8.52/3.64	YES
10.65/4.20	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
10.65/4.20	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.65/4.20	
10.65/4.20	
10.65/4.20	H-Termination with start terms of the given HASKELL could be proven:
10.65/4.20	
10.65/4.20	(0) HASKELL
10.65/4.20	(1) BR [EQUIVALENT, 0 ms]
10.65/4.20	(2) HASKELL
10.65/4.20	(3) COR [EQUIVALENT, 0 ms]
10.65/4.20	(4) HASKELL
10.65/4.20	(5) LetRed [EQUIVALENT, 3 ms]
10.65/4.20	(6) HASKELL
10.65/4.20	(7) NumRed [SOUND, 0 ms]
10.65/4.20	(8) HASKELL
10.65/4.20	(9) Narrow [SOUND, 0 ms]
10.65/4.20	(10) AND
10.65/4.20	    (11) QDP
10.65/4.20	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.65/4.20	        (13) YES
10.65/4.20	    (14) QDP
10.65/4.20	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.65/4.20	        (16) YES
10.65/4.20	    (17) QDP
10.65/4.20	        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
10.65/4.20	        (19) QDP
10.65/4.20	        (20) QDPSizeChangeProof [EQUIVALENT, 4 ms]
10.65/4.20	        (21) YES
10.65/4.20	
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(0)
10.65/4.20	Obligation:
10.65/4.20	mainModule Main 
10.65/4.20	module Main where {
10.65/4.20	import qualified Prelude;
10.65/4.20	}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(1) BR (EQUIVALENT)
10.65/4.20	Replaced joker patterns by fresh variables and removed binding patterns.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(2)
10.65/4.20	Obligation:
10.65/4.20	mainModule Main 
10.65/4.20	module Main where {
10.65/4.20	import qualified Prelude;
10.65/4.20	}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(3) COR (EQUIVALENT)
10.65/4.20	Cond Reductions:
10.65/4.20	The following Function with conditions
10.65/4.20	"undefined |Falseundefined;
10.65/4.20	"
10.65/4.20	is transformed to
10.65/4.20	"undefined  = undefined1;
10.65/4.20	"
10.65/4.20	"undefined0 True = undefined;
10.65/4.20	"
10.65/4.20	"undefined1  = undefined0 False;
10.65/4.20	"
10.65/4.20	The following Function with conditions
10.65/4.20	"power vz 0 = 1.0;
10.65/4.20	power x wu@(y+1) = fromInt x * power x y;
10.65/4.20	power x y = 1.0 / power x (`negate` y);
10.65/4.20	"
10.65/4.20	is transformed to
10.65/4.20	"power vz xu = power4 vz xu;
10.65/4.20	power x wu = power2 x wu;
10.65/4.20	power x y = power0 x y;
10.65/4.20	"
10.65/4.20	"power0 x y = 1.0 / power x (`negate` y);
10.65/4.20	"
10.65/4.20	"power1 True x wu = fromInt x * power x (wu - 1);
10.65/4.20	power1 wv ww wx = power0 ww wx;
10.65/4.20	"
10.65/4.20	"power2 x wu = power1 (wu >= 1) x wu;
10.65/4.20	power2 wy wz = power0 wy wz;
10.65/4.20	"
10.65/4.20	"power3 True vz xu = 1.0;
10.65/4.20	power3 xv xw xx = power2 xw xx;
10.65/4.20	"
10.65/4.20	"power4 vz xu = power3 (xu == 0) vz xu;
10.65/4.20	power4 xy xz = power2 xy xz;
10.65/4.20	"
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(4)
10.65/4.20	Obligation:
10.65/4.20	mainModule Main 
10.65/4.20	module Main where {
10.65/4.20	import qualified Prelude;
10.65/4.20	}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(5) LetRed (EQUIVALENT)
10.65/4.20	Let/Where Reductions:
10.65/4.20	The bindings of the following Let/Where expression
10.65/4.20	"fromInteger x * power 2 y where {
10.65/4.20	power vz xu = power4 vz xu;
10.65/4.20	power x wu = power2 x wu;
10.65/4.20	power x y = power0 x y;
10.65/4.20	;
10.65/4.20	power0 x y = 1.0 / power x (`negate` y);
10.65/4.20	;
10.65/4.20	power1 True x wu = fromInt x * power x (wu - 1);
10.65/4.20	power1 wv ww wx = power0 ww wx;
10.65/4.20	;
10.65/4.20	power2 x wu = power1 (wu >= 1) x wu;
10.65/4.20	power2 wy wz = power0 wy wz;
10.65/4.20	;
10.65/4.20	power3 True vz xu = 1.0;
10.65/4.20	power3 xv xw xx = power2 xw xx;
10.65/4.20	;
10.65/4.20	power4 vz xu = power3 (xu == 0) vz xu;
10.65/4.20	power4 xy xz = power2 xy xz;
10.65/4.20	} 
10.65/4.20	"
10.65/4.20	are unpacked to the following functions on top level
10.65/4.20	"primFloatEncodePower4 vz xu = primFloatEncodePower3 (xu == 0) vz xu;
10.65/4.20	primFloatEncodePower4 xy xz = primFloatEncodePower2 xy xz;
10.65/4.20	"
10.65/4.20	"primFloatEncodePower1 True x wu = fromInt x * primFloatEncodePower x (wu - 1);
10.65/4.20	primFloatEncodePower1 wv ww wx = primFloatEncodePower0 ww wx;
10.65/4.20	"
10.65/4.20	"primFloatEncodePower2 x wu = primFloatEncodePower1 (wu >= 1) x wu;
10.65/4.20	primFloatEncodePower2 wy wz = primFloatEncodePower0 wy wz;
10.65/4.20	"
10.65/4.20	"primFloatEncodePower vz xu = primFloatEncodePower4 vz xu;
10.65/4.20	primFloatEncodePower x wu = primFloatEncodePower2 x wu;
10.65/4.20	primFloatEncodePower x y = primFloatEncodePower0 x y;
10.65/4.20	"
10.65/4.20	"primFloatEncodePower0 x y = 1.0 / primFloatEncodePower x (`negate` y);
10.65/4.20	"
10.65/4.20	"primFloatEncodePower3 True vz xu = 1.0;
10.65/4.20	primFloatEncodePower3 xv xw xx = primFloatEncodePower2 xw xx;
10.65/4.20	"
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(6)
10.65/4.20	Obligation:
10.65/4.20	mainModule Main 
10.65/4.20	module Main where {
10.65/4.20	import qualified Prelude;
10.65/4.20	}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(7) NumRed (SOUND)
10.65/4.20	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(8)
10.65/4.20	Obligation:
10.65/4.20	mainModule Main 
10.65/4.20	module Main where {
10.65/4.20	import qualified Prelude;
10.65/4.20	}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(9) Narrow (SOUND)
10.65/4.20	Haskell To QDPs
10.65/4.20	
10.65/4.20	digraph dp_graph {
10.65/4.20	node [outthreshold=100, inthreshold=100];1[label="encodeFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.65/4.20	3[label="encodeFloat yu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.65/4.20	4[label="encodeFloat yu3 yu4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.65/4.20	5[label="primFloatEncode yu3 yu4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.65/4.20	6[label="fromInteger yu3 * primFloatEncodePower (Pos (Succ (Succ Zero))) yu4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.65/4.20	7[label="primMulFloat (fromInteger yu3) (primFloatEncodePower (Pos (Succ (Succ Zero))) yu4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.65/4.20	8[label="primMulFloat (primIntegerToFloat yu3) (primFloatEncodePower (Pos (Succ (Succ Zero))) yu4)",fontsize=16,color="burlywood",shape="box"];268[label="yu3/Integer yu30",fontsize=10,color="white",style="solid",shape="box"];8 -> 268[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	268 -> 9[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	9[label="primMulFloat (primIntegerToFloat (Integer yu30)) (primFloatEncodePower (Pos (Succ (Succ Zero))) yu4)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10.65/4.20	10[label="primMulFloat (primIntToFloat yu30) (primFloatEncodePower (Pos (Succ (Succ Zero))) yu4)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.65/4.20	11 -> 87[label="",style="dashed", color="red", weight=0];
10.65/4.20	11[label="primMulFloat (Float yu30 (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) yu4)",fontsize=16,color="magenta"];11 -> 88[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	88[label="primFloatEncodePower (Pos (Succ (Succ Zero))) yu4",fontsize=16,color="black",shape="triangle"];88 -> 133[label="",style="solid", color="black", weight=3];
10.65/4.20	87[label="primMulFloat (Float yu30 (Pos (Succ Zero))) yu6",fontsize=16,color="burlywood",shape="triangle"];269[label="yu6/Float yu60 yu61",fontsize=10,color="white",style="solid",shape="box"];87 -> 269[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	269 -> 134[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	133[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) yu4",fontsize=16,color="black",shape="box"];133 -> 135[label="",style="solid", color="black", weight=3];
10.65/4.20	134[label="primMulFloat (Float yu30 (Pos (Succ Zero))) (Float yu60 yu61)",fontsize=16,color="black",shape="box"];134 -> 136[label="",style="solid", color="black", weight=3];
10.65/4.20	135[label="primFloatEncodePower3 (yu4 == Pos Zero) (Pos (Succ (Succ Zero))) yu4",fontsize=16,color="black",shape="box"];135 -> 137[label="",style="solid", color="black", weight=3];
10.65/4.20	136[label="Float (yu30 * yu60) (Pos (Succ Zero) * yu61)",fontsize=16,color="green",shape="box"];136 -> 138[label="",style="dashed", color="green", weight=3];
10.65/4.20	136 -> 139[label="",style="dashed", color="green", weight=3];
10.65/4.20	137[label="primFloatEncodePower3 (primEqInt yu4 (Pos Zero)) (Pos (Succ (Succ Zero))) yu4",fontsize=16,color="burlywood",shape="box"];270[label="yu4/Pos yu40",fontsize=10,color="white",style="solid",shape="box"];137 -> 270[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	270 -> 140[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	271[label="yu4/Neg yu40",fontsize=10,color="white",style="solid",shape="box"];137 -> 271[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	271 -> 141[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	138[label="yu30 * yu60",fontsize=16,color="black",shape="triangle"];138 -> 142[label="",style="solid", color="black", weight=3];
10.65/4.20	139 -> 138[label="",style="dashed", color="red", weight=0];
10.65/4.20	139[label="Pos (Succ Zero) * yu61",fontsize=16,color="magenta"];139 -> 143[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	139 -> 144[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	140[label="primFloatEncodePower3 (primEqInt (Pos yu40) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos yu40)",fontsize=16,color="burlywood",shape="box"];272[label="yu40/Succ yu400",fontsize=10,color="white",style="solid",shape="box"];140 -> 272[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	272 -> 145[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	273[label="yu40/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 273[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	273 -> 146[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	141[label="primFloatEncodePower3 (primEqInt (Neg yu40) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg yu40)",fontsize=16,color="burlywood",shape="box"];274[label="yu40/Succ yu400",fontsize=10,color="white",style="solid",shape="box"];141 -> 274[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	274 -> 147[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	275[label="yu40/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 275[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	275 -> 148[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	142[label="primMulInt yu30 yu60",fontsize=16,color="burlywood",shape="box"];276[label="yu30/Pos yu300",fontsize=10,color="white",style="solid",shape="box"];142 -> 276[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	276 -> 149[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	277[label="yu30/Neg yu300",fontsize=10,color="white",style="solid",shape="box"];142 -> 277[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	277 -> 150[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	143[label="yu61",fontsize=16,color="green",shape="box"];144[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];145[label="primFloatEncodePower3 (primEqInt (Pos (Succ yu400)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];145 -> 151[label="",style="solid", color="black", weight=3];
10.65/4.20	146[label="primFloatEncodePower3 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="box"];146 -> 152[label="",style="solid", color="black", weight=3];
10.65/4.20	147[label="primFloatEncodePower3 (primEqInt (Neg (Succ yu400)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];147 -> 153[label="",style="solid", color="black", weight=3];
10.65/4.20	148[label="primFloatEncodePower3 (primEqInt (Neg Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg Zero)",fontsize=16,color="black",shape="box"];148 -> 154[label="",style="solid", color="black", weight=3];
10.65/4.20	149[label="primMulInt (Pos yu300) yu60",fontsize=16,color="burlywood",shape="box"];278[label="yu60/Pos yu600",fontsize=10,color="white",style="solid",shape="box"];149 -> 278[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	278 -> 155[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	279[label="yu60/Neg yu600",fontsize=10,color="white",style="solid",shape="box"];149 -> 279[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	279 -> 156[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	150[label="primMulInt (Neg yu300) yu60",fontsize=16,color="burlywood",shape="box"];280[label="yu60/Pos yu600",fontsize=10,color="white",style="solid",shape="box"];150 -> 280[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	280 -> 157[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	281[label="yu60/Neg yu600",fontsize=10,color="white",style="solid",shape="box"];150 -> 281[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	281 -> 158[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	151[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];151 -> 159[label="",style="solid", color="black", weight=3];
10.65/4.20	152[label="primFloatEncodePower3 True (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="box"];152 -> 160[label="",style="solid", color="black", weight=3];
10.65/4.20	153[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];153 -> 161[label="",style="solid", color="black", weight=3];
10.65/4.20	154[label="primFloatEncodePower3 True (Pos (Succ (Succ Zero))) (Neg Zero)",fontsize=16,color="black",shape="box"];154 -> 162[label="",style="solid", color="black", weight=3];
10.65/4.20	155[label="primMulInt (Pos yu300) (Pos yu600)",fontsize=16,color="black",shape="box"];155 -> 163[label="",style="solid", color="black", weight=3];
10.65/4.20	156[label="primMulInt (Pos yu300) (Neg yu600)",fontsize=16,color="black",shape="box"];156 -> 164[label="",style="solid", color="black", weight=3];
10.65/4.20	157[label="primMulInt (Neg yu300) (Pos yu600)",fontsize=16,color="black",shape="box"];157 -> 165[label="",style="solid", color="black", weight=3];
10.65/4.20	158[label="primMulInt (Neg yu300) (Neg yu600)",fontsize=16,color="black",shape="box"];158 -> 166[label="",style="solid", color="black", weight=3];
10.65/4.20	159[label="primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];159 -> 167[label="",style="solid", color="black", weight=3];
10.65/4.20	160[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];160 -> 168[label="",style="solid", color="black", weight=3];
10.65/4.20	161[label="primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];161 -> 169[label="",style="solid", color="black", weight=3];
10.65/4.20	162 -> 160[label="",style="dashed", color="red", weight=0];
10.65/4.20	162[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="magenta"];163[label="Pos (primMulNat yu300 yu600)",fontsize=16,color="green",shape="box"];163 -> 170[label="",style="dashed", color="green", weight=3];
10.65/4.20	164[label="Neg (primMulNat yu300 yu600)",fontsize=16,color="green",shape="box"];164 -> 171[label="",style="dashed", color="green", weight=3];
10.65/4.20	165[label="Neg (primMulNat yu300 yu600)",fontsize=16,color="green",shape="box"];165 -> 172[label="",style="dashed", color="green", weight=3];
10.65/4.20	166[label="Pos (primMulNat yu300 yu600)",fontsize=16,color="green",shape="box"];166 -> 173[label="",style="dashed", color="green", weight=3];
10.65/4.20	167[label="primFloatEncodePower1 (Pos (Succ yu400) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];167 -> 174[label="",style="solid", color="black", weight=3];
10.65/4.20	168[label="doubleToFloat (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];168 -> 175[label="",style="solid", color="black", weight=3];
10.65/4.20	169[label="primFloatEncodePower1 (Neg (Succ yu400) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];169 -> 176[label="",style="solid", color="black", weight=3];
10.65/4.20	170[label="primMulNat yu300 yu600",fontsize=16,color="burlywood",shape="triangle"];282[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];170 -> 282[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	282 -> 177[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	283[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];170 -> 283[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	283 -> 178[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	171 -> 170[label="",style="dashed", color="red", weight=0];
10.65/4.20	171[label="primMulNat yu300 yu600",fontsize=16,color="magenta"];171 -> 179[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	172 -> 170[label="",style="dashed", color="red", weight=0];
10.65/4.20	172[label="primMulNat yu300 yu600",fontsize=16,color="magenta"];172 -> 180[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	173 -> 170[label="",style="dashed", color="red", weight=0];
10.65/4.20	173[label="primMulNat yu300 yu600",fontsize=16,color="magenta"];173 -> 181[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	173 -> 182[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	174[label="primFloatEncodePower1 (compare (Pos (Succ yu400)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];174 -> 183[label="",style="solid", color="black", weight=3];
10.65/4.20	175[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];176[label="primFloatEncodePower1 (compare (Neg (Succ yu400)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];176 -> 184[label="",style="solid", color="black", weight=3];
10.65/4.20	177[label="primMulNat (Succ yu3000) yu600",fontsize=16,color="burlywood",shape="box"];284[label="yu600/Succ yu6000",fontsize=10,color="white",style="solid",shape="box"];177 -> 284[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	284 -> 185[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	285[label="yu600/Zero",fontsize=10,color="white",style="solid",shape="box"];177 -> 285[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	285 -> 186[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	178[label="primMulNat Zero yu600",fontsize=16,color="burlywood",shape="box"];286[label="yu600/Succ yu6000",fontsize=10,color="white",style="solid",shape="box"];178 -> 286[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	286 -> 187[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	287[label="yu600/Zero",fontsize=10,color="white",style="solid",shape="box"];178 -> 287[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	287 -> 188[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	179[label="yu600",fontsize=16,color="green",shape="box"];180[label="yu300",fontsize=16,color="green",shape="box"];181[label="yu600",fontsize=16,color="green",shape="box"];182[label="yu300",fontsize=16,color="green",shape="box"];183[label="primFloatEncodePower1 (not (compare (Pos (Succ yu400)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];183 -> 189[label="",style="solid", color="black", weight=3];
10.65/4.20	184[label="primFloatEncodePower1 (not (compare (Neg (Succ yu400)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];184 -> 190[label="",style="solid", color="black", weight=3];
10.65/4.20	185[label="primMulNat (Succ yu3000) (Succ yu6000)",fontsize=16,color="black",shape="box"];185 -> 191[label="",style="solid", color="black", weight=3];
10.65/4.20	186[label="primMulNat (Succ yu3000) Zero",fontsize=16,color="black",shape="box"];186 -> 192[label="",style="solid", color="black", weight=3];
10.65/4.20	187[label="primMulNat Zero (Succ yu6000)",fontsize=16,color="black",shape="box"];187 -> 193[label="",style="solid", color="black", weight=3];
10.65/4.20	188[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];188 -> 194[label="",style="solid", color="black", weight=3];
10.65/4.20	189[label="primFloatEncodePower1 (not (primCmpInt (Pos (Succ yu400)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];189 -> 195[label="",style="solid", color="black", weight=3];
10.65/4.20	190[label="primFloatEncodePower1 (not (primCmpInt (Neg (Succ yu400)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];190 -> 196[label="",style="solid", color="black", weight=3];
10.65/4.20	191 -> 197[label="",style="dashed", color="red", weight=0];
10.65/4.20	191[label="primPlusNat (primMulNat yu3000 (Succ yu6000)) (Succ yu6000)",fontsize=16,color="magenta"];191 -> 198[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	192[label="Zero",fontsize=16,color="green",shape="box"];193[label="Zero",fontsize=16,color="green",shape="box"];194[label="Zero",fontsize=16,color="green",shape="box"];195[label="primFloatEncodePower1 (not (primCmpNat (Succ yu400) (Succ Zero) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="black",shape="box"];195 -> 199[label="",style="solid", color="black", weight=3];
10.65/4.20	196[label="primFloatEncodePower1 (not (LT == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];196 -> 200[label="",style="solid", color="black", weight=3];
10.65/4.20	198 -> 170[label="",style="dashed", color="red", weight=0];
10.65/4.20	198[label="primMulNat yu3000 (Succ yu6000)",fontsize=16,color="magenta"];198 -> 201[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	198 -> 202[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	197[label="primPlusNat yu7 (Succ yu6000)",fontsize=16,color="burlywood",shape="triangle"];288[label="yu7/Succ yu70",fontsize=10,color="white",style="solid",shape="box"];197 -> 288[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	288 -> 203[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	289[label="yu7/Zero",fontsize=10,color="white",style="solid",shape="box"];197 -> 289[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	289 -> 204[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	199[label="primFloatEncodePower1 (not (primCmpNat yu400 Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yu400))",fontsize=16,color="burlywood",shape="box"];290[label="yu400/Succ yu4000",fontsize=10,color="white",style="solid",shape="box"];199 -> 290[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	290 -> 205[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	291[label="yu400/Zero",fontsize=10,color="white",style="solid",shape="box"];199 -> 291[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	291 -> 206[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	200[label="primFloatEncodePower1 (not True) (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];200 -> 207[label="",style="solid", color="black", weight=3];
10.65/4.20	201[label="Succ yu6000",fontsize=16,color="green",shape="box"];202[label="yu3000",fontsize=16,color="green",shape="box"];203[label="primPlusNat (Succ yu70) (Succ yu6000)",fontsize=16,color="black",shape="box"];203 -> 208[label="",style="solid", color="black", weight=3];
10.65/4.20	204[label="primPlusNat Zero (Succ yu6000)",fontsize=16,color="black",shape="box"];204 -> 209[label="",style="solid", color="black", weight=3];
10.65/4.20	205[label="primFloatEncodePower1 (not (primCmpNat (Succ yu4000) Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)))",fontsize=16,color="black",shape="box"];205 -> 210[label="",style="solid", color="black", weight=3];
10.65/4.20	206[label="primFloatEncodePower1 (not (primCmpNat Zero Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];206 -> 211[label="",style="solid", color="black", weight=3];
10.65/4.20	207[label="primFloatEncodePower1 False (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];207 -> 212[label="",style="solid", color="black", weight=3];
10.65/4.20	208[label="Succ (Succ (primPlusNat yu70 yu6000))",fontsize=16,color="green",shape="box"];208 -> 213[label="",style="dashed", color="green", weight=3];
10.65/4.20	209[label="Succ yu6000",fontsize=16,color="green",shape="box"];210[label="primFloatEncodePower1 (not (GT == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)))",fontsize=16,color="black",shape="box"];210 -> 214[label="",style="solid", color="black", weight=3];
10.65/4.20	211[label="primFloatEncodePower1 (not (EQ == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];211 -> 215[label="",style="solid", color="black", weight=3];
10.65/4.20	212[label="primFloatEncodePower0 (Pos (Succ (Succ Zero))) (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];212 -> 216[label="",style="solid", color="black", weight=3];
10.65/4.20	213[label="primPlusNat yu70 yu6000",fontsize=16,color="burlywood",shape="triangle"];292[label="yu70/Succ yu700",fontsize=10,color="white",style="solid",shape="box"];213 -> 292[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	292 -> 217[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	293[label="yu70/Zero",fontsize=10,color="white",style="solid",shape="box"];213 -> 293[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	293 -> 218[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	214[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)))",fontsize=16,color="black",shape="box"];214 -> 219[label="",style="solid", color="black", weight=3];
10.65/4.20	215[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];215 -> 220[label="",style="solid", color="black", weight=3];
10.65/4.20	216 -> 221[label="",style="dashed", color="red", weight=0];
10.65/4.20	216[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) / primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yu400))",fontsize=16,color="magenta"];216 -> 222[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	216 -> 223[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	217[label="primPlusNat (Succ yu700) yu6000",fontsize=16,color="burlywood",shape="box"];294[label="yu6000/Succ yu60000",fontsize=10,color="white",style="solid",shape="box"];217 -> 294[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	294 -> 224[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	295[label="yu6000/Zero",fontsize=10,color="white",style="solid",shape="box"];217 -> 295[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	295 -> 225[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	218[label="primPlusNat Zero yu6000",fontsize=16,color="burlywood",shape="box"];296[label="yu6000/Succ yu60000",fontsize=10,color="white",style="solid",shape="box"];218 -> 296[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	296 -> 226[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	297[label="yu6000/Zero",fontsize=10,color="white",style="solid",shape="box"];218 -> 297[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	297 -> 227[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	219[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)))",fontsize=16,color="black",shape="box"];219 -> 228[label="",style="solid", color="black", weight=3];
10.65/4.20	220[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];220 -> 229[label="",style="solid", color="black", weight=3];
10.65/4.20	222 -> 160[label="",style="dashed", color="red", weight=0];
10.65/4.20	222[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="magenta"];223 -> 88[label="",style="dashed", color="red", weight=0];
10.65/4.20	223[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yu400))",fontsize=16,color="magenta"];223 -> 230[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	221[label="yu9 / yu8",fontsize=16,color="black",shape="triangle"];221 -> 231[label="",style="solid", color="black", weight=3];
10.65/4.20	224[label="primPlusNat (Succ yu700) (Succ yu60000)",fontsize=16,color="black",shape="box"];224 -> 232[label="",style="solid", color="black", weight=3];
10.65/4.20	225[label="primPlusNat (Succ yu700) Zero",fontsize=16,color="black",shape="box"];225 -> 233[label="",style="solid", color="black", weight=3];
10.65/4.20	226[label="primPlusNat Zero (Succ yu60000)",fontsize=16,color="black",shape="box"];226 -> 234[label="",style="solid", color="black", weight=3];
10.65/4.20	227[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];227 -> 235[label="",style="solid", color="black", weight=3];
10.65/4.20	228 -> 236[label="",style="dashed", color="red", weight=0];
10.65/4.20	228[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)) - Pos (Succ Zero))",fontsize=16,color="magenta"];228 -> 237[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	229 -> 236[label="",style="dashed", color="red", weight=0];
10.65/4.20	229[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="magenta"];229 -> 238[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	230[label="`negate` Neg (Succ yu400)",fontsize=16,color="black",shape="box"];230 -> 239[label="",style="solid", color="black", weight=3];
10.65/4.20	231[label="primDivFloat yu9 yu8",fontsize=16,color="burlywood",shape="box"];298[label="yu9/Float yu90 yu91",fontsize=10,color="white",style="solid",shape="box"];231 -> 298[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	298 -> 240[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	232[label="Succ (Succ (primPlusNat yu700 yu60000))",fontsize=16,color="green",shape="box"];232 -> 241[label="",style="dashed", color="green", weight=3];
10.65/4.20	233[label="Succ yu700",fontsize=16,color="green",shape="box"];234[label="Succ yu60000",fontsize=16,color="green",shape="box"];235[label="Zero",fontsize=16,color="green",shape="box"];237 -> 88[label="",style="dashed", color="red", weight=0];
10.65/4.20	237[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yu4000)) - Pos (Succ Zero))",fontsize=16,color="magenta"];237 -> 242[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	236[label="fromInt (Pos (Succ (Succ Zero))) * yu10",fontsize=16,color="black",shape="triangle"];236 -> 243[label="",style="solid", color="black", weight=3];
10.65/4.20	238 -> 88[label="",style="dashed", color="red", weight=0];
10.65/4.20	238[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="magenta"];238 -> 244[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	239[label="primNegInt (Neg (Succ yu400))",fontsize=16,color="black",shape="box"];239 -> 245[label="",style="solid", color="black", weight=3];
10.65/4.20	240[label="primDivFloat (Float yu90 yu91) yu8",fontsize=16,color="burlywood",shape="box"];299[label="yu8/Float yu80 yu81",fontsize=10,color="white",style="solid",shape="box"];240 -> 299[label="",style="solid", color="burlywood", weight=9];
10.65/4.20	299 -> 246[label="",style="solid", color="burlywood", weight=3];
10.65/4.20	241 -> 213[label="",style="dashed", color="red", weight=0];
10.65/4.20	241[label="primPlusNat yu700 yu60000",fontsize=16,color="magenta"];241 -> 247[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	241 -> 248[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	242[label="Pos (Succ (Succ yu4000)) - Pos (Succ Zero)",fontsize=16,color="black",shape="box"];242 -> 249[label="",style="solid", color="black", weight=3];
10.65/4.20	243[label="primMulFloat (fromInt (Pos (Succ (Succ Zero)))) yu10",fontsize=16,color="black",shape="box"];243 -> 250[label="",style="solid", color="black", weight=3];
10.65/4.20	244[label="Pos (Succ Zero) - Pos (Succ Zero)",fontsize=16,color="black",shape="box"];244 -> 251[label="",style="solid", color="black", weight=3];
10.65/4.20	245[label="Pos (Succ yu400)",fontsize=16,color="green",shape="box"];246[label="primDivFloat (Float yu90 yu91) (Float yu80 yu81)",fontsize=16,color="black",shape="box"];246 -> 252[label="",style="solid", color="black", weight=3];
10.65/4.20	247[label="yu60000",fontsize=16,color="green",shape="box"];248[label="yu700",fontsize=16,color="green",shape="box"];249[label="primMinusInt (Pos (Succ (Succ yu4000))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];249 -> 253[label="",style="solid", color="black", weight=3];
10.65/4.20	250[label="primMulFloat (primIntToFloat (Pos (Succ (Succ Zero)))) yu10",fontsize=16,color="black",shape="box"];250 -> 254[label="",style="solid", color="black", weight=3];
10.65/4.20	251[label="primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];251 -> 255[label="",style="solid", color="black", weight=3];
10.65/4.20	252[label="Float (yu90 * yu81) (yu91 * yu80)",fontsize=16,color="green",shape="box"];252 -> 256[label="",style="dashed", color="green", weight=3];
10.65/4.20	252 -> 257[label="",style="dashed", color="green", weight=3];
10.65/4.20	253[label="primMinusNat (Succ (Succ yu4000)) (Succ Zero)",fontsize=16,color="black",shape="box"];253 -> 258[label="",style="solid", color="black", weight=3];
10.65/4.20	254 -> 87[label="",style="dashed", color="red", weight=0];
10.65/4.20	254[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) yu10",fontsize=16,color="magenta"];254 -> 259[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	254 -> 260[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	255[label="primMinusNat (Succ Zero) (Succ Zero)",fontsize=16,color="black",shape="box"];255 -> 261[label="",style="solid", color="black", weight=3];
10.65/4.20	256 -> 138[label="",style="dashed", color="red", weight=0];
10.65/4.20	256[label="yu90 * yu81",fontsize=16,color="magenta"];256 -> 262[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	256 -> 263[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	257 -> 138[label="",style="dashed", color="red", weight=0];
10.65/4.20	257[label="yu91 * yu80",fontsize=16,color="magenta"];257 -> 264[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	257 -> 265[label="",style="dashed", color="magenta", weight=3];
10.65/4.20	258[label="primMinusNat (Succ yu4000) Zero",fontsize=16,color="black",shape="box"];258 -> 266[label="",style="solid", color="black", weight=3];
10.65/4.20	259[label="yu10",fontsize=16,color="green",shape="box"];260[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];261[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];261 -> 267[label="",style="solid", color="black", weight=3];
10.65/4.20	262[label="yu81",fontsize=16,color="green",shape="box"];263[label="yu90",fontsize=16,color="green",shape="box"];264[label="yu80",fontsize=16,color="green",shape="box"];265[label="yu91",fontsize=16,color="green",shape="box"];266[label="Pos (Succ yu4000)",fontsize=16,color="green",shape="box"];267[label="Pos Zero",fontsize=16,color="green",shape="box"];}
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(10)
10.65/4.20	Complex Obligation (AND)
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(11)
10.65/4.20	Obligation:
10.65/4.20	Q DP problem:
10.65/4.20	The TRS P consists of the following rules:
10.65/4.20	
10.65/4.20	   new_primMulNat(Succ(yu3000), Succ(yu6000)) -> new_primMulNat(yu3000, Succ(yu6000))
10.65/4.20	
10.65/4.20	R is empty.
10.65/4.20	Q is empty.
10.65/4.20	We have to consider all minimal (P,Q,R)-chains.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(12) QDPSizeChangeProof (EQUIVALENT)
10.65/4.20	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. 
10.65/4.20	
10.65/4.20	From the DPs we obtained the following set of size-change graphs:
10.65/4.20	*new_primMulNat(Succ(yu3000), Succ(yu6000)) -> new_primMulNat(yu3000, Succ(yu6000))
10.65/4.20	The graph contains the following edges 1 > 1, 2 >= 2
10.65/4.20	
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(13)
10.65/4.20	YES
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(14)
10.65/4.20	Obligation:
10.65/4.20	Q DP problem:
10.65/4.20	The TRS P consists of the following rules:
10.65/4.20	
10.65/4.20	   new_primPlusNat(Succ(yu700), Succ(yu60000)) -> new_primPlusNat(yu700, yu60000)
10.65/4.20	
10.65/4.20	R is empty.
10.65/4.20	Q is empty.
10.65/4.20	We have to consider all minimal (P,Q,R)-chains.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(15) QDPSizeChangeProof (EQUIVALENT)
10.65/4.20	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. 
10.65/4.20	
10.65/4.20	From the DPs we obtained the following set of size-change graphs:
10.65/4.20	*new_primPlusNat(Succ(yu700), Succ(yu60000)) -> new_primPlusNat(yu700, yu60000)
10.65/4.20	The graph contains the following edges 1 > 1, 2 > 2
10.65/4.20	
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(16)
10.65/4.20	YES
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(17)
10.65/4.20	Obligation:
10.65/4.20	Q DP problem:
10.65/4.20	The TRS P consists of the following rules:
10.65/4.20	
10.65/4.20	   new_primFloatEncodePower(Pos(Succ(Zero))) -> new_primFloatEncodePower(Pos(Zero))
10.65/4.20	   new_primFloatEncodePower(Neg(Succ(yu400))) -> new_primFloatEncodePower(Pos(Succ(yu400)))
10.65/4.20	   new_primFloatEncodePower(Pos(Succ(Succ(yu4000)))) -> new_primFloatEncodePower(Pos(Succ(yu4000)))
10.65/4.20	
10.65/4.20	R is empty.
10.65/4.20	Q is empty.
10.65/4.20	We have to consider all minimal (P,Q,R)-chains.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(18) DependencyGraphProof (EQUIVALENT)
10.65/4.20	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(19)
10.65/4.20	Obligation:
10.65/4.20	Q DP problem:
10.65/4.20	The TRS P consists of the following rules:
10.65/4.20	
10.65/4.20	   new_primFloatEncodePower(Pos(Succ(Succ(yu4000)))) -> new_primFloatEncodePower(Pos(Succ(yu4000)))
10.65/4.20	
10.65/4.20	R is empty.
10.65/4.20	Q is empty.
10.65/4.20	We have to consider all minimal (P,Q,R)-chains.
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(20) QDPSizeChangeProof (EQUIVALENT)
10.65/4.20	We used the following order and afs together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
10.65/4.20	
10.65/4.20	Order:EMB rules!
10.65/4.20	
10.65/4.20	AFS: 
10.65/4.20	Pos(x1)  =  x1
10.65/4.20	
10.65/4.20	Succ(x1)  =  Succ(x1)
10.65/4.20	
10.65/4.20	
10.65/4.20	
10.65/4.20	
10.65/4.20	
10.65/4.20	From the DPs we obtained the following set of size-change graphs:
10.65/4.20	*new_primFloatEncodePower(Pos(Succ(Succ(yu4000)))) -> new_primFloatEncodePower(Pos(Succ(yu4000))) (allowed arguments on rhs = {1})
10.65/4.20	The graph contains the following edges 1 > 1
10.65/4.20	
10.65/4.20	
10.65/4.20	
10.65/4.20	We oriented the following set of usable rules [AAECC05,FROCOS05].
10.65/4.20	none
10.65/4.20	
10.65/4.20	----------------------------------------
10.65/4.20	
10.65/4.20	(21)
10.65/4.20	YES
10.65/4.24	EOF