8.45/3.72	YES
10.44/4.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.44/4.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.44/4.23	
10.44/4.23	
10.44/4.23	H-Termination with start terms of the given HASKELL could be proven:
10.44/4.23	
10.44/4.23	(0) HASKELL
10.44/4.23	(1) BR [EQUIVALENT, 0 ms]
10.44/4.23	(2) HASKELL
10.44/4.23	(3) COR [EQUIVALENT, 0 ms]
10.44/4.23	(4) HASKELL
10.44/4.23	(5) NumRed [SOUND, 4 ms]
10.44/4.23	(6) HASKELL
10.44/4.23	(7) Narrow [SOUND, 0 ms]
10.44/4.23	(8) AND
10.44/4.23	    (9) QDP
10.44/4.23	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.44/4.23	        (11) YES
10.44/4.23	    (12) QDP
10.44/4.23	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.44/4.23	        (14) YES
10.44/4.23	
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(0)
10.44/4.23	Obligation:
10.44/4.23	mainModule Main 
10.44/4.23	module Main where {
10.44/4.23	import qualified Prelude;
10.44/4.23	}
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(1) BR (EQUIVALENT)
10.44/4.23	Replaced joker patterns by fresh variables and removed binding patterns.
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(2)
10.44/4.23	Obligation:
10.44/4.23	mainModule Main 
10.44/4.23	module Main where {
10.44/4.23	import qualified Prelude;
10.44/4.23	}
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(3) COR (EQUIVALENT)
10.44/4.23	Cond Reductions:
10.44/4.23	The following Function with conditions
10.44/4.23	"undefined |Falseundefined;
10.44/4.23	"
10.44/4.23	is transformed to
10.44/4.23	"undefined  = undefined1;
10.44/4.23	"
10.44/4.23	"undefined0 True = undefined;
10.44/4.23	"
10.44/4.23	"undefined1  = undefined0 False;
10.44/4.23	"
10.44/4.23	The following Function with conditions
10.44/4.23	"signumReal x|x == 00|x > 01|otherwise-1;
10.44/4.23	"
10.44/4.23	is transformed to
10.44/4.23	"signumReal x = signumReal3 x;
10.44/4.23	"
10.44/4.23	"signumReal0 x True = -1;
10.44/4.23	"
10.44/4.23	"signumReal1 x True = 1;
10.44/4.23	signumReal1 x False = signumReal0 x otherwise;
10.44/4.23	"
10.44/4.23	"signumReal2 x True = 0;
10.44/4.23	signumReal2 x False = signumReal1 x (x > 0);
10.44/4.23	"
10.44/4.23	"signumReal3 x = signumReal2 x (x == 0);
10.44/4.23	"
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(4)
10.44/4.23	Obligation:
10.44/4.23	mainModule Main 
10.44/4.23	module Main where {
10.44/4.23	import qualified Prelude;
10.44/4.23	}
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(5) NumRed (SOUND)
10.44/4.23	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(6)
10.44/4.23	Obligation:
10.44/4.23	mainModule Main 
10.44/4.23	module Main where {
10.44/4.23	import qualified Prelude;
10.44/4.23	}
10.44/4.23	
10.44/4.23	----------------------------------------
10.44/4.23	
10.44/4.23	(7) Narrow (SOUND)
10.44/4.23	Haskell To QDPs
10.44/4.23	
10.44/4.23	digraph dp_graph {
10.44/4.24	node [outthreshold=100, inthreshold=100];1[label="signum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.44/4.24	3[label="signum vz3",fontsize=16,color="burlywood",shape="triangle"];363[label="vz3/vz30 :% vz31",fontsize=10,color="white",style="solid",shape="box"];3 -> 363[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	363 -> 4[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	4[label="signum (vz30 :% vz31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.44/4.24	5[label="signum vz30 :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
10.44/4.24	5 -> 7[label="",style="dashed", color="green", weight=3];
10.44/4.24	6[label="signum vz30",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.44/4.24	7[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];7 -> 9[label="",style="solid", color="black", weight=3];
10.44/4.24	8[label="signumReal vz30",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
10.44/4.24	9[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];10[label="signumReal3 vz30",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.44/4.24	11[label="signumReal2 vz30 (vz30 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
10.44/4.24	12[label="signumReal2 vz30 (primEqInt vz30 (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];364[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];12 -> 364[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	364 -> 13[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	365[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];12 -> 365[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	365 -> 14[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	13[label="signumReal2 (Pos vz300) (primEqInt (Pos vz300) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];366[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];13 -> 366[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	366 -> 15[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	367[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 367[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	367 -> 16[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	14[label="signumReal2 (Neg vz300) (primEqInt (Neg vz300) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];368[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];14 -> 368[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	368 -> 17[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	369[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 369[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	369 -> 18[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	15[label="signumReal2 (Pos (Succ vz3000)) (primEqInt (Pos (Succ vz3000)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
10.44/4.24	16[label="signumReal2 (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
10.44/4.24	17[label="signumReal2 (Neg (Succ vz3000)) (primEqInt (Neg (Succ vz3000)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
10.44/4.24	18[label="signumReal2 (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
10.44/4.24	19[label="signumReal2 (Pos (Succ vz3000)) (primEqInt (Pos (Succ vz3000)) (Pos Zero))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
10.44/4.24	20[label="signumReal2 (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
10.44/4.24	21[label="signumReal2 (Neg (Succ vz3000)) (primEqInt (Neg (Succ vz3000)) (Pos Zero))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
10.44/4.24	22[label="signumReal2 (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
10.44/4.24	23[label="signumReal2 (Pos (Succ vz3000)) False",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
10.44/4.24	24[label="signumReal2 (Pos Zero) True",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
10.44/4.24	25[label="signumReal2 (Neg (Succ vz3000)) False",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
10.44/4.24	26[label="signumReal2 (Neg Zero) True",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
10.44/4.24	27[label="signumReal1 (Pos (Succ vz3000)) (Pos (Succ vz3000) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
10.44/4.24	28[label="fromInt (Pos Zero)",fontsize=16,color="black",shape="triangle"];28 -> 32[label="",style="solid", color="black", weight=3];
10.44/4.24	29 -> 33[label="",style="dashed", color="red", weight=0];
10.44/4.24	29[label="signumReal1 (Neg (Succ vz3000)) (Neg (Succ vz3000) > fromInt (Pos Zero))",fontsize=16,color="magenta"];29 -> 34[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	30 -> 28[label="",style="dashed", color="red", weight=0];
10.44/4.24	30[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];31 -> 35[label="",style="dashed", color="red", weight=0];
10.44/4.24	31[label="signumReal1 (Pos (Succ vz3000)) (compare (Pos (Succ vz3000)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="magenta"];31 -> 36[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	32[label="Pos Zero",fontsize=16,color="green",shape="box"];34 -> 28[label="",style="dashed", color="red", weight=0];
10.44/4.24	34[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];33[label="signumReal1 (Neg (Succ vz3000)) (Neg (Succ vz3000) > vz4)",fontsize=16,color="black",shape="triangle"];33 -> 37[label="",style="solid", color="black", weight=3];
10.44/4.24	36 -> 28[label="",style="dashed", color="red", weight=0];
10.44/4.24	36[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];35[label="signumReal1 (Pos (Succ vz3000)) (compare (Pos (Succ vz3000)) vz5 == GT)",fontsize=16,color="black",shape="triangle"];35 -> 38[label="",style="solid", color="black", weight=3];
10.44/4.24	37[label="signumReal1 (Neg (Succ vz3000)) (compare (Neg (Succ vz3000)) vz4 == GT)",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
10.44/4.24	38[label="signumReal1 (Pos (Succ vz3000)) (primCmpInt (Pos (Succ vz3000)) vz5 == GT)",fontsize=16,color="burlywood",shape="box"];370[label="vz5/Pos vz50",fontsize=10,color="white",style="solid",shape="box"];38 -> 370[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	370 -> 40[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	371[label="vz5/Neg vz50",fontsize=10,color="white",style="solid",shape="box"];38 -> 371[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	371 -> 41[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	39[label="signumReal1 (Neg (Succ vz3000)) (primCmpInt (Neg (Succ vz3000)) vz4 == GT)",fontsize=16,color="burlywood",shape="box"];372[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];39 -> 372[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	372 -> 42[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	373[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];39 -> 373[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	373 -> 43[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	40[label="signumReal1 (Pos (Succ vz3000)) (primCmpInt (Pos (Succ vz3000)) (Pos vz50) == GT)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
10.44/4.24	41[label="signumReal1 (Pos (Succ vz3000)) (primCmpInt (Pos (Succ vz3000)) (Neg vz50) == GT)",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
10.44/4.24	42[label="signumReal1 (Neg (Succ vz3000)) (primCmpInt (Neg (Succ vz3000)) (Pos vz40) == GT)",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
10.44/4.24	43[label="signumReal1 (Neg (Succ vz3000)) (primCmpInt (Neg (Succ vz3000)) (Neg vz40) == GT)",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
10.44/4.24	44 -> 206[label="",style="dashed", color="red", weight=0];
10.44/4.24	44[label="signumReal1 (Pos (Succ vz3000)) (primCmpNat (Succ vz3000) vz50 == GT)",fontsize=16,color="magenta"];44 -> 207[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	44 -> 208[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	44 -> 209[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	45[label="signumReal1 (Pos (Succ vz3000)) (GT == GT)",fontsize=16,color="black",shape="triangle"];45 -> 50[label="",style="solid", color="black", weight=3];
10.44/4.24	46[label="signumReal1 (Neg (Succ vz3000)) (LT == GT)",fontsize=16,color="black",shape="triangle"];46 -> 51[label="",style="solid", color="black", weight=3];
10.44/4.24	47 -> 269[label="",style="dashed", color="red", weight=0];
10.44/4.24	47[label="signumReal1 (Neg (Succ vz3000)) (primCmpNat vz40 (Succ vz3000) == GT)",fontsize=16,color="magenta"];47 -> 270[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	47 -> 271[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	47 -> 272[label="",style="dashed", color="magenta", weight=3];
10.44/4.24	207[label="vz3000",fontsize=16,color="green",shape="box"];208[label="vz50",fontsize=16,color="green",shape="box"];209[label="Succ vz3000",fontsize=16,color="green",shape="box"];206[label="signumReal1 (Pos (Succ vz7)) (primCmpNat vz8 vz9 == GT)",fontsize=16,color="burlywood",shape="triangle"];374[label="vz8/Succ vz80",fontsize=10,color="white",style="solid",shape="box"];206 -> 374[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	374 -> 228[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	375[label="vz8/Zero",fontsize=10,color="white",style="solid",shape="box"];206 -> 375[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	375 -> 229[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	50[label="signumReal1 (Pos (Succ vz3000)) True",fontsize=16,color="black",shape="box"];50 -> 56[label="",style="solid", color="black", weight=3];
10.44/4.24	51[label="signumReal1 (Neg (Succ vz3000)) False",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3];
10.44/4.24	270[label="vz3000",fontsize=16,color="green",shape="box"];271[label="Succ vz3000",fontsize=16,color="green",shape="box"];272[label="vz40",fontsize=16,color="green",shape="box"];269[label="signumReal1 (Neg (Succ vz13)) (primCmpNat vz14 vz15 == GT)",fontsize=16,color="burlywood",shape="triangle"];376[label="vz14/Succ vz140",fontsize=10,color="white",style="solid",shape="box"];269 -> 376[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	376 -> 294[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	377[label="vz14/Zero",fontsize=10,color="white",style="solid",shape="box"];269 -> 377[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	377 -> 295[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	228[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) vz9 == GT)",fontsize=16,color="burlywood",shape="box"];378[label="vz9/Succ vz90",fontsize=10,color="white",style="solid",shape="box"];228 -> 378[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	378 -> 238[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	379[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];228 -> 379[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	379 -> 239[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	229[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero vz9 == GT)",fontsize=16,color="burlywood",shape="box"];380[label="vz9/Succ vz90",fontsize=10,color="white",style="solid",shape="box"];229 -> 380[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	380 -> 240[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	381[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];229 -> 381[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	381 -> 241[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	56 -> 7[label="",style="dashed", color="red", weight=0];
10.44/4.24	56[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];57[label="signumReal0 (Neg (Succ vz3000)) otherwise",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3];
10.44/4.24	294[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) vz15 == GT)",fontsize=16,color="burlywood",shape="box"];382[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];294 -> 382[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	382 -> 298[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	383[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];294 -> 383[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	383 -> 299[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	295[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero vz15 == GT)",fontsize=16,color="burlywood",shape="box"];384[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];295 -> 384[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	384 -> 300[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	385[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];295 -> 385[label="",style="solid", color="burlywood", weight=9];
10.44/4.24	385 -> 301[label="",style="solid", color="burlywood", weight=3];
10.44/4.24	238[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) (Succ vz90) == GT)",fontsize=16,color="black",shape="box"];238 -> 249[label="",style="solid", color="black", weight=3];
10.44/4.24	239[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) Zero == GT)",fontsize=16,color="black",shape="box"];239 -> 250[label="",style="solid", color="black", weight=3];
10.44/4.24	240[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero (Succ vz90) == GT)",fontsize=16,color="black",shape="box"];240 -> 251[label="",style="solid", color="black", weight=3];
10.44/4.24	241[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];241 -> 252[label="",style="solid", color="black", weight=3];
10.44/4.24	62[label="signumReal0 (Neg (Succ vz3000)) True",fontsize=16,color="black",shape="box"];62 -> 69[label="",style="solid", color="black", weight=3];
10.44/4.24	298[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) (Succ vz150) == GT)",fontsize=16,color="black",shape="box"];298 -> 308[label="",style="solid", color="black", weight=3];
10.44/4.24	299[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) Zero == GT)",fontsize=16,color="black",shape="box"];299 -> 309[label="",style="solid", color="black", weight=3];
10.44/4.24	300[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero (Succ vz150) == GT)",fontsize=16,color="black",shape="box"];300 -> 310[label="",style="solid", color="black", weight=3];
10.44/4.24	301[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];301 -> 311[label="",style="solid", color="black", weight=3];
10.44/4.24	249 -> 206[label="",style="dashed", color="red", weight=0];
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10.44/4.24	251[label="signumReal1 (Pos (Succ vz7)) (LT == GT)",fontsize=16,color="black",shape="box"];251 -> 262[label="",style="solid", color="black", weight=3];
10.44/4.24	252[label="signumReal1 (Pos (Succ vz7)) (EQ == GT)",fontsize=16,color="black",shape="box"];252 -> 263[label="",style="solid", color="black", weight=3];
10.44/4.24	69[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];69 -> 78[label="",style="solid", color="black", weight=3];
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10.44/4.24	308[label="signumReal1 (Neg (Succ vz13)) (primCmpNat vz140 vz150 == GT)",fontsize=16,color="magenta"];308 -> 317[label="",style="dashed", color="magenta", weight=3];
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10.44/4.24	309[label="signumReal1 (Neg (Succ vz13)) (GT == GT)",fontsize=16,color="black",shape="box"];309 -> 319[label="",style="solid", color="black", weight=3];
10.44/4.24	310[label="signumReal1 (Neg (Succ vz13)) (LT == GT)",fontsize=16,color="black",shape="box"];310 -> 320[label="",style="solid", color="black", weight=3];
10.44/4.24	311[label="signumReal1 (Neg (Succ vz13)) (EQ == GT)",fontsize=16,color="black",shape="box"];311 -> 321[label="",style="solid", color="black", weight=3];
10.44/4.24	259[label="vz90",fontsize=16,color="green",shape="box"];260[label="vz80",fontsize=16,color="green",shape="box"];261[label="signumReal1 (Pos (Succ vz7)) True",fontsize=16,color="black",shape="box"];261 -> 296[label="",style="solid", color="black", weight=3];
10.44/4.24	262[label="signumReal1 (Pos (Succ vz7)) False",fontsize=16,color="black",shape="triangle"];262 -> 297[label="",style="solid", color="black", weight=3];
10.44/4.24	263 -> 262[label="",style="dashed", color="red", weight=0];
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10.44/4.24	320[label="signumReal1 (Neg (Succ vz13)) False",fontsize=16,color="black",shape="triangle"];320 -> 331[label="",style="solid", color="black", weight=3];
10.44/4.24	321 -> 320[label="",style="dashed", color="red", weight=0];
10.44/4.24	321[label="signumReal1 (Neg (Succ vz13)) False",fontsize=16,color="magenta"];296[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];386[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];296 -> 386[label="",style="solid", color="blue", weight=9];
10.44/4.24	386 -> 302[label="",style="solid", color="blue", weight=3];
10.44/4.24	387[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];296 -> 387[label="",style="solid", color="blue", weight=9];
10.44/4.24	387 -> 303[label="",style="solid", color="blue", weight=3];
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10.44/4.24	389[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];296 -> 389[label="",style="solid", color="blue", weight=9];
10.44/4.24	389 -> 305[label="",style="solid", color="blue", weight=3];
10.44/4.24	390[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];296 -> 390[label="",style="solid", color="blue", weight=9];
10.44/4.24	390 -> 306[label="",style="solid", color="blue", weight=3];
10.44/4.24	297[label="signumReal0 (Pos (Succ vz7)) otherwise",fontsize=16,color="black",shape="box"];297 -> 307[label="",style="solid", color="black", weight=3];
10.44/4.24	330[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];391[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];330 -> 391[label="",style="solid", color="blue", weight=9];
10.44/4.24	391 -> 338[label="",style="solid", color="blue", weight=3];
10.44/4.24	392[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];330 -> 392[label="",style="solid", color="blue", weight=9];
10.44/4.24	392 -> 339[label="",style="solid", color="blue", weight=3];
10.44/4.24	393[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];330 -> 393[label="",style="solid", color="blue", weight=9];
10.44/4.24	393 -> 340[label="",style="solid", color="blue", weight=3];
10.44/4.24	394[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];330 -> 394[label="",style="solid", color="blue", weight=9];
10.44/4.24	394 -> 341[label="",style="solid", color="blue", weight=3];
10.44/4.24	395[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];330 -> 395[label="",style="solid", color="blue", weight=9];
10.44/4.24	395 -> 342[label="",style="solid", color="blue", weight=3];
10.44/4.24	331[label="signumReal0 (Neg (Succ vz13)) otherwise",fontsize=16,color="black",shape="box"];331 -> 343[label="",style="solid", color="black", weight=3];
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10.44/4.24	304[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];304 -> 314[label="",style="solid", color="black", weight=3];
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10.44/4.24	307[label="signumReal0 (Pos (Succ vz7)) True",fontsize=16,color="black",shape="box"];307 -> 316[label="",style="solid", color="black", weight=3];
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10.44/4.24	342[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];343[label="signumReal0 (Neg (Succ vz13)) True",fontsize=16,color="black",shape="box"];343 -> 351[label="",style="solid", color="black", weight=3];
10.44/4.24	312[label="primIntToDouble (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];312 -> 322[label="",style="solid", color="black", weight=3];
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10.44/4.24	315[label="Integer (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];316[label="fromInt (Neg (Succ Zero))",fontsize=16,color="blue",shape="box"];396[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];316 -> 396[label="",style="solid", color="blue", weight=9];
10.44/4.24	396 -> 325[label="",style="solid", color="blue", weight=3];
10.44/4.24	397[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];316 -> 397[label="",style="solid", color="blue", weight=9];
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10.44/4.24	398[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];316 -> 398[label="",style="solid", color="blue", weight=9];
10.44/4.24	398 -> 327[label="",style="solid", color="blue", weight=3];
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10.44/4.24	401 -> 354[label="",style="solid", color="blue", weight=3];
10.44/4.24	402[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];351 -> 402[label="",style="solid", color="blue", weight=9];
10.44/4.24	402 -> 355[label="",style="solid", color="blue", weight=3];
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10.44/4.24	403 -> 356[label="",style="solid", color="blue", weight=3];
10.44/4.24	404[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];351 -> 404[label="",style="solid", color="blue", weight=9];
10.44/4.24	404 -> 357[label="",style="solid", color="blue", weight=3];
10.44/4.24	405[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];351 -> 405[label="",style="solid", color="blue", weight=9];
10.44/4.24	405 -> 358[label="",style="solid", color="blue", weight=3];
10.44/4.24	322[label="Double (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];323[label="fromInt (Pos (Succ Zero)) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];323 -> 332[label="",style="dashed", color="green", weight=3];
10.44/4.24	323 -> 333[label="",style="dashed", color="green", weight=3];
10.44/4.24	324[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];325[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];325 -> 334[label="",style="solid", color="black", weight=3];
10.44/4.24	326[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];326 -> 335[label="",style="solid", color="black", weight=3];
10.44/4.24	327[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];327 -> 336[label="",style="solid", color="black", weight=3];
10.44/4.24	328 -> 69[label="",style="dashed", color="red", weight=0];
10.44/4.24	328[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];329[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];329 -> 337[label="",style="solid", color="black", weight=3];
10.44/4.24	354 -> 325[label="",style="dashed", color="red", weight=0];
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10.44/4.24	355[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];356 -> 327[label="",style="dashed", color="red", weight=0];
10.44/4.24	356[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];357 -> 69[label="",style="dashed", color="red", weight=0];
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10.44/4.24	358[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];332[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];406[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];332 -> 406[label="",style="solid", color="blue", weight=9];
10.44/4.24	406 -> 344[label="",style="solid", color="blue", weight=3];
10.44/4.24	407[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];332 -> 407[label="",style="solid", color="blue", weight=9];
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10.44/4.24	333[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];408[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];333 -> 408[label="",style="solid", color="blue", weight=9];
10.44/4.24	408 -> 346[label="",style="solid", color="blue", weight=3];
10.44/4.24	409[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];333 -> 409[label="",style="solid", color="blue", weight=9];
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10.44/4.24	335[label="intToRatio (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];335 -> 349[label="",style="solid", color="black", weight=3];
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10.44/4.24	360[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];361 -> 7[label="",style="dashed", color="red", weight=0];
10.44/4.24	361[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];362 -> 306[label="",style="dashed", color="red", weight=0];
10.44/4.24	362[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];}
10.44/4.24	
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(8)
10.44/4.24	Complex Obligation (AND)
10.44/4.24	
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(9)
10.44/4.24	Obligation:
10.44/4.24	Q DP problem:
10.44/4.24	The TRS P consists of the following rules:
10.44/4.24	
10.44/4.24	   new_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h)
10.44/4.24	
10.44/4.24	R is empty.
10.44/4.24	Q is empty.
10.44/4.24	We have to consider all minimal (P,Q,R)-chains.
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(10) QDPSizeChangeProof (EQUIVALENT)
10.44/4.24	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. 
10.44/4.24	
10.44/4.24	From the DPs we obtained the following set of size-change graphs:
10.44/4.24	*new_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h)
10.44/4.24	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4
10.44/4.24	
10.44/4.24	
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(11)
10.44/4.24	YES
10.44/4.24	
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(12)
10.44/4.24	Obligation:
10.44/4.24	Q DP problem:
10.44/4.24	The TRS P consists of the following rules:
10.44/4.24	
10.44/4.24	   new_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h)
10.44/4.24	
10.44/4.24	R is empty.
10.44/4.24	Q is empty.
10.44/4.24	We have to consider all minimal (P,Q,R)-chains.
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(13) QDPSizeChangeProof (EQUIVALENT)
10.44/4.24	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. 
10.44/4.24	
10.44/4.24	From the DPs we obtained the following set of size-change graphs:
10.44/4.24	*new_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h)
10.44/4.24	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4
10.44/4.24	
10.44/4.24	
10.44/4.24	----------------------------------------
10.44/4.24	
10.44/4.24	(14)
10.44/4.24	YES
10.54/4.28	EOF