8.99/3.90	MAYBE
11.11/4.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.11/4.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.11/4.50	
11.11/4.50	
11.11/4.50	H-Termination with start terms of the given HASKELL could not be shown:
11.11/4.50	
11.11/4.50	(0) HASKELL
11.11/4.50	(1) BR [EQUIVALENT, 0 ms]
11.11/4.50	(2) HASKELL
11.11/4.50	(3) COR [EQUIVALENT, 0 ms]
11.11/4.50	(4) HASKELL
11.11/4.50	(5) Narrow [SOUND, 0 ms]
11.11/4.50	(6) AND
11.11/4.50	    (7) QDP
11.11/4.50	        (8) MRRProof [EQUIVALENT, 121 ms]
11.11/4.50	        (9) QDP
11.11/4.50	        (10) NonTerminationLoopProof [COMPLETE, 0 ms]
11.11/4.50	        (11) NO
11.11/4.50	    (12) QDP
11.11/4.50	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.11/4.50	        (14) YES
11.11/4.50	(15) Narrow [COMPLETE, 0 ms]
11.11/4.50	(16) TRUE
11.11/4.50	
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(0)
11.11/4.50	Obligation:
11.11/4.50	mainModule Main 
11.11/4.50	module Main where {
11.11/4.50	import qualified Prelude;
11.11/4.50	data Float = Float MyInt MyInt ;
11.11/4.50	
11.11/4.50	data List a = Cons a (List a)  | Nil ;
11.11/4.50	
11.11/4.50	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
11.11/4.50	
11.11/4.50	data Main.Nat = Succ Main.Nat  | Zero ;
11.11/4.50	
11.11/4.50	data Main.WHNF a = WHNF a ;
11.11/4.50	
11.11/4.50	dsEm :: (b  ->  a)  ->  b  ->  a;
11.11/4.50	dsEm f x = Main.seq x (f x);
11.11/4.50	
11.11/4.50	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
11.11/4.50	enforceWHNF (Main.WHNF x) y = y;
11.11/4.50	
11.11/4.50	enumFromFloat :: Float  ->  List Float;
11.11/4.50	enumFromFloat = numericEnumFrom;
11.11/4.50	
11.11/4.50	fromIntFloat :: MyInt  ->  Float;
11.11/4.50	fromIntFloat = primIntToFloat;
11.11/4.50	
11.11/4.50	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psFloat n (fromIntFloat (Main.Pos (Main.Succ Main.Zero)))));
11.11/4.50	
11.11/4.50	primIntToFloat :: MyInt  ->  Float;
11.11/4.50	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
11.11/4.50	
11.11/4.50	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
11.11/4.50	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
11.11/4.50	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
11.11/4.50	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
11.11/4.50	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
11.11/4.50	
11.11/4.50	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
11.11/4.50	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
11.11/4.50	
11.11/4.50	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primMulNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
11.11/4.50	
11.11/4.50	primPlusFloat :: Float  ->  Float  ->  Float;
11.11/4.50	primPlusFloat (Float x1 x2) (Float y1 y2) = Float (psMyInt x1 y1) (srMyInt x2 y2);
11.11/4.50	
11.11/4.50	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
11.11/4.50	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
11.11/4.50	
11.11/4.50	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primPlusNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
11.11/4.50	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
11.11/4.50	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
11.11/4.50	
11.11/4.50	psFloat :: Float  ->  Float  ->  Float;
11.11/4.50	psFloat = primPlusFloat;
11.11/4.50	
11.11/4.50	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	psMyInt = primPlusInt;
11.11/4.50	
11.11/4.50	seq :: a  ->  b  ->  b;
11.11/4.50	seq x y = Main.enforceWHNF (Main.WHNF x) y;
11.11/4.50	
11.11/4.50	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	srMyInt = primMulInt;
11.11/4.50	
11.11/4.50	}
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(1) BR (EQUIVALENT)
11.11/4.50	Replaced joker patterns by fresh variables and removed binding patterns.
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(2)
11.11/4.50	Obligation:
11.11/4.50	mainModule Main 
11.11/4.50	module Main where {
11.11/4.50	import qualified Prelude;
11.11/4.50	data Float = Float MyInt MyInt ;
11.11/4.50	
11.11/4.50	data List a = Cons a (List a)  | Nil ;
11.11/4.50	
11.11/4.50	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
11.11/4.50	
11.11/4.50	data Main.Nat = Succ Main.Nat  | Zero ;
11.11/4.50	
11.11/4.50	data Main.WHNF a = WHNF a ;
11.11/4.50	
11.11/4.50	dsEm :: (a  ->  b)  ->  a  ->  b;
11.11/4.50	dsEm f x = Main.seq x (f x);
11.11/4.50	
11.11/4.50	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
11.11/4.50	enforceWHNF (Main.WHNF x) y = y;
11.11/4.50	
11.11/4.50	enumFromFloat :: Float  ->  List Float;
11.11/4.50	enumFromFloat = numericEnumFrom;
11.11/4.50	
11.11/4.50	fromIntFloat :: MyInt  ->  Float;
11.11/4.50	fromIntFloat = primIntToFloat;
11.11/4.50	
11.11/4.50	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psFloat n (fromIntFloat (Main.Pos (Main.Succ Main.Zero)))));
11.11/4.50	
11.11/4.50	primIntToFloat :: MyInt  ->  Float;
11.11/4.50	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
11.11/4.50	
11.11/4.50	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
11.11/4.50	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
11.11/4.50	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
11.11/4.50	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
11.11/4.50	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
11.11/4.50	
11.11/4.50	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
11.11/4.50	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
11.11/4.50	
11.11/4.50	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primMulNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
11.11/4.50	
11.11/4.50	primPlusFloat :: Float  ->  Float  ->  Float;
11.11/4.50	primPlusFloat (Float x1 x2) (Float y1 y2) = Float (psMyInt x1 y1) (srMyInt x2 y2);
11.11/4.50	
11.11/4.50	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
11.11/4.50	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
11.11/4.50	
11.11/4.50	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primPlusNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
11.11/4.50	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
11.11/4.50	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
11.11/4.50	
11.11/4.50	psFloat :: Float  ->  Float  ->  Float;
11.11/4.50	psFloat = primPlusFloat;
11.11/4.50	
11.11/4.50	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	psMyInt = primPlusInt;
11.11/4.50	
11.11/4.50	seq :: a  ->  b  ->  b;
11.11/4.50	seq x y = Main.enforceWHNF (Main.WHNF x) y;
11.11/4.50	
11.11/4.50	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	srMyInt = primMulInt;
11.11/4.50	
11.11/4.50	}
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(3) COR (EQUIVALENT)
11.11/4.50	Cond Reductions:
11.11/4.50	The following Function with conditions
11.11/4.50	"undefined |Falseundefined;
11.11/4.50	"
11.11/4.50	is transformed to
11.11/4.50	"undefined  = undefined1;
11.11/4.50	"
11.11/4.50	"undefined0 True = undefined;
11.11/4.50	"
11.11/4.50	"undefined1  = undefined0 False;
11.11/4.50	"
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(4)
11.11/4.50	Obligation:
11.11/4.50	mainModule Main 
11.11/4.50	module Main where {
11.11/4.50	import qualified Prelude;
11.11/4.50	data Float = Float MyInt MyInt ;
11.11/4.50	
11.11/4.50	data List a = Cons a (List a)  | Nil ;
11.11/4.50	
11.11/4.50	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
11.11/4.50	
11.11/4.50	data Main.Nat = Succ Main.Nat  | Zero ;
11.11/4.50	
11.11/4.50	data Main.WHNF a = WHNF a ;
11.11/4.50	
11.11/4.50	dsEm :: (a  ->  b)  ->  a  ->  b;
11.11/4.50	dsEm f x = Main.seq x (f x);
11.11/4.50	
11.11/4.50	enforceWHNF :: Main.WHNF a  ->  b  ->  b;
11.11/4.50	enforceWHNF (Main.WHNF x) y = y;
11.11/4.50	
11.11/4.50	enumFromFloat :: Float  ->  List Float;
11.11/4.50	enumFromFloat = numericEnumFrom;
11.11/4.50	
11.11/4.50	fromIntFloat :: MyInt  ->  Float;
11.11/4.50	fromIntFloat = primIntToFloat;
11.11/4.50	
11.11/4.50	numericEnumFrom n = Cons n (dsEm numericEnumFrom (psFloat n (fromIntFloat (Main.Pos (Main.Succ Main.Zero)))));
11.11/4.50	
11.11/4.50	primIntToFloat :: MyInt  ->  Float;
11.11/4.50	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
11.11/4.50	
11.11/4.50	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
11.11/4.50	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
11.11/4.50	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
11.11/4.50	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
11.11/4.50	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
11.11/4.50	
11.11/4.50	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
11.11/4.50	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
11.11/4.50	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
11.11/4.50	
11.11/4.50	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primMulNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
11.11/4.50	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
11.11/4.50	
11.11/4.50	primPlusFloat :: Float  ->  Float  ->  Float;
11.11/4.50	primPlusFloat (Float x1 x2) (Float y1 y2) = Float (psMyInt x1 y1) (srMyInt x2 y2);
11.11/4.50	
11.11/4.50	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
11.11/4.50	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
11.11/4.50	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
11.11/4.50	
11.11/4.50	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
11.11/4.50	primPlusNat Main.Zero Main.Zero = Main.Zero;
11.11/4.50	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
11.11/4.50	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
11.11/4.50	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
11.11/4.50	
11.11/4.50	psFloat :: Float  ->  Float  ->  Float;
11.11/4.50	psFloat = primPlusFloat;
11.11/4.50	
11.11/4.50	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	psMyInt = primPlusInt;
11.11/4.50	
11.11/4.50	seq :: a  ->  b  ->  b;
11.11/4.50	seq x y = Main.enforceWHNF (Main.WHNF x) y;
11.11/4.50	
11.11/4.50	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
11.11/4.50	srMyInt = primMulInt;
11.11/4.50	
11.11/4.50	}
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(5) Narrow (SOUND)
11.11/4.50	Haskell To QDPs
11.11/4.50	
11.11/4.50	digraph dp_graph {
11.11/4.50	node [outthreshold=100, inthreshold=100];1[label="enumFromFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.11/4.50	3[label="enumFromFloat vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
11.11/4.50	4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.11/4.50	5[label="Cons vx3 (dsEm numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
11.11/4.50	6[label="dsEm numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
11.11/4.50	7 -> 8[label="",style="dashed", color="red", weight=0];
11.11/4.50	7[label="seq (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))) (numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))))",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	9 -> 4[label="",style="dashed", color="red", weight=0];
11.11/4.50	9[label="numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))",fontsize=16,color="magenta"];9 -> 10[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	8[label="seq (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))) vx4",fontsize=16,color="black",shape="triangle"];8 -> 11[label="",style="solid", color="black", weight=3];
11.11/4.50	10[label="psFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3];
11.11/4.50	11 -> 13[label="",style="dashed", color="red", weight=0];
11.11/4.50	11[label="enforceWHNF (WHNF (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))) vx4",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	12[label="primPlusFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];59[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 59[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	59 -> 15[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	14 -> 10[label="",style="dashed", color="red", weight=0];
11.11/4.50	14[label="psFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
11.11/4.50	15[label="primPlusFloat (Float vx30 vx31) (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
11.11/4.50	16[label="vx4",fontsize=16,color="green",shape="box"];17[label="primPlusFloat (Float vx30 vx31) (primIntToFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
11.11/4.50	18[label="primPlusFloat (Float vx30 vx31) (Float (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
11.11/4.50	19[label="Float (psMyInt vx30 (Pos (Succ Zero))) (srMyInt vx31 (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="green", weight=3];
11.11/4.50	19 -> 21[label="",style="dashed", color="green", weight=3];
11.11/4.50	20[label="psMyInt vx30 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
11.11/4.50	21[label="srMyInt vx31 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
11.11/4.50	22[label="primPlusInt vx30 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];60[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 60[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	60 -> 24[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	61[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 61[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	61 -> 25[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	23[label="primMulInt vx31 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];62[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 62[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	62 -> 26[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	63[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 63[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	63 -> 27[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	24[label="primPlusInt (Pos vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
11.11/4.50	25[label="primPlusInt (Neg vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
11.11/4.50	26[label="primMulInt (Pos vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
11.11/4.50	27[label="primMulInt (Neg vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
11.11/4.50	28[label="Pos (primPlusNat vx300 (Succ Zero))",fontsize=16,color="green",shape="box"];28 -> 32[label="",style="dashed", color="green", weight=3];
11.11/4.50	29[label="primMinusNat (Succ Zero) vx300",fontsize=16,color="burlywood",shape="box"];64[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];29 -> 64[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	64 -> 33[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	65[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 65[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	65 -> 34[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	30[label="Pos (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];30 -> 35[label="",style="dashed", color="green", weight=3];
11.11/4.50	31[label="Neg (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];31 -> 36[label="",style="dashed", color="green", weight=3];
11.11/4.50	32[label="primPlusNat vx300 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];66[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];32 -> 66[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	66 -> 37[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	67[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 67[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	67 -> 38[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	33[label="primMinusNat (Succ Zero) (Succ vx3000)",fontsize=16,color="black",shape="box"];33 -> 39[label="",style="solid", color="black", weight=3];
11.11/4.50	34[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];34 -> 40[label="",style="solid", color="black", weight=3];
11.11/4.50	35[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];68[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 68[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	68 -> 41[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	69[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 69[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	69 -> 42[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	36 -> 35[label="",style="dashed", color="red", weight=0];
11.11/4.50	36[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="magenta"];36 -> 43[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	37[label="primPlusNat (Succ vx3000) (Succ Zero)",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
11.11/4.50	38[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3];
11.11/4.50	39[label="primMinusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];70[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];39 -> 70[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	70 -> 46[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	71[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 71[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	71 -> 47[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	40[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];41[label="primMulNat (Succ vx3100) (Succ Zero)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
11.11/4.50	42[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
11.11/4.50	43[label="vx310",fontsize=16,color="green",shape="box"];44[label="Succ (Succ (primPlusNat vx3000 Zero))",fontsize=16,color="green",shape="box"];44 -> 50[label="",style="dashed", color="green", weight=3];
11.11/4.50	45[label="Succ Zero",fontsize=16,color="green",shape="box"];46[label="primMinusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
11.11/4.50	47[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
11.11/4.50	48 -> 32[label="",style="dashed", color="red", weight=0];
11.11/4.50	48[label="primPlusNat (primMulNat vx3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];48 -> 53[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	49[label="Zero",fontsize=16,color="green",shape="box"];50[label="primPlusNat vx3000 Zero",fontsize=16,color="burlywood",shape="box"];72[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];50 -> 72[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	72 -> 54[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	73[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 73[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	73 -> 55[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	51[label="Neg (Succ vx30000)",fontsize=16,color="green",shape="box"];52[label="Pos Zero",fontsize=16,color="green",shape="box"];53 -> 35[label="",style="dashed", color="red", weight=0];
11.11/4.50	53[label="primMulNat vx3100 (Succ Zero)",fontsize=16,color="magenta"];53 -> 56[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	54[label="primPlusNat (Succ vx30000) Zero",fontsize=16,color="black",shape="box"];54 -> 57[label="",style="solid", color="black", weight=3];
11.11/4.50	55[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];55 -> 58[label="",style="solid", color="black", weight=3];
11.11/4.50	56[label="vx3100",fontsize=16,color="green",shape="box"];57[label="Succ vx30000",fontsize=16,color="green",shape="box"];58[label="Zero",fontsize=16,color="green",shape="box"];}
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(6)
11.11/4.50	Complex Obligation (AND)
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(7)
11.11/4.50	Obligation:
11.11/4.50	Q DP problem:
11.11/4.50	The TRS P consists of the following rules:
11.11/4.50	
11.11/4.50	   new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_psFloat(vx3))
11.11/4.50	
11.11/4.50	The TRS R consists of the following rules:
11.11/4.50	
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Zero))) -> Main.Pos(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Zero)) -> Main.Pos(Main.Succ(Main.Zero))
11.11/4.50	   new_primMulInt(Main.Pos(vx310)) -> Main.Pos(new_primMulNat0(vx310))
11.11/4.50	   new_primPlusNat(Main.Zero) -> Main.Succ(Main.Zero)
11.11/4.50	   new_primPlusNat(Main.Succ(vx3000)) -> Main.Succ(Main.Succ(new_primPlusNat0(vx3000)))
11.11/4.50	   new_psFloat(Float(vx30, vx31)) -> Float(new_primPlusInt(vx30), new_primMulInt(vx31))
11.11/4.50	   new_primPlusInt(Main.Pos(vx300)) -> Main.Pos(new_primPlusNat(vx300))
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Succ(vx30000)))) -> Main.Neg(Main.Succ(vx30000))
11.11/4.50	   new_primMulInt(Main.Neg(vx310)) -> Main.Neg(new_primMulNat0(vx310))
11.11/4.50	   new_primMulNat0(Main.Zero) -> Main.Zero
11.11/4.50	   new_primPlusNat0(Main.Succ(vx30000)) -> Main.Succ(vx30000)
11.11/4.50	   new_primMulNat0(Main.Succ(vx3100)) -> new_primPlusNat(new_primMulNat0(vx3100))
11.11/4.50	   new_primPlusNat0(Main.Zero) -> Main.Zero
11.11/4.50	
11.11/4.50	The set Q consists of the following terms:
11.11/4.50	
11.11/4.50	   new_primPlusNat0(Main.Zero)
11.11/4.50	   new_primPlusNat0(Main.Succ(x0))
11.11/4.50	   new_primMulNat0(Main.Succ(x0))
11.11/4.50	   new_primPlusInt(Main.Pos(x0))
11.11/4.50	   new_primPlusNat(Main.Succ(x0))
11.11/4.50	   new_psFloat(Float(x0, x1))
11.11/4.50	   new_primPlusNat(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Zero))
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Zero)))
11.11/4.50	   new_primMulNat0(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Succ(x0))))
11.11/4.50	   new_primMulInt(Main.Neg(x0))
11.11/4.50	   new_primMulInt(Main.Pos(x0))
11.11/4.50	
11.11/4.50	We have to consider all minimal (P,Q,R)-chains.
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(8) MRRProof (EQUIVALENT)
11.11/4.50	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.
11.11/4.50	
11.11/4.50	
11.11/4.50	Strictly oriented rules of the TRS R:
11.11/4.50	
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Zero))) -> Main.Pos(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Zero)) -> Main.Pos(Main.Succ(Main.Zero))
11.11/4.50	
11.11/4.50	Used ordering: Polynomial interpretation [POLO]:
11.11/4.50	
11.11/4.50	   POL(Float(x_1, x_2)) = 1 + x_1 + x_2
11.11/4.50	   POL(Main.Neg(x_1)) = 2*x_1
11.11/4.50	   POL(Main.Pos(x_1)) = x_1
11.11/4.50	   POL(Main.Succ(x_1)) = x_1
11.11/4.50	   POL(Main.Zero) = 2
11.11/4.50	   POL(new_numericEnumFrom(x_1)) = x_1
11.11/4.50	   POL(new_primMulInt(x_1)) = x_1
11.11/4.50	   POL(new_primMulNat0(x_1)) = x_1
11.11/4.50	   POL(new_primPlusInt(x_1)) = x_1
11.11/4.50	   POL(new_primPlusNat(x_1)) = x_1
11.11/4.50	   POL(new_primPlusNat0(x_1)) = x_1
11.11/4.50	   POL(new_psFloat(x_1)) = x_1
11.11/4.50	
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(9)
11.11/4.50	Obligation:
11.11/4.50	Q DP problem:
11.11/4.50	The TRS P consists of the following rules:
11.11/4.50	
11.11/4.50	   new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_psFloat(vx3))
11.11/4.50	
11.11/4.50	The TRS R consists of the following rules:
11.11/4.50	
11.11/4.50	   new_primMulInt(Main.Pos(vx310)) -> Main.Pos(new_primMulNat0(vx310))
11.11/4.50	   new_primPlusNat(Main.Zero) -> Main.Succ(Main.Zero)
11.11/4.50	   new_primPlusNat(Main.Succ(vx3000)) -> Main.Succ(Main.Succ(new_primPlusNat0(vx3000)))
11.11/4.50	   new_psFloat(Float(vx30, vx31)) -> Float(new_primPlusInt(vx30), new_primMulInt(vx31))
11.11/4.50	   new_primPlusInt(Main.Pos(vx300)) -> Main.Pos(new_primPlusNat(vx300))
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Succ(vx30000)))) -> Main.Neg(Main.Succ(vx30000))
11.11/4.50	   new_primMulInt(Main.Neg(vx310)) -> Main.Neg(new_primMulNat0(vx310))
11.11/4.50	   new_primMulNat0(Main.Zero) -> Main.Zero
11.11/4.50	   new_primPlusNat0(Main.Succ(vx30000)) -> Main.Succ(vx30000)
11.11/4.50	   new_primMulNat0(Main.Succ(vx3100)) -> new_primPlusNat(new_primMulNat0(vx3100))
11.11/4.50	   new_primPlusNat0(Main.Zero) -> Main.Zero
11.11/4.50	
11.11/4.50	The set Q consists of the following terms:
11.11/4.50	
11.11/4.50	   new_primPlusNat0(Main.Zero)
11.11/4.50	   new_primPlusNat0(Main.Succ(x0))
11.11/4.50	   new_primMulNat0(Main.Succ(x0))
11.11/4.50	   new_primPlusInt(Main.Pos(x0))
11.11/4.50	   new_primPlusNat(Main.Succ(x0))
11.11/4.50	   new_psFloat(Float(x0, x1))
11.11/4.50	   new_primPlusNat(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Zero))
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Zero)))
11.11/4.50	   new_primMulNat0(Main.Zero)
11.11/4.50	   new_primPlusInt(Main.Neg(Main.Succ(Main.Succ(x0))))
11.11/4.50	   new_primMulInt(Main.Neg(x0))
11.11/4.50	   new_primMulInt(Main.Pos(x0))
11.11/4.50	
11.11/4.50	We have to consider all minimal (P,Q,R)-chains.
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(10) NonTerminationLoopProof (COMPLETE)
11.11/4.50	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
11.11/4.50	Found a loop by semiunifying a rule from P directly.
11.11/4.50	
11.11/4.50	s = new_numericEnumFrom(vx3) evaluates to  t =new_numericEnumFrom(new_psFloat(vx3))
11.11/4.50	
11.11/4.50	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
11.11/4.50	* Matcher: [vx3 / new_psFloat(vx3)]
11.11/4.50	* Semiunifier: [ ]
11.11/4.50	
11.11/4.50	--------------------------------------------------------------------------------
11.11/4.50	Rewriting sequence
11.11/4.50	
11.11/4.50	The DP semiunifies directly so there is only one rewrite step from new_numericEnumFrom(vx3) to new_numericEnumFrom(new_psFloat(vx3)).
11.11/4.50	
11.11/4.50	
11.11/4.50	
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(11)
11.11/4.50	NO
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(12)
11.11/4.50	Obligation:
11.11/4.50	Q DP problem:
11.11/4.50	The TRS P consists of the following rules:
11.11/4.50	
11.11/4.50	   new_primMulNat(Main.Succ(vx3100)) -> new_primMulNat(vx3100)
11.11/4.50	
11.11/4.50	R is empty.
11.11/4.50	Q is empty.
11.11/4.50	We have to consider all minimal (P,Q,R)-chains.
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(13) QDPSizeChangeProof (EQUIVALENT)
11.11/4.50	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. 
11.11/4.50	
11.11/4.50	From the DPs we obtained the following set of size-change graphs:
11.11/4.50	*new_primMulNat(Main.Succ(vx3100)) -> new_primMulNat(vx3100)
11.11/4.50	The graph contains the following edges 1 > 1
11.11/4.50	
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(14)
11.11/4.50	YES
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(15) Narrow (COMPLETE)
11.11/4.50	Haskell To QDPs
11.11/4.50	
11.11/4.50	digraph dp_graph {
11.11/4.50	node [outthreshold=100, inthreshold=100];1[label="enumFromFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.11/4.50	3[label="enumFromFloat vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
11.11/4.50	4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.11/4.50	5[label="Cons vx3 (dsEm numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
11.11/4.50	6[label="dsEm numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
11.11/4.50	7 -> 8[label="",style="dashed", color="red", weight=0];
11.11/4.50	7[label="seq (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))) (numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))))",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	9 -> 4[label="",style="dashed", color="red", weight=0];
11.11/4.50	9[label="numericEnumFrom (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))",fontsize=16,color="magenta"];9 -> 10[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	8[label="seq (psFloat vx3 (fromIntFloat (Pos (Succ Zero)))) vx4",fontsize=16,color="black",shape="triangle"];8 -> 11[label="",style="solid", color="black", weight=3];
11.11/4.50	10[label="psFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3];
11.11/4.50	11 -> 13[label="",style="dashed", color="red", weight=0];
11.11/4.50	11[label="enforceWHNF (WHNF (psFloat vx3 (fromIntFloat (Pos (Succ Zero))))) vx4",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	12[label="primPlusFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];59[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 59[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	59 -> 15[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	14 -> 10[label="",style="dashed", color="red", weight=0];
11.11/4.50	14[label="psFloat vx3 (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
11.11/4.50	15[label="primPlusFloat (Float vx30 vx31) (fromIntFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
11.11/4.50	16[label="vx4",fontsize=16,color="green",shape="box"];17[label="primPlusFloat (Float vx30 vx31) (primIntToFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
11.11/4.50	18[label="primPlusFloat (Float vx30 vx31) (Float (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
11.11/4.50	19[label="Float (psMyInt vx30 (Pos (Succ Zero))) (srMyInt vx31 (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="green", weight=3];
11.11/4.50	19 -> 21[label="",style="dashed", color="green", weight=3];
11.11/4.50	20[label="psMyInt vx30 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
11.11/4.50	21[label="srMyInt vx31 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
11.11/4.50	22[label="primPlusInt vx30 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];60[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 60[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	60 -> 24[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	61[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 61[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	61 -> 25[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	23[label="primMulInt vx31 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];62[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 62[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	62 -> 26[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	63[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];23 -> 63[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	63 -> 27[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	24[label="primPlusInt (Pos vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
11.11/4.50	25[label="primPlusInt (Neg vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
11.11/4.50	26[label="primMulInt (Pos vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
11.11/4.50	27[label="primMulInt (Neg vx310) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
11.11/4.50	28[label="Pos (primPlusNat vx300 (Succ Zero))",fontsize=16,color="green",shape="box"];28 -> 32[label="",style="dashed", color="green", weight=3];
11.11/4.50	29[label="primMinusNat (Succ Zero) vx300",fontsize=16,color="burlywood",shape="box"];64[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];29 -> 64[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	64 -> 33[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	65[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 65[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	65 -> 34[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	30[label="Pos (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];30 -> 35[label="",style="dashed", color="green", weight=3];
11.11/4.50	31[label="Neg (primMulNat vx310 (Succ Zero))",fontsize=16,color="green",shape="box"];31 -> 36[label="",style="dashed", color="green", weight=3];
11.11/4.50	32[label="primPlusNat vx300 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];66[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];32 -> 66[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	66 -> 37[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	67[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 67[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	67 -> 38[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	33[label="primMinusNat (Succ Zero) (Succ vx3000)",fontsize=16,color="black",shape="box"];33 -> 39[label="",style="solid", color="black", weight=3];
11.11/4.50	34[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];34 -> 40[label="",style="solid", color="black", weight=3];
11.11/4.50	35[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];68[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];35 -> 68[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	68 -> 41[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	69[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 69[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	69 -> 42[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	36 -> 35[label="",style="dashed", color="red", weight=0];
11.11/4.50	36[label="primMulNat vx310 (Succ Zero)",fontsize=16,color="magenta"];36 -> 43[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	37[label="primPlusNat (Succ vx3000) (Succ Zero)",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
11.11/4.50	38[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3];
11.11/4.50	39[label="primMinusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];70[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];39 -> 70[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	70 -> 46[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	71[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 71[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	71 -> 47[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	40[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];41[label="primMulNat (Succ vx3100) (Succ Zero)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
11.11/4.50	42[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
11.11/4.50	43[label="vx310",fontsize=16,color="green",shape="box"];44[label="Succ (Succ (primPlusNat vx3000 Zero))",fontsize=16,color="green",shape="box"];44 -> 50[label="",style="dashed", color="green", weight=3];
11.11/4.50	45[label="Succ Zero",fontsize=16,color="green",shape="box"];46[label="primMinusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
11.11/4.50	47[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
11.11/4.50	48 -> 32[label="",style="dashed", color="red", weight=0];
11.11/4.50	48[label="primPlusNat (primMulNat vx3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];48 -> 53[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	49[label="Zero",fontsize=16,color="green",shape="box"];50[label="primPlusNat vx3000 Zero",fontsize=16,color="burlywood",shape="box"];72[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];50 -> 72[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	72 -> 54[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	73[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 73[label="",style="solid", color="burlywood", weight=9];
11.11/4.50	73 -> 55[label="",style="solid", color="burlywood", weight=3];
11.11/4.50	51[label="Neg (Succ vx30000)",fontsize=16,color="green",shape="box"];52[label="Pos Zero",fontsize=16,color="green",shape="box"];53 -> 35[label="",style="dashed", color="red", weight=0];
11.11/4.50	53[label="primMulNat vx3100 (Succ Zero)",fontsize=16,color="magenta"];53 -> 56[label="",style="dashed", color="magenta", weight=3];
11.11/4.50	54[label="primPlusNat (Succ vx30000) Zero",fontsize=16,color="black",shape="box"];54 -> 57[label="",style="solid", color="black", weight=3];
11.11/4.50	55[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];55 -> 58[label="",style="solid", color="black", weight=3];
11.11/4.50	56[label="vx3100",fontsize=16,color="green",shape="box"];57[label="Succ vx30000",fontsize=16,color="green",shape="box"];58[label="Zero",fontsize=16,color="green",shape="box"];}
11.11/4.50	
11.11/4.50	----------------------------------------
11.11/4.50	
11.11/4.50	(16)
11.11/4.50	TRUE
11.24/4.53	EOF