9.05/3.92	YES
11.38/4.52	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
11.38/4.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.38/4.52	
11.38/4.52	
11.38/4.52	H-Termination with start terms of the given HASKELL could be proven:
11.38/4.52	
11.38/4.52	(0) HASKELL
11.38/4.52	(1) LR [EQUIVALENT, 0 ms]
11.38/4.52	(2) HASKELL
11.38/4.52	(3) IPR [EQUIVALENT, 0 ms]
11.38/4.52	(4) HASKELL
11.38/4.52	(5) BR [EQUIVALENT, 0 ms]
11.38/4.52	(6) HASKELL
11.38/4.52	(7) COR [EQUIVALENT, 0 ms]
11.38/4.52	(8) HASKELL
11.38/4.52	(9) Narrow [SOUND, 0 ms]
11.38/4.52	(10) AND
11.38/4.52	    (11) QDP
11.38/4.52	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.38/4.52	        (13) YES
11.38/4.52	    (14) QDP
11.38/4.52	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.38/4.52	        (16) YES
11.38/4.52	
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(0)
11.38/4.52	Obligation:
11.38/4.52	mainModule Main 
11.38/4.52	module Maybe where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Main where {
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Monad where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Prelude;
11.38/4.52	mapAndUnzipM :: Monad c => (b  ->  c (a,d))  ->  [b]  ->  c ([a],[d]);
11.38/4.52	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
11.38/4.52	
11.38/4.52	}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(1) LR (EQUIVALENT)
11.38/4.52	Lambda Reductions:
11.38/4.52	The following Lambda expression
11.38/4.52	"\(a,b)~(as,bs)->(a : as,b : bs)"
11.38/4.52	is transformed to
11.38/4.52	"unzip0 (a,b) ~(as,bs) = (a : as,b : bs);
11.38/4.52	"
11.38/4.52	The following Lambda expression
11.38/4.52	"\xs->return (x : xs)"
11.38/4.52	is transformed to
11.38/4.52	"sequence0 x xs = return (x : xs);
11.38/4.52	"
11.38/4.52	The following Lambda expression
11.38/4.52	"\x->sequence cs >>= sequence0 x"
11.38/4.52	is transformed to
11.38/4.52	"sequence1 cs x = sequence cs >>= sequence0 x;
11.38/4.52	"
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(2)
11.38/4.52	Obligation:
11.38/4.52	mainModule Main 
11.38/4.52	module Maybe where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Main where {
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Monad where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Prelude;
11.38/4.52	mapAndUnzipM :: Monad b => (a  ->  b (d,c))  ->  [a]  ->  b ([d],[c]);
11.38/4.52	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
11.38/4.52	
11.38/4.52	}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(3) IPR (EQUIVALENT)
11.38/4.52	IrrPat Reductions:
11.38/4.52	The variables of the following irrefutable Pattern
11.38/4.52	"~(as,bs)"
11.38/4.52	are replaced by calls to these functions
11.38/4.52	"unzip00 (as,bs) = as;
11.38/4.52	"
11.38/4.52	"unzip01 (as,bs) = bs;
11.38/4.52	"
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(4)
11.38/4.52	Obligation:
11.38/4.52	mainModule Main 
11.38/4.52	module Maybe where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Main where {
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Monad where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Prelude;
11.38/4.52	mapAndUnzipM :: Monad a => (c  ->  a (b,d))  ->  [c]  ->  a ([b],[d]);
11.38/4.52	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
11.38/4.52	
11.38/4.52	}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(5) BR (EQUIVALENT)
11.38/4.52	Replaced joker patterns by fresh variables and removed binding patterns.
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(6)
11.38/4.52	Obligation:
11.38/4.52	mainModule Main 
11.38/4.52	module Maybe where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Main where {
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Monad where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Prelude;
11.38/4.52	mapAndUnzipM :: Monad d => (b  ->  d (a,c))  ->  [b]  ->  d ([a],[c]);
11.38/4.52	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
11.38/4.52	
11.38/4.52	}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(7) COR (EQUIVALENT)
11.38/4.52	Cond Reductions:
11.38/4.52	The following Function with conditions
11.38/4.52	"undefined |Falseundefined;
11.38/4.52	"
11.38/4.52	is transformed to
11.38/4.52	"undefined  = undefined1;
11.38/4.52	"
11.38/4.52	"undefined0 True = undefined;
11.38/4.52	"
11.38/4.52	"undefined1  = undefined0 False;
11.38/4.52	"
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(8)
11.38/4.52	Obligation:
11.38/4.52	mainModule Main 
11.38/4.52	module Maybe where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Main where {
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Monad;
11.38/4.52	import qualified Prelude;
11.38/4.52	}
11.38/4.52	module Monad where {
11.38/4.52	import qualified Main;
11.38/4.52	import qualified Maybe;
11.38/4.52	import qualified Prelude;
11.38/4.52	mapAndUnzipM :: Monad b => (c  ->  b (d,a))  ->  [c]  ->  b ([d],[a]);
11.38/4.52	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
11.38/4.52	
11.38/4.52	}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(9) Narrow (SOUND)
11.38/4.52	Haskell To QDPs
11.38/4.52	
11.38/4.52	digraph dp_graph {
11.38/4.52	node [outthreshold=100, inthreshold=100];1[label="Monad.mapAndUnzipM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.38/4.52	3[label="Monad.mapAndUnzipM vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.38/4.52	4[label="Monad.mapAndUnzipM vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.38/4.52	5[label="sequence (map vz3 vz4) >>= return . unzip",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
11.38/4.52	6 -> 174[label="",style="dashed", color="red", weight=0];
11.38/4.52	6[label="primbindIO (sequence (map vz3 vz4)) (return . unzip)",fontsize=16,color="magenta"];6 -> 175[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	175[label="sequence (map vz3 vz4)",fontsize=16,color="burlywood",shape="triangle"];325[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];175 -> 325[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	325 -> 260[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	326[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];175 -> 326[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	326 -> 261[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	174[label="primbindIO vz11 (return . unzip)",fontsize=16,color="burlywood",shape="triangle"];327[label="vz11/IO vz110",fontsize=10,color="white",style="solid",shape="box"];174 -> 327[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	327 -> 262[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	328[label="vz11/AProVE_IO vz110",fontsize=10,color="white",style="solid",shape="box"];174 -> 328[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	328 -> 263[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	329[label="vz11/AProVE_Exception vz110",fontsize=10,color="white",style="solid",shape="box"];174 -> 329[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	329 -> 264[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	330[label="vz11/AProVE_Error vz110",fontsize=10,color="white",style="solid",shape="box"];174 -> 330[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	330 -> 265[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	260[label="sequence (map vz3 (vz40 : vz41))",fontsize=16,color="black",shape="box"];260 -> 266[label="",style="solid", color="black", weight=3];
11.38/4.52	261[label="sequence (map vz3 [])",fontsize=16,color="black",shape="box"];261 -> 267[label="",style="solid", color="black", weight=3];
11.38/4.52	262[label="primbindIO (IO vz110) (return . unzip)",fontsize=16,color="black",shape="box"];262 -> 268[label="",style="solid", color="black", weight=3];
11.38/4.52	263[label="primbindIO (AProVE_IO vz110) (return . unzip)",fontsize=16,color="black",shape="box"];263 -> 269[label="",style="solid", color="black", weight=3];
11.38/4.52	264[label="primbindIO (AProVE_Exception vz110) (return . unzip)",fontsize=16,color="black",shape="box"];264 -> 270[label="",style="solid", color="black", weight=3];
11.38/4.52	265[label="primbindIO (AProVE_Error vz110) (return . unzip)",fontsize=16,color="black",shape="box"];265 -> 271[label="",style="solid", color="black", weight=3];
11.38/4.52	266[label="sequence (vz3 vz40 : map vz3 vz41)",fontsize=16,color="black",shape="box"];266 -> 272[label="",style="solid", color="black", weight=3];
11.38/4.52	267[label="sequence []",fontsize=16,color="black",shape="box"];267 -> 273[label="",style="solid", color="black", weight=3];
11.38/4.52	268[label="error []",fontsize=16,color="red",shape="box"];269[label="return . unzip",fontsize=16,color="black",shape="box"];269 -> 274[label="",style="solid", color="black", weight=3];
11.38/4.52	270[label="AProVE_Exception vz110",fontsize=16,color="green",shape="box"];271[label="AProVE_Error vz110",fontsize=16,color="green",shape="box"];272[label="vz3 vz40 >>= sequence1 (map vz3 vz41)",fontsize=16,color="black",shape="box"];272 -> 275[label="",style="solid", color="black", weight=3];
11.38/4.52	273[label="return []",fontsize=16,color="black",shape="box"];273 -> 276[label="",style="solid", color="black", weight=3];
11.38/4.52	274[label="return (unzip vz110)",fontsize=16,color="black",shape="box"];274 -> 277[label="",style="solid", color="black", weight=3];
11.38/4.52	275 -> 278[label="",style="dashed", color="red", weight=0];
11.38/4.52	275[label="primbindIO (vz3 vz40) (sequence1 (map vz3 vz41))",fontsize=16,color="magenta"];275 -> 279[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	276[label="primretIO []",fontsize=16,color="black",shape="box"];276 -> 280[label="",style="solid", color="black", weight=3];
11.38/4.52	277[label="primretIO (unzip vz110)",fontsize=16,color="black",shape="box"];277 -> 281[label="",style="solid", color="black", weight=3];
11.38/4.52	279[label="vz3 vz40",fontsize=16,color="green",shape="box"];279 -> 287[label="",style="dashed", color="green", weight=3];
11.38/4.52	278[label="primbindIO vz12 (sequence1 (map vz3 vz41))",fontsize=16,color="burlywood",shape="triangle"];331[label="vz12/IO vz120",fontsize=10,color="white",style="solid",shape="box"];278 -> 331[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	331 -> 283[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	332[label="vz12/AProVE_IO vz120",fontsize=10,color="white",style="solid",shape="box"];278 -> 332[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	332 -> 284[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	333[label="vz12/AProVE_Exception vz120",fontsize=10,color="white",style="solid",shape="box"];278 -> 333[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	333 -> 285[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	334[label="vz12/AProVE_Error vz120",fontsize=10,color="white",style="solid",shape="box"];278 -> 334[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	334 -> 286[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	280[label="AProVE_IO []",fontsize=16,color="green",shape="box"];281[label="AProVE_IO (unzip vz110)",fontsize=16,color="green",shape="box"];281 -> 288[label="",style="dashed", color="green", weight=3];
11.38/4.52	287[label="vz40",fontsize=16,color="green",shape="box"];283[label="primbindIO (IO vz120) (sequence1 (map vz3 vz41))",fontsize=16,color="black",shape="box"];283 -> 289[label="",style="solid", color="black", weight=3];
11.38/4.52	284[label="primbindIO (AProVE_IO vz120) (sequence1 (map vz3 vz41))",fontsize=16,color="black",shape="box"];284 -> 290[label="",style="solid", color="black", weight=3];
11.38/4.52	285[label="primbindIO (AProVE_Exception vz120) (sequence1 (map vz3 vz41))",fontsize=16,color="black",shape="box"];285 -> 291[label="",style="solid", color="black", weight=3];
11.38/4.52	286[label="primbindIO (AProVE_Error vz120) (sequence1 (map vz3 vz41))",fontsize=16,color="black",shape="box"];286 -> 292[label="",style="solid", color="black", weight=3];
11.38/4.52	288[label="unzip vz110",fontsize=16,color="black",shape="box"];288 -> 293[label="",style="solid", color="black", weight=3];
11.38/4.52	289[label="error []",fontsize=16,color="red",shape="box"];290[label="sequence1 (map vz3 vz41) vz120",fontsize=16,color="black",shape="box"];290 -> 294[label="",style="solid", color="black", weight=3];
11.38/4.52	291[label="AProVE_Exception vz120",fontsize=16,color="green",shape="box"];292[label="AProVE_Error vz120",fontsize=16,color="green",shape="box"];293[label="foldr unzip0 ([],[]) vz110",fontsize=16,color="burlywood",shape="triangle"];335[label="vz110/vz1100 : vz1101",fontsize=10,color="white",style="solid",shape="box"];293 -> 335[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	335 -> 295[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	336[label="vz110/[]",fontsize=10,color="white",style="solid",shape="box"];293 -> 336[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	336 -> 296[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	294 -> 297[label="",style="dashed", color="red", weight=0];
11.38/4.52	294[label="sequence (map vz3 vz41) >>= sequence0 vz120",fontsize=16,color="magenta"];294 -> 298[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	295[label="foldr unzip0 ([],[]) (vz1100 : vz1101)",fontsize=16,color="black",shape="box"];295 -> 299[label="",style="solid", color="black", weight=3];
11.38/4.52	296[label="foldr unzip0 ([],[]) []",fontsize=16,color="black",shape="box"];296 -> 300[label="",style="solid", color="black", weight=3];
11.38/4.52	298 -> 175[label="",style="dashed", color="red", weight=0];
11.38/4.52	298[label="sequence (map vz3 vz41)",fontsize=16,color="magenta"];298 -> 301[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	297[label="vz13 >>= sequence0 vz120",fontsize=16,color="black",shape="triangle"];297 -> 302[label="",style="solid", color="black", weight=3];
11.38/4.52	299 -> 303[label="",style="dashed", color="red", weight=0];
11.38/4.52	299[label="unzip0 vz1100 (foldr unzip0 ([],[]) vz1101)",fontsize=16,color="magenta"];299 -> 304[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	300[label="([],[])",fontsize=16,color="green",shape="box"];301[label="vz41",fontsize=16,color="green",shape="box"];302[label="primbindIO vz13 (sequence0 vz120)",fontsize=16,color="burlywood",shape="box"];337[label="vz13/IO vz130",fontsize=10,color="white",style="solid",shape="box"];302 -> 337[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	337 -> 305[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	338[label="vz13/AProVE_IO vz130",fontsize=10,color="white",style="solid",shape="box"];302 -> 338[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	338 -> 306[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	339[label="vz13/AProVE_Exception vz130",fontsize=10,color="white",style="solid",shape="box"];302 -> 339[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	339 -> 307[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	340[label="vz13/AProVE_Error vz130",fontsize=10,color="white",style="solid",shape="box"];302 -> 340[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	340 -> 308[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	304 -> 293[label="",style="dashed", color="red", weight=0];
11.38/4.52	304[label="foldr unzip0 ([],[]) vz1101",fontsize=16,color="magenta"];304 -> 309[label="",style="dashed", color="magenta", weight=3];
11.38/4.52	303[label="unzip0 vz1100 vz14",fontsize=16,color="burlywood",shape="triangle"];341[label="vz1100/(vz11000,vz11001)",fontsize=10,color="white",style="solid",shape="box"];303 -> 341[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	341 -> 310[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	305[label="primbindIO (IO vz130) (sequence0 vz120)",fontsize=16,color="black",shape="box"];305 -> 311[label="",style="solid", color="black", weight=3];
11.38/4.52	306[label="primbindIO (AProVE_IO vz130) (sequence0 vz120)",fontsize=16,color="black",shape="box"];306 -> 312[label="",style="solid", color="black", weight=3];
11.38/4.52	307[label="primbindIO (AProVE_Exception vz130) (sequence0 vz120)",fontsize=16,color="black",shape="box"];307 -> 313[label="",style="solid", color="black", weight=3];
11.38/4.52	308[label="primbindIO (AProVE_Error vz130) (sequence0 vz120)",fontsize=16,color="black",shape="box"];308 -> 314[label="",style="solid", color="black", weight=3];
11.38/4.52	309[label="vz1101",fontsize=16,color="green",shape="box"];310[label="unzip0 (vz11000,vz11001) vz14",fontsize=16,color="black",shape="box"];310 -> 315[label="",style="solid", color="black", weight=3];
11.38/4.52	311[label="error []",fontsize=16,color="red",shape="box"];312[label="sequence0 vz120 vz130",fontsize=16,color="black",shape="box"];312 -> 316[label="",style="solid", color="black", weight=3];
11.38/4.52	313[label="AProVE_Exception vz130",fontsize=16,color="green",shape="box"];314[label="AProVE_Error vz130",fontsize=16,color="green",shape="box"];315[label="(vz11000 : unzip00 vz14,vz11001 : unzip01 vz14)",fontsize=16,color="green",shape="box"];315 -> 317[label="",style="dashed", color="green", weight=3];
11.38/4.52	315 -> 318[label="",style="dashed", color="green", weight=3];
11.38/4.52	316[label="return (vz120 : vz130)",fontsize=16,color="black",shape="box"];316 -> 319[label="",style="solid", color="black", weight=3];
11.38/4.52	317[label="unzip00 vz14",fontsize=16,color="burlywood",shape="box"];342[label="vz14/(vz140,vz141)",fontsize=10,color="white",style="solid",shape="box"];317 -> 342[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	342 -> 320[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	318[label="unzip01 vz14",fontsize=16,color="burlywood",shape="box"];343[label="vz14/(vz140,vz141)",fontsize=10,color="white",style="solid",shape="box"];318 -> 343[label="",style="solid", color="burlywood", weight=9];
11.38/4.52	343 -> 321[label="",style="solid", color="burlywood", weight=3];
11.38/4.52	319[label="primretIO (vz120 : vz130)",fontsize=16,color="black",shape="box"];319 -> 322[label="",style="solid", color="black", weight=3];
11.38/4.52	320[label="unzip00 (vz140,vz141)",fontsize=16,color="black",shape="box"];320 -> 323[label="",style="solid", color="black", weight=3];
11.38/4.52	321[label="unzip01 (vz140,vz141)",fontsize=16,color="black",shape="box"];321 -> 324[label="",style="solid", color="black", weight=3];
11.38/4.52	322[label="AProVE_IO (vz120 : vz130)",fontsize=16,color="green",shape="box"];323[label="vz140",fontsize=16,color="green",shape="box"];324[label="vz141",fontsize=16,color="green",shape="box"];}
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(10)
11.38/4.52	Complex Obligation (AND)
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(11)
11.38/4.52	Obligation:
11.38/4.52	Q DP problem:
11.38/4.52	The TRS P consists of the following rules:
11.38/4.52	
11.38/4.52	   new_foldr(:(vz1100, vz1101), h, ba) -> new_foldr(vz1101, h, ba)
11.38/4.52	
11.38/4.52	R is empty.
11.38/4.52	Q is empty.
11.38/4.52	We have to consider all minimal (P,Q,R)-chains.
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(12) QDPSizeChangeProof (EQUIVALENT)
11.38/4.52	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. 
11.38/4.52	
11.38/4.52	From the DPs we obtained the following set of size-change graphs:
11.38/4.52	*new_foldr(:(vz1100, vz1101), h, ba) -> new_foldr(vz1101, h, ba)
11.38/4.52	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
11.38/4.52	
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(13)
11.38/4.52	YES
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(14)
11.38/4.52	Obligation:
11.38/4.52	Q DP problem:
11.38/4.52	The TRS P consists of the following rules:
11.38/4.52	
11.38/4.52	   new_sequence(vz3, :(vz40, vz41), h, ba, bb) -> new_primbindIO(vz3, vz41, h, ba, bb)
11.38/4.52	   new_primbindIO(vz3, vz41, h, ba, bb) -> new_sequence(vz3, vz41, h, ba, bb)
11.38/4.52	
11.38/4.52	R is empty.
11.38/4.52	Q is empty.
11.38/4.52	We have to consider all minimal (P,Q,R)-chains.
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(15) QDPSizeChangeProof (EQUIVALENT)
11.38/4.52	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. 
11.38/4.52	
11.38/4.52	From the DPs we obtained the following set of size-change graphs:
11.38/4.52	*new_primbindIO(vz3, vz41, h, ba, bb) -> new_sequence(vz3, vz41, h, ba, bb)
11.38/4.52	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
11.38/4.52	
11.38/4.52	
11.38/4.52	*new_sequence(vz3, :(vz40, vz41), h, ba, bb) -> new_primbindIO(vz3, vz41, h, ba, bb)
11.38/4.52	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
11.38/4.52	
11.38/4.52	
11.38/4.52	----------------------------------------
11.38/4.52	
11.38/4.52	(16)
11.38/4.52	YES
11.48/4.56	EOF