11.82/4.68	YES
13.37/5.19	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
13.37/5.19	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.37/5.19	
13.37/5.19	
13.37/5.19	H-Termination with start terms of the given HASKELL could be proven:
13.37/5.19	
13.37/5.19	(0) HASKELL
13.37/5.19	(1) BR [EQUIVALENT, 0 ms]
13.37/5.19	(2) HASKELL
13.37/5.19	(3) COR [EQUIVALENT, 0 ms]
13.37/5.19	(4) HASKELL
13.37/5.19	(5) Narrow [SOUND, 0 ms]
13.37/5.19	(6) AND
13.37/5.19	    (7) QDP
13.37/5.19	        (8) TransformationProof [EQUIVALENT, 0 ms]
13.37/5.19	        (9) QDP
13.37/5.19	        (10) UsableRulesProof [EQUIVALENT, 0 ms]
13.37/5.19	        (11) QDP
13.37/5.19	        (12) QReductionProof [EQUIVALENT, 0 ms]
13.37/5.19	        (13) QDP
13.37/5.19	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.37/5.19	        (15) YES
13.37/5.19	    (16) QDP
13.37/5.19	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.37/5.19	        (18) YES
13.37/5.19	    (19) QDP
13.37/5.19	        (20) TransformationProof [EQUIVALENT, 0 ms]
13.37/5.19	        (21) QDP
13.37/5.19	        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
13.37/5.19	        (23) TRUE
13.37/5.19	    (24) QDP
13.37/5.19	        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.37/5.19	        (26) YES
13.37/5.19	    (27) QDP
13.37/5.19	        (28) TransformationProof [EQUIVALENT, 0 ms]
13.37/5.19	        (29) QDP
13.37/5.19	        (30) UsableRulesProof [EQUIVALENT, 0 ms]
13.37/5.19	        (31) QDP
13.37/5.19	        (32) QReductionProof [EQUIVALENT, 0 ms]
13.37/5.19	        (33) QDP
13.37/5.19	        (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.37/5.19	        (35) YES
13.37/5.19	
13.37/5.19	
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(0)
13.37/5.19	Obligation:
13.37/5.19	mainModule Main 
13.37/5.19	module Maybe where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	module List where {
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isPrefixOf [] _ = True;
13.37/5.19	isPrefixOf _ [] = False;
13.37/5.19	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.37/5.19	
13.37/5.19	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.37/5.19	
13.37/5.19	}
13.37/5.19	module Main where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(1) BR (EQUIVALENT)
13.37/5.19	Replaced joker patterns by fresh variables and removed binding patterns.
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(2)
13.37/5.19	Obligation:
13.37/5.19	mainModule Main 
13.37/5.19	module Maybe where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	module List where {
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isPrefixOf [] wu = True;
13.37/5.19	isPrefixOf wv [] = False;
13.37/5.19	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.37/5.19	
13.37/5.19	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.37/5.19	
13.37/5.19	}
13.37/5.19	module Main where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(3) COR (EQUIVALENT)
13.37/5.19	Cond Reductions:
13.37/5.19	The following Function with conditions
13.37/5.19	"undefined |Falseundefined;
13.37/5.19	"
13.37/5.19	is transformed to
13.37/5.19	"undefined  = undefined1;
13.37/5.19	"
13.37/5.19	"undefined0 True = undefined;
13.37/5.19	"
13.37/5.19	"undefined1  = undefined0 False;
13.37/5.19	"
13.37/5.19	
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(4)
13.37/5.19	Obligation:
13.37/5.19	mainModule Main 
13.37/5.19	module Maybe where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	module List where {
13.37/5.19	import qualified Main;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isPrefixOf [] wu = True;
13.37/5.19	isPrefixOf wv [] = False;
13.37/5.19	isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;
13.37/5.19	
13.37/5.19	isSuffixOf :: Eq a => [a]  ->  [a]  ->  Bool;
13.37/5.19	isSuffixOf x y = reverse x `isPrefixOf` reverse y;
13.37/5.19	
13.37/5.19	}
13.37/5.19	module Main where {
13.37/5.19	import qualified List;
13.37/5.19	import qualified Maybe;
13.37/5.19	import qualified Prelude;
13.37/5.19	}
13.37/5.19	
13.37/5.19	----------------------------------------
13.37/5.19	
13.37/5.19	(5) Narrow (SOUND)
13.37/5.19	Haskell To QDPs
13.37/5.19	
13.37/5.19	digraph dp_graph {
13.37/5.19	node [outthreshold=100, inthreshold=100];1[label="List.isSuffixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.37/5.19	3[label="List.isSuffixOf ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.37/5.19	4[label="List.isSuffixOf ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
13.37/5.19	5[label="List.isPrefixOf (reverse ww3) (reverse ww4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
13.37/5.19	6[label="List.isPrefixOf (foldl (flip (:)) [] ww3) (reverse ww4)",fontsize=16,color="burlywood",shape="box"];504[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];6 -> 504[label="",style="solid", color="burlywood", weight=9];
13.37/5.19	504 -> 7[label="",style="solid", color="burlywood", weight=3];
13.37/5.19	505[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 505[label="",style="solid", color="burlywood", weight=9];
13.37/5.19	505 -> 8[label="",style="solid", color="burlywood", weight=3];
13.37/5.19	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];
13.37/5.19	8[label="List.isPrefixOf (foldl (flip (:)) [] []) (reverse ww4)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
13.37/5.19	9 -> 237[label="",style="dashed", color="red", weight=0];
13.37/5.19	9[label="List.isPrefixOf (foldl (flip (:)) (flip (:) [] ww30) ww31) (reverse ww4)",fontsize=16,color="magenta"];9 -> 238[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	9 -> 239[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	9 -> 240[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	9 -> 241[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	10[label="List.isPrefixOf [] (reverse ww4)",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
13.37/5.19	238[label="[]",fontsize=16,color="green",shape="box"];239[label="ww4",fontsize=16,color="green",shape="box"];240[label="ww31",fontsize=16,color="green",shape="box"];241[label="ww30",fontsize=16,color="green",shape="box"];237[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww15 ww16) ww17) (reverse ww18)",fontsize=16,color="burlywood",shape="triangle"];506[label="ww17/ww170 : ww171",fontsize=10,color="white",style="solid",shape="box"];237 -> 506[label="",style="solid", color="burlywood", weight=9];
13.37/5.19	506 -> 274[label="",style="solid", color="burlywood", weight=3];
13.37/5.19	507[label="ww17/[]",fontsize=10,color="white",style="solid",shape="box"];237 -> 507[label="",style="solid", color="burlywood", weight=9];
13.37/5.19	507 -> 275[label="",style="solid", color="burlywood", weight=3];
13.37/5.19	13[label="True",fontsize=16,color="green",shape="box"];274[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww15 ww16) (ww170 : ww171)) (reverse ww18)",fontsize=16,color="black",shape="box"];274 -> 276[label="",style="solid", color="black", weight=3];
13.37/5.19	275[label="List.isPrefixOf (foldl (flip (:)) (flip (:) ww15 ww16) []) (reverse ww18)",fontsize=16,color="black",shape="box"];275 -> 277[label="",style="solid", color="black", weight=3];
13.37/5.19	276 -> 237[label="",style="dashed", color="red", weight=0];
13.37/5.19	276[label="List.isPrefixOf (foldl (flip (:)) (flip (:) (flip (:) ww15 ww16) ww170) ww171) (reverse ww18)",fontsize=16,color="magenta"];276 -> 278[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	276 -> 279[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	276 -> 280[label="",style="dashed", color="magenta", weight=3];
13.37/5.19	277[label="List.isPrefixOf (flip (:) ww15 ww16) (reverse ww18)",fontsize=16,color="black",shape="box"];277 -> 281[label="",style="solid", color="black", weight=3];
13.37/5.20	278[label="flip (:) ww15 ww16",fontsize=16,color="black",shape="triangle"];278 -> 282[label="",style="solid", color="black", weight=3];
13.37/5.20	279[label="ww171",fontsize=16,color="green",shape="box"];280[label="ww170",fontsize=16,color="green",shape="box"];281[label="List.isPrefixOf ((:) ww16 ww15) (reverse ww18)",fontsize=16,color="black",shape="box"];281 -> 283[label="",style="solid", color="black", weight=3];
13.37/5.20	282[label="(:) ww16 ww15",fontsize=16,color="green",shape="box"];283 -> 288[label="",style="dashed", color="red", weight=0];
13.37/5.20	283[label="List.isPrefixOf ((:) ww16 ww15) (foldl (flip (:)) [] ww18)",fontsize=16,color="magenta"];283 -> 289[label="",style="dashed", color="magenta", weight=3];
13.37/5.20	283 -> 290[label="",style="dashed", color="magenta", weight=3];
13.37/5.20	289[label="[]",fontsize=16,color="green",shape="box"];290[label="ww18",fontsize=16,color="green",shape="box"];288[label="List.isPrefixOf ((:) ww16 ww15) (foldl (flip (:)) ww19 ww181)",fontsize=16,color="burlywood",shape="triangle"];508[label="ww181/ww1810 : ww1811",fontsize=10,color="white",style="solid",shape="box"];288 -> 508[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	508 -> 292[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	509[label="ww181/[]",fontsize=10,color="white",style="solid",shape="box"];288 -> 509[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	509 -> 293[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	292[label="List.isPrefixOf ((:) ww16 ww15) (foldl (flip (:)) ww19 (ww1810 : ww1811))",fontsize=16,color="black",shape="box"];292 -> 294[label="",style="solid", color="black", weight=3];
13.70/5.20	293[label="List.isPrefixOf ((:) ww16 ww15) (foldl (flip (:)) ww19 [])",fontsize=16,color="black",shape="box"];293 -> 295[label="",style="solid", color="black", weight=3];
13.70/5.20	294 -> 288[label="",style="dashed", color="red", weight=0];
13.70/5.20	294[label="List.isPrefixOf ((:) ww16 ww15) (foldl (flip (:)) (flip (:) ww19 ww1810) ww1811)",fontsize=16,color="magenta"];294 -> 296[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	294 -> 297[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	295[label="List.isPrefixOf ((:) ww16 ww15) ww19",fontsize=16,color="burlywood",shape="box"];510[label="ww19/ww190 : ww191",fontsize=10,color="white",style="solid",shape="box"];295 -> 510[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	510 -> 298[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	511[label="ww19/[]",fontsize=10,color="white",style="solid",shape="box"];295 -> 511[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	511 -> 299[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	296 -> 278[label="",style="dashed", color="red", weight=0];
13.70/5.20	296[label="flip (:) ww19 ww1810",fontsize=16,color="magenta"];296 -> 300[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	296 -> 301[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	297[label="ww1811",fontsize=16,color="green",shape="box"];298[label="List.isPrefixOf ((:) ww16 ww15) (ww190 : ww191)",fontsize=16,color="black",shape="box"];298 -> 302[label="",style="solid", color="black", weight=3];
13.70/5.20	299[label="List.isPrefixOf ((:) ww16 ww15) []",fontsize=16,color="black",shape="box"];299 -> 303[label="",style="solid", color="black", weight=3];
13.70/5.20	300[label="ww19",fontsize=16,color="green",shape="box"];301[label="ww1810",fontsize=16,color="green",shape="box"];302 -> 304[label="",style="dashed", color="red", weight=0];
13.70/5.20	302[label="ww16 == ww190 && List.isPrefixOf ww15 ww191",fontsize=16,color="magenta"];302 -> 305[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	302 -> 306[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	302 -> 307[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	303[label="False",fontsize=16,color="green",shape="box"];305[label="ww16 == ww190",fontsize=16,color="blue",shape="box"];512[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 512[label="",style="solid", color="blue", weight=9];
13.70/5.20	512 -> 308[label="",style="solid", color="blue", weight=3];
13.70/5.20	513[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 513[label="",style="solid", color="blue", weight=9];
13.70/5.20	513 -> 309[label="",style="solid", color="blue", weight=3];
13.70/5.20	514[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 514[label="",style="solid", color="blue", weight=9];
13.70/5.20	514 -> 310[label="",style="solid", color="blue", weight=3];
13.70/5.20	515[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 515[label="",style="solid", color="blue", weight=9];
13.70/5.20	515 -> 311[label="",style="solid", color="blue", weight=3];
13.70/5.20	516[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 516[label="",style="solid", color="blue", weight=9];
13.70/5.20	516 -> 312[label="",style="solid", color="blue", weight=3];
13.70/5.20	517[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 517[label="",style="solid", color="blue", weight=9];
13.70/5.20	517 -> 313[label="",style="solid", color="blue", weight=3];
13.70/5.20	518[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 518[label="",style="solid", color="blue", weight=9];
13.70/5.20	518 -> 314[label="",style="solid", color="blue", weight=3];
13.70/5.20	519[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 519[label="",style="solid", color="blue", weight=9];
13.70/5.20	519 -> 315[label="",style="solid", color="blue", weight=3];
13.70/5.20	520[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 520[label="",style="solid", color="blue", weight=9];
13.70/5.20	520 -> 316[label="",style="solid", color="blue", weight=3];
13.70/5.20	521[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 521[label="",style="solid", color="blue", weight=9];
13.70/5.20	521 -> 317[label="",style="solid", color="blue", weight=3];
13.70/5.20	522[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 522[label="",style="solid", color="blue", weight=9];
13.70/5.20	522 -> 318[label="",style="solid", color="blue", weight=3];
13.70/5.20	523[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 523[label="",style="solid", color="blue", weight=9];
13.70/5.20	523 -> 319[label="",style="solid", color="blue", weight=3];
13.70/5.20	524[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 524[label="",style="solid", color="blue", weight=9];
13.70/5.20	524 -> 320[label="",style="solid", color="blue", weight=3];
13.70/5.20	525[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 525[label="",style="solid", color="blue", weight=9];
13.70/5.20	525 -> 321[label="",style="solid", color="blue", weight=3];
13.70/5.20	306[label="ww15",fontsize=16,color="green",shape="box"];307[label="ww191",fontsize=16,color="green",shape="box"];304[label="ww24 && List.isPrefixOf ww25 ww26",fontsize=16,color="burlywood",shape="triangle"];526[label="ww24/False",fontsize=10,color="white",style="solid",shape="box"];304 -> 526[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	526 -> 322[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	527[label="ww24/True",fontsize=10,color="white",style="solid",shape="box"];304 -> 527[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	527 -> 323[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	308[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];308 -> 324[label="",style="solid", color="black", weight=3];
13.70/5.20	309[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];309 -> 325[label="",style="solid", color="black", weight=3];
13.70/5.20	310[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];310 -> 326[label="",style="solid", color="black", weight=3];
13.70/5.20	311[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];311 -> 327[label="",style="solid", color="black", weight=3];
13.70/5.20	312[label="ww16 == ww190",fontsize=16,color="burlywood",shape="triangle"];528[label="ww16/ww160 :% ww161",fontsize=10,color="white",style="solid",shape="box"];312 -> 528[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	528 -> 328[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	313[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];313 -> 329[label="",style="solid", color="black", weight=3];
13.70/5.20	314[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];314 -> 330[label="",style="solid", color="black", weight=3];
13.70/5.20	315[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];315 -> 331[label="",style="solid", color="black", weight=3];
13.70/5.20	316[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];316 -> 332[label="",style="solid", color="black", weight=3];
13.70/5.20	317[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];317 -> 333[label="",style="solid", color="black", weight=3];
13.70/5.20	318[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];318 -> 334[label="",style="solid", color="black", weight=3];
13.70/5.20	319[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];319 -> 335[label="",style="solid", color="black", weight=3];
13.70/5.20	320[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];320 -> 336[label="",style="solid", color="black", weight=3];
13.70/5.20	321[label="ww16 == ww190",fontsize=16,color="black",shape="triangle"];321 -> 337[label="",style="solid", color="black", weight=3];
13.70/5.20	322[label="False && List.isPrefixOf ww25 ww26",fontsize=16,color="black",shape="box"];322 -> 338[label="",style="solid", color="black", weight=3];
13.70/5.20	323[label="True && List.isPrefixOf ww25 ww26",fontsize=16,color="black",shape="box"];323 -> 339[label="",style="solid", color="black", weight=3];
13.70/5.20	324[label="error []",fontsize=16,color="red",shape="box"];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="ww160 :% ww161 == ww190",fontsize=16,color="burlywood",shape="box"];529[label="ww190/ww1900 :% ww1901",fontsize=10,color="white",style="solid",shape="box"];328 -> 529[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	529 -> 340[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	329[label="error []",fontsize=16,color="red",shape="box"];330[label="error []",fontsize=16,color="red",shape="box"];331[label="error []",fontsize=16,color="red",shape="box"];332[label="primEqInt ww16 ww190",fontsize=16,color="burlywood",shape="box"];530[label="ww16/Pos ww160",fontsize=10,color="white",style="solid",shape="box"];332 -> 530[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	530 -> 341[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	531[label="ww16/Neg ww160",fontsize=10,color="white",style="solid",shape="box"];332 -> 531[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	531 -> 342[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	333[label="error []",fontsize=16,color="red",shape="box"];334[label="error []",fontsize=16,color="red",shape="box"];335[label="error []",fontsize=16,color="red",shape="box"];336[label="error []",fontsize=16,color="red",shape="box"];337[label="error []",fontsize=16,color="red",shape="box"];338[label="False",fontsize=16,color="green",shape="box"];339[label="List.isPrefixOf ww25 ww26",fontsize=16,color="burlywood",shape="box"];532[label="ww25/ww250 : ww251",fontsize=10,color="white",style="solid",shape="box"];339 -> 532[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	532 -> 343[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	533[label="ww25/[]",fontsize=10,color="white",style="solid",shape="box"];339 -> 533[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	533 -> 344[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	340[label="ww160 :% ww161 == ww1900 :% ww1901",fontsize=16,color="black",shape="box"];340 -> 345[label="",style="solid", color="black", weight=3];
13.70/5.20	341[label="primEqInt (Pos ww160) ww190",fontsize=16,color="burlywood",shape="box"];534[label="ww160/Succ ww1600",fontsize=10,color="white",style="solid",shape="box"];341 -> 534[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	534 -> 346[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	535[label="ww160/Zero",fontsize=10,color="white",style="solid",shape="box"];341 -> 535[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	535 -> 347[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	342[label="primEqInt (Neg ww160) ww190",fontsize=16,color="burlywood",shape="box"];536[label="ww160/Succ ww1600",fontsize=10,color="white",style="solid",shape="box"];342 -> 536[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	536 -> 348[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	537[label="ww160/Zero",fontsize=10,color="white",style="solid",shape="box"];342 -> 537[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	537 -> 349[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	343[label="List.isPrefixOf (ww250 : ww251) ww26",fontsize=16,color="burlywood",shape="box"];538[label="ww26/ww260 : ww261",fontsize=10,color="white",style="solid",shape="box"];343 -> 538[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	538 -> 350[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	539[label="ww26/[]",fontsize=10,color="white",style="solid",shape="box"];343 -> 539[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	539 -> 351[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	344[label="List.isPrefixOf [] ww26",fontsize=16,color="black",shape="box"];344 -> 352[label="",style="solid", color="black", weight=3];
13.70/5.20	345 -> 353[label="",style="dashed", color="red", weight=0];
13.70/5.20	345[label="ww160 == ww1900 && ww161 == ww1901",fontsize=16,color="magenta"];345 -> 354[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	345 -> 355[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	345 -> 356[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	346[label="primEqInt (Pos (Succ ww1600)) ww190",fontsize=16,color="burlywood",shape="box"];540[label="ww190/Pos ww1900",fontsize=10,color="white",style="solid",shape="box"];346 -> 540[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	540 -> 357[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	541[label="ww190/Neg ww1900",fontsize=10,color="white",style="solid",shape="box"];346 -> 541[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	541 -> 358[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	347[label="primEqInt (Pos Zero) ww190",fontsize=16,color="burlywood",shape="box"];542[label="ww190/Pos ww1900",fontsize=10,color="white",style="solid",shape="box"];347 -> 542[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	542 -> 359[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	543[label="ww190/Neg ww1900",fontsize=10,color="white",style="solid",shape="box"];347 -> 543[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	543 -> 360[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	348[label="primEqInt (Neg (Succ ww1600)) ww190",fontsize=16,color="burlywood",shape="box"];544[label="ww190/Pos ww1900",fontsize=10,color="white",style="solid",shape="box"];348 -> 544[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	544 -> 361[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	545[label="ww190/Neg ww1900",fontsize=10,color="white",style="solid",shape="box"];348 -> 545[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	545 -> 362[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	349[label="primEqInt (Neg Zero) ww190",fontsize=16,color="burlywood",shape="box"];546[label="ww190/Pos ww1900",fontsize=10,color="white",style="solid",shape="box"];349 -> 546[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	546 -> 363[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	547[label="ww190/Neg ww1900",fontsize=10,color="white",style="solid",shape="box"];349 -> 547[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	547 -> 364[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	350[label="List.isPrefixOf (ww250 : ww251) (ww260 : ww261)",fontsize=16,color="black",shape="box"];350 -> 365[label="",style="solid", color="black", weight=3];
13.70/5.20	351[label="List.isPrefixOf (ww250 : ww251) []",fontsize=16,color="black",shape="box"];351 -> 366[label="",style="solid", color="black", weight=3];
13.70/5.20	352[label="True",fontsize=16,color="green",shape="box"];354[label="ww161",fontsize=16,color="green",shape="box"];355[label="ww160 == ww1900",fontsize=16,color="blue",shape="box"];548[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];355 -> 548[label="",style="solid", color="blue", weight=9];
13.70/5.20	548 -> 367[label="",style="solid", color="blue", weight=3];
13.70/5.20	549[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];355 -> 549[label="",style="solid", color="blue", weight=9];
13.70/5.20	549 -> 368[label="",style="solid", color="blue", weight=3];
13.70/5.20	356[label="ww1901",fontsize=16,color="green",shape="box"];353[label="ww31 && ww32 == ww33",fontsize=16,color="burlywood",shape="triangle"];550[label="ww31/False",fontsize=10,color="white",style="solid",shape="box"];353 -> 550[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	550 -> 369[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	551[label="ww31/True",fontsize=10,color="white",style="solid",shape="box"];353 -> 551[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	551 -> 370[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	357[label="primEqInt (Pos (Succ ww1600)) (Pos ww1900)",fontsize=16,color="burlywood",shape="box"];552[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];357 -> 552[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	552 -> 371[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	553[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];357 -> 553[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	553 -> 372[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	358[label="primEqInt (Pos (Succ ww1600)) (Neg ww1900)",fontsize=16,color="black",shape="box"];358 -> 373[label="",style="solid", color="black", weight=3];
13.70/5.20	359[label="primEqInt (Pos Zero) (Pos ww1900)",fontsize=16,color="burlywood",shape="box"];554[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];359 -> 554[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	554 -> 374[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	555[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];359 -> 555[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	555 -> 375[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	360[label="primEqInt (Pos Zero) (Neg ww1900)",fontsize=16,color="burlywood",shape="box"];556[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];360 -> 556[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	556 -> 376[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	557[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];360 -> 557[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	557 -> 377[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	361[label="primEqInt (Neg (Succ ww1600)) (Pos ww1900)",fontsize=16,color="black",shape="box"];361 -> 378[label="",style="solid", color="black", weight=3];
13.70/5.20	362[label="primEqInt (Neg (Succ ww1600)) (Neg ww1900)",fontsize=16,color="burlywood",shape="box"];558[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];362 -> 558[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	558 -> 379[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	559[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];362 -> 559[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	559 -> 380[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	363[label="primEqInt (Neg Zero) (Pos ww1900)",fontsize=16,color="burlywood",shape="box"];560[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];363 -> 560[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	560 -> 381[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	561[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];363 -> 561[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	561 -> 382[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	364[label="primEqInt (Neg Zero) (Neg ww1900)",fontsize=16,color="burlywood",shape="box"];562[label="ww1900/Succ ww19000",fontsize=10,color="white",style="solid",shape="box"];364 -> 562[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	562 -> 383[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	563[label="ww1900/Zero",fontsize=10,color="white",style="solid",shape="box"];364 -> 563[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	563 -> 384[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	365 -> 304[label="",style="dashed", color="red", weight=0];
13.70/5.20	365[label="ww250 == ww260 && List.isPrefixOf ww251 ww261",fontsize=16,color="magenta"];365 -> 385[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	365 -> 386[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	365 -> 387[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	366[label="False",fontsize=16,color="green",shape="box"];367 -> 316[label="",style="dashed", color="red", weight=0];
13.70/5.20	367[label="ww160 == ww1900",fontsize=16,color="magenta"];367 -> 388[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	367 -> 389[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	368 -> 317[label="",style="dashed", color="red", weight=0];
13.70/5.20	368[label="ww160 == ww1900",fontsize=16,color="magenta"];368 -> 390[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	368 -> 391[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	369[label="False && ww32 == ww33",fontsize=16,color="black",shape="box"];369 -> 392[label="",style="solid", color="black", weight=3];
13.70/5.20	370[label="True && ww32 == ww33",fontsize=16,color="black",shape="box"];370 -> 393[label="",style="solid", color="black", weight=3];
13.70/5.20	371[label="primEqInt (Pos (Succ ww1600)) (Pos (Succ ww19000))",fontsize=16,color="black",shape="box"];371 -> 394[label="",style="solid", color="black", weight=3];
13.70/5.20	372[label="primEqInt (Pos (Succ ww1600)) (Pos Zero)",fontsize=16,color="black",shape="box"];372 -> 395[label="",style="solid", color="black", weight=3];
13.70/5.20	373[label="False",fontsize=16,color="green",shape="box"];374[label="primEqInt (Pos Zero) (Pos (Succ ww19000))",fontsize=16,color="black",shape="box"];374 -> 396[label="",style="solid", color="black", weight=3];
13.70/5.20	375[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];375 -> 397[label="",style="solid", color="black", weight=3];
13.70/5.20	376[label="primEqInt (Pos Zero) (Neg (Succ ww19000))",fontsize=16,color="black",shape="box"];376 -> 398[label="",style="solid", color="black", weight=3];
13.70/5.20	377[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];377 -> 399[label="",style="solid", color="black", weight=3];
13.70/5.20	378[label="False",fontsize=16,color="green",shape="box"];379[label="primEqInt (Neg (Succ ww1600)) (Neg (Succ ww19000))",fontsize=16,color="black",shape="box"];379 -> 400[label="",style="solid", color="black", weight=3];
13.70/5.20	380[label="primEqInt (Neg (Succ ww1600)) (Neg Zero)",fontsize=16,color="black",shape="box"];380 -> 401[label="",style="solid", color="black", weight=3];
13.70/5.20	381[label="primEqInt (Neg Zero) (Pos (Succ ww19000))",fontsize=16,color="black",shape="box"];381 -> 402[label="",style="solid", color="black", weight=3];
13.70/5.20	382[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];382 -> 403[label="",style="solid", color="black", weight=3];
13.70/5.20	383[label="primEqInt (Neg Zero) (Neg (Succ ww19000))",fontsize=16,color="black",shape="box"];383 -> 404[label="",style="solid", color="black", weight=3];
13.70/5.20	384[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];384 -> 405[label="",style="solid", color="black", weight=3];
13.70/5.20	385[label="ww250 == ww260",fontsize=16,color="blue",shape="box"];564[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 564[label="",style="solid", color="blue", weight=9];
13.70/5.20	564 -> 406[label="",style="solid", color="blue", weight=3];
13.70/5.20	565[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 565[label="",style="solid", color="blue", weight=9];
13.70/5.20	565 -> 407[label="",style="solid", color="blue", weight=3];
13.70/5.20	566[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 566[label="",style="solid", color="blue", weight=9];
13.70/5.20	566 -> 408[label="",style="solid", color="blue", weight=3];
13.70/5.20	567[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 567[label="",style="solid", color="blue", weight=9];
13.70/5.20	567 -> 409[label="",style="solid", color="blue", weight=3];
13.70/5.20	568[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 568[label="",style="solid", color="blue", weight=9];
13.70/5.20	568 -> 410[label="",style="solid", color="blue", weight=3];
13.70/5.20	569[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 569[label="",style="solid", color="blue", weight=9];
13.70/5.20	569 -> 411[label="",style="solid", color="blue", weight=3];
13.70/5.20	570[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 570[label="",style="solid", color="blue", weight=9];
13.70/5.20	570 -> 412[label="",style="solid", color="blue", weight=3];
13.70/5.20	571[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 571[label="",style="solid", color="blue", weight=9];
13.70/5.20	571 -> 413[label="",style="solid", color="blue", weight=3];
13.70/5.20	572[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 572[label="",style="solid", color="blue", weight=9];
13.70/5.20	572 -> 414[label="",style="solid", color="blue", weight=3];
13.70/5.20	573[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 573[label="",style="solid", color="blue", weight=9];
13.70/5.20	573 -> 415[label="",style="solid", color="blue", weight=3];
13.70/5.20	574[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 574[label="",style="solid", color="blue", weight=9];
13.70/5.20	574 -> 416[label="",style="solid", color="blue", weight=3];
13.70/5.20	575[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 575[label="",style="solid", color="blue", weight=9];
13.70/5.20	575 -> 417[label="",style="solid", color="blue", weight=3];
13.70/5.20	576[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 576[label="",style="solid", color="blue", weight=9];
13.70/5.20	576 -> 418[label="",style="solid", color="blue", weight=3];
13.70/5.20	577[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];385 -> 577[label="",style="solid", color="blue", weight=9];
13.70/5.20	577 -> 419[label="",style="solid", color="blue", weight=3];
13.70/5.20	386[label="ww251",fontsize=16,color="green",shape="box"];387[label="ww261",fontsize=16,color="green",shape="box"];388[label="ww1900",fontsize=16,color="green",shape="box"];389[label="ww160",fontsize=16,color="green",shape="box"];390[label="ww1900",fontsize=16,color="green",shape="box"];391[label="ww160",fontsize=16,color="green",shape="box"];392[label="False",fontsize=16,color="green",shape="box"];393[label="ww32 == ww33",fontsize=16,color="blue",shape="box"];578[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 578[label="",style="solid", color="blue", weight=9];
13.70/5.20	578 -> 420[label="",style="solid", color="blue", weight=3];
13.70/5.20	579[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 579[label="",style="solid", color="blue", weight=9];
13.70/5.20	579 -> 421[label="",style="solid", color="blue", weight=3];
13.70/5.20	580[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 580[label="",style="solid", color="blue", weight=9];
13.70/5.20	580 -> 422[label="",style="solid", color="blue", weight=3];
13.70/5.20	581[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 581[label="",style="solid", color="blue", weight=9];
13.70/5.20	581 -> 423[label="",style="solid", color="blue", weight=3];
13.70/5.20	582[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 582[label="",style="solid", color="blue", weight=9];
13.70/5.20	582 -> 424[label="",style="solid", color="blue", weight=3];
13.70/5.20	583[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 583[label="",style="solid", color="blue", weight=9];
13.70/5.20	583 -> 425[label="",style="solid", color="blue", weight=3];
13.70/5.20	584[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 584[label="",style="solid", color="blue", weight=9];
13.70/5.20	584 -> 426[label="",style="solid", color="blue", weight=3];
13.70/5.20	585[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 585[label="",style="solid", color="blue", weight=9];
13.70/5.20	585 -> 427[label="",style="solid", color="blue", weight=3];
13.70/5.20	586[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 586[label="",style="solid", color="blue", weight=9];
13.70/5.20	586 -> 428[label="",style="solid", color="blue", weight=3];
13.70/5.20	587[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 587[label="",style="solid", color="blue", weight=9];
13.70/5.20	587 -> 429[label="",style="solid", color="blue", weight=3];
13.70/5.20	588[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 588[label="",style="solid", color="blue", weight=9];
13.70/5.20	588 -> 430[label="",style="solid", color="blue", weight=3];
13.70/5.20	589[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 589[label="",style="solid", color="blue", weight=9];
13.70/5.20	589 -> 431[label="",style="solid", color="blue", weight=3];
13.70/5.20	590[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 590[label="",style="solid", color="blue", weight=9];
13.70/5.20	590 -> 432[label="",style="solid", color="blue", weight=3];
13.70/5.20	591[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];393 -> 591[label="",style="solid", color="blue", weight=9];
13.70/5.20	591 -> 433[label="",style="solid", color="blue", weight=3];
13.70/5.20	394[label="primEqNat ww1600 ww19000",fontsize=16,color="burlywood",shape="triangle"];592[label="ww1600/Succ ww16000",fontsize=10,color="white",style="solid",shape="box"];394 -> 592[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	592 -> 434[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	593[label="ww1600/Zero",fontsize=10,color="white",style="solid",shape="box"];394 -> 593[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	593 -> 435[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	395[label="False",fontsize=16,color="green",shape="box"];396[label="False",fontsize=16,color="green",shape="box"];397[label="True",fontsize=16,color="green",shape="box"];398[label="False",fontsize=16,color="green",shape="box"];399[label="True",fontsize=16,color="green",shape="box"];400 -> 394[label="",style="dashed", color="red", weight=0];
13.70/5.20	400[label="primEqNat ww1600 ww19000",fontsize=16,color="magenta"];400 -> 436[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	400 -> 437[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	401[label="False",fontsize=16,color="green",shape="box"];402[label="False",fontsize=16,color="green",shape="box"];403[label="True",fontsize=16,color="green",shape="box"];404[label="False",fontsize=16,color="green",shape="box"];405[label="True",fontsize=16,color="green",shape="box"];406 -> 308[label="",style="dashed", color="red", weight=0];
13.70/5.20	406[label="ww250 == ww260",fontsize=16,color="magenta"];406 -> 438[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	406 -> 439[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	407 -> 309[label="",style="dashed", color="red", weight=0];
13.70/5.20	407[label="ww250 == ww260",fontsize=16,color="magenta"];407 -> 440[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	407 -> 441[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	408 -> 310[label="",style="dashed", color="red", weight=0];
13.70/5.20	408[label="ww250 == ww260",fontsize=16,color="magenta"];408 -> 442[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	408 -> 443[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	409 -> 311[label="",style="dashed", color="red", weight=0];
13.70/5.20	409[label="ww250 == ww260",fontsize=16,color="magenta"];409 -> 444[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	409 -> 445[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	410 -> 312[label="",style="dashed", color="red", weight=0];
13.70/5.20	410[label="ww250 == ww260",fontsize=16,color="magenta"];410 -> 446[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	410 -> 447[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	411 -> 313[label="",style="dashed", color="red", weight=0];
13.70/5.20	411[label="ww250 == ww260",fontsize=16,color="magenta"];411 -> 448[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	411 -> 449[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	412 -> 314[label="",style="dashed", color="red", weight=0];
13.70/5.20	412[label="ww250 == ww260",fontsize=16,color="magenta"];412 -> 450[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	412 -> 451[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	413 -> 315[label="",style="dashed", color="red", weight=0];
13.70/5.20	413[label="ww250 == ww260",fontsize=16,color="magenta"];413 -> 452[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	413 -> 453[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	414 -> 316[label="",style="dashed", color="red", weight=0];
13.70/5.20	414[label="ww250 == ww260",fontsize=16,color="magenta"];414 -> 454[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	414 -> 455[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	415 -> 317[label="",style="dashed", color="red", weight=0];
13.70/5.20	415[label="ww250 == ww260",fontsize=16,color="magenta"];415 -> 456[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	415 -> 457[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	416 -> 318[label="",style="dashed", color="red", weight=0];
13.70/5.20	416[label="ww250 == ww260",fontsize=16,color="magenta"];416 -> 458[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	416 -> 459[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	417 -> 319[label="",style="dashed", color="red", weight=0];
13.70/5.20	417[label="ww250 == ww260",fontsize=16,color="magenta"];417 -> 460[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	417 -> 461[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	418 -> 320[label="",style="dashed", color="red", weight=0];
13.70/5.20	418[label="ww250 == ww260",fontsize=16,color="magenta"];418 -> 462[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	418 -> 463[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	419 -> 321[label="",style="dashed", color="red", weight=0];
13.70/5.20	419[label="ww250 == ww260",fontsize=16,color="magenta"];419 -> 464[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	419 -> 465[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	420 -> 308[label="",style="dashed", color="red", weight=0];
13.70/5.20	420[label="ww32 == ww33",fontsize=16,color="magenta"];420 -> 466[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	420 -> 467[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	421 -> 309[label="",style="dashed", color="red", weight=0];
13.70/5.20	421[label="ww32 == ww33",fontsize=16,color="magenta"];421 -> 468[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	421 -> 469[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	422 -> 310[label="",style="dashed", color="red", weight=0];
13.70/5.20	422[label="ww32 == ww33",fontsize=16,color="magenta"];422 -> 470[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	422 -> 471[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	423 -> 311[label="",style="dashed", color="red", weight=0];
13.70/5.20	423[label="ww32 == ww33",fontsize=16,color="magenta"];423 -> 472[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	423 -> 473[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	424 -> 312[label="",style="dashed", color="red", weight=0];
13.70/5.20	424[label="ww32 == ww33",fontsize=16,color="magenta"];424 -> 474[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	424 -> 475[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	425 -> 313[label="",style="dashed", color="red", weight=0];
13.70/5.20	425[label="ww32 == ww33",fontsize=16,color="magenta"];425 -> 476[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	425 -> 477[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	426 -> 314[label="",style="dashed", color="red", weight=0];
13.70/5.20	426[label="ww32 == ww33",fontsize=16,color="magenta"];426 -> 478[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	426 -> 479[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	427 -> 315[label="",style="dashed", color="red", weight=0];
13.70/5.20	427[label="ww32 == ww33",fontsize=16,color="magenta"];427 -> 480[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	427 -> 481[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	428 -> 316[label="",style="dashed", color="red", weight=0];
13.70/5.20	428[label="ww32 == ww33",fontsize=16,color="magenta"];428 -> 482[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	428 -> 483[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	429 -> 317[label="",style="dashed", color="red", weight=0];
13.70/5.20	429[label="ww32 == ww33",fontsize=16,color="magenta"];429 -> 484[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	429 -> 485[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	430 -> 318[label="",style="dashed", color="red", weight=0];
13.70/5.20	430[label="ww32 == ww33",fontsize=16,color="magenta"];430 -> 486[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	430 -> 487[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	431 -> 319[label="",style="dashed", color="red", weight=0];
13.70/5.20	431[label="ww32 == ww33",fontsize=16,color="magenta"];431 -> 488[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	431 -> 489[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	432 -> 320[label="",style="dashed", color="red", weight=0];
13.70/5.20	432[label="ww32 == ww33",fontsize=16,color="magenta"];432 -> 490[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	432 -> 491[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	433 -> 321[label="",style="dashed", color="red", weight=0];
13.70/5.20	433[label="ww32 == ww33",fontsize=16,color="magenta"];433 -> 492[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	433 -> 493[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	434[label="primEqNat (Succ ww16000) ww19000",fontsize=16,color="burlywood",shape="box"];594[label="ww19000/Succ ww190000",fontsize=10,color="white",style="solid",shape="box"];434 -> 594[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	594 -> 494[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	595[label="ww19000/Zero",fontsize=10,color="white",style="solid",shape="box"];434 -> 595[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	595 -> 495[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	435[label="primEqNat Zero ww19000",fontsize=16,color="burlywood",shape="box"];596[label="ww19000/Succ ww190000",fontsize=10,color="white",style="solid",shape="box"];435 -> 596[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	596 -> 496[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	597[label="ww19000/Zero",fontsize=10,color="white",style="solid",shape="box"];435 -> 597[label="",style="solid", color="burlywood", weight=9];
13.70/5.20	597 -> 497[label="",style="solid", color="burlywood", weight=3];
13.70/5.20	436[label="ww1600",fontsize=16,color="green",shape="box"];437[label="ww19000",fontsize=16,color="green",shape="box"];438[label="ww260",fontsize=16,color="green",shape="box"];439[label="ww250",fontsize=16,color="green",shape="box"];440[label="ww260",fontsize=16,color="green",shape="box"];441[label="ww250",fontsize=16,color="green",shape="box"];442[label="ww260",fontsize=16,color="green",shape="box"];443[label="ww250",fontsize=16,color="green",shape="box"];444[label="ww260",fontsize=16,color="green",shape="box"];445[label="ww250",fontsize=16,color="green",shape="box"];446[label="ww260",fontsize=16,color="green",shape="box"];447[label="ww250",fontsize=16,color="green",shape="box"];448[label="ww260",fontsize=16,color="green",shape="box"];449[label="ww250",fontsize=16,color="green",shape="box"];450[label="ww260",fontsize=16,color="green",shape="box"];451[label="ww250",fontsize=16,color="green",shape="box"];452[label="ww260",fontsize=16,color="green",shape="box"];453[label="ww250",fontsize=16,color="green",shape="box"];454[label="ww260",fontsize=16,color="green",shape="box"];455[label="ww250",fontsize=16,color="green",shape="box"];456[label="ww260",fontsize=16,color="green",shape="box"];457[label="ww250",fontsize=16,color="green",shape="box"];458[label="ww260",fontsize=16,color="green",shape="box"];459[label="ww250",fontsize=16,color="green",shape="box"];460[label="ww260",fontsize=16,color="green",shape="box"];461[label="ww250",fontsize=16,color="green",shape="box"];462[label="ww260",fontsize=16,color="green",shape="box"];463[label="ww250",fontsize=16,color="green",shape="box"];464[label="ww260",fontsize=16,color="green",shape="box"];465[label="ww250",fontsize=16,color="green",shape="box"];466[label="ww33",fontsize=16,color="green",shape="box"];467[label="ww32",fontsize=16,color="green",shape="box"];468[label="ww33",fontsize=16,color="green",shape="box"];469[label="ww32",fontsize=16,color="green",shape="box"];470[label="ww33",fontsize=16,color="green",shape="box"];471[label="ww32",fontsize=16,color="green",shape="box"];472[label="ww33",fontsize=16,color="green",shape="box"];473[label="ww32",fontsize=16,color="green",shape="box"];474[label="ww33",fontsize=16,color="green",shape="box"];475[label="ww32",fontsize=16,color="green",shape="box"];476[label="ww33",fontsize=16,color="green",shape="box"];477[label="ww32",fontsize=16,color="green",shape="box"];478[label="ww33",fontsize=16,color="green",shape="box"];479[label="ww32",fontsize=16,color="green",shape="box"];480[label="ww33",fontsize=16,color="green",shape="box"];481[label="ww32",fontsize=16,color="green",shape="box"];482[label="ww33",fontsize=16,color="green",shape="box"];483[label="ww32",fontsize=16,color="green",shape="box"];484[label="ww33",fontsize=16,color="green",shape="box"];485[label="ww32",fontsize=16,color="green",shape="box"];486[label="ww33",fontsize=16,color="green",shape="box"];487[label="ww32",fontsize=16,color="green",shape="box"];488[label="ww33",fontsize=16,color="green",shape="box"];489[label="ww32",fontsize=16,color="green",shape="box"];490[label="ww33",fontsize=16,color="green",shape="box"];491[label="ww32",fontsize=16,color="green",shape="box"];492[label="ww33",fontsize=16,color="green",shape="box"];493[label="ww32",fontsize=16,color="green",shape="box"];494[label="primEqNat (Succ ww16000) (Succ ww190000)",fontsize=16,color="black",shape="box"];494 -> 498[label="",style="solid", color="black", weight=3];
13.70/5.20	495[label="primEqNat (Succ ww16000) Zero",fontsize=16,color="black",shape="box"];495 -> 499[label="",style="solid", color="black", weight=3];
13.70/5.20	496[label="primEqNat Zero (Succ ww190000)",fontsize=16,color="black",shape="box"];496 -> 500[label="",style="solid", color="black", weight=3];
13.70/5.20	497[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];497 -> 501[label="",style="solid", color="black", weight=3];
13.70/5.20	498 -> 394[label="",style="dashed", color="red", weight=0];
13.70/5.20	498[label="primEqNat ww16000 ww190000",fontsize=16,color="magenta"];498 -> 502[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	498 -> 503[label="",style="dashed", color="magenta", weight=3];
13.70/5.20	499[label="False",fontsize=16,color="green",shape="box"];500[label="False",fontsize=16,color="green",shape="box"];501[label="True",fontsize=16,color="green",shape="box"];502[label="ww16000",fontsize=16,color="green",shape="box"];503[label="ww190000",fontsize=16,color="green",shape="box"];}
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(6)
13.70/5.20	Complex Obligation (AND)
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(7)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, new_flip(ww19, ww1810, ba), ww1811, ba)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_flip(ww15, ww16, ba) -> :(ww16, ww15)
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(8) TransformationProof (EQUIVALENT)
13.70/5.20	By rewriting [LPAR04] the rule new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, new_flip(ww19, ww1810, ba), ww1811, ba) at position [2] we obtained the following new rules [LPAR04]:
13.70/5.20	
13.70/5.20	   (new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba),new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba))
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(9)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_flip(ww15, ww16, ba) -> :(ww16, ww15)
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(10) UsableRulesProof (EQUIVALENT)
13.70/5.20	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.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(11)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba)
13.70/5.20	
13.70/5.20	R is empty.
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(12) QReductionProof (EQUIVALENT)
13.70/5.20	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(13)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba)
13.70/5.20	
13.70/5.20	R is empty.
13.70/5.20	Q is empty.
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(14) QDPSizeChangeProof (EQUIVALENT)
13.70/5.20	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. 
13.70/5.20	
13.70/5.20	From the DPs we obtained the following set of size-change graphs:
13.70/5.20	*new_isPrefixOf(ww16, ww15, ww19, :(ww1810, ww1811), ba) -> new_isPrefixOf(ww16, ww15, :(ww1810, ww19), ww1811, ba)
13.70/5.20	The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(15)
13.70/5.20	YES
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(16)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_asAs0(True, :(ww250, ww251), :(ww260, ww261), ba) -> new_asAs0(new_esEs3(ww250, ww260, ba), ww251, ww261, ba)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_esEs3(ww250, ww260, ty_Bool) -> new_esEs12(ww250, ww260)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Ordering) -> new_esEs14(ww32, ww33)
13.70/5.20	   new_esEs15(ww16, ww190, ee, ef) -> error([])
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_esEs7(ww16, ww190, eb, ec) -> error([])
13.70/5.20	   new_esEs5(ww16, ww190) -> error([])
13.70/5.20	   new_esEs13(ww16, ww190) -> error([])
13.70/5.20	   new_esEs3(ww250, ww260, app(app(app(ty_@3, de), df), dg)) -> new_esEs11(ww250, ww260, de, df, dg)
13.70/5.20	   new_esEs1(ww16, ww190) -> error([])
13.70/5.20	   new_asAs1(True, ww32, ww33, app(ty_Ratio, bg)) -> new_esEs9(ww32, ww33, bg)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Int) -> new_esEs2(ww32, ww33)
13.70/5.20	   new_asAs1(True, ww32, ww33, app(app(ty_@2, cd), ce)) -> new_esEs15(ww32, ww33, cd, ce)
13.70/5.20	   new_esEs3(ww250, ww260, app(ty_[], db)) -> new_esEs6(ww250, ww260, db)
13.70/5.20	   new_esEs6(ww16, ww190, bb) -> error([])
13.70/5.20	   new_asAs1(True, ww32, ww33, app(app(ty_Either, bd), be)) -> new_esEs7(ww32, ww33, bd, be)
13.70/5.20	   new_esEs12(ww16, ww190) -> error([])
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs4(ww16, ww190) -> error([])
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Char) -> new_esEs13(ww32, ww33)
13.70/5.20	   new_esEs10(ww16, ww190, cf) -> error([])
13.70/5.20	   new_esEs3(ww250, ww260, ty_Int) -> new_esEs2(ww250, ww260)
13.70/5.20	   new_primEqNat0(Succ(ww16000), Zero) -> False
13.70/5.20	   new_primEqNat0(Zero, Succ(ww190000)) -> False
13.70/5.20	   new_esEs11(ww16, ww190, eg, eh, fa) -> error([])
13.70/5.20	   new_esEs3(ww250, ww260, ty_Double) -> new_esEs5(ww250, ww260)
13.70/5.20	   new_esEs3(ww250, ww260, app(app(ty_@2, dh), ea)) -> new_esEs15(ww250, ww260, dh, ea)
13.70/5.20	   new_esEs9(:%(ww160, ww161), :%(ww1900, ww1901), ed) -> new_asAs1(new_esEs0(ww160, ww1900, ed), ww161, ww1901, ed)
13.70/5.20	   new_asAs1(True, ww32, ww33, app(ty_Maybe, bh)) -> new_esEs10(ww32, ww33, bh)
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Int) -> new_esEs2(ww160, ww1900)
13.70/5.20	   new_asAs1(False, ww32, ww33, bc) -> False
13.70/5.20	   new_esEs3(ww250, ww260, ty_Char) -> new_esEs13(ww250, ww260)
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Integer) -> new_esEs1(ww160, ww1900)
13.70/5.20	   new_esEs8(ww16, ww190) -> error([])
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_@0) -> new_esEs4(ww32, ww33)
13.70/5.20	   new_esEs3(ww250, ww260, ty_Ordering) -> new_esEs14(ww250, ww260)
13.70/5.20	   new_esEs3(ww250, ww260, ty_Integer) -> new_esEs1(ww250, ww260)
13.70/5.20	   new_esEs3(ww250, ww260, app(ty_Ratio, dc)) -> new_esEs9(ww250, ww260, dc)
13.70/5.20	   new_primEqNat0(Zero, Zero) -> True
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Zero)) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_esEs3(ww250, ww260, app(ty_Maybe, dd)) -> new_esEs10(ww250, ww260, dd)
13.70/5.20	   new_esEs3(ww250, ww260, ty_@0) -> new_esEs4(ww250, ww260)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Float) -> new_esEs8(ww32, ww33)
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Neg(ww1900)) -> False
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Pos(ww1900)) -> False
13.70/5.20	   new_esEs3(ww250, ww260, app(app(ty_Either, cg), da)) -> new_esEs7(ww250, ww260, cg, da)
13.70/5.20	   new_asAs1(True, ww32, ww33, app(app(app(ty_@3, ca), cb), cc)) -> new_esEs11(ww32, ww33, ca, cb, cc)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Bool) -> new_esEs12(ww32, ww33)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Double) -> new_esEs5(ww32, ww33)
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero)) -> True
13.70/5.20	   new_esEs14(ww16, ww190) -> error([])
13.70/5.20	   new_primEqNat0(Succ(ww16000), Succ(ww190000)) -> new_primEqNat0(ww16000, ww190000)
13.70/5.20	   new_asAs1(True, ww32, ww33, ty_Integer) -> new_esEs1(ww32, ww33)
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Zero)) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_asAs1(True, ww32, ww33, app(ty_[], bf)) -> new_esEs6(ww32, ww33, bf)
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero)) -> True
13.70/5.20	   new_esEs3(ww250, ww260, ty_Float) -> new_esEs8(ww250, ww260)
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_esEs3(x0, x1, ty_@0)
13.70/5.20	   new_primEqNat0(Zero, Zero)
13.70/5.20	   new_esEs3(x0, x1, ty_Char)
13.70/5.20	   new_asAs1(True, x0, x1, ty_Double)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(x0)))
13.70/5.20	   new_asAs1(True, x0, x1, ty_@0)
13.70/5.20	   new_esEs3(x0, x1, app(ty_[], x2))
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Zero))
13.70/5.20	   new_esEs9(:%(x0, x1), :%(x2, x3), x4)
13.70/5.20	   new_esEs3(x0, x1, ty_Double)
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(x0)))
13.70/5.20	   new_asAs1(True, x0, x1, ty_Char)
13.70/5.20	   new_primEqNat0(Succ(x0), Succ(x1))
13.70/5.20	   new_asAs1(True, x0, x1, ty_Ordering)
13.70/5.20	   new_esEs5(x0, x1)
13.70/5.20	   new_esEs3(x0, x1, ty_Ordering)
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Succ(x1)))
13.70/5.20	   new_asAs1(False, x0, x1, x2)
13.70/5.20	   new_esEs11(x0, x1, x2, x3, x4)
13.70/5.20	   new_asAs1(True, x0, x1, app(ty_Maybe, x2))
13.70/5.20	   new_esEs3(x0, x1, app(app(ty_@2, x2), x3))
13.70/5.20	   new_esEs13(x0, x1)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero))
13.70/5.20	   new_esEs3(x0, x1, ty_Int)
13.70/5.20	   new_asAs1(True, x0, x1, ty_Int)
13.70/5.20	   new_asAs1(True, x0, x1, app(ty_Ratio, x2))
13.70/5.20	   new_esEs8(x0, x1)
13.70/5.20	   new_esEs3(x0, x1, app(ty_Maybe, x2))
13.70/5.20	   new_esEs7(x0, x1, x2, x3)
13.70/5.20	   new_esEs3(x0, x1, app(ty_Ratio, x2))
13.70/5.20	   new_esEs3(x0, x1, app(app(app(ty_@3, x2), x3), x4))
13.70/5.20	   new_esEs14(x0, x1)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero))
13.70/5.20	   new_esEs12(x0, x1)
13.70/5.20	   new_primEqNat0(Succ(x0), Zero)
13.70/5.20	   new_esEs0(x0, x1, ty_Integer)
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Zero))
13.70/5.20	   new_primEqNat0(Zero, Succ(x0))
13.70/5.20	   new_esEs0(x0, x1, ty_Int)
13.70/5.20	   new_esEs3(x0, x1, app(app(ty_Either, x2), x3))
13.70/5.20	   new_asAs1(True, x0, x1, app(ty_[], x2))
13.70/5.20	   new_asAs1(True, x0, x1, ty_Integer)
13.70/5.20	   new_esEs3(x0, x1, ty_Bool)
13.70/5.20	   new_esEs3(x0, x1, ty_Integer)
13.70/5.20	   new_esEs10(x0, x1, x2)
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Neg(x1))
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Pos(x1))
13.70/5.20	   new_esEs1(x0, x1)
13.70/5.20	   new_asAs1(True, x0, x1, ty_Bool)
13.70/5.20	   new_asAs1(True, x0, x1, app(app(ty_Either, x2), x3))
13.70/5.20	   new_asAs1(True, x0, x1, app(app(ty_@2, x2), x3))
13.70/5.20	   new_asAs1(True, x0, x1, ty_Float)
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Succ(x1)))
13.70/5.20	   new_esEs4(x0, x1)
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero))
13.70/5.20	   new_esEs3(x0, x1, ty_Float)
13.70/5.20	   new_esEs6(x0, x1, x2)
13.70/5.20	   new_esEs15(x0, x1, x2, x3)
13.70/5.20	   new_asAs1(True, x0, x1, app(app(app(ty_@3, x2), x3), x4))
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(17) QDPSizeChangeProof (EQUIVALENT)
13.70/5.20	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. 
13.70/5.20	
13.70/5.20	From the DPs we obtained the following set of size-change graphs:
13.70/5.20	*new_asAs0(True, :(ww250, ww251), :(ww260, ww261), ba) -> new_asAs0(new_esEs3(ww250, ww260, ba), ww251, ww261, ba)
13.70/5.20	The graph contains the following edges 2 > 2, 3 > 3, 4 >= 4
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(18)
13.70/5.20	YES
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(19)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_esEs(:%(ww160, ww161), :%(ww1900, ww1901), ba) -> new_asAs(new_esEs0(ww160, ww1900, ba), ww161, ww1901, ba)
13.70/5.20	   new_asAs(True, ww32, ww33, app(ty_Ratio, bb)) -> new_esEs(ww32, ww33, bb)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero)) -> True
13.70/5.20	   new_primEqNat0(Zero, Zero) -> True
13.70/5.20	   new_primEqNat0(Succ(ww16000), Zero) -> False
13.70/5.20	   new_primEqNat0(Zero, Succ(ww190000)) -> False
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Zero)) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_primEqNat0(Succ(ww16000), Succ(ww190000)) -> new_primEqNat0(ww16000, ww190000)
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Int) -> new_esEs2(ww160, ww1900)
13.70/5.20	   new_esEs1(ww16, ww190) -> error([])
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Integer) -> new_esEs1(ww160, ww1900)
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Neg(ww1900)) -> False
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Pos(ww1900)) -> False
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Zero)) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero)) -> True
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_primEqNat0(Zero, Zero)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(x0)))
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero))
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Succ(x1)))
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Neg(x1))
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Pos(x1))
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs1(x0, x1)
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Zero))
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Succ(x1)))
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(x0)))
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero))
13.70/5.20	   new_primEqNat0(Succ(x0), Zero)
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Zero))
13.70/5.20	   new_esEs0(x0, x1, ty_Integer)
13.70/5.20	   new_primEqNat0(Zero, Succ(x0))
13.70/5.20	   new_esEs0(x0, x1, ty_Int)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero))
13.70/5.20	   new_primEqNat0(Succ(x0), Succ(x1))
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(20) TransformationProof (EQUIVALENT)
13.70/5.20	By narrowing [LPAR04] the rule new_esEs(:%(ww160, ww161), :%(ww1900, ww1901), ba) -> new_asAs(new_esEs0(ww160, ww1900, ba), ww161, ww1901, ba) at position [0] we obtained the following new rules [LPAR04]:
13.70/5.20	
13.70/5.20	   (new_esEs(:%(x0, y1), :%(x1, y3), ty_Int) -> new_asAs(new_esEs2(x0, x1), y1, y3, ty_Int),new_esEs(:%(x0, y1), :%(x1, y3), ty_Int) -> new_asAs(new_esEs2(x0, x1), y1, y3, ty_Int))
13.70/5.20	   (new_esEs(:%(x0, y1), :%(x1, y3), ty_Integer) -> new_asAs(new_esEs1(x0, x1), y1, y3, ty_Integer),new_esEs(:%(x0, y1), :%(x1, y3), ty_Integer) -> new_asAs(new_esEs1(x0, x1), y1, y3, ty_Integer))
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(21)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_asAs(True, ww32, ww33, app(ty_Ratio, bb)) -> new_esEs(ww32, ww33, bb)
13.70/5.20	   new_esEs(:%(x0, y1), :%(x1, y3), ty_Int) -> new_asAs(new_esEs2(x0, x1), y1, y3, ty_Int)
13.70/5.20	   new_esEs(:%(x0, y1), :%(x1, y3), ty_Integer) -> new_asAs(new_esEs1(x0, x1), y1, y3, ty_Integer)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Succ(ww19000))) -> new_primEqNat0(ww1600, ww19000)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero)) -> True
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero)) -> True
13.70/5.20	   new_primEqNat0(Zero, Zero) -> True
13.70/5.20	   new_primEqNat0(Succ(ww16000), Zero) -> False
13.70/5.20	   new_primEqNat0(Zero, Succ(ww190000)) -> False
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Neg(Zero)) -> False
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(ww19000))) -> False
13.70/5.20	   new_primEqNat0(Succ(ww16000), Succ(ww190000)) -> new_primEqNat0(ww16000, ww190000)
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Int) -> new_esEs2(ww160, ww1900)
13.70/5.20	   new_esEs1(ww16, ww190) -> error([])
13.70/5.20	   new_esEs0(ww160, ww1900, ty_Integer) -> new_esEs1(ww160, ww1900)
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Neg(ww1900)) -> False
13.70/5.20	   new_esEs2(Neg(Succ(ww1600)), Pos(ww1900)) -> False
13.70/5.20	   new_esEs2(Pos(Succ(ww1600)), Pos(Zero)) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(ww19000))) -> False
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero)) -> True
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_primEqNat0(Zero, Zero)
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Succ(x0)))
13.70/5.20	   new_esEs2(Pos(Zero), Neg(Zero))
13.70/5.20	   new_esEs2(Neg(Zero), Pos(Zero))
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Succ(x1)))
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Neg(x1))
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Pos(x1))
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Succ(x0)))
13.70/5.20	   new_esEs1(x0, x1)
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Zero))
13.70/5.20	   new_esEs2(Pos(Succ(x0)), Pos(Succ(x1)))
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Succ(x0)))
13.70/5.20	   new_esEs2(Pos(Zero), Pos(Zero))
13.70/5.20	   new_primEqNat0(Succ(x0), Zero)
13.70/5.20	   new_esEs2(Neg(Succ(x0)), Neg(Zero))
13.70/5.20	   new_esEs0(x0, x1, ty_Integer)
13.70/5.20	   new_primEqNat0(Zero, Succ(x0))
13.70/5.20	   new_esEs0(x0, x1, ty_Int)
13.70/5.20	   new_esEs2(Neg(Zero), Neg(Zero))
13.70/5.20	   new_primEqNat0(Succ(x0), Succ(x1))
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(22) DependencyGraphProof (EQUIVALENT)
13.70/5.20	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(23)
13.70/5.20	TRUE
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(24)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_primEqNat(Succ(ww16000), Succ(ww190000)) -> new_primEqNat(ww16000, ww190000)
13.70/5.20	
13.70/5.20	R is empty.
13.70/5.20	Q is empty.
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(25) QDPSizeChangeProof (EQUIVALENT)
13.70/5.20	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. 
13.70/5.20	
13.70/5.20	From the DPs we obtained the following set of size-change graphs:
13.70/5.20	*new_primEqNat(Succ(ww16000), Succ(ww190000)) -> new_primEqNat(ww16000, ww190000)
13.70/5.20	The graph contains the following edges 1 > 1, 2 > 2
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(26)
13.70/5.20	YES
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(27)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(new_flip(ww15, ww16, ba), ww170, ww171, ww18, ba)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_flip(ww15, ww16, ba) -> :(ww16, ww15)
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(28) TransformationProof (EQUIVALENT)
13.70/5.20	By rewriting [LPAR04] the rule new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(new_flip(ww15, ww16, ba), ww170, ww171, ww18, ba) at position [0] we obtained the following new rules [LPAR04]:
13.70/5.20	
13.70/5.20	   (new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba),new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba))
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(29)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba)
13.70/5.20	
13.70/5.20	The TRS R consists of the following rules:
13.70/5.20	
13.70/5.20	   new_flip(ww15, ww16, ba) -> :(ww16, ww15)
13.70/5.20	
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(30) UsableRulesProof (EQUIVALENT)
13.70/5.20	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.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(31)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba)
13.70/5.20	
13.70/5.20	R is empty.
13.70/5.20	The set Q consists of the following terms:
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(32) QReductionProof (EQUIVALENT)
13.70/5.20	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
13.70/5.20	
13.70/5.20	   new_flip(x0, x1, x2)
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(33)
13.70/5.20	Obligation:
13.70/5.20	Q DP problem:
13.70/5.20	The TRS P consists of the following rules:
13.70/5.20	
13.70/5.20	   new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba)
13.70/5.20	
13.70/5.20	R is empty.
13.70/5.20	Q is empty.
13.70/5.20	We have to consider all minimal (P,Q,R)-chains.
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(34) QDPSizeChangeProof (EQUIVALENT)
13.70/5.20	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. 
13.70/5.20	
13.70/5.20	From the DPs we obtained the following set of size-change graphs:
13.70/5.20	*new_isPrefixOf0(ww15, ww16, :(ww170, ww171), ww18, ba) -> new_isPrefixOf0(:(ww16, ww15), ww170, ww171, ww18, ba)
13.70/5.20	The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
13.70/5.20	
13.70/5.20	
13.70/5.20	----------------------------------------
13.70/5.20	
13.70/5.20	(35)
13.70/5.20	YES
13.70/5.25	EOF