10.79/4.47	YES
12.94/5.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.94/5.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.94/5.08	
12.94/5.08	
12.94/5.08	H-Termination with start terms of the given HASKELL could be proven:
12.94/5.08	
12.94/5.08	(0) HASKELL
12.94/5.08	(1) LR [EQUIVALENT, 0 ms]
12.94/5.08	(2) HASKELL
12.94/5.08	(3) BR [EQUIVALENT, 0 ms]
12.94/5.08	(4) HASKELL
12.94/5.08	(5) COR [EQUIVALENT, 0 ms]
12.94/5.08	(6) HASKELL
12.94/5.08	(7) LetRed [EQUIVALENT, 0 ms]
12.94/5.08	(8) HASKELL
12.94/5.08	(9) NumRed [SOUND, 0 ms]
12.94/5.08	(10) HASKELL
12.94/5.08	(11) Narrow [SOUND, 0 ms]
12.94/5.08	(12) AND
12.94/5.08	    (13) QDP
12.94/5.08	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.08	        (15) YES
12.94/5.08	    (16) QDP
12.94/5.08	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.08	        (18) YES
12.94/5.08	    (19) QDP
12.94/5.08	        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
12.94/5.08	        (21) QDP
12.94/5.08	        (22) TransformationProof [EQUIVALENT, 0 ms]
12.94/5.08	        (23) QDP
12.94/5.08	        (24) UsableRulesProof [EQUIVALENT, 0 ms]
12.94/5.08	        (25) QDP
12.94/5.08	        (26) QReductionProof [EQUIVALENT, 0 ms]
12.94/5.08	        (27) QDP
12.94/5.08	        (28) TransformationProof [EQUIVALENT, 0 ms]
12.94/5.08	        (29) QDP
12.94/5.08	        (30) QDPPairToRuleProof [EQUIVALENT, 0 ms]
12.94/5.08	        (31) AND
12.94/5.08	            (32) QDP
12.94/5.08	                (33) DependencyGraphProof [EQUIVALENT, 0 ms]
12.94/5.08	                (34) QDP
12.94/5.08	                (35) TransformationProof [EQUIVALENT, 0 ms]
12.94/5.08	                (36) QDP
12.94/5.08	                (37) TransformationProof [EQUIVALENT, 0 ms]
12.94/5.08	                (38) QDP
12.94/5.08	                (39) DependencyGraphProof [EQUIVALENT, 0 ms]
12.94/5.08	                (40) QDP
12.94/5.08	                (41) UsableRulesProof [EQUIVALENT, 0 ms]
12.94/5.08	                (42) QDP
12.94/5.08	                (43) QReductionProof [EQUIVALENT, 0 ms]
12.94/5.08	                (44) QDP
12.94/5.08	                (45) TransformationProof [EQUIVALENT, 0 ms]
12.94/5.08	                (46) QDP
12.94/5.08	                (47) UsableRulesProof [EQUIVALENT, 0 ms]
12.94/5.08	                (48) QDP
12.94/5.08	                (49) QReductionProof [EQUIVALENT, 0 ms]
12.94/5.08	                (50) QDP
12.94/5.08	                (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.08	                (52) YES
12.94/5.08	            (53) QDP
12.94/5.08	                (54) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.94/5.08	                (55) YES
12.94/5.08	
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(0)
12.94/5.08	Obligation:
12.94/5.08	mainModule Main 
12.94/5.08	module Main where {
12.94/5.08	import qualified Prelude;
12.94/5.08	}
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(1) LR (EQUIVALENT)
12.94/5.08	Lambda Reductions:
12.94/5.08	The following Lambda expression
12.94/5.08	"\(m,_)->m"
12.94/5.08	is transformed to
12.94/5.08	"m0 (m,_) = m;
12.94/5.08	"
12.94/5.08	The following Lambda expression
12.94/5.08	"\(_,n)->n"
12.94/5.08	is transformed to
12.94/5.08	"n0 (_,n) = n;
12.94/5.08	"
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(2)
12.94/5.08	Obligation:
12.94/5.08	mainModule Main 
12.94/5.08	module Main where {
12.94/5.08	import qualified Prelude;
12.94/5.08	}
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(3) BR (EQUIVALENT)
12.94/5.08	Replaced joker patterns by fresh variables and removed binding patterns.
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(4)
12.94/5.08	Obligation:
12.94/5.08	mainModule Main 
12.94/5.08	module Main where {
12.94/5.08	import qualified Prelude;
12.94/5.08	}
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(5) COR (EQUIVALENT)
12.94/5.08	Cond Reductions:
12.94/5.08	The following Function with conditions
12.94/5.08	"undefined |Falseundefined;
12.94/5.08	"
12.94/5.08	is transformed to
12.94/5.08	"undefined  = undefined1;
12.94/5.08	"
12.94/5.08	"undefined0 True = undefined;
12.94/5.08	"
12.94/5.08	"undefined1  = undefined0 False;
12.94/5.08	"
12.94/5.08	The following Function with conditions
12.94/5.08	"power wv 0 = 1.0;
12.94/5.08	power x ww@(y+1) = fromInt x * power x y;
12.94/5.08	power x y = 1.0 / power x (`negate` y);
12.94/5.08	"
12.94/5.08	is transformed to
12.94/5.08	"power wv xw = power4 wv xw;
12.94/5.08	power x ww = power2 x ww;
12.94/5.08	power x y = power0 x y;
12.94/5.08	"
12.94/5.08	"power0 x y = 1.0 / power x (`negate` y);
12.94/5.08	"
12.94/5.08	"power1 True x ww = fromInt x * power x (ww - 1);
12.94/5.08	power1 wx wy wz = power0 wy wz;
12.94/5.08	"
12.94/5.08	"power2 x ww = power1 (ww >= 1) x ww;
12.94/5.08	power2 xu xv = power0 xu xv;
12.94/5.08	"
12.94/5.08	"power3 True wv xw = 1.0;
12.94/5.08	power3 xx xy xz = power2 xy xz;
12.94/5.08	"
12.94/5.08	"power4 wv xw = power3 (xw == 0) wv xw;
12.94/5.08	power4 yu yv = power2 yu yv;
12.94/5.08	"
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(6)
12.94/5.08	Obligation:
12.94/5.08	mainModule Main 
12.94/5.08	module Main where {
12.94/5.08	import qualified Prelude;
12.94/5.08	}
12.94/5.08	
12.94/5.08	----------------------------------------
12.94/5.08	
12.94/5.08	(7) LetRed (EQUIVALENT)
12.94/5.08	Let/Where Reductions:
12.94/5.08	The bindings of the following Let/Where expression
12.94/5.08	"encodeFloat m (n + k) where {
12.94/5.08	m  = m0 vu12;
12.94/5.08	;
12.94/5.08	m0 (m,vw) = m;
12.94/5.08	;
12.94/5.08	n  = n0 vu12;
12.94/5.08	;
12.94/5.08	n0 (vv,n) = n;
12.94/5.08	;
12.94/5.08	vu12  = decodeFloat x;
12.94/5.08	} 
12.94/5.08	"
12.94/5.08	are unpacked to the following functions on top level
12.94/5.08	"scaleFloatM yw = scaleFloatM0 yw (scaleFloatVu12 yw);
12.94/5.08	"
12.94/5.08	"scaleFloatVu12 yw = decodeFloat yw;
12.94/5.09	"
12.94/5.09	"scaleFloatN0 yw (vv,n) = n;
12.94/5.09	"
12.94/5.09	"scaleFloatM0 yw (m,vw) = m;
12.94/5.09	"
12.94/5.09	"scaleFloatN yw = scaleFloatN0 yw (scaleFloatVu12 yw);
12.94/5.09	"
12.94/5.09	The bindings of the following Let/Where expression
12.94/5.09	"fromInteger x * power 2 y where {
12.94/5.09	power wv xw = power4 wv xw;
12.94/5.09	power x ww = power2 x ww;
12.94/5.09	power x y = power0 x y;
12.94/5.09	;
12.94/5.09	power0 x y = 1.0 / power x (`negate` y);
12.94/5.09	;
12.94/5.09	power1 True x ww = fromInt x * power x (ww - 1);
12.94/5.09	power1 wx wy wz = power0 wy wz;
12.94/5.09	;
12.94/5.09	power2 x ww = power1 (ww >= 1) x ww;
12.94/5.09	power2 xu xv = power0 xu xv;
12.94/5.09	;
12.94/5.09	power3 True wv xw = 1.0;
12.94/5.09	power3 xx xy xz = power2 xy xz;
12.94/5.09	;
12.94/5.09	power4 wv xw = power3 (xw == 0) wv xw;
12.94/5.09	power4 yu yv = power2 yu yv;
12.94/5.09	} 
12.94/5.09	"
12.94/5.09	are unpacked to the following functions on top level
12.94/5.09	"primFloatEncodePower4 wv xw = primFloatEncodePower3 (xw == 0) wv xw;
12.94/5.09	primFloatEncodePower4 yu yv = primFloatEncodePower2 yu yv;
12.94/5.09	"
12.94/5.09	"primFloatEncodePower0 x y = 1.0 / primFloatEncodePower x (`negate` y);
12.94/5.09	"
12.94/5.09	"primFloatEncodePower wv xw = primFloatEncodePower4 wv xw;
12.94/5.09	primFloatEncodePower x ww = primFloatEncodePower2 x ww;
12.94/5.09	primFloatEncodePower x y = primFloatEncodePower0 x y;
12.94/5.09	"
12.94/5.09	"primFloatEncodePower1 True x ww = fromInt x * primFloatEncodePower x (ww - 1);
12.94/5.09	primFloatEncodePower1 wx wy wz = primFloatEncodePower0 wy wz;
12.94/5.09	"
12.94/5.09	"primFloatEncodePower3 True wv xw = 1.0;
12.94/5.09	primFloatEncodePower3 xx xy xz = primFloatEncodePower2 xy xz;
12.94/5.09	"
12.94/5.09	"primFloatEncodePower2 x ww = primFloatEncodePower1 (ww >= 1) x ww;
12.94/5.09	primFloatEncodePower2 xu xv = primFloatEncodePower0 xu xv;
12.94/5.09	"
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(8)
12.94/5.09	Obligation:
12.94/5.09	mainModule Main 
12.94/5.09	module Main where {
12.94/5.09	import qualified Prelude;
12.94/5.09	}
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(9) NumRed (SOUND)
12.94/5.09	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(10)
12.94/5.09	Obligation:
12.94/5.09	mainModule Main 
12.94/5.09	module Main where {
12.94/5.09	import qualified Prelude;
12.94/5.09	}
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(11) Narrow (SOUND)
12.94/5.09	Haskell To QDPs
12.94/5.09	
12.94/5.09	digraph dp_graph {
12.94/5.09	node [outthreshold=100, inthreshold=100];1[label="scaleFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.94/5.09	3[label="scaleFloat yx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.94/5.09	4[label="scaleFloat yx3 yx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.94/5.09	5[label="encodeFloat (scaleFloatM yx4) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
12.94/5.09	6[label="primFloatEncode (scaleFloatM yx4) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
12.94/5.09	7[label="fromInteger (scaleFloatM yx4) * primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
12.94/5.09	8[label="primMulFloat (fromInteger (scaleFloatM yx4)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
12.94/5.09	9[label="primMulFloat (primIntegerToFloat (scaleFloatM yx4)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
12.94/5.09	10 -> 15[label="",style="dashed", color="red", weight=0];
12.94/5.09	10[label="primMulFloat (primIntegerToFloat (scaleFloatM0 yx4 (scaleFloatVu12 yx4))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="magenta"];10 -> 16[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	16[label="scaleFloatVu12 yx4",fontsize=16,color="black",shape="triangle"];16 -> 21[label="",style="solid", color="black", weight=3];
12.94/5.09	15[label="primMulFloat (primIntegerToFloat (scaleFloatM0 yx4 yx5)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="burlywood",shape="triangle"];505[label="yx5/(yx50,yx51)",fontsize=10,color="white",style="solid",shape="box"];15 -> 505[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	505 -> 22[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	21[label="decodeFloat yx4",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
12.94/5.09	22[label="primMulFloat (primIntegerToFloat (scaleFloatM0 yx4 (yx50,yx51))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
12.94/5.09	24[label="primFloatDecode yx4",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
12.94/5.09	25[label="primMulFloat (primIntegerToFloat yx50) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="burlywood",shape="box"];506[label="yx50/Integer yx500",fontsize=10,color="white",style="solid",shape="box"];25 -> 506[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	506 -> 27[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	26[label="terminator yx4",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
12.94/5.09	27[label="primMulFloat (primIntegerToFloat (Integer yx500)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
12.94/5.09	28[label="ter1m yx4",fontsize=16,color="green",shape="box"];28 -> 30[label="",style="dashed", color="green", weight=3];
12.94/5.09	29[label="primMulFloat (primIntToFloat yx500) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
12.94/5.09	30[label="yx4",fontsize=16,color="green",shape="box"];31 -> 200[label="",style="dashed", color="red", weight=0];
12.94/5.09	31[label="primMulFloat (Float yx500 (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3))",fontsize=16,color="magenta"];31 -> 201[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	201[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];201 -> 294[label="",style="solid", color="black", weight=3];
12.94/5.09	200[label="primMulFloat (Float yx500 (Pos (Succ Zero))) yx10",fontsize=16,color="burlywood",shape="triangle"];507[label="yx10/Float yx100 yx101",fontsize=10,color="white",style="solid",shape="box"];200 -> 507[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	507 -> 295[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	294[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];294 -> 296[label="",style="solid", color="black", weight=3];
12.94/5.09	295[label="primMulFloat (Float yx500 (Pos (Succ Zero))) (Float yx100 yx101)",fontsize=16,color="black",shape="box"];295 -> 297[label="",style="solid", color="black", weight=3];
12.94/5.09	296[label="primFloatEncodePower3 (scaleFloatN yx4 + yx3 == Pos Zero) (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];296 -> 298[label="",style="solid", color="black", weight=3];
12.94/5.09	297[label="Float (yx500 * yx100) (Pos (Succ Zero) * yx101)",fontsize=16,color="green",shape="box"];297 -> 299[label="",style="dashed", color="green", weight=3];
12.94/5.09	297 -> 300[label="",style="dashed", color="green", weight=3];
12.94/5.09	298[label="primFloatEncodePower3 (primEqInt (scaleFloatN yx4 + yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (scaleFloatN yx4 + yx3)",fontsize=16,color="black",shape="box"];298 -> 301[label="",style="solid", color="black", weight=3];
12.94/5.09	299[label="yx500 * yx100",fontsize=16,color="black",shape="triangle"];299 -> 302[label="",style="solid", color="black", weight=3];
12.94/5.09	300 -> 299[label="",style="dashed", color="red", weight=0];
12.94/5.09	300[label="Pos (Succ Zero) * yx101",fontsize=16,color="magenta"];300 -> 303[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	300 -> 304[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	301[label="primFloatEncodePower3 (primEqInt (primPlusInt (scaleFloatN yx4) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (scaleFloatN yx4) yx3)",fontsize=16,color="black",shape="box"];301 -> 305[label="",style="solid", color="black", weight=3];
12.94/5.09	302[label="primMulInt yx500 yx100",fontsize=16,color="burlywood",shape="box"];508[label="yx500/Pos yx5000",fontsize=10,color="white",style="solid",shape="box"];302 -> 508[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	508 -> 306[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	509[label="yx500/Neg yx5000",fontsize=10,color="white",style="solid",shape="box"];302 -> 509[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	509 -> 307[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	303[label="yx101",fontsize=16,color="green",shape="box"];304[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];305 -> 308[label="",style="dashed", color="red", weight=0];
12.94/5.09	305[label="primFloatEncodePower3 (primEqInt (primPlusInt (scaleFloatN0 yx4 (scaleFloatVu12 yx4)) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (scaleFloatN0 yx4 (scaleFloatVu12 yx4)) yx3)",fontsize=16,color="magenta"];305 -> 309[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	305 -> 310[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	306[label="primMulInt (Pos yx5000) yx100",fontsize=16,color="burlywood",shape="box"];510[label="yx100/Pos yx1000",fontsize=10,color="white",style="solid",shape="box"];306 -> 510[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	510 -> 311[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	511[label="yx100/Neg yx1000",fontsize=10,color="white",style="solid",shape="box"];306 -> 511[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	511 -> 312[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	307[label="primMulInt (Neg yx5000) yx100",fontsize=16,color="burlywood",shape="box"];512[label="yx100/Pos yx1000",fontsize=10,color="white",style="solid",shape="box"];307 -> 512[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	512 -> 313[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	513[label="yx100/Neg yx1000",fontsize=10,color="white",style="solid",shape="box"];307 -> 513[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	513 -> 314[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	309 -> 16[label="",style="dashed", color="red", weight=0];
12.94/5.09	309[label="scaleFloatVu12 yx4",fontsize=16,color="magenta"];310 -> 16[label="",style="dashed", color="red", weight=0];
12.94/5.09	310[label="scaleFloatVu12 yx4",fontsize=16,color="magenta"];308[label="primFloatEncodePower3 (primEqInt (primPlusInt (scaleFloatN0 yx4 yx12) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (scaleFloatN0 yx4 yx11) yx3)",fontsize=16,color="burlywood",shape="triangle"];514[label="yx12/(yx120,yx121)",fontsize=10,color="white",style="solid",shape="box"];308 -> 514[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	514 -> 315[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	311[label="primMulInt (Pos yx5000) (Pos yx1000)",fontsize=16,color="black",shape="box"];311 -> 316[label="",style="solid", color="black", weight=3];
12.94/5.09	312[label="primMulInt (Pos yx5000) (Neg yx1000)",fontsize=16,color="black",shape="box"];312 -> 317[label="",style="solid", color="black", weight=3];
12.94/5.09	313[label="primMulInt (Neg yx5000) (Pos yx1000)",fontsize=16,color="black",shape="box"];313 -> 318[label="",style="solid", color="black", weight=3];
12.94/5.09	314[label="primMulInt (Neg yx5000) (Neg yx1000)",fontsize=16,color="black",shape="box"];314 -> 319[label="",style="solid", color="black", weight=3];
12.94/5.09	315[label="primFloatEncodePower3 (primEqInt (primPlusInt (scaleFloatN0 yx4 (yx120,yx121)) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (scaleFloatN0 yx4 yx11) yx3)",fontsize=16,color="black",shape="box"];315 -> 320[label="",style="solid", color="black", weight=3];
12.94/5.09	316[label="Pos (primMulNat yx5000 yx1000)",fontsize=16,color="green",shape="box"];316 -> 321[label="",style="dashed", color="green", weight=3];
12.94/5.09	317[label="Neg (primMulNat yx5000 yx1000)",fontsize=16,color="green",shape="box"];317 -> 322[label="",style="dashed", color="green", weight=3];
12.94/5.09	318[label="Neg (primMulNat yx5000 yx1000)",fontsize=16,color="green",shape="box"];318 -> 323[label="",style="dashed", color="green", weight=3];
12.94/5.09	319[label="Pos (primMulNat yx5000 yx1000)",fontsize=16,color="green",shape="box"];319 -> 324[label="",style="dashed", color="green", weight=3];
12.94/5.09	320[label="primFloatEncodePower3 (primEqInt (primPlusInt yx121 yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt yx121 yx3)",fontsize=16,color="burlywood",shape="box"];515[label="yx121/Pos yx1210",fontsize=10,color="white",style="solid",shape="box"];320 -> 515[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	515 -> 325[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	516[label="yx121/Neg yx1210",fontsize=10,color="white",style="solid",shape="box"];320 -> 516[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	516 -> 326[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	321[label="primMulNat yx5000 yx1000",fontsize=16,color="burlywood",shape="triangle"];517[label="yx5000/Succ yx50000",fontsize=10,color="white",style="solid",shape="box"];321 -> 517[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	517 -> 327[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	518[label="yx5000/Zero",fontsize=10,color="white",style="solid",shape="box"];321 -> 518[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	518 -> 328[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	322 -> 321[label="",style="dashed", color="red", weight=0];
12.94/5.09	322[label="primMulNat yx5000 yx1000",fontsize=16,color="magenta"];322 -> 329[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	323 -> 321[label="",style="dashed", color="red", weight=0];
12.94/5.09	323[label="primMulNat yx5000 yx1000",fontsize=16,color="magenta"];323 -> 330[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	324 -> 321[label="",style="dashed", color="red", weight=0];
12.94/5.09	324[label="primMulNat yx5000 yx1000",fontsize=16,color="magenta"];324 -> 331[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	324 -> 332[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	325[label="primFloatEncodePower3 (primEqInt (primPlusInt (Pos yx1210) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Pos yx1210) yx3)",fontsize=16,color="burlywood",shape="box"];519[label="yx3/Pos yx30",fontsize=10,color="white",style="solid",shape="box"];325 -> 519[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	519 -> 333[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	520[label="yx3/Neg yx30",fontsize=10,color="white",style="solid",shape="box"];325 -> 520[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	520 -> 334[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	326[label="primFloatEncodePower3 (primEqInt (primPlusInt (Neg yx1210) yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Neg yx1210) yx3)",fontsize=16,color="burlywood",shape="box"];521[label="yx3/Pos yx30",fontsize=10,color="white",style="solid",shape="box"];326 -> 521[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	521 -> 335[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	522[label="yx3/Neg yx30",fontsize=10,color="white",style="solid",shape="box"];326 -> 522[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	522 -> 336[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	327[label="primMulNat (Succ yx50000) yx1000",fontsize=16,color="burlywood",shape="box"];523[label="yx1000/Succ yx10000",fontsize=10,color="white",style="solid",shape="box"];327 -> 523[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	523 -> 337[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	524[label="yx1000/Zero",fontsize=10,color="white",style="solid",shape="box"];327 -> 524[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	524 -> 338[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	328[label="primMulNat Zero yx1000",fontsize=16,color="burlywood",shape="box"];525[label="yx1000/Succ yx10000",fontsize=10,color="white",style="solid",shape="box"];328 -> 525[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	525 -> 339[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	526[label="yx1000/Zero",fontsize=10,color="white",style="solid",shape="box"];328 -> 526[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	526 -> 340[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	329[label="yx1000",fontsize=16,color="green",shape="box"];330[label="yx5000",fontsize=16,color="green",shape="box"];331[label="yx1000",fontsize=16,color="green",shape="box"];332[label="yx5000",fontsize=16,color="green",shape="box"];333[label="primFloatEncodePower3 (primEqInt (primPlusInt (Pos yx1210) (Pos yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Pos yx1210) (Pos yx30))",fontsize=16,color="black",shape="box"];333 -> 341[label="",style="solid", color="black", weight=3];
12.94/5.09	334[label="primFloatEncodePower3 (primEqInt (primPlusInt (Pos yx1210) (Neg yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Pos yx1210) (Neg yx30))",fontsize=16,color="black",shape="box"];334 -> 342[label="",style="solid", color="black", weight=3];
12.94/5.09	335[label="primFloatEncodePower3 (primEqInt (primPlusInt (Neg yx1210) (Pos yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Neg yx1210) (Pos yx30))",fontsize=16,color="black",shape="box"];335 -> 343[label="",style="solid", color="black", weight=3];
12.94/5.09	336[label="primFloatEncodePower3 (primEqInt (primPlusInt (Neg yx1210) (Neg yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primPlusInt (Neg yx1210) (Neg yx30))",fontsize=16,color="black",shape="box"];336 -> 344[label="",style="solid", color="black", weight=3];
12.94/5.09	337[label="primMulNat (Succ yx50000) (Succ yx10000)",fontsize=16,color="black",shape="box"];337 -> 345[label="",style="solid", color="black", weight=3];
12.94/5.09	338[label="primMulNat (Succ yx50000) Zero",fontsize=16,color="black",shape="box"];338 -> 346[label="",style="solid", color="black", weight=3];
12.94/5.09	339[label="primMulNat Zero (Succ yx10000)",fontsize=16,color="black",shape="box"];339 -> 347[label="",style="solid", color="black", weight=3];
12.94/5.09	340[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];340 -> 348[label="",style="solid", color="black", weight=3];
12.94/5.09	341[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat yx1210 yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat yx1210 yx30))",fontsize=16,color="burlywood",shape="box"];527[label="yx1210/Succ yx12100",fontsize=10,color="white",style="solid",shape="box"];341 -> 527[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	527 -> 349[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	528[label="yx1210/Zero",fontsize=10,color="white",style="solid",shape="box"];341 -> 528[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	528 -> 350[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	342[label="primFloatEncodePower3 (primEqInt (primMinusNat yx1210 yx30) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat yx1210 yx30)",fontsize=16,color="burlywood",shape="triangle"];529[label="yx1210/Succ yx12100",fontsize=10,color="white",style="solid",shape="box"];342 -> 529[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	529 -> 351[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	530[label="yx1210/Zero",fontsize=10,color="white",style="solid",shape="box"];342 -> 530[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	530 -> 352[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	343 -> 342[label="",style="dashed", color="red", weight=0];
12.94/5.09	343[label="primFloatEncodePower3 (primEqInt (primMinusNat yx30 yx1210) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat yx30 yx1210)",fontsize=16,color="magenta"];343 -> 353[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	343 -> 354[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	344[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat yx1210 yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat yx1210 yx30))",fontsize=16,color="burlywood",shape="box"];531[label="yx1210/Succ yx12100",fontsize=10,color="white",style="solid",shape="box"];344 -> 531[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	531 -> 355[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	532[label="yx1210/Zero",fontsize=10,color="white",style="solid",shape="box"];344 -> 532[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	532 -> 356[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	345 -> 357[label="",style="dashed", color="red", weight=0];
12.94/5.09	345[label="primPlusNat (primMulNat yx50000 (Succ yx10000)) (Succ yx10000)",fontsize=16,color="magenta"];345 -> 358[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	346[label="Zero",fontsize=16,color="green",shape="box"];347[label="Zero",fontsize=16,color="green",shape="box"];348[label="Zero",fontsize=16,color="green",shape="box"];349[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat (Succ yx12100) yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat (Succ yx12100) yx30))",fontsize=16,color="burlywood",shape="box"];533[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];349 -> 533[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	533 -> 359[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	534[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];349 -> 534[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	534 -> 360[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	350[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat Zero yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat Zero yx30))",fontsize=16,color="burlywood",shape="box"];535[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];350 -> 535[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	535 -> 361[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	536[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];350 -> 536[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	536 -> 362[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	351[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ yx12100) yx30) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ yx12100) yx30)",fontsize=16,color="burlywood",shape="box"];537[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];351 -> 537[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	537 -> 363[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	538[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];351 -> 538[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	538 -> 364[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	352[label="primFloatEncodePower3 (primEqInt (primMinusNat Zero yx30) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat Zero yx30)",fontsize=16,color="burlywood",shape="box"];539[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];352 -> 539[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	539 -> 365[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	540[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];352 -> 540[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	540 -> 366[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	353[label="yx30",fontsize=16,color="green",shape="box"];354[label="yx1210",fontsize=16,color="green",shape="box"];355[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat (Succ yx12100) yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat (Succ yx12100) yx30))",fontsize=16,color="burlywood",shape="box"];541[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];355 -> 541[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	541 -> 367[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	542[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];355 -> 542[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	542 -> 368[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	356[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat Zero yx30)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat Zero yx30))",fontsize=16,color="burlywood",shape="box"];543[label="yx30/Succ yx300",fontsize=10,color="white",style="solid",shape="box"];356 -> 543[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	543 -> 369[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	544[label="yx30/Zero",fontsize=10,color="white",style="solid",shape="box"];356 -> 544[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	544 -> 370[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	358 -> 321[label="",style="dashed", color="red", weight=0];
12.94/5.09	358[label="primMulNat yx50000 (Succ yx10000)",fontsize=16,color="magenta"];358 -> 371[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	358 -> 372[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	357[label="primPlusNat yx13 (Succ yx10000)",fontsize=16,color="burlywood",shape="triangle"];545[label="yx13/Succ yx130",fontsize=10,color="white",style="solid",shape="box"];357 -> 545[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	545 -> 373[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	546[label="yx13/Zero",fontsize=10,color="white",style="solid",shape="box"];357 -> 546[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	546 -> 374[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	359[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat (Succ yx12100) (Succ yx300))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat (Succ yx12100) (Succ yx300)))",fontsize=16,color="black",shape="box"];359 -> 375[label="",style="solid", color="black", weight=3];
12.94/5.09	360[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat (Succ yx12100) Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat (Succ yx12100) Zero))",fontsize=16,color="black",shape="box"];360 -> 376[label="",style="solid", color="black", weight=3];
12.94/5.09	361[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat Zero (Succ yx300))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat Zero (Succ yx300)))",fontsize=16,color="black",shape="box"];361 -> 377[label="",style="solid", color="black", weight=3];
12.94/5.09	362[label="primFloatEncodePower3 (primEqInt (Pos (primPlusNat Zero Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (primPlusNat Zero Zero))",fontsize=16,color="black",shape="box"];362 -> 378[label="",style="solid", color="black", weight=3];
12.94/5.09	363[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ yx12100) (Succ yx300)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ yx12100) (Succ yx300))",fontsize=16,color="black",shape="box"];363 -> 379[label="",style="solid", color="black", weight=3];
12.94/5.09	364[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ yx12100) Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ yx12100) Zero)",fontsize=16,color="black",shape="box"];364 -> 380[label="",style="solid", color="black", weight=3];
12.94/5.09	365[label="primFloatEncodePower3 (primEqInt (primMinusNat Zero (Succ yx300)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat Zero (Succ yx300))",fontsize=16,color="black",shape="box"];365 -> 381[label="",style="solid", color="black", weight=3];
12.94/5.09	366[label="primFloatEncodePower3 (primEqInt (primMinusNat Zero Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat Zero Zero)",fontsize=16,color="black",shape="box"];366 -> 382[label="",style="solid", color="black", weight=3];
12.94/5.09	367[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat (Succ yx12100) (Succ yx300))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat (Succ yx12100) (Succ yx300)))",fontsize=16,color="black",shape="box"];367 -> 383[label="",style="solid", color="black", weight=3];
12.94/5.09	368[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat (Succ yx12100) Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat (Succ yx12100) Zero))",fontsize=16,color="black",shape="box"];368 -> 384[label="",style="solid", color="black", weight=3];
12.94/5.09	369[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat Zero (Succ yx300))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat Zero (Succ yx300)))",fontsize=16,color="black",shape="box"];369 -> 385[label="",style="solid", color="black", weight=3];
12.94/5.09	370[label="primFloatEncodePower3 (primEqInt (Neg (primPlusNat Zero Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (primPlusNat Zero Zero))",fontsize=16,color="black",shape="box"];370 -> 386[label="",style="solid", color="black", weight=3];
12.94/5.09	371[label="Succ yx10000",fontsize=16,color="green",shape="box"];372[label="yx50000",fontsize=16,color="green",shape="box"];373[label="primPlusNat (Succ yx130) (Succ yx10000)",fontsize=16,color="black",shape="box"];373 -> 387[label="",style="solid", color="black", weight=3];
12.94/5.09	374[label="primPlusNat Zero (Succ yx10000)",fontsize=16,color="black",shape="box"];374 -> 388[label="",style="solid", color="black", weight=3];
12.94/5.09	375[label="primFloatEncodePower3 (primEqInt (Pos (Succ (Succ (primPlusNat yx12100 yx300)))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ (primPlusNat yx12100 yx300))))",fontsize=16,color="black",shape="box"];375 -> 389[label="",style="solid", color="black", weight=3];
12.94/5.09	376[label="primFloatEncodePower3 (primEqInt (Pos (Succ yx12100)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="triangle"];376 -> 390[label="",style="solid", color="black", weight=3];
12.94/5.09	377 -> 376[label="",style="dashed", color="red", weight=0];
12.94/5.09	377[label="primFloatEncodePower3 (primEqInt (Pos (Succ yx300)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx300))",fontsize=16,color="magenta"];377 -> 391[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	378[label="primFloatEncodePower3 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="triangle"];378 -> 392[label="",style="solid", color="black", weight=3];
12.94/5.09	379 -> 342[label="",style="dashed", color="red", weight=0];
12.94/5.09	379[label="primFloatEncodePower3 (primEqInt (primMinusNat yx12100 yx300) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat yx12100 yx300)",fontsize=16,color="magenta"];379 -> 393[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	379 -> 394[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	380 -> 376[label="",style="dashed", color="red", weight=0];
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12.94/5.09	382 -> 378[label="",style="dashed", color="red", weight=0];
12.94/5.09	382[label="primFloatEncodePower3 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="magenta"];383 -> 381[label="",style="dashed", color="red", weight=0];
12.94/5.09	383[label="primFloatEncodePower3 (primEqInt (Neg (Succ (Succ (primPlusNat yx12100 yx300)))) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ (Succ (primPlusNat yx12100 yx300))))",fontsize=16,color="magenta"];383 -> 396[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	384 -> 381[label="",style="dashed", color="red", weight=0];
12.94/5.09	384[label="primFloatEncodePower3 (primEqInt (Neg (Succ yx12100)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yx12100))",fontsize=16,color="magenta"];384 -> 397[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	385 -> 381[label="",style="dashed", color="red", weight=0];
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12.94/5.09	387[label="Succ (Succ (primPlusNat yx130 yx10000))",fontsize=16,color="green",shape="box"];387 -> 399[label="",style="dashed", color="green", weight=3];
12.94/5.09	388[label="Succ yx10000",fontsize=16,color="green",shape="box"];389[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Pos (Succ (Succ (primPlusNat yx12100 yx300))))",fontsize=16,color="black",shape="box"];389 -> 400[label="",style="solid", color="black", weight=3];
12.94/5.09	390[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];390 -> 401[label="",style="solid", color="black", weight=3];
12.94/5.09	391[label="yx300",fontsize=16,color="green",shape="box"];392[label="primFloatEncodePower3 True (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="box"];392 -> 402[label="",style="solid", color="black", weight=3];
12.94/5.09	393[label="yx12100",fontsize=16,color="green",shape="box"];394[label="yx300",fontsize=16,color="green",shape="box"];395[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];395 -> 403[label="",style="solid", color="black", weight=3];
12.94/5.09	396[label="Succ (primPlusNat yx12100 yx300)",fontsize=16,color="green",shape="box"];396 -> 404[label="",style="dashed", color="green", weight=3];
12.94/5.09	397[label="yx12100",fontsize=16,color="green",shape="box"];398[label="primFloatEncodePower3 True (Pos (Succ (Succ Zero))) (Neg Zero)",fontsize=16,color="black",shape="box"];398 -> 405[label="",style="solid", color="black", weight=3];
12.94/5.09	399[label="primPlusNat yx130 yx10000",fontsize=16,color="burlywood",shape="triangle"];547[label="yx130/Succ yx1300",fontsize=10,color="white",style="solid",shape="box"];399 -> 547[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	547 -> 406[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	548[label="yx130/Zero",fontsize=10,color="white",style="solid",shape="box"];399 -> 548[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	548 -> 407[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	400 -> 408[label="",style="dashed", color="red", weight=0];
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12.94/5.09	401[label="primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="triangle"];401 -> 410[label="",style="solid", color="black", weight=3];
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12.94/5.09	403[label="primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];403 -> 412[label="",style="solid", color="black", weight=3];
12.94/5.09	404 -> 399[label="",style="dashed", color="red", weight=0];
12.94/5.09	404[label="primPlusNat yx12100 yx300",fontsize=16,color="magenta"];404 -> 413[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	404 -> 414[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	405 -> 402[label="",style="dashed", color="red", weight=0];
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12.94/5.09	549 -> 415[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	550[label="yx10000/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 550[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	550 -> 416[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	407[label="primPlusNat Zero yx10000",fontsize=16,color="burlywood",shape="box"];551[label="yx10000/Succ yx100000",fontsize=10,color="white",style="solid",shape="box"];407 -> 551[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	551 -> 417[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	552[label="yx10000/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 552[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	552 -> 418[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	409 -> 399[label="",style="dashed", color="red", weight=0];
12.94/5.09	409[label="primPlusNat yx12100 yx300",fontsize=16,color="magenta"];409 -> 419[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	409 -> 420[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	408 -> 401[label="",style="dashed", color="red", weight=0];
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12.94/5.09	410[label="primFloatEncodePower1 (Pos (Succ yx12100) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];410 -> 422[label="",style="solid", color="black", weight=3];
12.94/5.09	411[label="doubleToFloat (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];411 -> 423[label="",style="solid", color="black", weight=3];
12.94/5.09	412[label="primFloatEncodePower1 (Neg (Succ yx300) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];412 -> 424[label="",style="solid", color="black", weight=3];
12.94/5.09	413[label="yx12100",fontsize=16,color="green",shape="box"];414[label="yx300",fontsize=16,color="green",shape="box"];415[label="primPlusNat (Succ yx1300) (Succ yx100000)",fontsize=16,color="black",shape="box"];415 -> 425[label="",style="solid", color="black", weight=3];
12.94/5.09	416[label="primPlusNat (Succ yx1300) Zero",fontsize=16,color="black",shape="box"];416 -> 426[label="",style="solid", color="black", weight=3];
12.94/5.09	417[label="primPlusNat Zero (Succ yx100000)",fontsize=16,color="black",shape="box"];417 -> 427[label="",style="solid", color="black", weight=3];
12.94/5.09	418[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];418 -> 428[label="",style="solid", color="black", weight=3];
12.94/5.09	419[label="yx12100",fontsize=16,color="green",shape="box"];420[label="yx300",fontsize=16,color="green",shape="box"];421[label="Succ yx14",fontsize=16,color="green",shape="box"];422[label="primFloatEncodePower1 (compare (Pos (Succ yx12100)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];422 -> 429[label="",style="solid", color="black", weight=3];
12.94/5.09	423[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];424[label="primFloatEncodePower1 (compare (Neg (Succ yx300)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];424 -> 430[label="",style="solid", color="black", weight=3];
12.94/5.09	425[label="Succ (Succ (primPlusNat yx1300 yx100000))",fontsize=16,color="green",shape="box"];425 -> 431[label="",style="dashed", color="green", weight=3];
12.94/5.09	426[label="Succ yx1300",fontsize=16,color="green",shape="box"];427[label="Succ yx100000",fontsize=16,color="green",shape="box"];428[label="Zero",fontsize=16,color="green",shape="box"];429[label="primFloatEncodePower1 (not (compare (Pos (Succ yx12100)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];429 -> 432[label="",style="solid", color="black", weight=3];
12.94/5.09	430[label="primFloatEncodePower1 (not (compare (Neg (Succ yx300)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];430 -> 433[label="",style="solid", color="black", weight=3];
12.94/5.09	431 -> 399[label="",style="dashed", color="red", weight=0];
12.94/5.09	431[label="primPlusNat yx1300 yx100000",fontsize=16,color="magenta"];431 -> 434[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	431 -> 435[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	432[label="primFloatEncodePower1 (not (primCmpInt (Pos (Succ yx12100)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];432 -> 436[label="",style="solid", color="black", weight=3];
12.94/5.09	433[label="primFloatEncodePower1 (not (primCmpInt (Neg (Succ yx300)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];433 -> 437[label="",style="solid", color="black", weight=3];
12.94/5.09	434[label="yx1300",fontsize=16,color="green",shape="box"];435[label="yx100000",fontsize=16,color="green",shape="box"];436[label="primFloatEncodePower1 (not (primCmpNat (Succ yx12100) (Succ Zero) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="black",shape="box"];436 -> 438[label="",style="solid", color="black", weight=3];
12.94/5.09	437[label="primFloatEncodePower1 (not (LT == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];437 -> 439[label="",style="solid", color="black", weight=3];
12.94/5.09	438[label="primFloatEncodePower1 (not (primCmpNat yx12100 Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx12100))",fontsize=16,color="burlywood",shape="box"];553[label="yx12100/Succ yx121000",fontsize=10,color="white",style="solid",shape="box"];438 -> 553[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	553 -> 440[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	554[label="yx12100/Zero",fontsize=10,color="white",style="solid",shape="box"];438 -> 554[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	554 -> 441[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	439[label="primFloatEncodePower1 (not True) (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];439 -> 442[label="",style="solid", color="black", weight=3];
12.94/5.09	440[label="primFloatEncodePower1 (not (primCmpNat (Succ yx121000) Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)))",fontsize=16,color="black",shape="box"];440 -> 443[label="",style="solid", color="black", weight=3];
12.94/5.09	441[label="primFloatEncodePower1 (not (primCmpNat Zero Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];441 -> 444[label="",style="solid", color="black", weight=3];
12.94/5.09	442[label="primFloatEncodePower1 False (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];442 -> 445[label="",style="solid", color="black", weight=3];
12.94/5.09	443[label="primFloatEncodePower1 (not (GT == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)))",fontsize=16,color="black",shape="box"];443 -> 446[label="",style="solid", color="black", weight=3];
12.94/5.09	444[label="primFloatEncodePower1 (not (EQ == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];444 -> 447[label="",style="solid", color="black", weight=3];
12.94/5.09	445[label="primFloatEncodePower0 (Pos (Succ (Succ Zero))) (Neg (Succ yx300))",fontsize=16,color="black",shape="box"];445 -> 448[label="",style="solid", color="black", weight=3];
12.94/5.09	446[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)))",fontsize=16,color="black",shape="box"];446 -> 449[label="",style="solid", color="black", weight=3];
12.94/5.09	447[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];447 -> 450[label="",style="solid", color="black", weight=3];
12.94/5.09	448 -> 451[label="",style="dashed", color="red", weight=0];
12.94/5.09	448[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) / primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300))",fontsize=16,color="magenta"];448 -> 452[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	449[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)))",fontsize=16,color="black",shape="box"];449 -> 453[label="",style="solid", color="black", weight=3];
12.94/5.09	450[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];450 -> 454[label="",style="solid", color="black", weight=3];
12.94/5.09	452 -> 402[label="",style="dashed", color="red", weight=0];
12.94/5.09	452[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="magenta"];451[label="yx15 / primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300))",fontsize=16,color="black",shape="triangle"];451 -> 455[label="",style="solid", color="black", weight=3];
12.94/5.09	453[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];453 -> 456[label="",style="solid", color="black", weight=3];
12.94/5.09	454[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];454 -> 457[label="",style="solid", color="black", weight=3];
12.94/5.09	455[label="primDivFloat yx15 (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300)))",fontsize=16,color="burlywood",shape="box"];555[label="yx15/Float yx150 yx151",fontsize=10,color="white",style="solid",shape="box"];455 -> 555[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	555 -> 458[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	456[label="primMulFloat (fromInt (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];456 -> 459[label="",style="solid", color="black", weight=3];
12.94/5.09	457[label="primMulFloat (fromInt (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];457 -> 460[label="",style="solid", color="black", weight=3];
12.94/5.09	458[label="primDivFloat (Float yx150 yx151) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300)))",fontsize=16,color="black",shape="box"];458 -> 461[label="",style="solid", color="black", weight=3];
12.94/5.09	459[label="primMulFloat (primIntToFloat (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];459 -> 462[label="",style="solid", color="black", weight=3];
12.94/5.09	460[label="primMulFloat (primIntToFloat (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];460 -> 463[label="",style="solid", color="black", weight=3];
12.94/5.09	461 -> 478[label="",style="dashed", color="red", weight=0];
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12.94/5.09	462 -> 200[label="",style="dashed", color="red", weight=0];
12.94/5.09	462[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero)))",fontsize=16,color="magenta"];462 -> 465[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	462 -> 466[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	463 -> 200[label="",style="dashed", color="red", weight=0];
12.94/5.09	463[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="magenta"];463 -> 467[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	463 -> 468[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	479[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300))",fontsize=16,color="black",shape="box"];479 -> 484[label="",style="solid", color="black", weight=3];
12.94/5.09	478[label="primDivFloat (Float yx150 yx151) yx16",fontsize=16,color="burlywood",shape="triangle"];556[label="yx16/Float yx160 yx161",fontsize=10,color="white",style="solid",shape="box"];478 -> 556[label="",style="solid", color="burlywood", weight=9];
12.94/5.09	556 -> 485[label="",style="solid", color="burlywood", weight=3];
12.94/5.09	465[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];465 -> 470[label="",style="solid", color="black", weight=3];
12.94/5.09	466[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];467[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];467 -> 471[label="",style="solid", color="black", weight=3];
12.94/5.09	468[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];484[label="primFloatEncodePower3 (`negate` Neg (Succ yx300) == Pos Zero) (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300))",fontsize=16,color="black",shape="box"];484 -> 488[label="",style="solid", color="black", weight=3];
12.94/5.09	485[label="primDivFloat (Float yx150 yx151) (Float yx160 yx161)",fontsize=16,color="black",shape="box"];485 -> 489[label="",style="solid", color="black", weight=3];
12.94/5.09	470[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];470 -> 473[label="",style="solid", color="black", weight=3];
12.94/5.09	471[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];471 -> 474[label="",style="solid", color="black", weight=3];
12.94/5.09	488[label="primFloatEncodePower3 (primEqInt (`negate` Neg (Succ yx300)) (Pos Zero)) (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx300))",fontsize=16,color="black",shape="box"];488 -> 492[label="",style="solid", color="black", weight=3];
12.94/5.09	489[label="Float (yx150 * yx161) (yx151 * yx160)",fontsize=16,color="green",shape="box"];489 -> 493[label="",style="dashed", color="green", weight=3];
12.94/5.09	489 -> 494[label="",style="dashed", color="green", weight=3];
12.94/5.09	473[label="primFloatEncodePower3 (Pos (Succ (Succ yx121000)) - Pos (Succ Zero) == Pos Zero) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];473 -> 476[label="",style="solid", color="black", weight=3];
12.94/5.09	474[label="primFloatEncodePower3 (Pos (Succ Zero) - Pos (Succ Zero) == Pos Zero) (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];474 -> 477[label="",style="solid", color="black", weight=3];
12.94/5.09	492[label="primFloatEncodePower3 (primEqInt (primNegInt (Neg (Succ yx300))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt (Neg (Succ yx300)))",fontsize=16,color="black",shape="box"];492 -> 499[label="",style="solid", color="black", weight=3];
12.94/5.09	493 -> 299[label="",style="dashed", color="red", weight=0];
12.94/5.09	493[label="yx150 * yx161",fontsize=16,color="magenta"];493 -> 500[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	493 -> 501[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	494 -> 299[label="",style="dashed", color="red", weight=0];
12.94/5.09	494[label="yx151 * yx160",fontsize=16,color="magenta"];494 -> 502[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	494 -> 503[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	476[label="primFloatEncodePower3 (primEqInt (Pos (Succ (Succ yx121000)) - Pos (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx121000)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];476 -> 486[label="",style="solid", color="black", weight=3];
12.94/5.09	477[label="primFloatEncodePower3 (primEqInt (Pos (Succ Zero) - Pos (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];477 -> 487[label="",style="solid", color="black", weight=3];
12.94/5.09	499 -> 376[label="",style="dashed", color="red", weight=0];
12.94/5.09	499[label="primFloatEncodePower3 (primEqInt (Pos (Succ yx300)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx300))",fontsize=16,color="magenta"];499 -> 504[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	500[label="yx161",fontsize=16,color="green",shape="box"];501[label="yx150",fontsize=16,color="green",shape="box"];502[label="yx160",fontsize=16,color="green",shape="box"];503[label="yx151",fontsize=16,color="green",shape="box"];486[label="primFloatEncodePower3 (primEqInt (primMinusInt (Pos (Succ (Succ yx121000))) (Pos (Succ Zero))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusInt (Pos (Succ (Succ yx121000))) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];486 -> 490[label="",style="solid", color="black", weight=3];
12.94/5.09	487[label="primFloatEncodePower3 (primEqInt (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];487 -> 491[label="",style="solid", color="black", weight=3];
12.94/5.09	504[label="yx300",fontsize=16,color="green",shape="box"];490 -> 342[label="",style="dashed", color="red", weight=0];
12.94/5.09	490[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ (Succ yx121000)) (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ (Succ yx121000)) (Succ Zero))",fontsize=16,color="magenta"];490 -> 495[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	490 -> 496[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	491 -> 342[label="",style="dashed", color="red", weight=0];
12.94/5.09	491[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ Zero) (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ Zero) (Succ Zero))",fontsize=16,color="magenta"];491 -> 497[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	491 -> 498[label="",style="dashed", color="magenta", weight=3];
12.94/5.09	495[label="Succ (Succ yx121000)",fontsize=16,color="green",shape="box"];496[label="Succ Zero",fontsize=16,color="green",shape="box"];497[label="Succ Zero",fontsize=16,color="green",shape="box"];498[label="Succ Zero",fontsize=16,color="green",shape="box"];}
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(12)
12.94/5.09	Complex Obligation (AND)
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(13)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primMulNat(Succ(yx50000), Succ(yx10000)) -> new_primMulNat(yx50000, Succ(yx10000))
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(14) QDPSizeChangeProof (EQUIVALENT)
12.94/5.09	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. 
12.94/5.09	
12.94/5.09	From the DPs we obtained the following set of size-change graphs:
12.94/5.09	*new_primMulNat(Succ(yx50000), Succ(yx10000)) -> new_primMulNat(yx50000, Succ(yx10000))
12.94/5.09	The graph contains the following edges 1 > 1, 2 >= 2
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(15)
12.94/5.09	YES
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(16)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primPlusNat(Succ(yx1300), Succ(yx100000)) -> new_primPlusNat(yx1300, yx100000)
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(17) QDPSizeChangeProof (EQUIVALENT)
12.94/5.09	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. 
12.94/5.09	
12.94/5.09	From the DPs we obtained the following set of size-change graphs:
12.94/5.09	*new_primPlusNat(Succ(yx1300), Succ(yx100000)) -> new_primPlusNat(yx1300, yx100000)
12.94/5.09	The graph contains the following edges 1 > 1, 2 > 2
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(18)
12.94/5.09	YES
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(19)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower31(yx300) -> new_fs(new_fromDouble, yx300)
12.94/5.09	   new_primFloatEncodePower2(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower2(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(new_fromDouble, yx300)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_fromDouble -> Float(Pos(Succ(Zero)), Pos(Succ(Zero)))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_fromDouble
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(20) DependencyGraphProof (EQUIVALENT)
12.94/5.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(21)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(new_fromDouble, yx300)
12.94/5.09	   new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_fromDouble -> Float(Pos(Succ(Zero)), Pos(Succ(Zero)))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_fromDouble
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(22) TransformationProof (EQUIVALENT)
12.94/5.09	By rewriting [LPAR04] the rule new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(new_fromDouble, yx300) at position [0] we obtained the following new rules [LPAR04]:
12.94/5.09	
12.94/5.09	   (new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300),new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(23)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300)
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_fromDouble -> Float(Pos(Succ(Zero)), Pos(Succ(Zero)))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_fromDouble
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(24) UsableRulesProof (EQUIVALENT)
12.94/5.09	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(25)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300)
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_fromDouble
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(26) QReductionProof (EQUIVALENT)
12.94/5.09	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.94/5.09	
12.94/5.09	   new_fromDouble
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(27)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300)
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(28) TransformationProof (EQUIVALENT)
12.94/5.09	By instantiating [LPAR04] the rule new_fs(Float(yx150, yx151), yx300) -> new_primFloatEncodePower30(yx300) we obtained the following new rules [LPAR04]:
12.94/5.09	
12.94/5.09	   (new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0),new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(29)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	   new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0)
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(30) QDPPairToRuleProof (EQUIVALENT)
12.94/5.09	The dependency pair new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300) was transformed to the following new rules:
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	the following new pairs maintain the fan-in:
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(anew_new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero)))
12.94/5.09	   new_primFloatEncodePower30(Zero) -> H(anew_new_primFloatEncodePower3(Succ(Zero), Succ(Zero)))
12.94/5.09	
12.94/5.09	the following new pairs maintain the fan-out:
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Zero, Succ(yx300))) -> new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(31)
12.94/5.09	Complex Obligation (AND)
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(32)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> new_primFloatEncodePower3(Succ(Zero), Succ(Zero))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	   new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(anew_new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero)))
12.94/5.09	   new_primFloatEncodePower30(Zero) -> H(anew_new_primFloatEncodePower3(Succ(Zero), Succ(Zero)))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Zero, Succ(yx300))) -> new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(33) DependencyGraphProof (EQUIVALENT)
12.94/5.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(34)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(anew_new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero)))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> H(anew_new_primFloatEncodePower3(Succ(Zero), Succ(Zero)))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Zero, Succ(yx300))) -> new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	   new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(35) TransformationProof (EQUIVALENT)
12.94/5.09	By rewriting [LPAR04] the rule new_primFloatEncodePower30(Succ(yx121000)) -> H(anew_new_primFloatEncodePower3(Succ(Succ(yx121000)), Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
12.94/5.09	
12.94/5.09	   (new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero)),new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero)))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(36)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Zero) -> H(anew_new_primFloatEncodePower3(Succ(Zero), Succ(Zero)))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Zero, Succ(yx300))) -> new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	   new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(37) TransformationProof (EQUIVALENT)
12.94/5.09	By rewriting [LPAR04] the rule new_primFloatEncodePower30(Zero) -> H(anew_new_primFloatEncodePower3(Succ(Zero), Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
12.94/5.09	
12.94/5.09	   (new_primFloatEncodePower30(Zero) -> H(new_new_primFloatEncodePower3(Zero, Zero)),new_primFloatEncodePower30(Zero) -> H(new_new_primFloatEncodePower3(Zero, Zero)))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(38)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Zero, Succ(yx300))) -> new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	   new_primFloatEncodePower3(Zero, Succ(yx300)) -> new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), yx300)
12.94/5.09	   new_fs(Float(Pos(Succ(Zero)), Pos(Succ(Zero))), z0) -> new_primFloatEncodePower30(z0)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	   new_primFloatEncodePower30(Zero) -> H(new_new_primFloatEncodePower3(Zero, Zero))
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(39) DependencyGraphProof (EQUIVALENT)
12.94/5.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(40)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(yx300)) -> cons_new_primFloatEncodePower3(Zero, Succ(yx300))
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(41) UsableRulesProof (EQUIVALENT)
12.94/5.09	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(42)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(43) QReductionProof (EQUIVALENT)
12.94/5.09	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.94/5.09	
12.94/5.09	   anew_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(44)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(45) TransformationProof (EQUIVALENT)
12.94/5.09	By rewriting [LPAR04] the rule new_primFloatEncodePower30(Succ(yx121000)) -> H(new_new_primFloatEncodePower3(Succ(yx121000), Zero)) at position [0] we obtained the following new rules [LPAR04]:
12.94/5.09	
12.94/5.09	   (new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero)),new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero)))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(46)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	
12.94/5.09	The TRS R consists of the following rules:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(yx12100), Zero) -> cons_new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(47) UsableRulesProof (EQUIVALENT)
12.94/5.09	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(48)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	The set Q consists of the following terms:
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(49) QReductionProof (EQUIVALENT)
12.94/5.09	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
12.94/5.09	
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Succ(x1))
12.94/5.09	   new_new_primFloatEncodePower3(Succ(x0), Zero)
12.94/5.09	   new_new_primFloatEncodePower3(Zero, Succ(x0))
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(50)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100)
12.94/5.09	   H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero)
12.94/5.09	   new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero))
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(51) QDPSizeChangeProof (EQUIVALENT)
12.94/5.09	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. 
12.94/5.09	
12.94/5.09	Order:EMB rules!
12.94/5.09	
12.94/5.09	AFS: 
12.94/5.09	Zero  =  Zero
12.94/5.09	
12.94/5.09	Succ(x1)  =  Succ(x1)
12.94/5.09	
12.94/5.09	cons_new_primFloatEncodePower3(x1, x2)  =  x1
12.94/5.09	
12.94/5.09	
12.94/5.09	
12.94/5.09	
12.94/5.09	
12.94/5.09	From the DPs we obtained the following set of size-change graphs:
12.94/5.09	*new_primFloatEncodePower30(Succ(yx121000)) -> H(cons_new_primFloatEncodePower3(Succ(yx121000), Zero)) (allowed arguments on rhs = {1})
12.94/5.09	The graph contains the following edges 1 >= 1
12.94/5.09	
12.94/5.09	
12.94/5.09	*H(cons_new_primFloatEncodePower3(Succ(yx12100), Zero)) -> new_primFloatEncodePower3(Succ(yx12100), Zero) (allowed arguments on rhs = {1, 2})
12.94/5.09	The graph contains the following edges 1 >= 1
12.94/5.09	
12.94/5.09	
12.94/5.09	*new_primFloatEncodePower3(Succ(yx12100), Zero) -> new_primFloatEncodePower30(yx12100) (allowed arguments on rhs = {1})
12.94/5.09	The graph contains the following edges 1 > 1
12.94/5.09	
12.94/5.09	
12.94/5.09	
12.94/5.09	We oriented the following set of usable rules [AAECC05,FROCOS05].
12.94/5.09	none
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(52)
12.94/5.09	YES
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(53)
12.94/5.09	Obligation:
12.94/5.09	Q DP problem:
12.94/5.09	The TRS P consists of the following rules:
12.94/5.09	
12.94/5.09	   new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	
12.94/5.09	R is empty.
12.94/5.09	Q is empty.
12.94/5.09	We have to consider all minimal (P,Q,R)-chains.
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(54) QDPSizeChangeProof (EQUIVALENT)
12.94/5.09	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. 
12.94/5.09	
12.94/5.09	From the DPs we obtained the following set of size-change graphs:
12.94/5.09	*new_primFloatEncodePower3(Succ(yx12100), Succ(yx300)) -> new_primFloatEncodePower3(yx12100, yx300)
12.94/5.09	The graph contains the following edges 1 > 1, 2 > 2
12.94/5.09	
12.94/5.09	
12.94/5.09	----------------------------------------
12.94/5.09	
12.94/5.09	(55)
12.94/5.09	YES
12.94/5.12	EOF