)
13.36/5.20	   new_esEs(x0, x1, ty_Float)
13.36/5.20	   new_esEs3(x0, x1, x2)
13.36/5.20	   new_esEs9(x0, x1)
13.36/5.20	   new_esEs(x0, x1, ty_Bool)
13.36/5.20	   new_esEs(x0, x1, app(ty_Ratio, x2))
13.36/5.20	   new_primPlusNat0(Succ(x0), Zero)
13.36/5.20	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
13.36/5.20	   new_primEqNat0(Succ(x0), Zero)
13.36/5.20	   new_esEs11(x0, x1, x2, x3, x4)
13.36/5.20	   new_esEs6(Pos(Zero), Pos(Succ(x0)))
13.36/5.20	   new_esEs8(x0, x1)
13.36/5.20	   new_esEs6(Pos(Succ(x0)), Pos(Zero))
13.36/5.20	   new_esEs(x0, x1, ty_Ordering)
13.36/5.20	   new_primMulNat0(Zero, Succ(x0))
13.36/5.20	   new_primPlusNat1(Zero, x0)
13.36/5.20	   new_primEqNat0(Succ(x0), Succ(x1))
13.36/5.20	   new_esEs6(Pos(Zero), Neg(Succ(x0)))
13.36/5.20	   new_esEs6(Neg(Zero), Pos(Succ(x0)))
13.36/5.20	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
13.36/5.20	   new_esEs4(x0, x1, x2)
13.36/5.20	   new_esEs6(Neg(Succ(x0)), Neg(Zero))
13.36/5.20	   new_esEs7(x0, x1, x2, x3)
13.36/5.20	   new_esEs5(Float(x0, x1), Float(x2, x3))
13.36/5.20	   new_primEqNat0(Zero, Succ(x0))
13.36/5.20	   new_primPlusNat1(Succ(x0), x1)
13.36/5.20	   new_esEs6(Neg(Zero), Neg(Zero))
13.36/5.20	   new_esEs(x0, x1, ty_Double)
13.36/5.20	   new_esEs10(x0, x1, x2, x3)
13.36/5.20	   new_sr(Pos(x0), Pos(x1))
13.36/5.20	   new_primPlusNat0(Zero, Succ(x0))
13.36/5.20	   new_esEs0(x0, x1, x2)
13.36/5.20	   new_sr(Pos(x0), Neg(x1))
13.36/5.20	   new_sr(Neg(x0), Pos(x1))
13.36/5.20	   new_esEs(x0, x1, ty_Char)
13.36/5.20	   new_esEs13(x0, x1)
13.36/5.20	   new_esEs6(Neg(Zero), Neg(Succ(x0)))
13.36/5.20	   new_primPlusNat0(Zero, Zero)
13.36/5.20	   new_esEs6(Pos(Succ(x0)), Neg(x1))
13.36/5.20	   new_esEs6(Neg(Succ(x0)), Pos(x1))
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(20) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_asAs(True, :(ww240, ww241), :(ww250, ww251), ba) -> new_asAs(new_esEs(ww240, ww250, ba), ww241, ww251, ba)
13.36/5.20	The graph contains the following edges 2 > 2, 3 > 3, 4 >= 4
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(21)
13.36/5.20	YES
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(22)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_primPlusNat(Succ(ww2600), Succ(ww1801000)) -> new_primPlusNat(ww2600, ww1801000)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	Q is empty.
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(23) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_primPlusNat(Succ(ww2600), Succ(ww1801000)) -> new_primPlusNat(ww2600, ww1801000)
13.36/5.20	The graph contains the following edges 1 > 1, 2 > 2
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(24)
13.36/5.20	YES
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(25)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_primEqNat(Succ(ww15000), Succ(ww180000)) -> new_primEqNat(ww15000, ww180000)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	Q is empty.
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(26) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_primEqNat(Succ(ww15000), Succ(ww180000)) -> new_primEqNat(ww15000, ww180000)
13.36/5.20	The graph contains the following edges 1 > 1, 2 > 2
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(27)
13.36/5.20	YES
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(28)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(new_flip(ww14, ww15, ba), ww160, ww161, ww17, ba)
13.36/5.20	
13.36/5.20	The TRS R consists of the following rules:
13.36/5.20	
13.36/5.20	   new_flip(ww14, ww15, ba) -> :(ww15, ww14)
13.36/5.20	
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(29) TransformationProof (EQUIVALENT)
13.36/5.20	By rewriting [LPAR04] the rule new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(new_flip(ww14, ww15, ba), ww160, ww161, ww17, ba) at position [0] we obtained the following new rules [LPAR04]:
13.36/5.20	
13.36/5.20	   (new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba),new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba))
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(30)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba)
13.36/5.20	
13.36/5.20	The TRS R consists of the following rules:
13.36/5.20	
13.36/5.20	   new_flip(ww14, ww15, ba) -> :(ww15, ww14)
13.36/5.20	
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(31) UsableRulesProof (EQUIVALENT)
13.36/5.20	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.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(32)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	The set Q consists of the following terms:
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(33) QReductionProof (EQUIVALENT)
13.36/5.20	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
13.36/5.20	
13.36/5.20	   new_flip(x0, x1, x2)
13.36/5.20	
13.36/5.20	
13.36/5.20	----------------------------------------
13.36/5.20	
13.36/5.20	(34)
13.36/5.20	Obligation:
13.36/5.20	Q DP problem:
13.36/5.20	The TRS P consists of the following rules:
13.36/5.20	
13.36/5.20	   new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba)
13.36/5.20	
13.36/5.20	R is empty.
13.36/5.20	Q is empty.
13.36/5.20	We have to consider all minimal (P,Q,R)-chains.
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13.36/5.20	
13.36/5.20	(35) QDPSizeChangeProof (EQUIVALENT)
13.36/5.20	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. 
13.36/5.20	
13.36/5.20	From the DPs we obtained the following set of size-change graphs:
13.36/5.20	*new_isPrefixOf0(ww14, ww15, :(ww160, ww161), ww17, ba) -> new_isPrefixOf0(:(ww15, ww14), ww160, ww161, ww17, ba)
13.36/5.20	The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
13.36/5.20	
13.36/5.20	
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13.36/5.20	
13.36/5.20	(36)
13.36/5.20	YES
13.36/5.23	EOF