8.53/3.69	YES
10.16/4.22	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.16/4.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.16/4.22	
10.16/4.22	
10.16/4.22	H-Termination with start terms of the given HASKELL could be proven:
10.16/4.22	
10.16/4.22	(0) HASKELL
10.16/4.22	(1) BR [EQUIVALENT, 0 ms]
10.16/4.22	(2) HASKELL
10.16/4.22	(3) COR [EQUIVALENT, 0 ms]
10.16/4.22	(4) HASKELL
10.16/4.22	(5) Narrow [SOUND, 0 ms]
10.16/4.22	(6) AND
10.16/4.22	    (7) QDP
10.16/4.22	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.16/4.22	        (9) YES
10.16/4.22	    (10) QDP
10.16/4.22	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.16/4.22	        (12) YES
10.16/4.22	    (13) QDP
10.16/4.22	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.16/4.22	        (15) YES
10.16/4.22	
10.16/4.22	
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(0)
10.16/4.22	Obligation:
10.16/4.22	mainModule Main 
10.16/4.22	module Main where {
10.16/4.22	import qualified Prelude;
10.16/4.22	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.16/4.22	
10.16/4.22	data Main.Nat = Succ Main.Nat  | Zero ;
10.16/4.22	
10.16/4.22	data Ordering = LT  | EQ  | GT ;
10.16/4.22	
10.16/4.22	data Ratio a = CnPc a a ;
10.16/4.22	
10.16/4.22	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	compareMyInt = primCmpInt;
10.16/4.22	
10.16/4.22	compareRatio :: Ratio MyInt  ->  Ratio MyInt  ->  Ordering;
10.16/4.22	compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y);
10.16/4.22	
10.16/4.22	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.16/4.22	
10.16/4.22	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.16/4.22	primCmpNat Main.Zero Main.Zero = EQ;
10.16/4.22	primCmpNat Main.Zero (Main.Succ y) = LT;
10.16/4.22	primCmpNat (Main.Succ x) Main.Zero = GT;
10.16/4.22	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.16/4.22	
10.16/4.22	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
10.16/4.22	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
10.16/4.22	
10.16/4.22	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primMulNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
10.16/4.22	
10.16/4.22	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.16/4.22	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.16/4.22	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.16/4.22	
10.16/4.22	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	srMyInt = primMulInt;
10.16/4.22	
10.16/4.22	}
10.16/4.22	
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(1) BR (EQUIVALENT)
10.16/4.22	Replaced joker patterns by fresh variables and removed binding patterns.
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(2)
10.16/4.22	Obligation:
10.16/4.22	mainModule Main 
10.16/4.22	module Main where {
10.16/4.22	import qualified Prelude;
10.16/4.22	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.16/4.22	
10.16/4.22	data Main.Nat = Succ Main.Nat  | Zero ;
10.16/4.22	
10.16/4.22	data Ordering = LT  | EQ  | GT ;
10.16/4.22	
10.16/4.22	data Ratio a = CnPc a a ;
10.16/4.22	
10.16/4.22	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	compareMyInt = primCmpInt;
10.16/4.22	
10.16/4.22	compareRatio :: Ratio MyInt  ->  Ratio MyInt  ->  Ordering;
10.16/4.22	compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y);
10.16/4.22	
10.16/4.22	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.16/4.22	
10.16/4.22	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.16/4.22	primCmpNat Main.Zero Main.Zero = EQ;
10.16/4.22	primCmpNat Main.Zero (Main.Succ y) = LT;
10.16/4.22	primCmpNat (Main.Succ x) Main.Zero = GT;
10.16/4.22	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.16/4.22	
10.16/4.22	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
10.16/4.22	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
10.16/4.22	
10.16/4.22	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primMulNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
10.16/4.22	
10.16/4.22	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.16/4.22	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.16/4.22	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.16/4.22	
10.16/4.22	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	srMyInt = primMulInt;
10.16/4.22	
10.16/4.22	}
10.16/4.22	
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(3) COR (EQUIVALENT)
10.16/4.22	Cond Reductions:
10.16/4.22	The following Function with conditions
10.16/4.22	"undefined |Falseundefined;
10.16/4.22	"
10.16/4.22	is transformed to
10.16/4.22	"undefined  = undefined1;
10.16/4.22	"
10.16/4.22	"undefined0 True = undefined;
10.16/4.22	"
10.16/4.22	"undefined1  = undefined0 False;
10.16/4.22	"
10.16/4.22	
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(4)
10.16/4.22	Obligation:
10.16/4.22	mainModule Main 
10.16/4.22	module Main where {
10.16/4.22	import qualified Prelude;
10.16/4.22	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.16/4.22	
10.16/4.22	data Main.Nat = Succ Main.Nat  | Zero ;
10.16/4.22	
10.16/4.22	data Ordering = LT  | EQ  | GT ;
10.16/4.22	
10.16/4.22	data Ratio a = CnPc a a ;
10.16/4.22	
10.16/4.22	compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	compareMyInt = primCmpInt;
10.16/4.22	
10.16/4.22	compareRatio :: Ratio MyInt  ->  Ratio MyInt  ->  Ordering;
10.16/4.22	compareRatio (CnPc x y) (CnPc x' y') = compareMyInt (srMyInt x y') (srMyInt x' y);
10.16/4.22	
10.16/4.22	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
10.16/4.22	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
10.16/4.22	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
10.16/4.22	
10.16/4.22	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
10.16/4.22	primCmpNat Main.Zero Main.Zero = EQ;
10.16/4.22	primCmpNat Main.Zero (Main.Succ y) = LT;
10.16/4.22	primCmpNat (Main.Succ x) Main.Zero = GT;
10.16/4.22	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
10.16/4.22	
10.16/4.22	primMulInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
10.16/4.22	primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
10.16/4.22	primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);
10.16/4.22	
10.16/4.22	primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primMulNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primMulNat Main.Zero (Main.Succ y) = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) Main.Zero = Main.Zero;
10.16/4.22	primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);
10.16/4.22	
10.16/4.22	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.16/4.22	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.16/4.22	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.16/4.22	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.16/4.22	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.16/4.22	
10.16/4.22	srMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.16/4.22	srMyInt = primMulInt;
10.16/4.22	
10.16/4.22	}
10.16/4.22	
10.16/4.22	----------------------------------------
10.16/4.22	
10.16/4.22	(5) Narrow (SOUND)
10.16/4.22	Haskell To QDPs
10.16/4.22	
10.16/4.22	digraph dp_graph {
10.16/4.22	node [outthreshold=100, inthreshold=100];1[label="compareRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.16/4.22	3[label="compareRatio vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.16/4.22	4[label="compareRatio vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];504[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 504[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	504 -> 5[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	5[label="compareRatio (CnPc vx30 vx31) vx4",fontsize=16,color="burlywood",shape="box"];505[label="vx4/CnPc vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];5 -> 505[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	505 -> 6[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	6[label="compareRatio (CnPc vx30 vx31) (CnPc vx40 vx41)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.16/4.22	7[label="compareMyInt (srMyInt vx30 vx41) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.16/4.22	8[label="primCmpInt (srMyInt vx30 vx41) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
10.16/4.22	9[label="primCmpInt (primMulInt vx30 vx41) (srMyInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];506[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];9 -> 506[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	506 -> 10[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	507[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];9 -> 507[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	507 -> 11[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	10[label="primCmpInt (primMulInt (Pos vx300) vx41) (srMyInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];508[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];10 -> 508[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	508 -> 12[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	509[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];10 -> 509[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	509 -> 13[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	11[label="primCmpInt (primMulInt (Neg vx300) vx41) (srMyInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];510[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];11 -> 510[label="",style="solid", color="burlywood", weight=9];
10.16/4.22	510 -> 14[label="",style="solid", color="burlywood", weight=3];
10.16/4.22	511[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];11 -> 511[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	511 -> 15[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	12[label="primCmpInt (primMulInt (Pos vx300) (Pos vx410)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
10.16/4.23	13[label="primCmpInt (primMulInt (Pos vx300) (Neg vx410)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
10.16/4.23	14[label="primCmpInt (primMulInt (Neg vx300) (Pos vx410)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
10.16/4.23	15[label="primCmpInt (primMulInt (Neg vx300) (Neg vx410)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
10.16/4.23	16 -> 263[label="",style="dashed", color="red", weight=0];
10.16/4.23	16[label="primCmpInt (Pos (primMulNat vx300 vx410)) (srMyInt vx40 vx31)",fontsize=16,color="magenta"];16 -> 264[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	17 -> 339[label="",style="dashed", color="red", weight=0];
10.16/4.23	17[label="primCmpInt (Neg (primMulNat vx300 vx410)) (srMyInt vx40 vx31)",fontsize=16,color="magenta"];17 -> 340[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	18 -> 339[label="",style="dashed", color="red", weight=0];
10.16/4.23	18[label="primCmpInt (Neg (primMulNat vx300 vx410)) (srMyInt vx40 vx31)",fontsize=16,color="magenta"];18 -> 341[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	19 -> 263[label="",style="dashed", color="red", weight=0];
10.16/4.23	19[label="primCmpInt (Pos (primMulNat vx300 vx410)) (srMyInt vx40 vx31)",fontsize=16,color="magenta"];19 -> 265[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	264[label="primMulNat vx300 vx410",fontsize=16,color="burlywood",shape="triangle"];512[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];264 -> 512[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	512 -> 276[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	513[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];264 -> 513[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	513 -> 277[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	263[label="primCmpInt (Pos vx10) (srMyInt vx40 vx31)",fontsize=16,color="burlywood",shape="triangle"];514[label="vx10/Succ vx100",fontsize=10,color="white",style="solid",shape="box"];263 -> 514[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	514 -> 278[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	515[label="vx10/Zero",fontsize=10,color="white",style="solid",shape="box"];263 -> 515[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	515 -> 279[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	340 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	340[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];340 -> 352[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	339[label="primCmpInt (Neg vx15) (srMyInt vx40 vx31)",fontsize=16,color="burlywood",shape="triangle"];516[label="vx15/Succ vx150",fontsize=10,color="white",style="solid",shape="box"];339 -> 516[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	516 -> 353[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	517[label="vx15/Zero",fontsize=10,color="white",style="solid",shape="box"];339 -> 517[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	517 -> 354[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	341 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	341[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];341 -> 355[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	265 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	265[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];265 -> 280[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	265 -> 281[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	276[label="primMulNat (Succ vx3000) vx410",fontsize=16,color="burlywood",shape="box"];518[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];276 -> 518[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	518 -> 296[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	519[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];276 -> 519[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	519 -> 297[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	277[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];520[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];277 -> 520[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	520 -> 298[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	521[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];277 -> 521[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	521 -> 299[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	278[label="primCmpInt (Pos (Succ vx100)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];278 -> 300[label="",style="solid", color="black", weight=3];
10.16/4.23	279[label="primCmpInt (Pos Zero) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];279 -> 301[label="",style="solid", color="black", weight=3];
10.16/4.23	352[label="vx410",fontsize=16,color="green",shape="box"];353[label="primCmpInt (Neg (Succ vx150)) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];353 -> 366[label="",style="solid", color="black", weight=3];
10.16/4.23	354[label="primCmpInt (Neg Zero) (srMyInt vx40 vx31)",fontsize=16,color="black",shape="box"];354 -> 367[label="",style="solid", color="black", weight=3];
10.16/4.23	355[label="vx300",fontsize=16,color="green",shape="box"];280[label="vx300",fontsize=16,color="green",shape="box"];281[label="vx410",fontsize=16,color="green",shape="box"];296[label="primMulNat (Succ vx3000) (Succ vx4100)",fontsize=16,color="black",shape="box"];296 -> 312[label="",style="solid", color="black", weight=3];
10.16/4.23	297[label="primMulNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];297 -> 313[label="",style="solid", color="black", weight=3];
10.16/4.23	298[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];298 -> 314[label="",style="solid", color="black", weight=3];
10.16/4.23	299[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];299 -> 315[label="",style="solid", color="black", weight=3];
10.16/4.23	300[label="primCmpInt (Pos (Succ vx100)) (primMulInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];522[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];300 -> 522[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	522 -> 316[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	523[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];300 -> 523[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	523 -> 317[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	301[label="primCmpInt (Pos Zero) (primMulInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];524[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];301 -> 524[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	524 -> 318[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	525[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];301 -> 525[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	525 -> 319[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	366[label="primCmpInt (Neg (Succ vx150)) (primMulInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];526[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];366 -> 526[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	526 -> 371[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	527[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];366 -> 527[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	527 -> 372[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	367[label="primCmpInt (Neg Zero) (primMulInt vx40 vx31)",fontsize=16,color="burlywood",shape="box"];528[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];367 -> 528[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	528 -> 373[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	529[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];367 -> 529[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	529 -> 374[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	312 -> 325[label="",style="dashed", color="red", weight=0];
10.16/4.23	312[label="primPlusNat (primMulNat vx3000 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];312 -> 326[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	313[label="Zero",fontsize=16,color="green",shape="box"];314[label="Zero",fontsize=16,color="green",shape="box"];315[label="Zero",fontsize=16,color="green",shape="box"];316[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) vx31)",fontsize=16,color="burlywood",shape="box"];530[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];316 -> 530[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	530 -> 327[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	531[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];316 -> 531[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	531 -> 328[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	317[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) vx31)",fontsize=16,color="burlywood",shape="box"];532[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];317 -> 532[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	532 -> 329[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	533[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];317 -> 533[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	533 -> 330[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	318[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) vx31)",fontsize=16,color="burlywood",shape="box"];534[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];318 -> 534[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	534 -> 331[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	535[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];318 -> 535[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	535 -> 332[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	319[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) vx31)",fontsize=16,color="burlywood",shape="box"];536[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];319 -> 536[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	536 -> 333[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	537[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];319 -> 537[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	537 -> 334[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	371[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) vx31)",fontsize=16,color="burlywood",shape="box"];538[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];371 -> 538[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	538 -> 378[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	539[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];371 -> 539[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	539 -> 379[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	372[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) vx31)",fontsize=16,color="burlywood",shape="box"];540[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];372 -> 540[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	540 -> 380[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	541[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];372 -> 541[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	541 -> 381[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	373[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) vx31)",fontsize=16,color="burlywood",shape="box"];542[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];373 -> 542[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	542 -> 382[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	543[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];373 -> 543[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	543 -> 383[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	374[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) vx31)",fontsize=16,color="burlywood",shape="box"];544[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];374 -> 544[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	544 -> 384[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	545[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];374 -> 545[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	545 -> 385[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	326 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	326[label="primMulNat vx3000 (Succ vx4100)",fontsize=16,color="magenta"];326 -> 335[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	326 -> 336[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	325[label="primPlusNat vx14 (Succ vx4100)",fontsize=16,color="burlywood",shape="triangle"];546[label="vx14/Succ vx140",fontsize=10,color="white",style="solid",shape="box"];325 -> 546[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	546 -> 337[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	547[label="vx14/Zero",fontsize=10,color="white",style="solid",shape="box"];325 -> 547[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	547 -> 338[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	327[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];327 -> 356[label="",style="solid", color="black", weight=3];
10.16/4.23	328[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];328 -> 357[label="",style="solid", color="black", weight=3];
10.16/4.23	329[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];329 -> 358[label="",style="solid", color="black", weight=3];
10.16/4.23	330[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];330 -> 359[label="",style="solid", color="black", weight=3];
10.16/4.23	331[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];331 -> 360[label="",style="solid", color="black", weight=3];
10.16/4.23	332[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];332 -> 361[label="",style="solid", color="black", weight=3];
10.16/4.23	333[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];333 -> 362[label="",style="solid", color="black", weight=3];
10.16/4.23	334[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];334 -> 363[label="",style="solid", color="black", weight=3];
10.16/4.23	378[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];378 -> 389[label="",style="solid", color="black", weight=3];
10.16/4.23	379[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];379 -> 390[label="",style="solid", color="black", weight=3];
10.16/4.23	380[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];380 -> 391[label="",style="solid", color="black", weight=3];
10.16/4.23	381[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];381 -> 392[label="",style="solid", color="black", weight=3];
10.16/4.23	382[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];382 -> 393[label="",style="solid", color="black", weight=3];
10.16/4.23	383[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];383 -> 394[label="",style="solid", color="black", weight=3];
10.16/4.23	384[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) (Pos vx310))",fontsize=16,color="black",shape="box"];384 -> 395[label="",style="solid", color="black", weight=3];
10.16/4.23	385[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) (Neg vx310))",fontsize=16,color="black",shape="box"];385 -> 396[label="",style="solid", color="black", weight=3];
10.16/4.23	335[label="vx3000",fontsize=16,color="green",shape="box"];336[label="Succ vx4100",fontsize=16,color="green",shape="box"];337[label="primPlusNat (Succ vx140) (Succ vx4100)",fontsize=16,color="black",shape="box"];337 -> 364[label="",style="solid", color="black", weight=3];
10.16/4.23	338[label="primPlusNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];338 -> 365[label="",style="solid", color="black", weight=3];
10.16/4.23	356 -> 368[label="",style="dashed", color="red", weight=0];
10.16/4.23	356[label="primCmpInt (Pos (Succ vx100)) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];356 -> 369[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	357 -> 375[label="",style="dashed", color="red", weight=0];
10.16/4.23	357[label="primCmpInt (Pos (Succ vx100)) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];357 -> 376[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	358 -> 375[label="",style="dashed", color="red", weight=0];
10.16/4.23	358[label="primCmpInt (Pos (Succ vx100)) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];358 -> 377[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	359 -> 368[label="",style="dashed", color="red", weight=0];
10.16/4.23	359[label="primCmpInt (Pos (Succ vx100)) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];359 -> 370[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	360 -> 386[label="",style="dashed", color="red", weight=0];
10.16/4.23	360[label="primCmpInt (Pos Zero) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];360 -> 387[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	361 -> 397[label="",style="dashed", color="red", weight=0];
10.16/4.23	361[label="primCmpInt (Pos Zero) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];361 -> 398[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	362 -> 397[label="",style="dashed", color="red", weight=0];
10.16/4.23	362[label="primCmpInt (Pos Zero) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];362 -> 399[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	363 -> 386[label="",style="dashed", color="red", weight=0];
10.16/4.23	363[label="primCmpInt (Pos Zero) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];363 -> 388[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	389 -> 400[label="",style="dashed", color="red", weight=0];
10.16/4.23	389[label="primCmpInt (Neg (Succ vx150)) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];389 -> 401[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	390 -> 403[label="",style="dashed", color="red", weight=0];
10.16/4.23	390[label="primCmpInt (Neg (Succ vx150)) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];390 -> 404[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	391 -> 403[label="",style="dashed", color="red", weight=0];
10.16/4.23	391[label="primCmpInt (Neg (Succ vx150)) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];391 -> 405[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	392 -> 400[label="",style="dashed", color="red", weight=0];
10.16/4.23	392[label="primCmpInt (Neg (Succ vx150)) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];392 -> 402[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	393 -> 406[label="",style="dashed", color="red", weight=0];
10.16/4.23	393[label="primCmpInt (Neg Zero) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];393 -> 407[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	394 -> 409[label="",style="dashed", color="red", weight=0];
10.16/4.23	394[label="primCmpInt (Neg Zero) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];394 -> 410[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	395 -> 409[label="",style="dashed", color="red", weight=0];
10.16/4.23	395[label="primCmpInt (Neg Zero) (Neg (primMulNat vx400 vx310))",fontsize=16,color="magenta"];395 -> 411[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	396 -> 406[label="",style="dashed", color="red", weight=0];
10.16/4.23	396[label="primCmpInt (Neg Zero) (Pos (primMulNat vx400 vx310))",fontsize=16,color="magenta"];396 -> 408[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	364[label="Succ (Succ (primPlusNat vx140 vx4100))",fontsize=16,color="green",shape="box"];364 -> 412[label="",style="dashed", color="green", weight=3];
10.16/4.23	365[label="Succ vx4100",fontsize=16,color="green",shape="box"];369 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	369[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];369 -> 413[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	369 -> 414[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	368[label="primCmpInt (Pos (Succ vx100)) (Pos vx16)",fontsize=16,color="black",shape="triangle"];368 -> 415[label="",style="solid", color="black", weight=3];
10.16/4.23	376 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	376[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];376 -> 416[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	376 -> 417[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	375[label="primCmpInt (Pos (Succ vx100)) (Neg vx17)",fontsize=16,color="black",shape="triangle"];375 -> 418[label="",style="solid", color="black", weight=3];
10.16/4.23	377 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	377[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];377 -> 419[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	377 -> 420[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	370 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	370[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];370 -> 421[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	370 -> 422[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	387 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	387[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];387 -> 423[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	387 -> 424[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	386[label="primCmpInt (Pos Zero) (Pos vx18)",fontsize=16,color="burlywood",shape="triangle"];548[label="vx18/Succ vx180",fontsize=10,color="white",style="solid",shape="box"];386 -> 548[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	548 -> 425[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	549[label="vx18/Zero",fontsize=10,color="white",style="solid",shape="box"];386 -> 549[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	549 -> 426[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	398 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	398[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];398 -> 427[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	398 -> 428[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	397[label="primCmpInt (Pos Zero) (Neg vx19)",fontsize=16,color="burlywood",shape="triangle"];550[label="vx19/Succ vx190",fontsize=10,color="white",style="solid",shape="box"];397 -> 550[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	550 -> 429[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	551[label="vx19/Zero",fontsize=10,color="white",style="solid",shape="box"];397 -> 551[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	551 -> 430[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	399 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	399[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];399 -> 431[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	399 -> 432[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	388 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	388[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];388 -> 433[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	388 -> 434[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	401 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	401[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];401 -> 435[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	401 -> 436[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	400[label="primCmpInt (Neg (Succ vx150)) (Pos vx20)",fontsize=16,color="black",shape="triangle"];400 -> 437[label="",style="solid", color="black", weight=3];
10.16/4.23	404 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	404[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];404 -> 438[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	404 -> 439[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	403[label="primCmpInt (Neg (Succ vx150)) (Neg vx21)",fontsize=16,color="black",shape="triangle"];403 -> 440[label="",style="solid", color="black", weight=3];
10.16/4.23	405 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	405[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];405 -> 441[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	405 -> 442[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	402 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	402[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];402 -> 443[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	402 -> 444[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	407 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	407[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];407 -> 445[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	407 -> 446[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	406[label="primCmpInt (Neg Zero) (Pos vx22)",fontsize=16,color="burlywood",shape="triangle"];552[label="vx22/Succ vx220",fontsize=10,color="white",style="solid",shape="box"];406 -> 552[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	552 -> 447[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	553[label="vx22/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 553[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	553 -> 448[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	410 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	410[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];410 -> 449[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	410 -> 450[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	409[label="primCmpInt (Neg Zero) (Neg vx23)",fontsize=16,color="burlywood",shape="triangle"];554[label="vx23/Succ vx230",fontsize=10,color="white",style="solid",shape="box"];409 -> 554[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	554 -> 451[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	555[label="vx23/Zero",fontsize=10,color="white",style="solid",shape="box"];409 -> 555[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	555 -> 452[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	411 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	411[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];411 -> 453[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	411 -> 454[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	408 -> 264[label="",style="dashed", color="red", weight=0];
10.16/4.23	408[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];408 -> 455[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	408 -> 456[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	412[label="primPlusNat vx140 vx4100",fontsize=16,color="burlywood",shape="triangle"];556[label="vx140/Succ vx1400",fontsize=10,color="white",style="solid",shape="box"];412 -> 556[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	556 -> 457[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	557[label="vx140/Zero",fontsize=10,color="white",style="solid",shape="box"];412 -> 557[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	557 -> 458[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	413[label="vx400",fontsize=16,color="green",shape="box"];414[label="vx310",fontsize=16,color="green",shape="box"];415[label="primCmpNat (Succ vx100) vx16",fontsize=16,color="burlywood",shape="triangle"];558[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];415 -> 558[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	558 -> 459[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	559[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];415 -> 559[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	559 -> 460[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	416[label="vx400",fontsize=16,color="green",shape="box"];417[label="vx310",fontsize=16,color="green",shape="box"];418[label="GT",fontsize=16,color="green",shape="box"];419[label="vx400",fontsize=16,color="green",shape="box"];420[label="vx310",fontsize=16,color="green",shape="box"];421[label="vx400",fontsize=16,color="green",shape="box"];422[label="vx310",fontsize=16,color="green",shape="box"];423[label="vx400",fontsize=16,color="green",shape="box"];424[label="vx310",fontsize=16,color="green",shape="box"];425[label="primCmpInt (Pos Zero) (Pos (Succ vx180))",fontsize=16,color="black",shape="box"];425 -> 461[label="",style="solid", color="black", weight=3];
10.16/4.23	426[label="primCmpInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];426 -> 462[label="",style="solid", color="black", weight=3];
10.16/4.23	427[label="vx400",fontsize=16,color="green",shape="box"];428[label="vx310",fontsize=16,color="green",shape="box"];429[label="primCmpInt (Pos Zero) (Neg (Succ vx190))",fontsize=16,color="black",shape="box"];429 -> 463[label="",style="solid", color="black", weight=3];
10.16/4.23	430[label="primCmpInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];430 -> 464[label="",style="solid", color="black", weight=3];
10.16/4.23	431[label="vx400",fontsize=16,color="green",shape="box"];432[label="vx310",fontsize=16,color="green",shape="box"];433[label="vx400",fontsize=16,color="green",shape="box"];434[label="vx310",fontsize=16,color="green",shape="box"];435[label="vx400",fontsize=16,color="green",shape="box"];436[label="vx310",fontsize=16,color="green",shape="box"];437[label="LT",fontsize=16,color="green",shape="box"];438[label="vx400",fontsize=16,color="green",shape="box"];439[label="vx310",fontsize=16,color="green",shape="box"];440[label="primCmpNat vx21 (Succ vx150)",fontsize=16,color="burlywood",shape="triangle"];560[label="vx21/Succ vx210",fontsize=10,color="white",style="solid",shape="box"];440 -> 560[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	560 -> 465[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	561[label="vx21/Zero",fontsize=10,color="white",style="solid",shape="box"];440 -> 561[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	561 -> 466[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	441[label="vx400",fontsize=16,color="green",shape="box"];442[label="vx310",fontsize=16,color="green",shape="box"];443[label="vx400",fontsize=16,color="green",shape="box"];444[label="vx310",fontsize=16,color="green",shape="box"];445[label="vx400",fontsize=16,color="green",shape="box"];446[label="vx310",fontsize=16,color="green",shape="box"];447[label="primCmpInt (Neg Zero) (Pos (Succ vx220))",fontsize=16,color="black",shape="box"];447 -> 467[label="",style="solid", color="black", weight=3];
10.16/4.23	448[label="primCmpInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];448 -> 468[label="",style="solid", color="black", weight=3];
10.16/4.23	449[label="vx400",fontsize=16,color="green",shape="box"];450[label="vx310",fontsize=16,color="green",shape="box"];451[label="primCmpInt (Neg Zero) (Neg (Succ vx230))",fontsize=16,color="black",shape="box"];451 -> 469[label="",style="solid", color="black", weight=3];
10.16/4.23	452[label="primCmpInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];452 -> 470[label="",style="solid", color="black", weight=3];
10.16/4.23	453[label="vx400",fontsize=16,color="green",shape="box"];454[label="vx310",fontsize=16,color="green",shape="box"];455[label="vx400",fontsize=16,color="green",shape="box"];456[label="vx310",fontsize=16,color="green",shape="box"];457[label="primPlusNat (Succ vx1400) vx4100",fontsize=16,color="burlywood",shape="box"];562[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];457 -> 562[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	562 -> 471[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	563[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];457 -> 563[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	563 -> 472[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	458[label="primPlusNat Zero vx4100",fontsize=16,color="burlywood",shape="box"];564[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];458 -> 564[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	564 -> 473[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	565[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];458 -> 565[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	565 -> 474[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	459[label="primCmpNat (Succ vx100) (Succ vx160)",fontsize=16,color="black",shape="box"];459 -> 475[label="",style="solid", color="black", weight=3];
10.16/4.23	460[label="primCmpNat (Succ vx100) Zero",fontsize=16,color="black",shape="box"];460 -> 476[label="",style="solid", color="black", weight=3];
10.16/4.23	461 -> 440[label="",style="dashed", color="red", weight=0];
10.16/4.23	461[label="primCmpNat Zero (Succ vx180)",fontsize=16,color="magenta"];461 -> 477[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	461 -> 478[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	462[label="EQ",fontsize=16,color="green",shape="box"];463[label="GT",fontsize=16,color="green",shape="box"];464[label="EQ",fontsize=16,color="green",shape="box"];465[label="primCmpNat (Succ vx210) (Succ vx150)",fontsize=16,color="black",shape="box"];465 -> 479[label="",style="solid", color="black", weight=3];
10.16/4.23	466[label="primCmpNat Zero (Succ vx150)",fontsize=16,color="black",shape="box"];466 -> 480[label="",style="solid", color="black", weight=3];
10.16/4.23	467[label="LT",fontsize=16,color="green",shape="box"];468[label="EQ",fontsize=16,color="green",shape="box"];469 -> 415[label="",style="dashed", color="red", weight=0];
10.16/4.23	469[label="primCmpNat (Succ vx230) Zero",fontsize=16,color="magenta"];469 -> 481[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	469 -> 482[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	470[label="EQ",fontsize=16,color="green",shape="box"];471[label="primPlusNat (Succ vx1400) (Succ vx41000)",fontsize=16,color="black",shape="box"];471 -> 483[label="",style="solid", color="black", weight=3];
10.16/4.23	472[label="primPlusNat (Succ vx1400) Zero",fontsize=16,color="black",shape="box"];472 -> 484[label="",style="solid", color="black", weight=3];
10.16/4.23	473[label="primPlusNat Zero (Succ vx41000)",fontsize=16,color="black",shape="box"];473 -> 485[label="",style="solid", color="black", weight=3];
10.16/4.23	474[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];474 -> 486[label="",style="solid", color="black", weight=3];
10.16/4.23	475[label="primCmpNat vx100 vx160",fontsize=16,color="burlywood",shape="triangle"];566[label="vx100/Succ vx1000",fontsize=10,color="white",style="solid",shape="box"];475 -> 566[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	566 -> 487[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	567[label="vx100/Zero",fontsize=10,color="white",style="solid",shape="box"];475 -> 567[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	567 -> 488[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	476[label="GT",fontsize=16,color="green",shape="box"];477[label="vx180",fontsize=16,color="green",shape="box"];478[label="Zero",fontsize=16,color="green",shape="box"];479 -> 475[label="",style="dashed", color="red", weight=0];
10.16/4.23	479[label="primCmpNat vx210 vx150",fontsize=16,color="magenta"];479 -> 489[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	479 -> 490[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	480[label="LT",fontsize=16,color="green",shape="box"];481[label="Zero",fontsize=16,color="green",shape="box"];482[label="vx230",fontsize=16,color="green",shape="box"];483[label="Succ (Succ (primPlusNat vx1400 vx41000))",fontsize=16,color="green",shape="box"];483 -> 491[label="",style="dashed", color="green", weight=3];
10.16/4.23	484[label="Succ vx1400",fontsize=16,color="green",shape="box"];485[label="Succ vx41000",fontsize=16,color="green",shape="box"];486[label="Zero",fontsize=16,color="green",shape="box"];487[label="primCmpNat (Succ vx1000) vx160",fontsize=16,color="burlywood",shape="box"];568[label="vx160/Succ vx1600",fontsize=10,color="white",style="solid",shape="box"];487 -> 568[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	568 -> 492[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	569[label="vx160/Zero",fontsize=10,color="white",style="solid",shape="box"];487 -> 569[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	569 -> 493[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	488[label="primCmpNat Zero vx160",fontsize=16,color="burlywood",shape="box"];570[label="vx160/Succ vx1600",fontsize=10,color="white",style="solid",shape="box"];488 -> 570[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	570 -> 494[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	571[label="vx160/Zero",fontsize=10,color="white",style="solid",shape="box"];488 -> 571[label="",style="solid", color="burlywood", weight=9];
10.16/4.23	571 -> 495[label="",style="solid", color="burlywood", weight=3];
10.16/4.23	489[label="vx150",fontsize=16,color="green",shape="box"];490[label="vx210",fontsize=16,color="green",shape="box"];491 -> 412[label="",style="dashed", color="red", weight=0];
10.16/4.23	491[label="primPlusNat vx1400 vx41000",fontsize=16,color="magenta"];491 -> 496[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	491 -> 497[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	492[label="primCmpNat (Succ vx1000) (Succ vx1600)",fontsize=16,color="black",shape="box"];492 -> 498[label="",style="solid", color="black", weight=3];
10.16/4.23	493[label="primCmpNat (Succ vx1000) Zero",fontsize=16,color="black",shape="box"];493 -> 499[label="",style="solid", color="black", weight=3];
10.16/4.23	494[label="primCmpNat Zero (Succ vx1600)",fontsize=16,color="black",shape="box"];494 -> 500[label="",style="solid", color="black", weight=3];
10.16/4.23	495[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];495 -> 501[label="",style="solid", color="black", weight=3];
10.16/4.23	496[label="vx1400",fontsize=16,color="green",shape="box"];497[label="vx41000",fontsize=16,color="green",shape="box"];498 -> 475[label="",style="dashed", color="red", weight=0];
10.16/4.23	498[label="primCmpNat vx1000 vx1600",fontsize=16,color="magenta"];498 -> 502[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	498 -> 503[label="",style="dashed", color="magenta", weight=3];
10.16/4.23	499[label="GT",fontsize=16,color="green",shape="box"];500[label="LT",fontsize=16,color="green",shape="box"];501[label="EQ",fontsize=16,color="green",shape="box"];502[label="vx1600",fontsize=16,color="green",shape="box"];503[label="vx1000",fontsize=16,color="green",shape="box"];}
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(6)
10.16/4.23	Complex Obligation (AND)
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(7)
10.16/4.23	Obligation:
10.16/4.23	Q DP problem:
10.16/4.23	The TRS P consists of the following rules:
10.16/4.23	
10.16/4.23	   new_primCmpNat(Main.Succ(vx1000), Main.Succ(vx1600)) -> new_primCmpNat(vx1000, vx1600)
10.16/4.23	
10.16/4.23	R is empty.
10.16/4.23	Q is empty.
10.16/4.23	We have to consider all minimal (P,Q,R)-chains.
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(8) QDPSizeChangeProof (EQUIVALENT)
10.16/4.23	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. 
10.16/4.23	
10.16/4.23	From the DPs we obtained the following set of size-change graphs:
10.16/4.23	*new_primCmpNat(Main.Succ(vx1000), Main.Succ(vx1600)) -> new_primCmpNat(vx1000, vx1600)
10.16/4.23	The graph contains the following edges 1 > 1, 2 > 2
10.16/4.23	
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(9)
10.16/4.23	YES
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(10)
10.16/4.23	Obligation:
10.16/4.23	Q DP problem:
10.16/4.23	The TRS P consists of the following rules:
10.16/4.23	
10.16/4.23	   new_primMulNat(Main.Succ(vx3000), Main.Succ(vx4100)) -> new_primMulNat(vx3000, Main.Succ(vx4100))
10.16/4.23	
10.16/4.23	R is empty.
10.16/4.23	Q is empty.
10.16/4.23	We have to consider all minimal (P,Q,R)-chains.
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(11) QDPSizeChangeProof (EQUIVALENT)
10.16/4.23	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. 
10.16/4.23	
10.16/4.23	From the DPs we obtained the following set of size-change graphs:
10.16/4.23	*new_primMulNat(Main.Succ(vx3000), Main.Succ(vx4100)) -> new_primMulNat(vx3000, Main.Succ(vx4100))
10.16/4.23	The graph contains the following edges 1 > 1, 2 >= 2
10.16/4.23	
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(12)
10.16/4.23	YES
10.16/4.23	
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(13)
10.16/4.23	Obligation:
10.16/4.23	Q DP problem:
10.16/4.23	The TRS P consists of the following rules:
10.16/4.23	
10.16/4.23	   new_primPlusNat(Main.Succ(vx1400), Main.Succ(vx41000)) -> new_primPlusNat(vx1400, vx41000)
10.16/4.23	
10.16/4.23	R is empty.
10.16/4.23	Q is empty.
10.16/4.23	We have to consider all minimal (P,Q,R)-chains.
10.16/4.23	----------------------------------------
10.16/4.23	
10.16/4.23	(14) QDPSizeChangeProof (EQUIVALENT)
10.16/4.23	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. 
10.16/4.23	
10.16/4.23	From the DPs we obtained the following set of size-change graphs:
10.16/4.23	*new_primPlusNat(Main.Succ(vx1400), Main.Succ(vx41000)) -> new_primPlusNat(vx1400, vx41000)
10.16/4.23	The graph contains the following edges 1 > 1, 2 > 2
10.16/4.23	
10.16/4.23	
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10.16/4.23	
10.16/4.23	(15)
10.16/4.23	YES
10.46/4.27	EOF