7.89/3.53	YES
9.65/4.02	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.65/4.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.65/4.02	
9.65/4.02	
9.65/4.02	H-Termination with start terms of the given HASKELL could be proven:
9.65/4.02	
9.65/4.02	(0) HASKELL
9.65/4.02	(1) BR [EQUIVALENT, 0 ms]
9.65/4.02	(2) HASKELL
9.65/4.02	(3) COR [EQUIVALENT, 0 ms]
9.65/4.02	(4) HASKELL
9.65/4.02	(5) Narrow [SOUND, 0 ms]
9.65/4.02	(6) AND
9.65/4.02	    (7) QDP
9.65/4.02	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.65/4.02	        (9) YES
9.65/4.02	    (10) QDP
9.65/4.02	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.65/4.02	        (12) YES
9.65/4.02	
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(0)
9.65/4.02	Obligation:
9.65/4.02	mainModule Main 
9.65/4.02	module Main where {
9.65/4.02	import qualified Prelude;
9.65/4.02	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.65/4.02	
9.65/4.02	data Main.Nat = Succ Main.Nat  | Zero ;
9.65/4.02	
9.65/4.02	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
9.65/4.02	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
9.65/4.02	
9.65/4.02	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primMulNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
9.65/4.02	
9.65/4.02	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.65/4.02	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.65/4.02	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.65/4.02	
9.65/4.02	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	srMyInt = primMulInt;
9.65/4.02	
9.65/4.02	}
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(1) BR (EQUIVALENT)
9.65/4.02	Replaced joker patterns by fresh variables and removed binding patterns.
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(2)
9.65/4.02	Obligation:
9.65/4.02	mainModule Main 
9.65/4.02	module Main where {
9.65/4.02	import qualified Prelude;
9.65/4.02	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.65/4.02	
9.65/4.02	data Main.Nat = Succ Main.Nat  | Zero ;
9.65/4.02	
9.65/4.02	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
9.65/4.02	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
9.65/4.02	
9.65/4.02	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primMulNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
9.65/4.02	
9.65/4.02	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.65/4.02	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.65/4.02	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.65/4.02	
9.65/4.02	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	srMyInt = primMulInt;
9.65/4.02	
9.65/4.02	}
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(3) COR (EQUIVALENT)
9.65/4.02	Cond Reductions:
9.65/4.02	The following Function with conditions
9.65/4.02	"undefined |Falseundefined;
9.65/4.02	"
9.65/4.02	is transformed to
9.65/4.02	"undefined  = undefined1;
9.65/4.02	"
9.65/4.02	"undefined0 True = undefined;
9.65/4.02	"
9.65/4.02	"undefined1  = undefined0 False;
9.65/4.02	"
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(4)
9.65/4.02	Obligation:
9.65/4.02	mainModule Main 
9.65/4.02	module Main where {
9.65/4.02	import qualified Prelude;
9.65/4.02	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.65/4.02	
9.65/4.02	data Main.Nat = Succ Main.Nat  | Zero ;
9.65/4.02	
9.65/4.02	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
9.65/4.02	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
9.65/4.02	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
9.65/4.02	
9.65/4.02	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primMulNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
9.65/4.02	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
9.65/4.02	
9.65/4.02	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.65/4.02	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.65/4.02	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.65/4.02	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.65/4.02	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.65/4.02	
9.65/4.02	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.65/4.02	srMyInt = primMulInt;
9.65/4.02	
9.65/4.02	}
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(5) Narrow (SOUND)
9.65/4.02	Haskell To QDPs
9.65/4.02	
9.65/4.02	digraph dp_graph {
9.65/4.02	node [outthreshold=100, inthreshold=100];1[label="srMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.65/4.02	3[label="srMyInt vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.65/4.02	4[label="srMyInt vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.65/4.02	5[label="primMulInt vx3 vx4",fontsize=16,color="burlywood",shape="box"];56[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 56[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	56 -> 6[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	57[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 57[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	57 -> 7[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	6[label="primMulInt (Pos vx30) vx4",fontsize=16,color="burlywood",shape="box"];58[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 58[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	58 -> 8[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	59[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 59[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	59 -> 9[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	7[label="primMulInt (Neg vx30) vx4",fontsize=16,color="burlywood",shape="box"];60[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	60 -> 10[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	61[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 61[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	61 -> 11[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	8[label="primMulInt (Pos vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9.65/4.02	9[label="primMulInt (Pos vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.65/4.02	10[label="primMulInt (Neg vx30) (Pos vx40)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.65/4.02	11[label="primMulInt (Neg vx30) (Neg vx40)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.65/4.02	12[label="Pos (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];12 -> 16[label="",style="dashed", color="green", weight=3];
9.65/4.02	13[label="Neg (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];13 -> 17[label="",style="dashed", color="green", weight=3];
9.65/4.02	14[label="Neg (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];14 -> 18[label="",style="dashed", color="green", weight=3];
9.65/4.02	15[label="Pos (primMulNat vx30 vx40)",fontsize=16,color="green",shape="box"];15 -> 19[label="",style="dashed", color="green", weight=3];
9.65/4.02	16[label="primMulNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];62[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 62[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	62 -> 20[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	63[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 63[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	63 -> 21[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	17 -> 16[label="",style="dashed", color="red", weight=0];
9.65/4.02	17[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];17 -> 22[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	18 -> 16[label="",style="dashed", color="red", weight=0];
9.65/4.02	18[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];18 -> 23[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	19 -> 16[label="",style="dashed", color="red", weight=0];
9.65/4.02	19[label="primMulNat vx30 vx40",fontsize=16,color="magenta"];19 -> 24[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	19 -> 25[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	20[label="primMulNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];64[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 64[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	64 -> 26[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	65[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 65[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	65 -> 27[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	21[label="primMulNat Zero vx40",fontsize=16,color="burlywood",shape="box"];66[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];21 -> 66[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	66 -> 28[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	67[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 67[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	67 -> 29[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	22[label="vx40",fontsize=16,color="green",shape="box"];23[label="vx30",fontsize=16,color="green",shape="box"];24[label="vx40",fontsize=16,color="green",shape="box"];25[label="vx30",fontsize=16,color="green",shape="box"];26[label="primMulNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
9.65/4.02	27[label="primMulNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
9.65/4.02	28[label="primMulNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
9.65/4.02	29[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
9.65/4.02	30 -> 34[label="",style="dashed", color="red", weight=0];
9.65/4.02	30[label="primPlusNat (primMulNat vx300 (Succ vx400)) (Succ vx400)",fontsize=16,color="magenta"];30 -> 35[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	31[label="Zero",fontsize=16,color="green",shape="box"];32[label="Zero",fontsize=16,color="green",shape="box"];33[label="Zero",fontsize=16,color="green",shape="box"];35 -> 16[label="",style="dashed", color="red", weight=0];
9.65/4.02	35[label="primMulNat vx300 (Succ vx400)",fontsize=16,color="magenta"];35 -> 36[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	35 -> 37[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	34[label="primPlusNat vx5 (Succ vx400)",fontsize=16,color="burlywood",shape="triangle"];68[label="vx5/Succ vx50",fontsize=10,color="white",style="solid",shape="box"];34 -> 68[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	68 -> 38[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	69[label="vx5/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 69[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	69 -> 39[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	36[label="Succ vx400",fontsize=16,color="green",shape="box"];37[label="vx300",fontsize=16,color="green",shape="box"];38[label="primPlusNat (Succ vx50) (Succ vx400)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
9.65/4.02	39[label="primPlusNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
9.65/4.02	40[label="Succ (Succ (primPlusNat vx50 vx400))",fontsize=16,color="green",shape="box"];40 -> 42[label="",style="dashed", color="green", weight=3];
9.65/4.02	41[label="Succ vx400",fontsize=16,color="green",shape="box"];42[label="primPlusNat vx50 vx400",fontsize=16,color="burlywood",shape="triangle"];70[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];42 -> 70[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	70 -> 43[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	71[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];42 -> 71[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	71 -> 44[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	43[label="primPlusNat (Succ vx500) vx400",fontsize=16,color="burlywood",shape="box"];72[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];43 -> 72[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	72 -> 45[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	73[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 73[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	73 -> 46[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	44[label="primPlusNat Zero vx400",fontsize=16,color="burlywood",shape="box"];74[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];44 -> 74[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	74 -> 47[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	75[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];44 -> 75[label="",style="solid", color="burlywood", weight=9];
9.65/4.02	75 -> 48[label="",style="solid", color="burlywood", weight=3];
9.65/4.02	45[label="primPlusNat (Succ vx500) (Succ vx4000)",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
9.65/4.02	46[label="primPlusNat (Succ vx500) Zero",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3];
9.65/4.02	47[label="primPlusNat Zero (Succ vx4000)",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3];
9.65/4.02	48[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3];
9.65/4.02	49[label="Succ (Succ (primPlusNat vx500 vx4000))",fontsize=16,color="green",shape="box"];49 -> 53[label="",style="dashed", color="green", weight=3];
9.65/4.02	50[label="Succ vx500",fontsize=16,color="green",shape="box"];51[label="Succ vx4000",fontsize=16,color="green",shape="box"];52[label="Zero",fontsize=16,color="green",shape="box"];53 -> 42[label="",style="dashed", color="red", weight=0];
9.65/4.02	53[label="primPlusNat vx500 vx4000",fontsize=16,color="magenta"];53 -> 54[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	53 -> 55[label="",style="dashed", color="magenta", weight=3];
9.65/4.02	54[label="vx500",fontsize=16,color="green",shape="box"];55[label="vx4000",fontsize=16,color="green",shape="box"];}
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(6)
9.65/4.02	Complex Obligation (AND)
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(7)
9.65/4.02	Obligation:
9.65/4.02	Q DP problem:
9.65/4.02	The TRS P consists of the following rules:
9.65/4.02	
9.65/4.02	   new_primMulNat(Main.Succ(vx300), Main.Succ(vx400)) -> new_primMulNat(vx300, Main.Succ(vx400))
9.65/4.02	
9.65/4.02	R is empty.
9.65/4.02	Q is empty.
9.65/4.02	We have to consider all minimal (P,Q,R)-chains.
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(8) QDPSizeChangeProof (EQUIVALENT)
9.65/4.02	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. 
9.65/4.02	
9.65/4.02	From the DPs we obtained the following set of size-change graphs:
9.65/4.02	*new_primMulNat(Main.Succ(vx300), Main.Succ(vx400)) -> new_primMulNat(vx300, Main.Succ(vx400))
9.65/4.02	The graph contains the following edges 1 > 1, 2 >= 2
9.65/4.02	
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(9)
9.65/4.02	YES
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(10)
9.65/4.02	Obligation:
9.65/4.02	Q DP problem:
9.65/4.02	The TRS P consists of the following rules:
9.65/4.02	
9.65/4.02	   new_primPlusNat(Main.Succ(vx500), Main.Succ(vx4000)) -> new_primPlusNat(vx500, vx4000)
9.65/4.02	
9.65/4.02	R is empty.
9.65/4.02	Q is empty.
9.65/4.02	We have to consider all minimal (P,Q,R)-chains.
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(11) QDPSizeChangeProof (EQUIVALENT)
9.65/4.02	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. 
9.65/4.02	
9.65/4.02	From the DPs we obtained the following set of size-change graphs:
9.65/4.02	*new_primPlusNat(Main.Succ(vx500), Main.Succ(vx4000)) -> new_primPlusNat(vx500, vx4000)
9.65/4.02	The graph contains the following edges 1 > 1, 2 > 2
9.65/4.02	
9.65/4.02	
9.65/4.02	----------------------------------------
9.65/4.02	
9.65/4.02	(12)
9.65/4.02	YES
9.65/4.06	EOF