9.05/3.80	YES
11.00/4.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.00/4.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.00/4.39	
11.00/4.39	
11.00/4.39	H-Termination with start terms of the given HASKELL could be proven:
11.00/4.39	
11.00/4.39	(0) HASKELL
11.00/4.39	(1) IFR [EQUIVALENT, 0 ms]
11.00/4.39	(2) HASKELL
11.00/4.39	(3) BR [EQUIVALENT, 0 ms]
11.00/4.39	(4) HASKELL
11.00/4.39	(5) COR [EQUIVALENT, 0 ms]
11.00/4.39	(6) HASKELL
11.00/4.39	(7) NumRed [SOUND, 0 ms]
11.00/4.39	(8) HASKELL
11.00/4.39	(9) Narrow [SOUND, 0 ms]
11.00/4.39	(10) AND
11.00/4.39	    (11) QDP
11.00/4.39	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.00/4.39	        (13) YES
11.00/4.39	    (14) QDP
11.00/4.39	        (15) DependencyGraphProof [EQUIVALENT, 0 ms]
11.00/4.39	        (16) AND
11.00/4.39	            (17) QDP
11.00/4.39	                (18) MRRProof [EQUIVALENT, 7 ms]
11.00/4.39	                (19) QDP
11.00/4.39	                (20) PisEmptyProof [EQUIVALENT, 0 ms]
11.00/4.39	                (21) YES
11.00/4.39	            (22) QDP
11.00/4.39	                (23) QDPSizeChangeProof [EQUIVALENT, 11 ms]
11.00/4.39	                (24) YES
11.00/4.39	    (25) QDP
11.00/4.39	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.00/4.39	        (27) YES
11.00/4.39	    (28) QDP
11.00/4.39	        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.00/4.39	        (30) YES
11.00/4.39	    (31) QDP
11.00/4.39	        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.00/4.39	        (33) YES
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(0)
11.00/4.39	Obligation:
11.00/4.39	mainModule Main 
11.00/4.39	module Main where {
11.00/4.39	import qualified Prelude;
11.00/4.39	}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(1) IFR (EQUIVALENT)
11.00/4.39	If Reductions:
11.00/4.39	The following If expression
11.00/4.39	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
11.00/4.39	is transformed to
11.00/4.39	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
11.00/4.39	primDivNatS0 x y False = Zero;
11.00/4.39	"
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(2)
11.00/4.39	Obligation:
11.00/4.39	mainModule Main 
11.00/4.39	module Main where {
11.00/4.39	import qualified Prelude;
11.00/4.39	}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(3) BR (EQUIVALENT)
11.00/4.39	Replaced joker patterns by fresh variables and removed binding patterns.
11.00/4.39	
11.00/4.39	Binding Reductions:
11.00/4.39	The bind variable of the following binding Pattern
11.00/4.39	"frac@(Float vy vz)"
11.00/4.39	is replaced by the following term
11.00/4.39	"Float vy vz"
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(4)
11.00/4.39	Obligation:
11.00/4.39	mainModule Main 
11.00/4.39	module Main where {
11.00/4.39	import qualified Prelude;
11.00/4.39	}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(5) COR (EQUIVALENT)
11.00/4.39	Cond Reductions:
11.00/4.39	The following Function with conditions
11.00/4.39	"undefined |Falseundefined;
11.00/4.39	"
11.00/4.39	is transformed to
11.00/4.39	"undefined  = undefined1;
11.00/4.39	"
11.00/4.39	"undefined0 True = undefined;
11.00/4.39	"
11.00/4.39	"undefined1  = undefined0 False;
11.00/4.39	"
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(6)
11.00/4.39	Obligation:
11.00/4.39	mainModule Main 
11.00/4.39	module Main where {
11.00/4.39	import qualified Prelude;
11.00/4.39	}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(7) NumRed (SOUND)
11.00/4.39	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(8)
11.00/4.39	Obligation:
11.00/4.39	mainModule Main 
11.00/4.39	module Main where {
11.00/4.39	import qualified Prelude;
11.00/4.39	}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(9) Narrow (SOUND)
11.00/4.39	Haskell To QDPs
11.00/4.39	
11.00/4.39	digraph dp_graph {
11.00/4.39	node [outthreshold=100, inthreshold=100];1[label="properFraction",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.00/4.39	3[label="properFraction wv3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
11.00/4.39	4[label="floatProperFractionFloat wv3",fontsize=16,color="burlywood",shape="box"];545[label="wv3/Float wv30 wv31",fontsize=10,color="white",style="solid",shape="box"];4 -> 545[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	545 -> 5[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	5[label="floatProperFractionFloat (Float wv30 wv31)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
11.00/4.39	6[label="(fromInt (wv30 `quot` wv31),Float wv30 wv31 - fromInt (wv30 `quot` wv31))",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
11.00/4.39	6 -> 8[label="",style="dashed", color="green", weight=3];
11.00/4.39	7[label="fromInt (wv30 `quot` wv31)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
11.00/4.39	8[label="Float wv30 wv31 - fromInt (wv30 `quot` wv31)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
11.00/4.39	9[label="wv30 `quot` wv31",fontsize=16,color="black",shape="triangle"];9 -> 11[label="",style="solid", color="black", weight=3];
11.00/4.39	10 -> 12[label="",style="dashed", color="red", weight=0];
11.00/4.39	10[label="primMinusFloat (Float wv30 wv31) (fromInt (wv30 `quot` wv31))",fontsize=16,color="magenta"];10 -> 13[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	11[label="primQuotInt wv30 wv31",fontsize=16,color="burlywood",shape="box"];546[label="wv30/Pos wv300",fontsize=10,color="white",style="solid",shape="box"];11 -> 546[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	546 -> 14[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	547[label="wv30/Neg wv300",fontsize=10,color="white",style="solid",shape="box"];11 -> 547[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	547 -> 15[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	13 -> 9[label="",style="dashed", color="red", weight=0];
11.00/4.39	13[label="wv30 `quot` wv31",fontsize=16,color="magenta"];12[label="primMinusFloat (Float wv30 wv31) (fromInt wv4)",fontsize=16,color="black",shape="triangle"];12 -> 16[label="",style="solid", color="black", weight=3];
11.00/4.39	14[label="primQuotInt (Pos wv300) wv31",fontsize=16,color="burlywood",shape="box"];548[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];14 -> 548[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	548 -> 17[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	549[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];14 -> 549[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	549 -> 18[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	15[label="primQuotInt (Neg wv300) wv31",fontsize=16,color="burlywood",shape="box"];550[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];15 -> 550[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	550 -> 19[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	551[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];15 -> 551[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	551 -> 20[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	16[label="primMinusFloat (Float wv30 wv31) (primIntToFloat wv4)",fontsize=16,color="black",shape="box"];16 -> 21[label="",style="solid", color="black", weight=3];
11.00/4.39	17[label="primQuotInt (Pos wv300) (Pos wv310)",fontsize=16,color="burlywood",shape="box"];552[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];17 -> 552[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	552 -> 22[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	553[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 553[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	553 -> 23[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	18[label="primQuotInt (Pos wv300) (Neg wv310)",fontsize=16,color="burlywood",shape="box"];554[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];18 -> 554[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	554 -> 24[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	555[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 555[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	555 -> 25[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	19[label="primQuotInt (Neg wv300) (Pos wv310)",fontsize=16,color="burlywood",shape="box"];556[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];19 -> 556[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	556 -> 26[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	557[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 557[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	557 -> 27[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	20[label="primQuotInt (Neg wv300) (Neg wv310)",fontsize=16,color="burlywood",shape="box"];558[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];20 -> 558[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	558 -> 28[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	559[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 559[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	559 -> 29[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	21[label="primMinusFloat (Float wv30 wv31) (Float wv4 (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
11.00/4.39	22[label="primQuotInt (Pos wv300) (Pos (Succ wv3100))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
11.00/4.39	23[label="primQuotInt (Pos wv300) (Pos Zero)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
11.00/4.39	24[label="primQuotInt (Pos wv300) (Neg (Succ wv3100))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
11.00/4.39	25[label="primQuotInt (Pos wv300) (Neg Zero)",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
11.00/4.39	26[label="primQuotInt (Neg wv300) (Pos (Succ wv3100))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
11.00/4.39	27[label="primQuotInt (Neg wv300) (Pos Zero)",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
11.00/4.39	28[label="primQuotInt (Neg wv300) (Neg (Succ wv3100))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
11.00/4.39	29[label="primQuotInt (Neg wv300) (Neg Zero)",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
11.00/4.39	30[label="Float (wv30 * Pos (Succ Zero) - wv4 * wv31) (wv31 * Pos (Succ Zero))",fontsize=16,color="green",shape="box"];30 -> 39[label="",style="dashed", color="green", weight=3];
11.00/4.39	30 -> 40[label="",style="dashed", color="green", weight=3];
11.00/4.39	31[label="Pos (primDivNatS wv300 (Succ wv3100))",fontsize=16,color="green",shape="box"];31 -> 41[label="",style="dashed", color="green", weight=3];
11.00/4.39	32[label="error []",fontsize=16,color="black",shape="triangle"];32 -> 42[label="",style="solid", color="black", weight=3];
11.00/4.39	33[label="Neg (primDivNatS wv300 (Succ wv3100))",fontsize=16,color="green",shape="box"];33 -> 43[label="",style="dashed", color="green", weight=3];
11.00/4.39	34 -> 32[label="",style="dashed", color="red", weight=0];
11.00/4.39	34[label="error []",fontsize=16,color="magenta"];35[label="Neg (primDivNatS wv300 (Succ wv3100))",fontsize=16,color="green",shape="box"];35 -> 44[label="",style="dashed", color="green", weight=3];
11.00/4.39	36 -> 32[label="",style="dashed", color="red", weight=0];
11.00/4.39	36[label="error []",fontsize=16,color="magenta"];37[label="Pos (primDivNatS wv300 (Succ wv3100))",fontsize=16,color="green",shape="box"];37 -> 45[label="",style="dashed", color="green", weight=3];
11.00/4.39	38 -> 32[label="",style="dashed", color="red", weight=0];
11.00/4.39	38[label="error []",fontsize=16,color="magenta"];39[label="wv30 * Pos (Succ Zero) - wv4 * wv31",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
11.00/4.39	40[label="wv31 * Pos (Succ Zero)",fontsize=16,color="black",shape="triangle"];40 -> 47[label="",style="solid", color="black", weight=3];
11.00/4.39	41[label="primDivNatS wv300 (Succ wv3100)",fontsize=16,color="burlywood",shape="triangle"];560[label="wv300/Succ wv3000",fontsize=10,color="white",style="solid",shape="box"];41 -> 560[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	560 -> 48[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	561[label="wv300/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 561[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	561 -> 49[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	42[label="error []",fontsize=16,color="red",shape="box"];43 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	43[label="primDivNatS wv300 (Succ wv3100)",fontsize=16,color="magenta"];43 -> 50[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	44 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	44[label="primDivNatS wv300 (Succ wv3100)",fontsize=16,color="magenta"];44 -> 51[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	45 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	45[label="primDivNatS wv300 (Succ wv3100)",fontsize=16,color="magenta"];45 -> 52[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	45 -> 53[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	46 -> 54[label="",style="dashed", color="red", weight=0];
11.00/4.39	46[label="primMinusInt (wv30 * Pos (Succ Zero)) (wv4 * wv31)",fontsize=16,color="magenta"];46 -> 55[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	47[label="primMulInt wv31 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];562[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];47 -> 562[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	562 -> 56[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	563[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];47 -> 563[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	563 -> 57[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	48[label="primDivNatS (Succ wv3000) (Succ wv3100)",fontsize=16,color="black",shape="box"];48 -> 58[label="",style="solid", color="black", weight=3];
11.00/4.39	49[label="primDivNatS Zero (Succ wv3100)",fontsize=16,color="black",shape="box"];49 -> 59[label="",style="solid", color="black", weight=3];
11.00/4.39	50[label="wv3100",fontsize=16,color="green",shape="box"];51[label="wv300",fontsize=16,color="green",shape="box"];52[label="wv300",fontsize=16,color="green",shape="box"];53[label="wv3100",fontsize=16,color="green",shape="box"];55 -> 40[label="",style="dashed", color="red", weight=0];
11.00/4.39	55[label="wv30 * Pos (Succ Zero)",fontsize=16,color="magenta"];55 -> 60[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	54[label="primMinusInt wv5 (wv4 * wv31)",fontsize=16,color="burlywood",shape="triangle"];564[label="wv5/Pos wv50",fontsize=10,color="white",style="solid",shape="box"];54 -> 564[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	564 -> 61[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	565[label="wv5/Neg wv50",fontsize=10,color="white",style="solid",shape="box"];54 -> 565[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	565 -> 62[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	56[label="primMulInt (Pos wv310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];56 -> 63[label="",style="solid", color="black", weight=3];
11.00/4.39	57[label="primMulInt (Neg wv310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];57 -> 64[label="",style="solid", color="black", weight=3];
11.00/4.39	58[label="primDivNatS0 wv3000 wv3100 (primGEqNatS wv3000 wv3100)",fontsize=16,color="burlywood",shape="box"];566[label="wv3000/Succ wv30000",fontsize=10,color="white",style="solid",shape="box"];58 -> 566[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	566 -> 65[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	567[label="wv3000/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 567[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	567 -> 66[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	59[label="Zero",fontsize=16,color="green",shape="box"];60[label="wv30",fontsize=16,color="green",shape="box"];61[label="primMinusInt (Pos wv50) (wv4 * wv31)",fontsize=16,color="black",shape="box"];61 -> 67[label="",style="solid", color="black", weight=3];
11.00/4.39	62[label="primMinusInt (Neg wv50) (wv4 * wv31)",fontsize=16,color="black",shape="box"];62 -> 68[label="",style="solid", color="black", weight=3];
11.00/4.39	63[label="Pos (primMulNat wv310 (Succ Zero))",fontsize=16,color="green",shape="box"];63 -> 69[label="",style="dashed", color="green", weight=3];
11.00/4.39	64[label="Neg (primMulNat wv310 (Succ Zero))",fontsize=16,color="green",shape="box"];64 -> 70[label="",style="dashed", color="green", weight=3];
11.00/4.39	65[label="primDivNatS0 (Succ wv30000) wv3100 (primGEqNatS (Succ wv30000) wv3100)",fontsize=16,color="burlywood",shape="box"];568[label="wv3100/Succ wv31000",fontsize=10,color="white",style="solid",shape="box"];65 -> 568[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	568 -> 71[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	569[label="wv3100/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 569[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	569 -> 72[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	66[label="primDivNatS0 Zero wv3100 (primGEqNatS Zero wv3100)",fontsize=16,color="burlywood",shape="box"];570[label="wv3100/Succ wv31000",fontsize=10,color="white",style="solid",shape="box"];66 -> 570[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	570 -> 73[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	571[label="wv3100/Zero",fontsize=10,color="white",style="solid",shape="box"];66 -> 571[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	571 -> 74[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	67[label="primMinusInt (Pos wv50) (primMulInt wv4 wv31)",fontsize=16,color="burlywood",shape="box"];572[label="wv4/Pos wv40",fontsize=10,color="white",style="solid",shape="box"];67 -> 572[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	572 -> 75[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	573[label="wv4/Neg wv40",fontsize=10,color="white",style="solid",shape="box"];67 -> 573[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	573 -> 76[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	68[label="primMinusInt (Neg wv50) (primMulInt wv4 wv31)",fontsize=16,color="burlywood",shape="box"];574[label="wv4/Pos wv40",fontsize=10,color="white",style="solid",shape="box"];68 -> 574[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	574 -> 77[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	575[label="wv4/Neg wv40",fontsize=10,color="white",style="solid",shape="box"];68 -> 575[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	575 -> 78[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	69[label="primMulNat wv310 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];576[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];69 -> 576[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	576 -> 79[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	577[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 577[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	577 -> 80[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	70 -> 69[label="",style="dashed", color="red", weight=0];
11.00/4.39	70[label="primMulNat wv310 (Succ Zero)",fontsize=16,color="magenta"];70 -> 81[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	71[label="primDivNatS0 (Succ wv30000) (Succ wv31000) (primGEqNatS (Succ wv30000) (Succ wv31000))",fontsize=16,color="black",shape="box"];71 -> 82[label="",style="solid", color="black", weight=3];
11.00/4.39	72[label="primDivNatS0 (Succ wv30000) Zero (primGEqNatS (Succ wv30000) Zero)",fontsize=16,color="black",shape="box"];72 -> 83[label="",style="solid", color="black", weight=3];
11.00/4.39	73[label="primDivNatS0 Zero (Succ wv31000) (primGEqNatS Zero (Succ wv31000))",fontsize=16,color="black",shape="box"];73 -> 84[label="",style="solid", color="black", weight=3];
11.00/4.39	74[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];74 -> 85[label="",style="solid", color="black", weight=3];
11.00/4.39	75[label="primMinusInt (Pos wv50) (primMulInt (Pos wv40) wv31)",fontsize=16,color="burlywood",shape="box"];578[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];75 -> 578[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	578 -> 86[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	579[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];75 -> 579[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	579 -> 87[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	76[label="primMinusInt (Pos wv50) (primMulInt (Neg wv40) wv31)",fontsize=16,color="burlywood",shape="box"];580[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];76 -> 580[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	580 -> 88[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	581[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];76 -> 581[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	581 -> 89[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	77[label="primMinusInt (Neg wv50) (primMulInt (Pos wv40) wv31)",fontsize=16,color="burlywood",shape="box"];582[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];77 -> 582[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	582 -> 90[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	583[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];77 -> 583[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	583 -> 91[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	78[label="primMinusInt (Neg wv50) (primMulInt (Neg wv40) wv31)",fontsize=16,color="burlywood",shape="box"];584[label="wv31/Pos wv310",fontsize=10,color="white",style="solid",shape="box"];78 -> 584[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	584 -> 92[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	585[label="wv31/Neg wv310",fontsize=10,color="white",style="solid",shape="box"];78 -> 585[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	585 -> 93[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	79[label="primMulNat (Succ wv3100) (Succ Zero)",fontsize=16,color="black",shape="box"];79 -> 94[label="",style="solid", color="black", weight=3];
11.00/4.39	80[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];80 -> 95[label="",style="solid", color="black", weight=3];
11.00/4.39	81[label="wv310",fontsize=16,color="green",shape="box"];82 -> 482[label="",style="dashed", color="red", weight=0];
11.00/4.39	82[label="primDivNatS0 (Succ wv30000) (Succ wv31000) (primGEqNatS wv30000 wv31000)",fontsize=16,color="magenta"];82 -> 483[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	82 -> 484[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	82 -> 485[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	82 -> 486[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	83[label="primDivNatS0 (Succ wv30000) Zero True",fontsize=16,color="black",shape="box"];83 -> 98[label="",style="solid", color="black", weight=3];
11.00/4.39	84[label="primDivNatS0 Zero (Succ wv31000) False",fontsize=16,color="black",shape="box"];84 -> 99[label="",style="solid", color="black", weight=3];
11.00/4.39	85[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];85 -> 100[label="",style="solid", color="black", weight=3];
11.00/4.39	86[label="primMinusInt (Pos wv50) (primMulInt (Pos wv40) (Pos wv310))",fontsize=16,color="black",shape="box"];86 -> 101[label="",style="solid", color="black", weight=3];
11.00/4.39	87[label="primMinusInt (Pos wv50) (primMulInt (Pos wv40) (Neg wv310))",fontsize=16,color="black",shape="box"];87 -> 102[label="",style="solid", color="black", weight=3];
11.00/4.39	88[label="primMinusInt (Pos wv50) (primMulInt (Neg wv40) (Pos wv310))",fontsize=16,color="black",shape="box"];88 -> 103[label="",style="solid", color="black", weight=3];
11.00/4.39	89[label="primMinusInt (Pos wv50) (primMulInt (Neg wv40) (Neg wv310))",fontsize=16,color="black",shape="box"];89 -> 104[label="",style="solid", color="black", weight=3];
11.00/4.39	90[label="primMinusInt (Neg wv50) (primMulInt (Pos wv40) (Pos wv310))",fontsize=16,color="black",shape="box"];90 -> 105[label="",style="solid", color="black", weight=3];
11.00/4.39	91[label="primMinusInt (Neg wv50) (primMulInt (Pos wv40) (Neg wv310))",fontsize=16,color="black",shape="box"];91 -> 106[label="",style="solid", color="black", weight=3];
11.00/4.39	92[label="primMinusInt (Neg wv50) (primMulInt (Neg wv40) (Pos wv310))",fontsize=16,color="black",shape="box"];92 -> 107[label="",style="solid", color="black", weight=3];
11.00/4.39	93[label="primMinusInt (Neg wv50) (primMulInt (Neg wv40) (Neg wv310))",fontsize=16,color="black",shape="box"];93 -> 108[label="",style="solid", color="black", weight=3];
11.00/4.39	94 -> 319[label="",style="dashed", color="red", weight=0];
11.00/4.39	94[label="primPlusNat (primMulNat wv3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];94 -> 320[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	94 -> 321[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	95[label="Zero",fontsize=16,color="green",shape="box"];483[label="wv31000",fontsize=16,color="green",shape="box"];484[label="wv30000",fontsize=16,color="green",shape="box"];485[label="wv31000",fontsize=16,color="green",shape="box"];486[label="wv30000",fontsize=16,color="green",shape="box"];482[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS wv32 wv33)",fontsize=16,color="burlywood",shape="triangle"];586[label="wv32/Succ wv320",fontsize=10,color="white",style="solid",shape="box"];482 -> 586[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	586 -> 515[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	587[label="wv32/Zero",fontsize=10,color="white",style="solid",shape="box"];482 -> 587[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	587 -> 516[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	98[label="Succ (primDivNatS (primMinusNatS (Succ wv30000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];98 -> 115[label="",style="dashed", color="green", weight=3];
11.00/4.39	99[label="Zero",fontsize=16,color="green",shape="box"];100[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];100 -> 116[label="",style="dashed", color="green", weight=3];
11.00/4.39	101[label="primMinusInt (Pos wv50) (Pos (primMulNat wv40 wv310))",fontsize=16,color="black",shape="triangle"];101 -> 117[label="",style="solid", color="black", weight=3];
11.00/4.39	102[label="primMinusInt (Pos wv50) (Neg (primMulNat wv40 wv310))",fontsize=16,color="black",shape="triangle"];102 -> 118[label="",style="solid", color="black", weight=3];
11.00/4.39	103 -> 102[label="",style="dashed", color="red", weight=0];
11.00/4.39	103[label="primMinusInt (Pos wv50) (Neg (primMulNat wv40 wv310))",fontsize=16,color="magenta"];103 -> 119[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	103 -> 120[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	104 -> 101[label="",style="dashed", color="red", weight=0];
11.00/4.39	104[label="primMinusInt (Pos wv50) (Pos (primMulNat wv40 wv310))",fontsize=16,color="magenta"];104 -> 121[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	104 -> 122[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	105[label="primMinusInt (Neg wv50) (Pos (primMulNat wv40 wv310))",fontsize=16,color="black",shape="triangle"];105 -> 123[label="",style="solid", color="black", weight=3];
11.00/4.39	106[label="primMinusInt (Neg wv50) (Neg (primMulNat wv40 wv310))",fontsize=16,color="black",shape="triangle"];106 -> 124[label="",style="solid", color="black", weight=3];
11.00/4.39	107 -> 106[label="",style="dashed", color="red", weight=0];
11.00/4.39	107[label="primMinusInt (Neg wv50) (Neg (primMulNat wv40 wv310))",fontsize=16,color="magenta"];107 -> 125[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	107 -> 126[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	108 -> 105[label="",style="dashed", color="red", weight=0];
11.00/4.39	108[label="primMinusInt (Neg wv50) (Pos (primMulNat wv40 wv310))",fontsize=16,color="magenta"];108 -> 127[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	108 -> 128[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	320 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	320[label="primMulNat wv3100 (Succ Zero)",fontsize=16,color="magenta"];320 -> 333[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	320 -> 334[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	321[label="Zero",fontsize=16,color="green",shape="box"];319[label="primPlusNat wv12 (Succ wv3100)",fontsize=16,color="burlywood",shape="triangle"];588[label="wv12/Succ wv120",fontsize=10,color="white",style="solid",shape="box"];319 -> 588[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	588 -> 335[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	589[label="wv12/Zero",fontsize=10,color="white",style="solid",shape="box"];319 -> 589[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	589 -> 336[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	515[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS (Succ wv320) wv33)",fontsize=16,color="burlywood",shape="box"];590[label="wv33/Succ wv330",fontsize=10,color="white",style="solid",shape="box"];515 -> 590[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	590 -> 517[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	591[label="wv33/Zero",fontsize=10,color="white",style="solid",shape="box"];515 -> 591[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	591 -> 518[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	516[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS Zero wv33)",fontsize=16,color="burlywood",shape="box"];592[label="wv33/Succ wv330",fontsize=10,color="white",style="solid",shape="box"];516 -> 592[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	592 -> 519[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	593[label="wv33/Zero",fontsize=10,color="white",style="solid",shape="box"];516 -> 593[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	593 -> 520[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	115 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	115[label="primDivNatS (primMinusNatS (Succ wv30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];115 -> 136[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	115 -> 137[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	116 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	116[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];116 -> 138[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	116 -> 139[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	117[label="primMinusNat wv50 (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="box"];594[label="wv50/Succ wv500",fontsize=10,color="white",style="solid",shape="box"];117 -> 594[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	594 -> 140[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	595[label="wv50/Zero",fontsize=10,color="white",style="solid",shape="box"];117 -> 595[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	595 -> 141[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	118[label="Pos (primPlusNat wv50 (primMulNat wv40 wv310))",fontsize=16,color="green",shape="box"];118 -> 142[label="",style="dashed", color="green", weight=3];
11.00/4.39	119[label="wv310",fontsize=16,color="green",shape="box"];120[label="wv40",fontsize=16,color="green",shape="box"];121[label="wv40",fontsize=16,color="green",shape="box"];122[label="wv310",fontsize=16,color="green",shape="box"];123[label="Neg (primPlusNat wv50 (primMulNat wv40 wv310))",fontsize=16,color="green",shape="box"];123 -> 143[label="",style="dashed", color="green", weight=3];
11.00/4.39	124[label="primMinusNat (primMulNat wv40 wv310) wv50",fontsize=16,color="burlywood",shape="box"];596[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];124 -> 596[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	596 -> 144[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	597[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];124 -> 597[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	597 -> 145[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	125[label="wv310",fontsize=16,color="green",shape="box"];126[label="wv40",fontsize=16,color="green",shape="box"];127[label="wv40",fontsize=16,color="green",shape="box"];128[label="wv310",fontsize=16,color="green",shape="box"];333[label="wv3100",fontsize=16,color="green",shape="box"];334[label="Zero",fontsize=16,color="green",shape="box"];270[label="primMulNat wv400 (Succ wv3100)",fontsize=16,color="burlywood",shape="triangle"];598[label="wv400/Succ wv4000",fontsize=10,color="white",style="solid",shape="box"];270 -> 598[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	598 -> 273[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	599[label="wv400/Zero",fontsize=10,color="white",style="solid",shape="box"];270 -> 599[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	599 -> 274[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	335[label="primPlusNat (Succ wv120) (Succ wv3100)",fontsize=16,color="black",shape="box"];335 -> 358[label="",style="solid", color="black", weight=3];
11.00/4.39	336[label="primPlusNat Zero (Succ wv3100)",fontsize=16,color="black",shape="box"];336 -> 359[label="",style="solid", color="black", weight=3];
11.00/4.39	517[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS (Succ wv320) (Succ wv330))",fontsize=16,color="black",shape="box"];517 -> 521[label="",style="solid", color="black", weight=3];
11.00/4.39	518[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS (Succ wv320) Zero)",fontsize=16,color="black",shape="box"];518 -> 522[label="",style="solid", color="black", weight=3];
11.00/4.39	519[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS Zero (Succ wv330))",fontsize=16,color="black",shape="box"];519 -> 523[label="",style="solid", color="black", weight=3];
11.00/4.39	520[label="primDivNatS0 (Succ wv30) (Succ wv31) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];520 -> 524[label="",style="solid", color="black", weight=3];
11.00/4.39	136[label="primMinusNatS (Succ wv30000) Zero",fontsize=16,color="black",shape="triangle"];136 -> 153[label="",style="solid", color="black", weight=3];
11.00/4.39	137[label="Zero",fontsize=16,color="green",shape="box"];138[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];138 -> 154[label="",style="solid", color="black", weight=3];
11.00/4.39	139[label="Zero",fontsize=16,color="green",shape="box"];140[label="primMinusNat (Succ wv500) (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="box"];600[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];140 -> 600[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	600 -> 155[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	601[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 601[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	601 -> 156[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	141[label="primMinusNat Zero (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="box"];602[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];141 -> 602[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	602 -> 157[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	603[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 603[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	603 -> 158[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	142[label="primPlusNat wv50 (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="triangle"];604[label="wv50/Succ wv500",fontsize=10,color="white",style="solid",shape="box"];142 -> 604[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	604 -> 159[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	605[label="wv50/Zero",fontsize=10,color="white",style="solid",shape="box"];142 -> 605[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	605 -> 160[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	143 -> 142[label="",style="dashed", color="red", weight=0];
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11.00/4.39	143 -> 162[label="",style="dashed", color="magenta", weight=3];
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11.00/4.39	606 -> 163[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	607[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];144 -> 607[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	607 -> 164[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	145[label="primMinusNat (primMulNat Zero wv310) wv50",fontsize=16,color="burlywood",shape="box"];608[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];145 -> 608[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	608 -> 165[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	609[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];145 -> 609[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	609 -> 166[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	273[label="primMulNat (Succ wv4000) (Succ wv3100)",fontsize=16,color="black",shape="box"];273 -> 292[label="",style="solid", color="black", weight=3];
11.00/4.39	274[label="primMulNat Zero (Succ wv3100)",fontsize=16,color="black",shape="box"];274 -> 293[label="",style="solid", color="black", weight=3];
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11.00/4.39	359[label="Succ wv3100",fontsize=16,color="green",shape="box"];521 -> 482[label="",style="dashed", color="red", weight=0];
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11.00/4.39	521 -> 526[label="",style="dashed", color="magenta", weight=3];
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11.00/4.39	523[label="primDivNatS0 (Succ wv30) (Succ wv31) False",fontsize=16,color="black",shape="box"];523 -> 528[label="",style="solid", color="black", weight=3];
11.00/4.39	524 -> 522[label="",style="dashed", color="red", weight=0];
11.00/4.39	524[label="primDivNatS0 (Succ wv30) (Succ wv31) True",fontsize=16,color="magenta"];153[label="Succ wv30000",fontsize=16,color="green",shape="box"];154[label="Zero",fontsize=16,color="green",shape="box"];155[label="primMinusNat (Succ wv500) (primMulNat (Succ wv400) wv310)",fontsize=16,color="burlywood",shape="box"];610[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];155 -> 610[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	610 -> 174[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	611[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];155 -> 611[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	611 -> 175[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	156[label="primMinusNat (Succ wv500) (primMulNat Zero wv310)",fontsize=16,color="burlywood",shape="box"];612[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];156 -> 612[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	612 -> 176[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	613[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];156 -> 613[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	613 -> 177[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	157[label="primMinusNat Zero (primMulNat (Succ wv400) wv310)",fontsize=16,color="burlywood",shape="box"];614[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];157 -> 614[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	614 -> 178[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	615[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];157 -> 615[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	615 -> 179[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	158[label="primMinusNat Zero (primMulNat Zero wv310)",fontsize=16,color="burlywood",shape="box"];616[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];158 -> 616[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	616 -> 180[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	617[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];158 -> 617[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	617 -> 181[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	159[label="primPlusNat (Succ wv500) (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="box"];618[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];159 -> 618[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	618 -> 182[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	619[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];159 -> 619[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	619 -> 183[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	160[label="primPlusNat Zero (primMulNat wv40 wv310)",fontsize=16,color="burlywood",shape="box"];620[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];160 -> 620[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	620 -> 184[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	621[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];160 -> 621[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	621 -> 185[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	161[label="wv310",fontsize=16,color="green",shape="box"];162[label="wv50",fontsize=16,color="green",shape="box"];163[label="primMinusNat (primMulNat (Succ wv400) (Succ wv3100)) wv50",fontsize=16,color="black",shape="box"];163 -> 186[label="",style="solid", color="black", weight=3];
11.00/4.39	164[label="primMinusNat (primMulNat (Succ wv400) Zero) wv50",fontsize=16,color="black",shape="box"];164 -> 187[label="",style="solid", color="black", weight=3];
11.00/4.39	165[label="primMinusNat (primMulNat Zero (Succ wv3100)) wv50",fontsize=16,color="black",shape="box"];165 -> 188[label="",style="solid", color="black", weight=3];
11.00/4.39	166[label="primMinusNat (primMulNat Zero Zero) wv50",fontsize=16,color="black",shape="box"];166 -> 189[label="",style="solid", color="black", weight=3];
11.00/4.39	292 -> 319[label="",style="dashed", color="red", weight=0];
11.00/4.39	292[label="primPlusNat (primMulNat wv4000 (Succ wv3100)) (Succ wv3100)",fontsize=16,color="magenta"];292 -> 329[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	292 -> 330[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	293[label="Zero",fontsize=16,color="green",shape="box"];375 -> 360[label="",style="dashed", color="red", weight=0];
11.00/4.39	375[label="primPlusNat wv120 wv3100",fontsize=16,color="magenta"];375 -> 395[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	525[label="wv320",fontsize=16,color="green",shape="box"];526[label="wv330",fontsize=16,color="green",shape="box"];527[label="Succ (primDivNatS (primMinusNatS (Succ wv30) (Succ wv31)) (Succ (Succ wv31)))",fontsize=16,color="green",shape="box"];527 -> 529[label="",style="dashed", color="green", weight=3];
11.00/4.39	528[label="Zero",fontsize=16,color="green",shape="box"];174[label="primMinusNat (Succ wv500) (primMulNat (Succ wv400) (Succ wv3100))",fontsize=16,color="black",shape="box"];174 -> 200[label="",style="solid", color="black", weight=3];
11.00/4.39	175[label="primMinusNat (Succ wv500) (primMulNat (Succ wv400) Zero)",fontsize=16,color="black",shape="box"];175 -> 201[label="",style="solid", color="black", weight=3];
11.00/4.39	176[label="primMinusNat (Succ wv500) (primMulNat Zero (Succ wv3100))",fontsize=16,color="black",shape="box"];176 -> 202[label="",style="solid", color="black", weight=3];
11.00/4.39	177[label="primMinusNat (Succ wv500) (primMulNat Zero Zero)",fontsize=16,color="black",shape="box"];177 -> 203[label="",style="solid", color="black", weight=3];
11.00/4.39	178[label="primMinusNat Zero (primMulNat (Succ wv400) (Succ wv3100))",fontsize=16,color="black",shape="box"];178 -> 204[label="",style="solid", color="black", weight=3];
11.00/4.39	179[label="primMinusNat Zero (primMulNat (Succ wv400) Zero)",fontsize=16,color="black",shape="box"];179 -> 205[label="",style="solid", color="black", weight=3];
11.00/4.39	180[label="primMinusNat Zero (primMulNat Zero (Succ wv3100))",fontsize=16,color="black",shape="box"];180 -> 206[label="",style="solid", color="black", weight=3];
11.00/4.39	181[label="primMinusNat Zero (primMulNat Zero Zero)",fontsize=16,color="black",shape="box"];181 -> 207[label="",style="solid", color="black", weight=3];
11.00/4.39	182[label="primPlusNat (Succ wv500) (primMulNat (Succ wv400) wv310)",fontsize=16,color="burlywood",shape="box"];622[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];182 -> 622[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	622 -> 208[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	623[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];182 -> 623[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	623 -> 209[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	183[label="primPlusNat (Succ wv500) (primMulNat Zero wv310)",fontsize=16,color="burlywood",shape="box"];624[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];183 -> 624[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	624 -> 210[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	625[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];183 -> 625[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	625 -> 211[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	184[label="primPlusNat Zero (primMulNat (Succ wv400) wv310)",fontsize=16,color="burlywood",shape="box"];626[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];184 -> 626[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	626 -> 212[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	627[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];184 -> 627[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	627 -> 213[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	185[label="primPlusNat Zero (primMulNat Zero wv310)",fontsize=16,color="burlywood",shape="box"];628[label="wv310/Succ wv3100",fontsize=10,color="white",style="solid",shape="box"];185 -> 628[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	628 -> 214[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	629[label="wv310/Zero",fontsize=10,color="white",style="solid",shape="box"];185 -> 629[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	629 -> 215[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	186 -> 269[label="",style="dashed", color="red", weight=0];
11.00/4.39	186[label="primMinusNat (primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100)) wv50",fontsize=16,color="magenta"];186 -> 270[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	187[label="primMinusNat Zero wv50",fontsize=16,color="burlywood",shape="triangle"];630[label="wv50/Succ wv500",fontsize=10,color="white",style="solid",shape="box"];187 -> 630[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	630 -> 218[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	631[label="wv50/Zero",fontsize=10,color="white",style="solid",shape="box"];187 -> 631[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	631 -> 219[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	188 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	188[label="primMinusNat Zero wv50",fontsize=16,color="magenta"];189 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	189[label="primMinusNat Zero wv50",fontsize=16,color="magenta"];329 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	329[label="primMulNat wv4000 (Succ wv3100)",fontsize=16,color="magenta"];329 -> 346[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	330[label="wv3100",fontsize=16,color="green",shape="box"];395[label="wv120",fontsize=16,color="green",shape="box"];360[label="primPlusNat wv100 wv3100",fontsize=16,color="burlywood",shape="triangle"];632[label="wv100/Succ wv1000",fontsize=10,color="white",style="solid",shape="box"];360 -> 632[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	632 -> 376[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	633[label="wv100/Zero",fontsize=10,color="white",style="solid",shape="box"];360 -> 633[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	633 -> 377[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	529 -> 41[label="",style="dashed", color="red", weight=0];
11.00/4.39	529[label="primDivNatS (primMinusNatS (Succ wv30) (Succ wv31)) (Succ (Succ wv31))",fontsize=16,color="magenta"];529 -> 530[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	529 -> 531[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	200 -> 285[label="",style="dashed", color="red", weight=0];
11.00/4.39	200[label="primMinusNat (Succ wv500) (primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100))",fontsize=16,color="magenta"];200 -> 286[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	201[label="primMinusNat (Succ wv500) Zero",fontsize=16,color="black",shape="triangle"];201 -> 231[label="",style="solid", color="black", weight=3];
11.00/4.39	202 -> 201[label="",style="dashed", color="red", weight=0];
11.00/4.39	202[label="primMinusNat (Succ wv500) Zero",fontsize=16,color="magenta"];203 -> 201[label="",style="dashed", color="red", weight=0];
11.00/4.39	203[label="primMinusNat (Succ wv500) Zero",fontsize=16,color="magenta"];204 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	204[label="primMinusNat Zero (primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100))",fontsize=16,color="magenta"];204 -> 232[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	205 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	205[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];205 -> 233[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	206 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	206[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];206 -> 234[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	207 -> 187[label="",style="dashed", color="red", weight=0];
11.00/4.39	207[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];207 -> 235[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	208[label="primPlusNat (Succ wv500) (primMulNat (Succ wv400) (Succ wv3100))",fontsize=16,color="black",shape="box"];208 -> 236[label="",style="solid", color="black", weight=3];
11.00/4.39	209[label="primPlusNat (Succ wv500) (primMulNat (Succ wv400) Zero)",fontsize=16,color="black",shape="box"];209 -> 237[label="",style="solid", color="black", weight=3];
11.00/4.39	210[label="primPlusNat (Succ wv500) (primMulNat Zero (Succ wv3100))",fontsize=16,color="black",shape="box"];210 -> 238[label="",style="solid", color="black", weight=3];
11.00/4.39	211[label="primPlusNat (Succ wv500) (primMulNat Zero Zero)",fontsize=16,color="black",shape="box"];211 -> 239[label="",style="solid", color="black", weight=3];
11.00/4.39	212[label="primPlusNat Zero (primMulNat (Succ wv400) (Succ wv3100))",fontsize=16,color="black",shape="box"];212 -> 240[label="",style="solid", color="black", weight=3];
11.00/4.39	213[label="primPlusNat Zero (primMulNat (Succ wv400) Zero)",fontsize=16,color="black",shape="box"];213 -> 241[label="",style="solid", color="black", weight=3];
11.00/4.39	214[label="primPlusNat Zero (primMulNat Zero (Succ wv3100))",fontsize=16,color="black",shape="box"];214 -> 242[label="",style="solid", color="black", weight=3];
11.00/4.39	215[label="primPlusNat Zero (primMulNat Zero Zero)",fontsize=16,color="black",shape="box"];215 -> 243[label="",style="solid", color="black", weight=3];
11.00/4.39	269[label="primMinusNat (primPlusNat wv9 (Succ wv3100)) wv50",fontsize=16,color="burlywood",shape="triangle"];634[label="wv9/Succ wv90",fontsize=10,color="white",style="solid",shape="box"];269 -> 634[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	634 -> 275[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	635[label="wv9/Zero",fontsize=10,color="white",style="solid",shape="box"];269 -> 635[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	635 -> 276[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	218[label="primMinusNat Zero (Succ wv500)",fontsize=16,color="black",shape="box"];218 -> 246[label="",style="solid", color="black", weight=3];
11.00/4.39	219[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];219 -> 247[label="",style="solid", color="black", weight=3];
11.00/4.39	346[label="wv4000",fontsize=16,color="green",shape="box"];376[label="primPlusNat (Succ wv1000) wv3100",fontsize=16,color="burlywood",shape="box"];636[label="wv3100/Succ wv31000",fontsize=10,color="white",style="solid",shape="box"];376 -> 636[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	636 -> 396[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	637[label="wv3100/Zero",fontsize=10,color="white",style="solid",shape="box"];376 -> 637[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	637 -> 397[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	377[label="primPlusNat Zero wv3100",fontsize=16,color="burlywood",shape="box"];638[label="wv3100/Succ wv31000",fontsize=10,color="white",style="solid",shape="box"];377 -> 638[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	638 -> 398[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	639[label="wv3100/Zero",fontsize=10,color="white",style="solid",shape="box"];377 -> 639[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	639 -> 399[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	530[label="primMinusNatS (Succ wv30) (Succ wv31)",fontsize=16,color="black",shape="box"];530 -> 532[label="",style="solid", color="black", weight=3];
11.00/4.39	531[label="Succ wv31",fontsize=16,color="green",shape="box"];286 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	286[label="primMulNat wv400 (Succ wv3100)",fontsize=16,color="magenta"];286 -> 289[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	285[label="primMinusNat (Succ wv500) (primPlusNat wv10 (Succ wv3100))",fontsize=16,color="burlywood",shape="triangle"];640[label="wv10/Succ wv100",fontsize=10,color="white",style="solid",shape="box"];285 -> 640[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	640 -> 290[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	641[label="wv10/Zero",fontsize=10,color="white",style="solid",shape="box"];285 -> 641[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	641 -> 291[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	231[label="Pos (Succ wv500)",fontsize=16,color="green",shape="box"];232 -> 319[label="",style="dashed", color="red", weight=0];
11.00/4.39	232[label="primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100)",fontsize=16,color="magenta"];232 -> 324[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	233[label="Zero",fontsize=16,color="green",shape="box"];234[label="Zero",fontsize=16,color="green",shape="box"];235[label="Zero",fontsize=16,color="green",shape="box"];236 -> 259[label="",style="dashed", color="red", weight=0];
11.00/4.39	236[label="primPlusNat (Succ wv500) (primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100))",fontsize=16,color="magenta"];236 -> 260[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	237 -> 259[label="",style="dashed", color="red", weight=0];
11.00/4.39	237[label="primPlusNat (Succ wv500) Zero",fontsize=16,color="magenta"];237 -> 261[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	238 -> 259[label="",style="dashed", color="red", weight=0];
11.00/4.39	238[label="primPlusNat (Succ wv500) Zero",fontsize=16,color="magenta"];238 -> 262[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	239 -> 259[label="",style="dashed", color="red", weight=0];
11.00/4.39	239[label="primPlusNat (Succ wv500) Zero",fontsize=16,color="magenta"];239 -> 263[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	240 -> 264[label="",style="dashed", color="red", weight=0];
11.00/4.39	240[label="primPlusNat Zero (primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100))",fontsize=16,color="magenta"];240 -> 265[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	241 -> 264[label="",style="dashed", color="red", weight=0];
11.00/4.39	241[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];241 -> 266[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	242 -> 264[label="",style="dashed", color="red", weight=0];
11.00/4.39	242[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];242 -> 267[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	243 -> 264[label="",style="dashed", color="red", weight=0];
11.00/4.39	243[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];243 -> 268[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	275[label="primMinusNat (primPlusNat (Succ wv90) (Succ wv3100)) wv50",fontsize=16,color="black",shape="box"];275 -> 294[label="",style="solid", color="black", weight=3];
11.00/4.39	276[label="primMinusNat (primPlusNat Zero (Succ wv3100)) wv50",fontsize=16,color="black",shape="box"];276 -> 295[label="",style="solid", color="black", weight=3];
11.00/4.39	246[label="Neg (Succ wv500)",fontsize=16,color="green",shape="box"];247[label="Pos Zero",fontsize=16,color="green",shape="box"];396[label="primPlusNat (Succ wv1000) (Succ wv31000)",fontsize=16,color="black",shape="box"];396 -> 411[label="",style="solid", color="black", weight=3];
11.00/4.39	397[label="primPlusNat (Succ wv1000) Zero",fontsize=16,color="black",shape="box"];397 -> 412[label="",style="solid", color="black", weight=3];
11.00/4.39	398[label="primPlusNat Zero (Succ wv31000)",fontsize=16,color="black",shape="box"];398 -> 413[label="",style="solid", color="black", weight=3];
11.00/4.39	399[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];399 -> 414[label="",style="solid", color="black", weight=3];
11.00/4.39	532[label="primMinusNatS wv30 wv31",fontsize=16,color="burlywood",shape="triangle"];642[label="wv30/Succ wv300",fontsize=10,color="white",style="solid",shape="box"];532 -> 642[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	642 -> 533[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	643[label="wv30/Zero",fontsize=10,color="white",style="solid",shape="box"];532 -> 643[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	643 -> 534[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	289[label="wv3100",fontsize=16,color="green",shape="box"];290[label="primMinusNat (Succ wv500) (primPlusNat (Succ wv100) (Succ wv3100))",fontsize=16,color="black",shape="box"];290 -> 311[label="",style="solid", color="black", weight=3];
11.00/4.39	291[label="primMinusNat (Succ wv500) (primPlusNat Zero (Succ wv3100))",fontsize=16,color="black",shape="box"];291 -> 312[label="",style="solid", color="black", weight=3];
11.00/4.39	324 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	324[label="primMulNat wv400 (Succ wv3100)",fontsize=16,color="magenta"];324 -> 337[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	260 -> 319[label="",style="dashed", color="red", weight=0];
11.00/4.39	260[label="primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100)",fontsize=16,color="magenta"];260 -> 325[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	260 -> 326[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	259[label="primPlusNat (Succ wv500) wv7",fontsize=16,color="burlywood",shape="triangle"];644[label="wv7/Succ wv70",fontsize=10,color="white",style="solid",shape="box"];259 -> 644[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	644 -> 299[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	645[label="wv7/Zero",fontsize=10,color="white",style="solid",shape="box"];259 -> 645[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	645 -> 300[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	261[label="Zero",fontsize=16,color="green",shape="box"];262[label="Zero",fontsize=16,color="green",shape="box"];263[label="Zero",fontsize=16,color="green",shape="box"];265 -> 319[label="",style="dashed", color="red", weight=0];
11.00/4.39	265[label="primPlusNat (primMulNat wv400 (Succ wv3100)) (Succ wv3100)",fontsize=16,color="magenta"];265 -> 327[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	265 -> 328[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	264[label="primPlusNat Zero wv8",fontsize=16,color="burlywood",shape="triangle"];646[label="wv8/Succ wv80",fontsize=10,color="white",style="solid",shape="box"];264 -> 646[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	646 -> 302[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	647[label="wv8/Zero",fontsize=10,color="white",style="solid",shape="box"];264 -> 647[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	647 -> 303[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	266[label="Zero",fontsize=16,color="green",shape="box"];267[label="Zero",fontsize=16,color="green",shape="box"];268[label="Zero",fontsize=16,color="green",shape="box"];294[label="primMinusNat (Succ (Succ (primPlusNat wv90 wv3100))) wv50",fontsize=16,color="burlywood",shape="box"];648[label="wv50/Succ wv500",fontsize=10,color="white",style="solid",shape="box"];294 -> 648[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	648 -> 315[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	649[label="wv50/Zero",fontsize=10,color="white",style="solid",shape="box"];294 -> 649[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	649 -> 316[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	295[label="primMinusNat (Succ wv3100) wv50",fontsize=16,color="burlywood",shape="triangle"];650[label="wv50/Succ wv500",fontsize=10,color="white",style="solid",shape="box"];295 -> 650[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	650 -> 317[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	651[label="wv50/Zero",fontsize=10,color="white",style="solid",shape="box"];295 -> 651[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	651 -> 318[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	411[label="Succ (Succ (primPlusNat wv1000 wv31000))",fontsize=16,color="green",shape="box"];411 -> 425[label="",style="dashed", color="green", weight=3];
11.00/4.39	412[label="Succ wv1000",fontsize=16,color="green",shape="box"];413[label="Succ wv31000",fontsize=16,color="green",shape="box"];414[label="Zero",fontsize=16,color="green",shape="box"];533[label="primMinusNatS (Succ wv300) wv31",fontsize=16,color="burlywood",shape="box"];652[label="wv31/Succ wv310",fontsize=10,color="white",style="solid",shape="box"];533 -> 652[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	652 -> 535[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	653[label="wv31/Zero",fontsize=10,color="white",style="solid",shape="box"];533 -> 653[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	653 -> 536[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	534[label="primMinusNatS Zero wv31",fontsize=16,color="burlywood",shape="box"];654[label="wv31/Succ wv310",fontsize=10,color="white",style="solid",shape="box"];534 -> 654[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	654 -> 537[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	655[label="wv31/Zero",fontsize=10,color="white",style="solid",shape="box"];534 -> 655[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	655 -> 538[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	311 -> 295[label="",style="dashed", color="red", weight=0];
11.00/4.39	311[label="primMinusNat (Succ wv500) (Succ (Succ (primPlusNat wv100 wv3100)))",fontsize=16,color="magenta"];311 -> 338[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	311 -> 339[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	312 -> 295[label="",style="dashed", color="red", weight=0];
11.00/4.39	312[label="primMinusNat (Succ wv500) (Succ wv3100)",fontsize=16,color="magenta"];312 -> 340[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	312 -> 341[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	337[label="wv3100",fontsize=16,color="green",shape="box"];325 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	325[label="primMulNat wv400 (Succ wv3100)",fontsize=16,color="magenta"];326[label="wv3100",fontsize=16,color="green",shape="box"];299[label="primPlusNat (Succ wv500) (Succ wv70)",fontsize=16,color="black",shape="box"];299 -> 342[label="",style="solid", color="black", weight=3];
11.00/4.39	300[label="primPlusNat (Succ wv500) Zero",fontsize=16,color="black",shape="box"];300 -> 343[label="",style="solid", color="black", weight=3];
11.00/4.39	327 -> 270[label="",style="dashed", color="red", weight=0];
11.00/4.39	327[label="primMulNat wv400 (Succ wv3100)",fontsize=16,color="magenta"];328[label="wv3100",fontsize=16,color="green",shape="box"];302[label="primPlusNat Zero (Succ wv80)",fontsize=16,color="black",shape="box"];302 -> 344[label="",style="solid", color="black", weight=3];
11.00/4.39	303[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];303 -> 345[label="",style="solid", color="black", weight=3];
11.00/4.39	315[label="primMinusNat (Succ (Succ (primPlusNat wv90 wv3100))) (Succ wv500)",fontsize=16,color="black",shape="box"];315 -> 347[label="",style="solid", color="black", weight=3];
11.00/4.39	316[label="primMinusNat (Succ (Succ (primPlusNat wv90 wv3100))) Zero",fontsize=16,color="black",shape="box"];316 -> 348[label="",style="solid", color="black", weight=3];
11.00/4.39	317[label="primMinusNat (Succ wv3100) (Succ wv500)",fontsize=16,color="black",shape="box"];317 -> 349[label="",style="solid", color="black", weight=3];
11.00/4.39	318[label="primMinusNat (Succ wv3100) Zero",fontsize=16,color="black",shape="box"];318 -> 350[label="",style="solid", color="black", weight=3];
11.00/4.39	425 -> 360[label="",style="dashed", color="red", weight=0];
11.00/4.39	425[label="primPlusNat wv1000 wv31000",fontsize=16,color="magenta"];425 -> 430[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	425 -> 431[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	535[label="primMinusNatS (Succ wv300) (Succ wv310)",fontsize=16,color="black",shape="box"];535 -> 539[label="",style="solid", color="black", weight=3];
11.00/4.39	536[label="primMinusNatS (Succ wv300) Zero",fontsize=16,color="black",shape="box"];536 -> 540[label="",style="solid", color="black", weight=3];
11.00/4.39	537[label="primMinusNatS Zero (Succ wv310)",fontsize=16,color="black",shape="box"];537 -> 541[label="",style="solid", color="black", weight=3];
11.00/4.39	538[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];538 -> 542[label="",style="solid", color="black", weight=3];
11.00/4.39	338[label="wv500",fontsize=16,color="green",shape="box"];339[label="Succ (Succ (primPlusNat wv100 wv3100))",fontsize=16,color="green",shape="box"];339 -> 360[label="",style="dashed", color="green", weight=3];
11.00/4.39	340[label="wv500",fontsize=16,color="green",shape="box"];341[label="Succ wv3100",fontsize=16,color="green",shape="box"];342[label="Succ (Succ (primPlusNat wv500 wv70))",fontsize=16,color="green",shape="box"];342 -> 361[label="",style="dashed", color="green", weight=3];
11.00/4.39	343[label="Succ wv500",fontsize=16,color="green",shape="box"];344[label="Succ wv80",fontsize=16,color="green",shape="box"];345[label="Zero",fontsize=16,color="green",shape="box"];347 -> 295[label="",style="dashed", color="red", weight=0];
11.00/4.39	347[label="primMinusNat (Succ (primPlusNat wv90 wv3100)) wv500",fontsize=16,color="magenta"];347 -> 362[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	347 -> 363[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	348[label="Pos (Succ (Succ (primPlusNat wv90 wv3100)))",fontsize=16,color="green",shape="box"];348 -> 364[label="",style="dashed", color="green", weight=3];
11.00/4.39	349[label="primMinusNat wv3100 wv500",fontsize=16,color="burlywood",shape="triangle"];656[label="wv3100/Succ wv31000",fontsize=10,color="white",style="solid",shape="box"];349 -> 656[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	656 -> 365[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	657[label="wv3100/Zero",fontsize=10,color="white",style="solid",shape="box"];349 -> 657[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	657 -> 366[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	350[label="Pos (Succ wv3100)",fontsize=16,color="green",shape="box"];430[label="wv1000",fontsize=16,color="green",shape="box"];431[label="wv31000",fontsize=16,color="green",shape="box"];539 -> 532[label="",style="dashed", color="red", weight=0];
11.00/4.39	539[label="primMinusNatS wv300 wv310",fontsize=16,color="magenta"];539 -> 543[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	539 -> 544[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	540[label="Succ wv300",fontsize=16,color="green",shape="box"];541[label="Zero",fontsize=16,color="green",shape="box"];542[label="Zero",fontsize=16,color="green",shape="box"];361 -> 360[label="",style="dashed", color="red", weight=0];
11.00/4.39	361[label="primPlusNat wv500 wv70",fontsize=16,color="magenta"];361 -> 378[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	361 -> 379[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	362 -> 360[label="",style="dashed", color="red", weight=0];
11.00/4.39	362[label="primPlusNat wv90 wv3100",fontsize=16,color="magenta"];362 -> 380[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	362 -> 381[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	363[label="wv500",fontsize=16,color="green",shape="box"];364 -> 360[label="",style="dashed", color="red", weight=0];
11.00/4.39	364[label="primPlusNat wv90 wv3100",fontsize=16,color="magenta"];364 -> 382[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	364 -> 383[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	365[label="primMinusNat (Succ wv31000) wv500",fontsize=16,color="burlywood",shape="box"];658[label="wv500/Succ wv5000",fontsize=10,color="white",style="solid",shape="box"];365 -> 658[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	658 -> 384[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	659[label="wv500/Zero",fontsize=10,color="white",style="solid",shape="box"];365 -> 659[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	659 -> 385[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	366[label="primMinusNat Zero wv500",fontsize=16,color="burlywood",shape="box"];660[label="wv500/Succ wv5000",fontsize=10,color="white",style="solid",shape="box"];366 -> 660[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	660 -> 386[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	661[label="wv500/Zero",fontsize=10,color="white",style="solid",shape="box"];366 -> 661[label="",style="solid", color="burlywood", weight=9];
11.00/4.39	661 -> 387[label="",style="solid", color="burlywood", weight=3];
11.00/4.39	543[label="wv310",fontsize=16,color="green",shape="box"];544[label="wv300",fontsize=16,color="green",shape="box"];378[label="wv500",fontsize=16,color="green",shape="box"];379[label="wv70",fontsize=16,color="green",shape="box"];380[label="wv90",fontsize=16,color="green",shape="box"];381[label="wv3100",fontsize=16,color="green",shape="box"];382[label="wv90",fontsize=16,color="green",shape="box"];383[label="wv3100",fontsize=16,color="green",shape="box"];384[label="primMinusNat (Succ wv31000) (Succ wv5000)",fontsize=16,color="black",shape="box"];384 -> 400[label="",style="solid", color="black", weight=3];
11.00/4.39	385[label="primMinusNat (Succ wv31000) Zero",fontsize=16,color="black",shape="box"];385 -> 401[label="",style="solid", color="black", weight=3];
11.00/4.39	386[label="primMinusNat Zero (Succ wv5000)",fontsize=16,color="black",shape="box"];386 -> 402[label="",style="solid", color="black", weight=3];
11.00/4.39	387[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];387 -> 403[label="",style="solid", color="black", weight=3];
11.00/4.39	400 -> 349[label="",style="dashed", color="red", weight=0];
11.00/4.39	400[label="primMinusNat wv31000 wv5000",fontsize=16,color="magenta"];400 -> 415[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	400 -> 416[label="",style="dashed", color="magenta", weight=3];
11.00/4.39	401[label="Pos (Succ wv31000)",fontsize=16,color="green",shape="box"];402[label="Neg (Succ wv5000)",fontsize=16,color="green",shape="box"];403[label="Pos Zero",fontsize=16,color="green",shape="box"];415[label="wv31000",fontsize=16,color="green",shape="box"];416[label="wv5000",fontsize=16,color="green",shape="box"];}
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(10)
11.00/4.39	Complex Obligation (AND)
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(11)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMulNat(Succ(wv4000), wv3100) -> new_primMulNat(wv4000, wv3100)
11.00/4.39	
11.00/4.39	R is empty.
11.00/4.39	Q is empty.
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(12) QDPSizeChangeProof (EQUIVALENT)
11.00/4.39	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
11.00/4.39	
11.00/4.39	From the DPs we obtained the following set of size-change graphs:
11.00/4.39	*new_primMulNat(Succ(wv4000), wv3100) -> new_primMulNat(wv4000, wv3100)
11.00/4.39	The graph contains the following edges 1 > 1, 2 >= 2
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(13)
11.00/4.39	YES
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(14)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primDivNatS(Succ(Succ(wv30000)), Succ(wv31000)) -> new_primDivNatS0(wv30000, wv31000, wv30000, wv31000)
11.00/4.39	   new_primDivNatS0(wv30, wv31, Succ(wv320), Zero) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31))
11.00/4.39	   new_primDivNatS0(wv30, wv31, Zero, Zero) -> new_primDivNatS00(wv30, wv31)
11.00/4.39	   new_primDivNatS0(wv30, wv31, Succ(wv320), Succ(wv330)) -> new_primDivNatS0(wv30, wv31, wv320, wv330)
11.00/4.39	   new_primDivNatS(Succ(Zero), Zero) -> new_primDivNatS(new_primMinusNatS2, Zero)
11.00/4.39	   new_primDivNatS(Succ(Succ(wv30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(wv30000), Zero)
11.00/4.39	   new_primDivNatS00(wv30, wv31) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31))
11.00/4.39	
11.00/4.39	The TRS R consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Succ(wv310)) -> Zero
11.00/4.39	   new_primMinusNatS0(Zero, Zero) -> Zero
11.00/4.39	   new_primMinusNatS1(wv30000) -> Succ(wv30000)
11.00/4.39	   new_primMinusNatS2 -> Zero
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Succ(wv310)) -> new_primMinusNatS0(wv300, wv310)
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Zero) -> Succ(wv300)
11.00/4.39	
11.00/4.39	The set Q consists of the following terms:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Zero)
11.00/4.39	   new_primMinusNatS2
11.00/4.39	   new_primMinusNatS1(x0)
11.00/4.39	   new_primMinusNatS0(Succ(x0), Zero)
11.00/4.39	   new_primMinusNatS0(Zero, Succ(x0))
11.00/4.39	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.00/4.39	
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(15) DependencyGraphProof (EQUIVALENT)
11.00/4.39	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(16)
11.00/4.39	Complex Obligation (AND)
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(17)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primDivNatS(Succ(Succ(wv30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(wv30000), Zero)
11.00/4.39	
11.00/4.39	The TRS R consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Succ(wv310)) -> Zero
11.00/4.39	   new_primMinusNatS0(Zero, Zero) -> Zero
11.00/4.39	   new_primMinusNatS1(wv30000) -> Succ(wv30000)
11.00/4.39	   new_primMinusNatS2 -> Zero
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Succ(wv310)) -> new_primMinusNatS0(wv300, wv310)
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Zero) -> Succ(wv300)
11.00/4.39	
11.00/4.39	The set Q consists of the following terms:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Zero)
11.00/4.39	   new_primMinusNatS2
11.00/4.39	   new_primMinusNatS1(x0)
11.00/4.39	   new_primMinusNatS0(Succ(x0), Zero)
11.00/4.39	   new_primMinusNatS0(Zero, Succ(x0))
11.00/4.39	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.00/4.39	
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(18) MRRProof (EQUIVALENT)
11.00/4.39	By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
11.00/4.39	
11.00/4.39	Strictly oriented dependency pairs:
11.00/4.39	
11.00/4.39	   new_primDivNatS(Succ(Succ(wv30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(wv30000), Zero)
11.00/4.39	
11.00/4.39	Strictly oriented rules of the TRS R:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Succ(wv310)) -> Zero
11.00/4.39	   new_primMinusNatS0(Zero, Zero) -> Zero
11.00/4.39	   new_primMinusNatS1(wv30000) -> Succ(wv30000)
11.00/4.39	   new_primMinusNatS2 -> Zero
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Succ(wv310)) -> new_primMinusNatS0(wv300, wv310)
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Zero) -> Succ(wv300)
11.00/4.39	
11.00/4.39	Used ordering: Polynomial interpretation [POLO]:
11.00/4.39	
11.00/4.39	   POL(Succ(x_1)) = 1 + 2*x_1
11.00/4.39	   POL(Zero) = 1
11.00/4.39	   POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2
11.00/4.39	   POL(new_primMinusNatS0(x_1, x_2)) = x_1 + x_2
11.00/4.39	   POL(new_primMinusNatS1(x_1)) = 2 + 2*x_1
11.00/4.39	   POL(new_primMinusNatS2) = 2
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(19)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	P is empty.
11.00/4.39	R is empty.
11.00/4.39	The set Q consists of the following terms:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Zero)
11.00/4.39	   new_primMinusNatS2
11.00/4.39	   new_primMinusNatS1(x0)
11.00/4.39	   new_primMinusNatS0(Succ(x0), Zero)
11.00/4.39	   new_primMinusNatS0(Zero, Succ(x0))
11.00/4.39	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.00/4.39	
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(20) PisEmptyProof (EQUIVALENT)
11.00/4.39	The TRS P is empty. Hence, there is no (P,Q,R) chain.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(21)
11.00/4.39	YES
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(22)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primDivNatS0(wv30, wv31, Succ(wv320), Zero) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31))
11.00/4.39	   new_primDivNatS(Succ(Succ(wv30000)), Succ(wv31000)) -> new_primDivNatS0(wv30000, wv31000, wv30000, wv31000)
11.00/4.39	   new_primDivNatS0(wv30, wv31, Zero, Zero) -> new_primDivNatS00(wv30, wv31)
11.00/4.39	   new_primDivNatS00(wv30, wv31) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31))
11.00/4.39	   new_primDivNatS0(wv30, wv31, Succ(wv320), Succ(wv330)) -> new_primDivNatS0(wv30, wv31, wv320, wv330)
11.00/4.39	
11.00/4.39	The TRS R consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Succ(wv310)) -> Zero
11.00/4.39	   new_primMinusNatS0(Zero, Zero) -> Zero
11.00/4.39	   new_primMinusNatS1(wv30000) -> Succ(wv30000)
11.00/4.39	   new_primMinusNatS2 -> Zero
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Succ(wv310)) -> new_primMinusNatS0(wv300, wv310)
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Zero) -> Succ(wv300)
11.00/4.39	
11.00/4.39	The set Q consists of the following terms:
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Zero)
11.00/4.39	   new_primMinusNatS2
11.00/4.39	   new_primMinusNatS1(x0)
11.00/4.39	   new_primMinusNatS0(Succ(x0), Zero)
11.00/4.39	   new_primMinusNatS0(Zero, Succ(x0))
11.00/4.39	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.00/4.39	
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(23) QDPSizeChangeProof (EQUIVALENT)
11.00/4.39	We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
11.00/4.39	
11.00/4.39	Order:Polynomial interpretation [POLO]:
11.00/4.39	
11.00/4.39	   POL(Succ(x_1)) = 1 + x_1
11.00/4.39	   POL(Zero) = 1
11.00/4.39	   POL(new_primMinusNatS0(x_1, x_2)) = x_1
11.00/4.39	
11.00/4.39	
11.00/4.39	
11.00/4.39	
11.00/4.39	From the DPs we obtained the following set of size-change graphs:
11.00/4.39	*new_primDivNatS(Succ(Succ(wv30000)), Succ(wv31000)) -> new_primDivNatS0(wv30000, wv31000, wv30000, wv31000) (allowed arguments on rhs = {1, 2, 3, 4})
11.00/4.39	The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4
11.00/4.39	
11.00/4.39	
11.00/4.39	*new_primDivNatS0(wv30, wv31, Succ(wv320), Succ(wv330)) -> new_primDivNatS0(wv30, wv31, wv320, wv330) (allowed arguments on rhs = {1, 2, 3, 4})
11.00/4.39	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
11.00/4.39	
11.00/4.39	
11.00/4.39	*new_primDivNatS0(wv30, wv31, Succ(wv320), Zero) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31)) (allowed arguments on rhs = {1, 2})
11.00/4.39	The graph contains the following edges 1 >= 1
11.00/4.39	
11.00/4.39	
11.00/4.39	*new_primDivNatS0(wv30, wv31, Zero, Zero) -> new_primDivNatS00(wv30, wv31) (allowed arguments on rhs = {1, 2})
11.00/4.39	The graph contains the following edges 1 >= 1, 2 >= 2
11.00/4.39	
11.00/4.39	
11.00/4.39	*new_primDivNatS00(wv30, wv31) -> new_primDivNatS(new_primMinusNatS0(wv30, wv31), Succ(wv31)) (allowed arguments on rhs = {1, 2})
11.00/4.39	The graph contains the following edges 1 >= 1
11.00/4.39	
11.00/4.39	
11.00/4.39	
11.00/4.39	We oriented the following set of usable rules [AAECC05,FROCOS05].
11.00/4.39	
11.00/4.39	   new_primMinusNatS0(Zero, Zero) -> Zero
11.00/4.39	   new_primMinusNatS0(Zero, Succ(wv310)) -> Zero
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Zero) -> Succ(wv300)
11.00/4.39	   new_primMinusNatS0(Succ(wv300), Succ(wv310)) -> new_primMinusNatS0(wv300, wv310)
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(24)
11.00/4.39	YES
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(25)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMinusNatS(Succ(wv300), Succ(wv310)) -> new_primMinusNatS(wv300, wv310)
11.00/4.39	
11.00/4.39	R is empty.
11.00/4.39	Q is empty.
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(26) QDPSizeChangeProof (EQUIVALENT)
11.00/4.39	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
11.00/4.39	
11.00/4.39	From the DPs we obtained the following set of size-change graphs:
11.00/4.39	*new_primMinusNatS(Succ(wv300), Succ(wv310)) -> new_primMinusNatS(wv300, wv310)
11.00/4.39	The graph contains the following edges 1 > 1, 2 > 2
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(27)
11.00/4.39	YES
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(28)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primPlusNat(Succ(wv1000), Succ(wv31000)) -> new_primPlusNat(wv1000, wv31000)
11.00/4.39	
11.00/4.39	R is empty.
11.00/4.39	Q is empty.
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(29) QDPSizeChangeProof (EQUIVALENT)
11.00/4.39	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
11.00/4.39	
11.00/4.39	From the DPs we obtained the following set of size-change graphs:
11.00/4.39	*new_primPlusNat(Succ(wv1000), Succ(wv31000)) -> new_primPlusNat(wv1000, wv31000)
11.00/4.39	The graph contains the following edges 1 > 1, 2 > 2
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(30)
11.00/4.39	YES
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(31)
11.00/4.39	Obligation:
11.00/4.39	Q DP problem:
11.00/4.39	The TRS P consists of the following rules:
11.00/4.39	
11.00/4.39	   new_primMinusNat(Succ(wv31000), Succ(wv5000)) -> new_primMinusNat(wv31000, wv5000)
11.00/4.39	
11.00/4.39	R is empty.
11.00/4.39	Q is empty.
11.00/4.39	We have to consider all minimal (P,Q,R)-chains.
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(32) QDPSizeChangeProof (EQUIVALENT)
11.00/4.39	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
11.00/4.39	
11.00/4.39	From the DPs we obtained the following set of size-change graphs:
11.00/4.39	*new_primMinusNat(Succ(wv31000), Succ(wv5000)) -> new_primMinusNat(wv31000, wv5000)
11.00/4.39	The graph contains the following edges 1 > 1, 2 > 2
11.00/4.39	
11.00/4.39	
11.00/4.39	----------------------------------------
11.00/4.39	
11.00/4.39	(33)
11.00/4.39	YES
11.00/4.43	EOF