8.70/3.71	YES
10.91/4.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.91/4.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.91/4.26	
10.91/4.26	
10.91/4.26	H-Termination with start terms of the given HASKELL could be proven:
10.91/4.26	
10.91/4.26	(0) HASKELL
10.91/4.26	(1) LR [EQUIVALENT, 0 ms]
10.91/4.26	(2) HASKELL
10.91/4.26	(3) BR [EQUIVALENT, 0 ms]
10.91/4.26	(4) HASKELL
10.91/4.26	(5) COR [EQUIVALENT, 0 ms]
10.91/4.26	(6) HASKELL
10.91/4.26	(7) NumRed [SOUND, 0 ms]
10.91/4.26	(8) HASKELL
10.91/4.26	(9) Narrow [SOUND, 0 ms]
10.91/4.26	(10) QDP
10.91/4.26	(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.91/4.26	(12) YES
10.91/4.26	
10.91/4.26	
10.91/4.26	----------------------------------------
10.91/4.26	
10.91/4.26	(0)
10.91/4.26	Obligation:
10.91/4.26	mainModule Main 
10.91/4.26	module Main where {
10.91/4.26	import qualified Prelude;
10.91/4.26	}
10.91/4.26	
10.91/4.26	----------------------------------------
10.91/4.26	
10.91/4.26	(1) LR (EQUIVALENT)
10.91/4.26	Lambda Reductions:
10.91/4.26	The following Lambda expression
10.91/4.26	"\_->q"
10.91/4.26	is transformed to
10.91/4.26	"gtGt0 q _ = q;
10.91/4.26	"
10.91/4.26	
10.91/4.26	----------------------------------------
10.91/4.26	
10.91/4.26	(2)
10.91/4.26	Obligation:
10.91/4.26	mainModule Main 
10.91/4.26	module Main where {
10.91/4.26	import qualified Prelude;
10.91/4.26	}
10.91/4.26	
10.91/4.26	----------------------------------------
10.91/4.26	
10.91/4.26	(3) BR (EQUIVALENT)
10.91/4.26	Replaced joker patterns by fresh variables and removed binding patterns.
10.91/4.26	----------------------------------------
10.91/4.27	
10.91/4.27	(4)
10.91/4.27	Obligation:
10.91/4.27	mainModule Main 
10.91/4.27	module Main where {
10.91/4.27	import qualified Prelude;
10.91/4.27	}
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(5) COR (EQUIVALENT)
10.91/4.27	Cond Reductions:
10.91/4.27	The following Function with conditions
10.91/4.27	"randomSelect (x : []) = x;
10.91/4.27	randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
10.91/4.27	"
10.91/4.27	is transformed to
10.91/4.27	"randomSelect (x : []) = randomSelect3 (x : []);
10.91/4.27	randomSelect (x : xs) = randomSelect2 (x : xs);
10.91/4.27	"
10.91/4.27	"randomSelect0 x xs True = x;
10.91/4.27	"
10.91/4.27	"randomSelect1 x xs True = randomSelect xs;
10.91/4.27	randomSelect1 x xs False = randomSelect0 x xs otherwise;
10.91/4.27	"
10.91/4.27	"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
10.91/4.27	"
10.91/4.27	"randomSelect3 (x : []) = x;
10.91/4.27	randomSelect3 wv = randomSelect2 wv;
10.91/4.27	"
10.91/4.27	The following Function with conditions
10.91/4.27	"undefined |Falseundefined;
10.91/4.27	"
10.91/4.27	is transformed to
10.91/4.27	"undefined  = undefined1;
10.91/4.27	"
10.91/4.27	"undefined0 True = undefined;
10.91/4.27	"
10.91/4.27	"undefined1  = undefined0 False;
10.91/4.27	"
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(6)
10.91/4.27	Obligation:
10.91/4.27	mainModule Main 
10.91/4.27	module Main where {
10.91/4.27	import qualified Prelude;
10.91/4.27	}
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(7) NumRed (SOUND)
10.91/4.27	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(8)
10.91/4.27	Obligation:
10.91/4.27	mainModule Main 
10.91/4.27	module Main where {
10.91/4.27	import qualified Prelude;
10.91/4.27	}
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(9) Narrow (SOUND)
10.91/4.27	Haskell To QDPs
10.91/4.27	
10.91/4.27	digraph dp_graph {
10.91/4.27	node [outthreshold=100, inthreshold=100];1[label="print",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.91/4.27	3[label="print ww3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.91/4.27	4[label="putStrLn . show",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.91/4.27	5[label="putStrLn (show ww3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.91/4.27	6 -> 7[label="",style="dashed", color="red", weight=0];
10.91/4.27	6[label="putStr (show ww3) >> putChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	6 -> 9[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	8[label="ww3",fontsize=16,color="green",shape="box"];9[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];7[label="putStr (show ww5) >> putChar (Char (Succ ww6))",fontsize=16,color="black",shape="triangle"];7 -> 10[label="",style="solid", color="black", weight=3];
10.91/4.27	10[label="putStr (show ww5) >>= gtGt0 (putChar (Char (Succ ww6)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.91/4.27	11 -> 165[label="",style="dashed", color="red", weight=0];
10.91/4.27	11[label="primbindIO (putStr (show ww5)) (gtGt0 (putChar (Char (Succ ww6))))",fontsize=16,color="magenta"];11 -> 166[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	11 -> 167[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	166[label="putChar (Char (Succ ww6))",fontsize=16,color="black",shape="box"];166 -> 270[label="",style="solid", color="black", weight=3];
10.91/4.27	167 -> 271[label="",style="dashed", color="red", weight=0];
10.91/4.27	167[label="putStr (show ww5)",fontsize=16,color="magenta"];167 -> 272[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	165[label="primbindIO ww19 (gtGt0 ww18)",fontsize=16,color="burlywood",shape="triangle"];393[label="ww19/IO ww190",fontsize=10,color="white",style="solid",shape="box"];165 -> 393[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	393 -> 273[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	394[label="ww19/AProVE_IO ww190",fontsize=10,color="white",style="solid",shape="box"];165 -> 394[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	394 -> 274[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	395[label="ww19/AProVE_Exception ww190",fontsize=10,color="white",style="solid",shape="box"];165 -> 395[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	395 -> 275[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	396[label="ww19/AProVE_Error ww190",fontsize=10,color="white",style="solid",shape="box"];165 -> 396[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	396 -> 276[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	270 -> 369[label="",style="dashed", color="red", weight=0];
10.91/4.27	270[label="(seq Char (Succ ww6) output)",fontsize=16,color="magenta"];270 -> 370[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	270 -> 371[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	272[label="show ww5",fontsize=16,color="blue",shape="box"];397[label="show :: (Maybe a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 397[label="",style="solid", color="blue", weight=9];
10.91/4.27	397 -> 278[label="",style="solid", color="blue", weight=3];
10.91/4.27	398[label="show :: Bool -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 398[label="",style="solid", color="blue", weight=9];
10.91/4.27	398 -> 279[label="",style="solid", color="blue", weight=3];
10.91/4.27	399[label="show :: () -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 399[label="",style="solid", color="blue", weight=9];
10.91/4.27	399 -> 280[label="",style="solid", color="blue", weight=3];
10.91/4.27	400[label="show :: (IO a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 400[label="",style="solid", color="blue", weight=9];
10.91/4.27	400 -> 281[label="",style="solid", color="blue", weight=3];
10.91/4.27	401[label="show :: IOErrorKind -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 401[label="",style="solid", color="blue", weight=9];
10.91/4.27	401 -> 282[label="",style="solid", color="blue", weight=3];
10.91/4.27	402[label="show :: Double -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 402[label="",style="solid", color="blue", weight=9];
10.91/4.27	402 -> 283[label="",style="solid", color="blue", weight=3];
10.91/4.27	403[label="show :: ([] a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 403[label="",style="solid", color="blue", weight=9];
10.91/4.27	403 -> 284[label="",style="solid", color="blue", weight=3];
10.91/4.27	404[label="show :: Integer -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 404[label="",style="solid", color="blue", weight=9];
10.91/4.27	404 -> 285[label="",style="solid", color="blue", weight=3];
10.91/4.27	405[label="show :: ((@3) a b c) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 405[label="",style="solid", color="blue", weight=9];
10.91/4.27	405 -> 286[label="",style="solid", color="blue", weight=3];
10.91/4.27	406[label="show :: Int -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 406[label="",style="solid", color="blue", weight=9];
10.91/4.27	406 -> 287[label="",style="solid", color="blue", weight=3];
10.91/4.27	407[label="show :: Ordering -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 407[label="",style="solid", color="blue", weight=9];
10.91/4.27	407 -> 288[label="",style="solid", color="blue", weight=3];
10.91/4.27	408[label="show :: (Ratio a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 408[label="",style="solid", color="blue", weight=9];
10.91/4.27	408 -> 289[label="",style="solid", color="blue", weight=3];
10.91/4.27	409[label="show :: (Either a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 409[label="",style="solid", color="blue", weight=9];
10.91/4.27	409 -> 290[label="",style="solid", color="blue", weight=3];
10.91/4.27	410[label="show :: HugsException -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 410[label="",style="solid", color="blue", weight=9];
10.91/4.27	410 -> 291[label="",style="solid", color="blue", weight=3];
10.91/4.27	411[label="show :: Float -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 411[label="",style="solid", color="blue", weight=9];
10.91/4.27	411 -> 292[label="",style="solid", color="blue", weight=3];
10.91/4.27	412[label="show :: IOError -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 412[label="",style="solid", color="blue", weight=9];
10.91/4.27	412 -> 293[label="",style="solid", color="blue", weight=3];
10.91/4.27	413[label="show :: ((@2) a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 413[label="",style="solid", color="blue", weight=9];
10.91/4.27	413 -> 294[label="",style="solid", color="blue", weight=3];
10.91/4.27	414[label="show :: Char -> [] Char",fontsize=10,color="white",style="solid",shape="box"];272 -> 414[label="",style="solid", color="blue", weight=9];
10.91/4.27	414 -> 295[label="",style="solid", color="blue", weight=3];
10.91/4.27	271[label="putStr ww22",fontsize=16,color="burlywood",shape="triangle"];415[label="ww22/ww220 : ww221",fontsize=10,color="white",style="solid",shape="box"];271 -> 415[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	415 -> 296[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	416[label="ww22/[]",fontsize=10,color="white",style="solid",shape="box"];271 -> 416[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	416 -> 297[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	273[label="primbindIO (IO ww190) (gtGt0 ww18)",fontsize=16,color="black",shape="box"];273 -> 298[label="",style="solid", color="black", weight=3];
10.91/4.27	274[label="primbindIO (AProVE_IO ww190) (gtGt0 ww18)",fontsize=16,color="black",shape="box"];274 -> 299[label="",style="solid", color="black", weight=3];
10.91/4.27	275[label="primbindIO (AProVE_Exception ww190) (gtGt0 ww18)",fontsize=16,color="black",shape="box"];275 -> 300[label="",style="solid", color="black", weight=3];
10.91/4.27	276[label="primbindIO (AProVE_Error ww190) (gtGt0 ww18)",fontsize=16,color="black",shape="box"];276 -> 301[label="",style="solid", color="black", weight=3];
10.91/4.27	370 -> 302[label="",style="dashed", color="red", weight=0];
10.91/4.27	370[label="output",fontsize=16,color="magenta"];371[label="Char (Succ ww6)",fontsize=16,color="green",shape="box"];369[label="(seq ww220 ww29)",fontsize=16,color="black",shape="triangle"];369 -> 373[label="",style="solid", color="black", weight=3];
10.91/4.27	278[label="show ww5",fontsize=16,color="black",shape="box"];278 -> 303[label="",style="solid", color="black", weight=3];
10.91/4.27	279[label="show ww5",fontsize=16,color="black",shape="box"];279 -> 304[label="",style="solid", color="black", weight=3];
10.91/4.27	280[label="show ww5",fontsize=16,color="black",shape="box"];280 -> 305[label="",style="solid", color="black", weight=3];
10.91/4.27	281[label="show ww5",fontsize=16,color="black",shape="box"];281 -> 306[label="",style="solid", color="black", weight=3];
10.91/4.27	282[label="show ww5",fontsize=16,color="black",shape="box"];282 -> 307[label="",style="solid", color="black", weight=3];
10.91/4.27	283[label="show ww5",fontsize=16,color="black",shape="box"];283 -> 308[label="",style="solid", color="black", weight=3];
10.91/4.27	284[label="show ww5",fontsize=16,color="black",shape="box"];284 -> 309[label="",style="solid", color="black", weight=3];
10.91/4.27	285[label="show ww5",fontsize=16,color="black",shape="box"];285 -> 310[label="",style="solid", color="black", weight=3];
10.91/4.27	286[label="show ww5",fontsize=16,color="black",shape="box"];286 -> 311[label="",style="solid", color="black", weight=3];
10.91/4.27	287[label="show ww5",fontsize=16,color="black",shape="box"];287 -> 312[label="",style="solid", color="black", weight=3];
10.91/4.27	288[label="show ww5",fontsize=16,color="black",shape="box"];288 -> 313[label="",style="solid", color="black", weight=3];
10.91/4.27	289[label="show ww5",fontsize=16,color="black",shape="box"];289 -> 314[label="",style="solid", color="black", weight=3];
10.91/4.27	290[label="show ww5",fontsize=16,color="black",shape="box"];290 -> 315[label="",style="solid", color="black", weight=3];
10.91/4.27	291[label="show ww5",fontsize=16,color="black",shape="box"];291 -> 316[label="",style="solid", color="black", weight=3];
10.91/4.27	292[label="show ww5",fontsize=16,color="black",shape="box"];292 -> 317[label="",style="solid", color="black", weight=3];
10.91/4.27	293[label="show ww5",fontsize=16,color="black",shape="box"];293 -> 318[label="",style="solid", color="black", weight=3];
10.91/4.27	294[label="show ww5",fontsize=16,color="black",shape="box"];294 -> 319[label="",style="solid", color="black", weight=3];
10.91/4.27	295[label="show ww5",fontsize=16,color="black",shape="box"];295 -> 320[label="",style="solid", color="black", weight=3];
10.91/4.27	296[label="putStr (ww220 : ww221)",fontsize=16,color="black",shape="box"];296 -> 321[label="",style="solid", color="black", weight=3];
10.91/4.27	297[label="putStr []",fontsize=16,color="black",shape="box"];297 -> 322[label="",style="solid", color="black", weight=3];
10.91/4.27	298[label="error []",fontsize=16,color="red",shape="box"];299[label="gtGt0 ww18 ww190",fontsize=16,color="black",shape="box"];299 -> 323[label="",style="solid", color="black", weight=3];
10.91/4.27	300[label="AProVE_Exception ww190",fontsize=16,color="green",shape="box"];301[label="AProVE_Error ww190",fontsize=16,color="green",shape="box"];302[label="output",fontsize=16,color="black",shape="triangle"];302 -> 324[label="",style="solid", color="black", weight=3];
10.91/4.27	373[label="enforceWHNF (WHNF ww220) ww29",fontsize=16,color="black",shape="box"];373 -> 377[label="",style="solid", color="black", weight=3];
10.91/4.27	303[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];303 -> 325[label="",style="solid", color="black", weight=3];
10.91/4.27	304[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];304 -> 326[label="",style="solid", color="black", weight=3];
10.91/4.27	305[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="burlywood",shape="box"];417[label="ww5/()",fontsize=10,color="white",style="solid",shape="box"];305 -> 417[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	417 -> 327[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	306[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];306 -> 328[label="",style="solid", color="black", weight=3];
10.91/4.27	307[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];307 -> 329[label="",style="solid", color="black", weight=3];
10.91/4.27	308[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];308 -> 330[label="",style="solid", color="black", weight=3];
10.91/4.27	309[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];309 -> 331[label="",style="solid", color="black", weight=3];
10.91/4.27	310[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];310 -> 332[label="",style="solid", color="black", weight=3];
10.91/4.27	311[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];311 -> 333[label="",style="solid", color="black", weight=3];
10.91/4.27	312[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];312 -> 334[label="",style="solid", color="black", weight=3];
10.91/4.27	313[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];313 -> 335[label="",style="solid", color="black", weight=3];
10.91/4.27	314[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];314 -> 336[label="",style="solid", color="black", weight=3];
10.91/4.27	315[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];315 -> 337[label="",style="solid", color="black", weight=3];
10.91/4.27	316[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];316 -> 338[label="",style="solid", color="black", weight=3];
10.91/4.27	317[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];317 -> 339[label="",style="solid", color="black", weight=3];
10.91/4.27	318[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];318 -> 340[label="",style="solid", color="black", weight=3];
10.91/4.27	319[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];319 -> 341[label="",style="solid", color="black", weight=3];
10.91/4.27	320[label="showsPrec (Pos Zero) ww5 []",fontsize=16,color="black",shape="box"];320 -> 342[label="",style="solid", color="black", weight=3];
10.91/4.27	321 -> 343[label="",style="dashed", color="red", weight=0];
10.91/4.27	321[label="putChar ww220 >> putStr ww221",fontsize=16,color="magenta"];321 -> 344[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	322 -> 302[label="",style="dashed", color="red", weight=0];
10.91/4.27	322[label="output",fontsize=16,color="magenta"];323[label="ww18",fontsize=16,color="green",shape="box"];324[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];324 -> 345[label="",style="solid", color="black", weight=3];
10.91/4.27	377[label="ww29",fontsize=16,color="green",shape="box"];325[label="error []",fontsize=16,color="red",shape="box"];326[label="error []",fontsize=16,color="red",shape="box"];327[label="showsPrec (Pos Zero) () []",fontsize=16,color="black",shape="box"];327 -> 346[label="",style="solid", color="black", weight=3];
10.91/4.27	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="error []",fontsize=16,color="red",shape="box"];332[label="error []",fontsize=16,color="red",shape="box"];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="error []",fontsize=16,color="red",shape="box"];339[label="error []",fontsize=16,color="red",shape="box"];340[label="error []",fontsize=16,color="red",shape="box"];341[label="error []",fontsize=16,color="red",shape="box"];342[label="error []",fontsize=16,color="red",shape="box"];344 -> 271[label="",style="dashed", color="red", weight=0];
10.91/4.27	344[label="putStr ww221",fontsize=16,color="magenta"];344 -> 347[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	343[label="putChar ww220 >> ww23",fontsize=16,color="black",shape="triangle"];343 -> 348[label="",style="solid", color="black", weight=3];
10.91/4.27	345[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];345 -> 349[label="",style="solid", color="black", weight=3];
10.91/4.27	346 -> 354[label="",style="dashed", color="red", weight=0];
10.91/4.27	346[label="showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))) : []) []",fontsize=16,color="magenta"];346 -> 355[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	346 -> 356[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	347[label="ww221",fontsize=16,color="green",shape="box"];348[label="putChar ww220 >>= gtGt0 ww23",fontsize=16,color="black",shape="box"];348 -> 352[label="",style="solid", color="black", weight=3];
10.91/4.27	349[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];349 -> 353[label="",style="solid", color="black", weight=3];
10.91/4.27	355[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];356[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];354[label="showString (Char (Succ ww27) : Char (Succ ww28) : []) []",fontsize=16,color="black",shape="triangle"];354 -> 359[label="",style="solid", color="black", weight=3];
10.91/4.27	352 -> 165[label="",style="dashed", color="red", weight=0];
10.91/4.27	352[label="primbindIO (putChar ww220) (gtGt0 ww23)",fontsize=16,color="magenta"];352 -> 360[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	352 -> 361[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	353[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter5m",fontsize=16,color="burlywood",shape="box"];418[label="ter5m/False",fontsize=10,color="white",style="solid",shape="box"];353 -> 418[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	418 -> 362[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	419[label="ter5m/True",fontsize=10,color="white",style="solid",shape="box"];353 -> 419[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	419 -> 363[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	359[label="(++) (Char (Succ ww27) : Char (Succ ww28) : []) []",fontsize=16,color="black",shape="box"];359 -> 364[label="",style="solid", color="black", weight=3];
10.91/4.27	360[label="ww23",fontsize=16,color="green",shape="box"];361[label="putChar ww220",fontsize=16,color="black",shape="box"];361 -> 365[label="",style="solid", color="black", weight=3];
10.91/4.27	362[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];362 -> 366[label="",style="solid", color="black", weight=3];
10.91/4.27	363[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];363 -> 367[label="",style="solid", color="black", weight=3];
10.91/4.27	364[label="Char (Succ ww27) : (Char (Succ ww28) : []) ++ []",fontsize=16,color="green",shape="box"];364 -> 368[label="",style="dashed", color="green", weight=3];
10.91/4.27	365 -> 369[label="",style="dashed", color="red", weight=0];
10.91/4.27	365[label="(seq ww220 output)",fontsize=16,color="magenta"];365 -> 372[label="",style="dashed", color="magenta", weight=3];
10.91/4.27	366[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];366 -> 375[label="",style="solid", color="black", weight=3];
10.91/4.27	367[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];367 -> 376[label="",style="solid", color="black", weight=3];
10.91/4.27	368[label="(Char (Succ ww28) : []) ++ []",fontsize=16,color="black",shape="box"];368 -> 374[label="",style="solid", color="black", weight=3];
10.91/4.27	372 -> 302[label="",style="dashed", color="red", weight=0];
10.91/4.27	372[label="output",fontsize=16,color="magenta"];375[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];375 -> 379[label="",style="solid", color="black", weight=3];
10.91/4.27	376[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];376 -> 380[label="",style="solid", color="black", weight=3];
10.91/4.27	374[label="Char (Succ ww28) : [] ++ []",fontsize=16,color="green",shape="box"];374 -> 378[label="",style="dashed", color="green", weight=3];
10.91/4.27	379[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];379 -> 382[label="",style="solid", color="black", weight=3];
10.91/4.27	380[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];380 -> 383[label="",style="solid", color="black", weight=3];
10.91/4.27	378[label="[] ++ []",fontsize=16,color="black",shape="box"];378 -> 381[label="",style="solid", color="black", weight=3];
10.91/4.27	382[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];383[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter6m",fontsize=16,color="burlywood",shape="box"];420[label="ter6m/False",fontsize=10,color="white",style="solid",shape="box"];383 -> 420[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	420 -> 384[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	421[label="ter6m/True",fontsize=10,color="white",style="solid",shape="box"];383 -> 421[label="",style="solid", color="burlywood", weight=9];
10.91/4.27	421 -> 385[label="",style="solid", color="burlywood", weight=3];
10.91/4.27	381[label="[]",fontsize=16,color="green",shape="box"];384[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];384 -> 386[label="",style="solid", color="black", weight=3];
10.91/4.27	385[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];385 -> 387[label="",style="solid", color="black", weight=3];
10.91/4.27	386[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];386 -> 388[label="",style="solid", color="black", weight=3];
10.91/4.27	387[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];387 -> 389[label="",style="solid", color="black", weight=3];
10.91/4.27	388[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];388 -> 390[label="",style="solid", color="black", weight=3];
10.91/4.27	389[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];389 -> 391[label="",style="solid", color="black", weight=3];
10.91/4.27	390[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];390 -> 392[label="",style="solid", color="black", weight=3];
10.91/4.27	391[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];392[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];}
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(10)
10.91/4.27	Obligation:
10.91/4.27	Q DP problem:
10.91/4.27	The TRS P consists of the following rules:
10.91/4.27	
10.91/4.27	   new_putStr(:(ww220, ww221)) -> new_putStr(ww221)
10.91/4.27	
10.91/4.27	R is empty.
10.91/4.27	Q is empty.
10.91/4.27	We have to consider all minimal (P,Q,R)-chains.
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(11) QDPSizeChangeProof (EQUIVALENT)
10.91/4.27	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. 
10.91/4.27	
10.91/4.27	From the DPs we obtained the following set of size-change graphs:
10.91/4.27	*new_putStr(:(ww220, ww221)) -> new_putStr(ww221)
10.91/4.27	The graph contains the following edges 1 > 1
10.91/4.27	
10.91/4.27	
10.91/4.27	----------------------------------------
10.91/4.27	
10.91/4.27	(12)
10.91/4.27	YES
10.91/4.30	EOF