8.77/3.83	YES
11.34/4.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.34/4.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.34/4.52	
11.34/4.52	
11.34/4.52	H-Termination with start terms of the given HASKELL could be proven:
11.34/4.52	
11.34/4.52	(0) HASKELL
11.34/4.52	(1) LR [EQUIVALENT, 0 ms]
11.34/4.52	(2) HASKELL
11.34/4.52	(3) IFR [EQUIVALENT, 0 ms]
11.34/4.52	(4) HASKELL
11.34/4.52	(5) BR [EQUIVALENT, 0 ms]
11.34/4.52	(6) HASKELL
11.34/4.52	(7) COR [EQUIVALENT, 0 ms]
11.34/4.52	(8) HASKELL
11.34/4.52	(9) LetRed [EQUIVALENT, 0 ms]
11.34/4.52	(10) HASKELL
11.34/4.52	(11) NumRed [SOUND, 0 ms]
11.34/4.52	(12) HASKELL
11.34/4.52	(13) Narrow [SOUND, 0 ms]
11.34/4.52	(14) AND
11.34/4.52	    (15) QDP
11.34/4.52	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
11.34/4.52	        (17) AND
11.34/4.52	            (18) QDP
11.34/4.52	                (19) MRRProof [EQUIVALENT, 0 ms]
11.34/4.52	                (20) QDP
11.34/4.52	                (21) PisEmptyProof [EQUIVALENT, 0 ms]
11.34/4.52	                (22) YES
11.34/4.52	            (23) QDP
11.34/4.52	                (24) QDPSizeChangeProof [EQUIVALENT, 9 ms]
11.34/4.52	                (25) YES
11.34/4.52	    (26) QDP
11.34/4.52	        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.34/4.52	        (28) YES
11.34/4.52	
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(0)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(1) LR (EQUIVALENT)
11.34/4.52	Lambda Reductions:
11.34/4.52	The following Lambda expression
11.34/4.52	"\(m,_)->m"
11.34/4.52	is transformed to
11.34/4.52	"m0 (m,_) = m;
11.34/4.52	"
11.34/4.52	The following Lambda expression
11.34/4.52	"\(q,_)->q"
11.34/4.52	is transformed to
11.34/4.52	"q1 (q,_) = q;
11.34/4.52	"
11.34/4.52	The following Lambda expression
11.34/4.52	"\(_,r)->r"
11.34/4.52	is transformed to
11.34/4.52	"r0 (_,r) = r;
11.34/4.52	"
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(2)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(3) IFR (EQUIVALENT)
11.34/4.52	If Reductions:
11.34/4.52	The following If expression
11.34/4.52	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
11.34/4.52	is transformed to
11.34/4.52	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
11.34/4.52	primDivNatS0 x y False = Zero;
11.34/4.52	"
11.34/4.52	The following If expression
11.34/4.52	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
11.34/4.52	is transformed to
11.34/4.52	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
11.34/4.52	primModNatS0 x y False = Succ x;
11.34/4.52	"
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(4)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(5) BR (EQUIVALENT)
11.34/4.52	Replaced joker patterns by fresh variables and removed binding patterns.
11.34/4.52	
11.34/4.52	Binding Reductions:
11.34/4.52	The bind variable of the following binding Pattern
11.34/4.52	"frac@(Float vz wu)"
11.34/4.52	is replaced by the following term
11.34/4.52	"Float vz wu"
11.34/4.52	The bind variable of the following binding Pattern
11.34/4.52	"frac@(Double xu xv)"
11.34/4.52	is replaced by the following term
11.34/4.52	"Double xu xv"
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(6)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(7) COR (EQUIVALENT)
11.34/4.52	Cond Reductions:
11.34/4.52	The following Function with conditions
11.34/4.52	"undefined |Falseundefined;
11.34/4.52	"
11.34/4.52	is transformed to
11.34/4.52	"undefined  = undefined1;
11.34/4.52	"
11.34/4.52	"undefined0 True = undefined;
11.34/4.52	"
11.34/4.52	"undefined1  = undefined0 False;
11.34/4.52	"
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(8)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(9) LetRed (EQUIVALENT)
11.34/4.52	Let/Where Reductions:
11.34/4.52	The bindings of the following Let/Where expression
11.34/4.52	"m where {
11.34/4.52	m  = m0 vu6;
11.34/4.52	;
11.34/4.52	m0 (m,vv) = m;
11.34/4.52	;
11.34/4.52	vu6  = properFraction x;
11.34/4.52	} 
11.34/4.52	"
11.34/4.52	are unpacked to the following functions on top level
11.34/4.52	"truncateM xw = truncateM0 xw (truncateVu6 xw);
11.34/4.52	"
11.34/4.52	"truncateVu6 xw = properFraction xw;
11.34/4.52	"
11.34/4.52	"truncateM0 xw (m,vv) = m;
11.34/4.52	"
11.34/4.52	The bindings of the following Let/Where expression
11.34/4.52	"(fromIntegral q,r :% y) where {
11.34/4.52	q  = q1 vu30;
11.34/4.52	;
11.34/4.52	q1 (q,vw) = q;
11.34/4.52	;
11.34/4.52	r  = r0 vu30;
11.34/4.52	;
11.34/4.52	r0 (vx,r) = r;
11.34/4.52	;
11.34/4.52	vu30  = quotRem x y;
11.34/4.52	} 
11.34/4.52	"
11.34/4.52	are unpacked to the following functions on top level
11.34/4.52	"properFractionQ xx xy = properFractionQ1 xx xy (properFractionVu30 xx xy);
11.34/4.52	"
11.34/4.52	"properFractionVu30 xx xy = quotRem xx xy;
11.34/4.52	"
11.34/4.52	"properFractionR0 xx xy (vx,r) = r;
11.34/4.52	"
11.34/4.52	"properFractionR xx xy = properFractionR0 xx xy (properFractionVu30 xx xy);
11.34/4.52	"
11.34/4.52	"properFractionQ1 xx xy (q,vw) = q;
11.34/4.52	"
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(10)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(11) NumRed (SOUND)
11.34/4.52	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(12)
11.34/4.52	Obligation:
11.34/4.52	mainModule Main 
11.34/4.52	module Main where {
11.34/4.52	import qualified Prelude;
11.34/4.52	}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(13) Narrow (SOUND)
11.34/4.52	Haskell To QDPs
11.34/4.52	
11.34/4.52	digraph dp_graph {
11.34/4.52	node [outthreshold=100, inthreshold=100];1[label="fromEnum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.34/4.52	3[label="fromEnum xz3",fontsize=16,color="blue",shape="box"];354[label="fromEnum :: Char -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 354[label="",style="solid", color="blue", weight=9];
11.34/4.52	354 -> 4[label="",style="solid", color="blue", weight=3];
11.34/4.52	355[label="fromEnum :: Bool -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 355[label="",style="solid", color="blue", weight=9];
11.34/4.52	355 -> 5[label="",style="solid", color="blue", weight=3];
11.34/4.52	356[label="fromEnum :: (Ratio a) -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 356[label="",style="solid", color="blue", weight=9];
11.34/4.52	356 -> 6[label="",style="solid", color="blue", weight=3];
11.34/4.52	357[label="fromEnum :: Float -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 357[label="",style="solid", color="blue", weight=9];
11.34/4.52	357 -> 7[label="",style="solid", color="blue", weight=3];
11.34/4.52	358[label="fromEnum :: Double -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 358[label="",style="solid", color="blue", weight=9];
11.34/4.52	358 -> 8[label="",style="solid", color="blue", weight=3];
11.34/4.52	359[label="fromEnum :: Ordering -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 359[label="",style="solid", color="blue", weight=9];
11.34/4.52	359 -> 9[label="",style="solid", color="blue", weight=3];
11.34/4.52	360[label="fromEnum :: () -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 360[label="",style="solid", color="blue", weight=9];
11.34/4.52	360 -> 10[label="",style="solid", color="blue", weight=3];
11.34/4.52	361[label="fromEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 361[label="",style="solid", color="blue", weight=9];
11.34/4.52	361 -> 11[label="",style="solid", color="blue", weight=3];
11.34/4.52	362[label="fromEnum :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 362[label="",style="solid", color="blue", weight=9];
11.34/4.52	362 -> 12[label="",style="solid", color="blue", weight=3];
11.34/4.52	4[label="fromEnum xz3",fontsize=16,color="black",shape="box"];4 -> 13[label="",style="solid", color="black", weight=3];
11.34/4.52	5[label="fromEnum xz3",fontsize=16,color="burlywood",shape="box"];363[label="xz3/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 363[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	363 -> 14[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	364[label="xz3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 364[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	364 -> 15[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	6[label="fromEnum xz3",fontsize=16,color="black",shape="box"];6 -> 16[label="",style="solid", color="black", weight=3];
11.34/4.52	7[label="fromEnum xz3",fontsize=16,color="black",shape="box"];7 -> 17[label="",style="solid", color="black", weight=3];
11.34/4.52	8[label="fromEnum xz3",fontsize=16,color="black",shape="box"];8 -> 18[label="",style="solid", color="black", weight=3];
11.34/4.52	9[label="fromEnum xz3",fontsize=16,color="burlywood",shape="box"];365[label="xz3/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 365[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	365 -> 19[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	366[label="xz3/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 366[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	366 -> 20[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	367[label="xz3/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 367[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	367 -> 21[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	10[label="fromEnum xz3",fontsize=16,color="burlywood",shape="box"];368[label="xz3/()",fontsize=10,color="white",style="solid",shape="box"];10 -> 368[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	368 -> 22[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	11[label="fromEnum xz3",fontsize=16,color="black",shape="box"];11 -> 23[label="",style="solid", color="black", weight=3];
11.34/4.52	12[label="fromEnum xz3",fontsize=16,color="burlywood",shape="box"];369[label="xz3/Integer xz30",fontsize=10,color="white",style="solid",shape="box"];12 -> 369[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	369 -> 24[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	13[label="primCharToInt xz3",fontsize=16,color="burlywood",shape="box"];370[label="xz3/Char xz30",fontsize=10,color="white",style="solid",shape="box"];13 -> 370[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	370 -> 25[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	14[label="fromEnum False",fontsize=16,color="black",shape="box"];14 -> 26[label="",style="solid", color="black", weight=3];
11.34/4.52	15[label="fromEnum True",fontsize=16,color="black",shape="box"];15 -> 27[label="",style="solid", color="black", weight=3];
11.34/4.52	16[label="truncate xz3",fontsize=16,color="black",shape="box"];16 -> 28[label="",style="solid", color="black", weight=3];
11.34/4.52	17[label="truncate xz3",fontsize=16,color="black",shape="box"];17 -> 29[label="",style="solid", color="black", weight=3];
11.34/4.52	18[label="truncate xz3",fontsize=16,color="black",shape="box"];18 -> 30[label="",style="solid", color="black", weight=3];
11.34/4.52	19[label="fromEnum LT",fontsize=16,color="black",shape="box"];19 -> 31[label="",style="solid", color="black", weight=3];
11.34/4.52	20[label="fromEnum EQ",fontsize=16,color="black",shape="box"];20 -> 32[label="",style="solid", color="black", weight=3];
11.34/4.52	21[label="fromEnum GT",fontsize=16,color="black",shape="box"];21 -> 33[label="",style="solid", color="black", weight=3];
11.34/4.52	22[label="fromEnum ()",fontsize=16,color="black",shape="box"];22 -> 34[label="",style="solid", color="black", weight=3];
11.34/4.52	23[label="id xz3",fontsize=16,color="black",shape="box"];23 -> 35[label="",style="solid", color="black", weight=3];
11.34/4.52	24[label="fromEnum (Integer xz30)",fontsize=16,color="black",shape="box"];24 -> 36[label="",style="solid", color="black", weight=3];
11.34/4.52	25[label="primCharToInt (Char xz30)",fontsize=16,color="black",shape="box"];25 -> 37[label="",style="solid", color="black", weight=3];
11.34/4.52	26[label="Pos Zero",fontsize=16,color="green",shape="box"];27[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];28[label="truncateM xz3",fontsize=16,color="black",shape="box"];28 -> 38[label="",style="solid", color="black", weight=3];
11.34/4.52	29[label="truncateM xz3",fontsize=16,color="black",shape="box"];29 -> 39[label="",style="solid", color="black", weight=3];
11.34/4.52	30[label="truncateM xz3",fontsize=16,color="black",shape="box"];30 -> 40[label="",style="solid", color="black", weight=3];
11.34/4.52	31[label="Pos Zero",fontsize=16,color="green",shape="box"];32[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];33[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];34[label="Pos Zero",fontsize=16,color="green",shape="box"];35[label="xz3",fontsize=16,color="green",shape="box"];36[label="xz30",fontsize=16,color="green",shape="box"];37[label="Pos xz30",fontsize=16,color="green",shape="box"];38[label="truncateM0 xz3 (truncateVu6 xz3)",fontsize=16,color="black",shape="box"];38 -> 41[label="",style="solid", color="black", weight=3];
11.34/4.52	39[label="truncateM0 xz3 (truncateVu6 xz3)",fontsize=16,color="black",shape="box"];39 -> 42[label="",style="solid", color="black", weight=3];
11.34/4.52	40[label="truncateM0 xz3 (truncateVu6 xz3)",fontsize=16,color="black",shape="box"];40 -> 43[label="",style="solid", color="black", weight=3];
11.34/4.52	41[label="truncateM0 xz3 (properFraction xz3)",fontsize=16,color="burlywood",shape="box"];371[label="xz3/xz30 :% xz31",fontsize=10,color="white",style="solid",shape="box"];41 -> 371[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	371 -> 44[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	42[label="truncateM0 xz3 (properFraction xz3)",fontsize=16,color="black",shape="box"];42 -> 45[label="",style="solid", color="black", weight=3];
11.34/4.52	43[label="truncateM0 xz3 (properFraction xz3)",fontsize=16,color="black",shape="box"];43 -> 46[label="",style="solid", color="black", weight=3];
11.34/4.52	44[label="truncateM0 (xz30 :% xz31) (properFraction (xz30 :% xz31))",fontsize=16,color="black",shape="box"];44 -> 47[label="",style="solid", color="black", weight=3];
11.34/4.52	45[label="truncateM0 xz3 (floatProperFractionFloat xz3)",fontsize=16,color="burlywood",shape="box"];372[label="xz3/Float xz30 xz31",fontsize=10,color="white",style="solid",shape="box"];45 -> 372[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	372 -> 48[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	46[label="truncateM0 xz3 (floatProperFractionDouble xz3)",fontsize=16,color="burlywood",shape="box"];373[label="xz3/Double xz30 xz31",fontsize=10,color="white",style="solid",shape="box"];46 -> 373[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	373 -> 49[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	47[label="truncateM0 (xz30 :% xz31) (fromIntegral (properFractionQ xz30 xz31),properFractionR xz30 xz31 :% xz31)",fontsize=16,color="black",shape="box"];47 -> 50[label="",style="solid", color="black", weight=3];
11.34/4.52	48[label="truncateM0 (Float xz30 xz31) (floatProperFractionFloat (Float xz30 xz31))",fontsize=16,color="black",shape="box"];48 -> 51[label="",style="solid", color="black", weight=3];
11.34/4.52	49[label="truncateM0 (Double xz30 xz31) (floatProperFractionDouble (Double xz30 xz31))",fontsize=16,color="black",shape="box"];49 -> 52[label="",style="solid", color="black", weight=3];
11.34/4.52	50[label="fromIntegral (properFractionQ xz30 xz31)",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3];
11.34/4.52	51[label="truncateM0 (Float xz30 xz31) (fromInt (xz30 `quot` xz31),Float xz30 xz31 - fromInt (xz30 `quot` xz31))",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
11.34/4.52	52[label="truncateM0 (Double xz30 xz31) (fromInt (xz30 `quot` xz31),Double xz30 xz31 - fromInt (xz30 `quot` xz31))",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3];
11.34/4.52	53[label="fromInteger . toInteger",fontsize=16,color="black",shape="box"];53 -> 56[label="",style="solid", color="black", weight=3];
11.34/4.52	54[label="fromInt (xz30 `quot` xz31)",fontsize=16,color="black",shape="triangle"];54 -> 57[label="",style="solid", color="black", weight=3];
11.34/4.52	55 -> 54[label="",style="dashed", color="red", weight=0];
11.34/4.52	55[label="fromInt (xz30 `quot` xz31)",fontsize=16,color="magenta"];55 -> 58[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	55 -> 59[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	56[label="fromInteger (toInteger (properFractionQ xz30 xz31))",fontsize=16,color="blue",shape="box"];374[label="toInteger :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];56 -> 374[label="",style="solid", color="blue", weight=9];
11.34/4.52	374 -> 60[label="",style="solid", color="blue", weight=3];
11.34/4.52	375[label="toInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];56 -> 375[label="",style="solid", color="blue", weight=9];
11.34/4.52	375 -> 61[label="",style="solid", color="blue", weight=3];
11.34/4.52	57[label="xz30 `quot` xz31",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3];
11.34/4.52	58[label="xz31",fontsize=16,color="green",shape="box"];59[label="xz30",fontsize=16,color="green",shape="box"];60[label="fromInteger (toInteger (properFractionQ xz30 xz31))",fontsize=16,color="black",shape="box"];60 -> 63[label="",style="solid", color="black", weight=3];
11.34/4.52	61[label="fromInteger (toInteger (properFractionQ xz30 xz31))",fontsize=16,color="black",shape="box"];61 -> 64[label="",style="solid", color="black", weight=3];
11.34/4.52	62[label="primQuotInt xz30 xz31",fontsize=16,color="burlywood",shape="triangle"];376[label="xz30/Pos xz300",fontsize=10,color="white",style="solid",shape="box"];62 -> 376[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	376 -> 65[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	377[label="xz30/Neg xz300",fontsize=10,color="white",style="solid",shape="box"];62 -> 377[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	377 -> 66[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	63[label="fromInteger (Integer (properFractionQ xz30 xz31))",fontsize=16,color="black",shape="box"];63 -> 67[label="",style="solid", color="black", weight=3];
11.34/4.52	64[label="fromInteger (properFractionQ xz30 xz31)",fontsize=16,color="black",shape="box"];64 -> 68[label="",style="solid", color="black", weight=3];
11.34/4.52	65[label="primQuotInt (Pos xz300) xz31",fontsize=16,color="burlywood",shape="box"];378[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];65 -> 378[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	378 -> 69[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	379[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];65 -> 379[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	379 -> 70[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	66[label="primQuotInt (Neg xz300) xz31",fontsize=16,color="burlywood",shape="box"];380[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];66 -> 380[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	380 -> 71[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	381[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];66 -> 381[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	381 -> 72[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	67[label="properFractionQ xz30 xz31",fontsize=16,color="black",shape="box"];67 -> 73[label="",style="solid", color="black", weight=3];
11.34/4.52	68[label="fromInteger (properFractionQ1 xz30 xz31 (properFractionVu30 xz30 xz31))",fontsize=16,color="black",shape="box"];68 -> 74[label="",style="solid", color="black", weight=3];
11.34/4.52	69[label="primQuotInt (Pos xz300) (Pos xz310)",fontsize=16,color="burlywood",shape="box"];382[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];69 -> 382[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	382 -> 75[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	383[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 383[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	383 -> 76[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	70[label="primQuotInt (Pos xz300) (Neg xz310)",fontsize=16,color="burlywood",shape="box"];384[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];70 -> 384[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	384 -> 77[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	385[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 385[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	385 -> 78[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	71[label="primQuotInt (Neg xz300) (Pos xz310)",fontsize=16,color="burlywood",shape="box"];386[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];71 -> 386[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	386 -> 79[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	387[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 387[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	387 -> 80[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	72[label="primQuotInt (Neg xz300) (Neg xz310)",fontsize=16,color="burlywood",shape="box"];388[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];72 -> 388[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	388 -> 81[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	389[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 389[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	389 -> 82[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	73[label="properFractionQ1 xz30 xz31 (properFractionVu30 xz30 xz31)",fontsize=16,color="black",shape="box"];73 -> 83[label="",style="solid", color="black", weight=3];
11.34/4.52	74[label="fromInteger (properFractionQ1 xz30 xz31 (quotRem xz30 xz31))",fontsize=16,color="burlywood",shape="box"];390[label="xz30/Integer xz300",fontsize=10,color="white",style="solid",shape="box"];74 -> 390[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	390 -> 84[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	75[label="primQuotInt (Pos xz300) (Pos (Succ xz3100))",fontsize=16,color="black",shape="box"];75 -> 85[label="",style="solid", color="black", weight=3];
11.34/4.52	76[label="primQuotInt (Pos xz300) (Pos Zero)",fontsize=16,color="black",shape="box"];76 -> 86[label="",style="solid", color="black", weight=3];
11.34/4.52	77[label="primQuotInt (Pos xz300) (Neg (Succ xz3100))",fontsize=16,color="black",shape="box"];77 -> 87[label="",style="solid", color="black", weight=3];
11.34/4.52	78[label="primQuotInt (Pos xz300) (Neg Zero)",fontsize=16,color="black",shape="box"];78 -> 88[label="",style="solid", color="black", weight=3];
11.34/4.52	79[label="primQuotInt (Neg xz300) (Pos (Succ xz3100))",fontsize=16,color="black",shape="box"];79 -> 89[label="",style="solid", color="black", weight=3];
11.34/4.52	80[label="primQuotInt (Neg xz300) (Pos Zero)",fontsize=16,color="black",shape="box"];80 -> 90[label="",style="solid", color="black", weight=3];
11.34/4.52	81[label="primQuotInt (Neg xz300) (Neg (Succ xz3100))",fontsize=16,color="black",shape="box"];81 -> 91[label="",style="solid", color="black", weight=3];
11.34/4.52	82[label="primQuotInt (Neg xz300) (Neg Zero)",fontsize=16,color="black",shape="box"];82 -> 92[label="",style="solid", color="black", weight=3];
11.34/4.52	83[label="properFractionQ1 xz30 xz31 (quotRem xz30 xz31)",fontsize=16,color="black",shape="box"];83 -> 93[label="",style="solid", color="black", weight=3];
11.34/4.52	84[label="fromInteger (properFractionQ1 (Integer xz300) xz31 (quotRem (Integer xz300) xz31))",fontsize=16,color="burlywood",shape="box"];391[label="xz31/Integer xz310",fontsize=10,color="white",style="solid",shape="box"];84 -> 391[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	391 -> 94[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	85[label="Pos (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="green",shape="box"];85 -> 95[label="",style="dashed", color="green", weight=3];
11.34/4.52	86[label="error []",fontsize=16,color="black",shape="triangle"];86 -> 96[label="",style="solid", color="black", weight=3];
11.34/4.52	87[label="Neg (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="green",shape="box"];87 -> 97[label="",style="dashed", color="green", weight=3];
11.34/4.52	88 -> 86[label="",style="dashed", color="red", weight=0];
11.34/4.52	88[label="error []",fontsize=16,color="magenta"];89[label="Neg (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="green",shape="box"];89 -> 98[label="",style="dashed", color="green", weight=3];
11.34/4.52	90 -> 86[label="",style="dashed", color="red", weight=0];
11.34/4.52	90[label="error []",fontsize=16,color="magenta"];91[label="Pos (primDivNatS xz300 (Succ xz3100))",fontsize=16,color="green",shape="box"];91 -> 99[label="",style="dashed", color="green", weight=3];
11.34/4.52	92 -> 86[label="",style="dashed", color="red", weight=0];
11.34/4.52	92[label="error []",fontsize=16,color="magenta"];93[label="properFractionQ1 xz30 xz31 (primQrmInt xz30 xz31)",fontsize=16,color="black",shape="box"];93 -> 100[label="",style="solid", color="black", weight=3];
11.34/4.52	94[label="fromInteger (properFractionQ1 (Integer xz300) (Integer xz310) (quotRem (Integer xz300) (Integer xz310)))",fontsize=16,color="black",shape="box"];94 -> 101[label="",style="solid", color="black", weight=3];
11.34/4.52	95[label="primDivNatS xz300 (Succ xz3100)",fontsize=16,color="burlywood",shape="triangle"];392[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];95 -> 392[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	392 -> 102[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	393[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];95 -> 393[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	393 -> 103[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	96[label="error []",fontsize=16,color="red",shape="box"];97 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	97[label="primDivNatS xz300 (Succ xz3100)",fontsize=16,color="magenta"];97 -> 104[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	98 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	98[label="primDivNatS xz300 (Succ xz3100)",fontsize=16,color="magenta"];98 -> 105[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	99 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	99[label="primDivNatS xz300 (Succ xz3100)",fontsize=16,color="magenta"];99 -> 106[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	99 -> 107[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	100 -> 108[label="",style="dashed", color="red", weight=0];
11.34/4.52	100[label="properFractionQ1 xz30 xz31 (primQuotInt xz30 xz31,primRemInt xz30 xz31)",fontsize=16,color="magenta"];100 -> 109[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	101 -> 110[label="",style="dashed", color="red", weight=0];
11.34/4.52	101[label="fromInteger (properFractionQ1 (Integer xz300) (Integer xz310) (Integer (primQuotInt xz300 xz310),Integer (primRemInt xz300 xz310)))",fontsize=16,color="magenta"];101 -> 111[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	102[label="primDivNatS (Succ xz3000) (Succ xz3100)",fontsize=16,color="black",shape="box"];102 -> 112[label="",style="solid", color="black", weight=3];
11.34/4.52	103[label="primDivNatS Zero (Succ xz3100)",fontsize=16,color="black",shape="box"];103 -> 113[label="",style="solid", color="black", weight=3];
11.34/4.52	104[label="xz3100",fontsize=16,color="green",shape="box"];105[label="xz300",fontsize=16,color="green",shape="box"];106[label="xz300",fontsize=16,color="green",shape="box"];107[label="xz3100",fontsize=16,color="green",shape="box"];109 -> 62[label="",style="dashed", color="red", weight=0];
11.34/4.52	109[label="primQuotInt xz30 xz31",fontsize=16,color="magenta"];109 -> 114[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	109 -> 115[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	108[label="properFractionQ1 xz30 xz31 (xz6,primRemInt xz30 xz31)",fontsize=16,color="black",shape="triangle"];108 -> 116[label="",style="solid", color="black", weight=3];
11.34/4.52	111 -> 62[label="",style="dashed", color="red", weight=0];
11.34/4.52	111[label="primQuotInt xz300 xz310",fontsize=16,color="magenta"];111 -> 117[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	111 -> 118[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	110[label="fromInteger (properFractionQ1 (Integer xz300) (Integer xz310) (Integer xz7,Integer (primRemInt xz300 xz310)))",fontsize=16,color="black",shape="triangle"];110 -> 119[label="",style="solid", color="black", weight=3];
11.34/4.52	112[label="primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100)",fontsize=16,color="burlywood",shape="box"];394[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];112 -> 394[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	394 -> 120[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	395[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];112 -> 395[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	395 -> 121[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	113[label="Zero",fontsize=16,color="green",shape="box"];114[label="xz31",fontsize=16,color="green",shape="box"];115[label="xz30",fontsize=16,color="green",shape="box"];116[label="xz6",fontsize=16,color="green",shape="box"];117[label="xz310",fontsize=16,color="green",shape="box"];118[label="xz300",fontsize=16,color="green",shape="box"];119[label="fromInteger (Integer xz7)",fontsize=16,color="black",shape="box"];119 -> 122[label="",style="solid", color="black", weight=3];
11.34/4.52	120[label="primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100)",fontsize=16,color="burlywood",shape="box"];396[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];120 -> 396[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	396 -> 123[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	397[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];120 -> 397[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	397 -> 124[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	121[label="primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100)",fontsize=16,color="burlywood",shape="box"];398[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];121 -> 398[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	398 -> 125[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	399[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 399[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	399 -> 126[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	122[label="xz7",fontsize=16,color="green",shape="box"];123[label="primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000))",fontsize=16,color="black",shape="box"];123 -> 127[label="",style="solid", color="black", weight=3];
11.34/4.52	124[label="primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero)",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3];
11.34/4.52	125[label="primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000))",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3];
11.34/4.52	126[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
11.34/4.52	127 -> 291[label="",style="dashed", color="red", weight=0];
11.34/4.52	127[label="primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000)",fontsize=16,color="magenta"];127 -> 292[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	127 -> 293[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	127 -> 294[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	127 -> 295[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	128[label="primDivNatS0 (Succ xz30000) Zero True",fontsize=16,color="black",shape="box"];128 -> 133[label="",style="solid", color="black", weight=3];
11.34/4.52	129[label="primDivNatS0 Zero (Succ xz31000) False",fontsize=16,color="black",shape="box"];129 -> 134[label="",style="solid", color="black", weight=3];
11.34/4.52	130[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];130 -> 135[label="",style="solid", color="black", weight=3];
11.34/4.52	292[label="xz31000",fontsize=16,color="green",shape="box"];293[label="xz30000",fontsize=16,color="green",shape="box"];294[label="xz30000",fontsize=16,color="green",shape="box"];295[label="xz31000",fontsize=16,color="green",shape="box"];291[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS xz26 xz27)",fontsize=16,color="burlywood",shape="triangle"];400[label="xz26/Succ xz260",fontsize=10,color="white",style="solid",shape="box"];291 -> 400[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	400 -> 324[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	401[label="xz26/Zero",fontsize=10,color="white",style="solid",shape="box"];291 -> 401[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	401 -> 325[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	133[label="Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];133 -> 140[label="",style="dashed", color="green", weight=3];
11.34/4.52	134[label="Zero",fontsize=16,color="green",shape="box"];135[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];135 -> 141[label="",style="dashed", color="green", weight=3];
11.34/4.52	324[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS (Succ xz260) xz27)",fontsize=16,color="burlywood",shape="box"];402[label="xz27/Succ xz270",fontsize=10,color="white",style="solid",shape="box"];324 -> 402[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	402 -> 326[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	403[label="xz27/Zero",fontsize=10,color="white",style="solid",shape="box"];324 -> 403[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	403 -> 327[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	325[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS Zero xz27)",fontsize=16,color="burlywood",shape="box"];404[label="xz27/Succ xz270",fontsize=10,color="white",style="solid",shape="box"];325 -> 404[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	404 -> 328[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	405[label="xz27/Zero",fontsize=10,color="white",style="solid",shape="box"];325 -> 405[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	405 -> 329[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	140 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	140[label="primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];140 -> 146[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	140 -> 147[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	141 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	141[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];141 -> 148[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	141 -> 149[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	326[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS (Succ xz260) (Succ xz270))",fontsize=16,color="black",shape="box"];326 -> 330[label="",style="solid", color="black", weight=3];
11.34/4.52	327[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS (Succ xz260) Zero)",fontsize=16,color="black",shape="box"];327 -> 331[label="",style="solid", color="black", weight=3];
11.34/4.52	328[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS Zero (Succ xz270))",fontsize=16,color="black",shape="box"];328 -> 332[label="",style="solid", color="black", weight=3];
11.34/4.52	329[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];329 -> 333[label="",style="solid", color="black", weight=3];
11.34/4.52	146[label="primMinusNatS (Succ xz30000) Zero",fontsize=16,color="black",shape="triangle"];146 -> 155[label="",style="solid", color="black", weight=3];
11.34/4.52	147[label="Zero",fontsize=16,color="green",shape="box"];148[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];148 -> 156[label="",style="solid", color="black", weight=3];
11.34/4.52	149[label="Zero",fontsize=16,color="green",shape="box"];330 -> 291[label="",style="dashed", color="red", weight=0];
11.34/4.52	330[label="primDivNatS0 (Succ xz24) (Succ xz25) (primGEqNatS xz260 xz270)",fontsize=16,color="magenta"];330 -> 334[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	330 -> 335[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	331[label="primDivNatS0 (Succ xz24) (Succ xz25) True",fontsize=16,color="black",shape="triangle"];331 -> 336[label="",style="solid", color="black", weight=3];
11.34/4.52	332[label="primDivNatS0 (Succ xz24) (Succ xz25) False",fontsize=16,color="black",shape="box"];332 -> 337[label="",style="solid", color="black", weight=3];
11.34/4.52	333 -> 331[label="",style="dashed", color="red", weight=0];
11.34/4.52	333[label="primDivNatS0 (Succ xz24) (Succ xz25) True",fontsize=16,color="magenta"];155[label="Succ xz30000",fontsize=16,color="green",shape="box"];156[label="Zero",fontsize=16,color="green",shape="box"];334[label="xz260",fontsize=16,color="green",shape="box"];335[label="xz270",fontsize=16,color="green",shape="box"];336[label="Succ (primDivNatS (primMinusNatS (Succ xz24) (Succ xz25)) (Succ (Succ xz25)))",fontsize=16,color="green",shape="box"];336 -> 338[label="",style="dashed", color="green", weight=3];
11.34/4.52	337[label="Zero",fontsize=16,color="green",shape="box"];338 -> 95[label="",style="dashed", color="red", weight=0];
11.34/4.52	338[label="primDivNatS (primMinusNatS (Succ xz24) (Succ xz25)) (Succ (Succ xz25))",fontsize=16,color="magenta"];338 -> 339[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	338 -> 340[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	339[label="primMinusNatS (Succ xz24) (Succ xz25)",fontsize=16,color="black",shape="box"];339 -> 341[label="",style="solid", color="black", weight=3];
11.34/4.52	340[label="Succ xz25",fontsize=16,color="green",shape="box"];341[label="primMinusNatS xz24 xz25",fontsize=16,color="burlywood",shape="triangle"];406[label="xz24/Succ xz240",fontsize=10,color="white",style="solid",shape="box"];341 -> 406[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	406 -> 342[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	407[label="xz24/Zero",fontsize=10,color="white",style="solid",shape="box"];341 -> 407[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	407 -> 343[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	342[label="primMinusNatS (Succ xz240) xz25",fontsize=16,color="burlywood",shape="box"];408[label="xz25/Succ xz250",fontsize=10,color="white",style="solid",shape="box"];342 -> 408[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	408 -> 344[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	409[label="xz25/Zero",fontsize=10,color="white",style="solid",shape="box"];342 -> 409[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	409 -> 345[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	343[label="primMinusNatS Zero xz25",fontsize=16,color="burlywood",shape="box"];410[label="xz25/Succ xz250",fontsize=10,color="white",style="solid",shape="box"];343 -> 410[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	410 -> 346[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	411[label="xz25/Zero",fontsize=10,color="white",style="solid",shape="box"];343 -> 411[label="",style="solid", color="burlywood", weight=9];
11.34/4.52	411 -> 347[label="",style="solid", color="burlywood", weight=3];
11.34/4.52	344[label="primMinusNatS (Succ xz240) (Succ xz250)",fontsize=16,color="black",shape="box"];344 -> 348[label="",style="solid", color="black", weight=3];
11.34/4.52	345[label="primMinusNatS (Succ xz240) Zero",fontsize=16,color="black",shape="box"];345 -> 349[label="",style="solid", color="black", weight=3];
11.34/4.52	346[label="primMinusNatS Zero (Succ xz250)",fontsize=16,color="black",shape="box"];346 -> 350[label="",style="solid", color="black", weight=3];
11.34/4.52	347[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];347 -> 351[label="",style="solid", color="black", weight=3];
11.34/4.52	348 -> 341[label="",style="dashed", color="red", weight=0];
11.34/4.52	348[label="primMinusNatS xz240 xz250",fontsize=16,color="magenta"];348 -> 352[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	348 -> 353[label="",style="dashed", color="magenta", weight=3];
11.34/4.52	349[label="Succ xz240",fontsize=16,color="green",shape="box"];350[label="Zero",fontsize=16,color="green",shape="box"];351[label="Zero",fontsize=16,color="green",shape="box"];352[label="xz250",fontsize=16,color="green",shape="box"];353[label="xz240",fontsize=16,color="green",shape="box"];}
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(14)
11.34/4.52	Complex Obligation (AND)
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(15)
11.34/4.52	Obligation:
11.34/4.52	Q DP problem:
11.34/4.52	The TRS P consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primDivNatS(Succ(Succ(xz30000)), Succ(xz31000)) -> new_primDivNatS0(xz30000, xz31000, xz30000, xz31000)
11.34/4.52	   new_primDivNatS0(xz24, xz25, Succ(xz260), Zero) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25))
11.34/4.52	   new_primDivNatS0(xz24, xz25, Zero, Zero) -> new_primDivNatS00(xz24, xz25)
11.34/4.52	   new_primDivNatS0(xz24, xz25, Succ(xz260), Succ(xz270)) -> new_primDivNatS0(xz24, xz25, xz260, xz270)
11.34/4.52	   new_primDivNatS(Succ(Zero), Zero) -> new_primDivNatS(new_primMinusNatS2, Zero)
11.34/4.52	   new_primDivNatS(Succ(Succ(xz30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(xz30000), Zero)
11.34/4.52	   new_primDivNatS00(xz24, xz25) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25))
11.34/4.52	
11.34/4.52	The TRS R consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(xz250)) -> Zero
11.34/4.52	   new_primMinusNatS0(Zero, Zero) -> Zero
11.34/4.52	   new_primMinusNatS1(xz30000) -> Succ(xz30000)
11.34/4.52	   new_primMinusNatS2 -> Zero
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Succ(xz250)) -> new_primMinusNatS0(xz240, xz250)
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Zero) -> Succ(xz240)
11.34/4.52	
11.34/4.52	The set Q consists of the following terms:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(x0))
11.34/4.52	   new_primMinusNatS0(Zero, Zero)
11.34/4.52	   new_primMinusNatS2
11.34/4.52	   new_primMinusNatS1(x0)
11.34/4.52	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.34/4.52	   new_primMinusNatS0(Succ(x0), Zero)
11.34/4.52	
11.34/4.52	We have to consider all minimal (P,Q,R)-chains.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(16) DependencyGraphProof (EQUIVALENT)
11.34/4.52	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(17)
11.34/4.52	Complex Obligation (AND)
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(18)
11.34/4.52	Obligation:
11.34/4.52	Q DP problem:
11.34/4.52	The TRS P consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primDivNatS(Succ(Succ(xz30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(xz30000), Zero)
11.34/4.52	
11.34/4.52	The TRS R consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(xz250)) -> Zero
11.34/4.52	   new_primMinusNatS0(Zero, Zero) -> Zero
11.34/4.52	   new_primMinusNatS1(xz30000) -> Succ(xz30000)
11.34/4.52	   new_primMinusNatS2 -> Zero
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Succ(xz250)) -> new_primMinusNatS0(xz240, xz250)
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Zero) -> Succ(xz240)
11.34/4.52	
11.34/4.52	The set Q consists of the following terms:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(x0))
11.34/4.52	   new_primMinusNatS0(Zero, Zero)
11.34/4.52	   new_primMinusNatS2
11.34/4.52	   new_primMinusNatS1(x0)
11.34/4.52	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.34/4.52	   new_primMinusNatS0(Succ(x0), Zero)
11.34/4.52	
11.34/4.52	We have to consider all minimal (P,Q,R)-chains.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(19) MRRProof (EQUIVALENT)
11.34/4.52	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.
11.34/4.52	
11.34/4.52	Strictly oriented dependency pairs:
11.34/4.52	
11.34/4.52	   new_primDivNatS(Succ(Succ(xz30000)), Zero) -> new_primDivNatS(new_primMinusNatS1(xz30000), Zero)
11.34/4.52	
11.34/4.52	Strictly oriented rules of the TRS R:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(xz250)) -> Zero
11.34/4.52	   new_primMinusNatS0(Zero, Zero) -> Zero
11.34/4.52	   new_primMinusNatS1(xz30000) -> Succ(xz30000)
11.34/4.52	   new_primMinusNatS2 -> Zero
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Succ(xz250)) -> new_primMinusNatS0(xz240, xz250)
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Zero) -> Succ(xz240)
11.34/4.52	
11.34/4.52	Used ordering: Polynomial interpretation [POLO]:
11.34/4.52	
11.34/4.52	   POL(Succ(x_1)) = 1 + 2*x_1
11.34/4.52	   POL(Zero) = 1
11.34/4.52	   POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2
11.34/4.52	   POL(new_primMinusNatS0(x_1, x_2)) = x_1 + x_2
11.34/4.52	   POL(new_primMinusNatS1(x_1)) = 2 + 2*x_1
11.34/4.52	   POL(new_primMinusNatS2) = 2
11.34/4.52	
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(20)
11.34/4.52	Obligation:
11.34/4.52	Q DP problem:
11.34/4.52	P is empty.
11.34/4.52	R is empty.
11.34/4.52	The set Q consists of the following terms:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(x0))
11.34/4.52	   new_primMinusNatS0(Zero, Zero)
11.34/4.52	   new_primMinusNatS2
11.34/4.52	   new_primMinusNatS1(x0)
11.34/4.52	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.34/4.52	   new_primMinusNatS0(Succ(x0), Zero)
11.34/4.52	
11.34/4.52	We have to consider all minimal (P,Q,R)-chains.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(21) PisEmptyProof (EQUIVALENT)
11.34/4.52	The TRS P is empty. Hence, there is no (P,Q,R) chain.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(22)
11.34/4.52	YES
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(23)
11.34/4.52	Obligation:
11.34/4.52	Q DP problem:
11.34/4.52	The TRS P consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primDivNatS0(xz24, xz25, Succ(xz260), Zero) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25))
11.34/4.52	   new_primDivNatS(Succ(Succ(xz30000)), Succ(xz31000)) -> new_primDivNatS0(xz30000, xz31000, xz30000, xz31000)
11.34/4.52	   new_primDivNatS0(xz24, xz25, Zero, Zero) -> new_primDivNatS00(xz24, xz25)
11.34/4.52	   new_primDivNatS00(xz24, xz25) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25))
11.34/4.52	   new_primDivNatS0(xz24, xz25, Succ(xz260), Succ(xz270)) -> new_primDivNatS0(xz24, xz25, xz260, xz270)
11.34/4.52	
11.34/4.52	The TRS R consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(xz250)) -> Zero
11.34/4.52	   new_primMinusNatS0(Zero, Zero) -> Zero
11.34/4.52	   new_primMinusNatS1(xz30000) -> Succ(xz30000)
11.34/4.52	   new_primMinusNatS2 -> Zero
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Succ(xz250)) -> new_primMinusNatS0(xz240, xz250)
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Zero) -> Succ(xz240)
11.34/4.52	
11.34/4.52	The set Q consists of the following terms:
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Succ(x0))
11.34/4.52	   new_primMinusNatS0(Zero, Zero)
11.34/4.52	   new_primMinusNatS2
11.34/4.52	   new_primMinusNatS1(x0)
11.34/4.52	   new_primMinusNatS0(Succ(x0), Succ(x1))
11.34/4.52	   new_primMinusNatS0(Succ(x0), Zero)
11.34/4.52	
11.34/4.52	We have to consider all minimal (P,Q,R)-chains.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(24) QDPSizeChangeProof (EQUIVALENT)
11.34/4.52	We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
11.34/4.52	
11.34/4.52	Order:Polynomial interpretation [POLO]:
11.34/4.52	
11.34/4.52	   POL(Succ(x_1)) = 1 + x_1
11.34/4.52	   POL(Zero) = 1
11.34/4.52	   POL(new_primMinusNatS0(x_1, x_2)) = x_1
11.34/4.52	
11.34/4.52	
11.34/4.52	
11.34/4.52	
11.34/4.52	From the DPs we obtained the following set of size-change graphs:
11.34/4.52	*new_primDivNatS(Succ(Succ(xz30000)), Succ(xz31000)) -> new_primDivNatS0(xz30000, xz31000, xz30000, xz31000) (allowed arguments on rhs = {1, 2, 3, 4})
11.34/4.52	The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4
11.34/4.52	
11.34/4.52	
11.34/4.52	*new_primDivNatS0(xz24, xz25, Succ(xz260), Succ(xz270)) -> new_primDivNatS0(xz24, xz25, xz260, xz270) (allowed arguments on rhs = {1, 2, 3, 4})
11.34/4.52	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
11.34/4.52	
11.34/4.52	
11.34/4.52	*new_primDivNatS0(xz24, xz25, Succ(xz260), Zero) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25)) (allowed arguments on rhs = {1, 2})
11.34/4.52	The graph contains the following edges 1 >= 1
11.34/4.52	
11.34/4.52	
11.34/4.52	*new_primDivNatS0(xz24, xz25, Zero, Zero) -> new_primDivNatS00(xz24, xz25) (allowed arguments on rhs = {1, 2})
11.34/4.52	The graph contains the following edges 1 >= 1, 2 >= 2
11.34/4.52	
11.34/4.52	
11.34/4.52	*new_primDivNatS00(xz24, xz25) -> new_primDivNatS(new_primMinusNatS0(xz24, xz25), Succ(xz25)) (allowed arguments on rhs = {1, 2})
11.34/4.52	The graph contains the following edges 1 >= 1
11.34/4.52	
11.34/4.52	
11.34/4.52	
11.34/4.52	We oriented the following set of usable rules [AAECC05,FROCOS05].
11.34/4.52	
11.34/4.52	   new_primMinusNatS0(Zero, Zero) -> Zero
11.34/4.52	   new_primMinusNatS0(Zero, Succ(xz250)) -> Zero
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Zero) -> Succ(xz240)
11.34/4.52	   new_primMinusNatS0(Succ(xz240), Succ(xz250)) -> new_primMinusNatS0(xz240, xz250)
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(25)
11.34/4.52	YES
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(26)
11.34/4.52	Obligation:
11.34/4.52	Q DP problem:
11.34/4.52	The TRS P consists of the following rules:
11.34/4.52	
11.34/4.52	   new_primMinusNatS(Succ(xz240), Succ(xz250)) -> new_primMinusNatS(xz240, xz250)
11.34/4.52	
11.34/4.52	R is empty.
11.34/4.52	Q is empty.
11.34/4.52	We have to consider all minimal (P,Q,R)-chains.
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(27) QDPSizeChangeProof (EQUIVALENT)
11.34/4.52	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
11.34/4.52	
11.34/4.52	From the DPs we obtained the following set of size-change graphs:
11.34/4.52	*new_primMinusNatS(Succ(xz240), Succ(xz250)) -> new_primMinusNatS(xz240, xz250)
11.34/4.52	The graph contains the following edges 1 > 1, 2 > 2
11.34/4.52	
11.34/4.52	
11.34/4.52	----------------------------------------
11.34/4.52	
11.34/4.52	(28)
11.34/4.52	YES
11.53/4.56	EOF