8.95/4.00	MAYBE
10.95/4.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.95/4.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.95/4.55	
10.95/4.55	
10.95/4.55	H-Termination with start terms of the given HASKELL could not be shown:
10.95/4.55	
10.95/4.55	(0) HASKELL
10.95/4.55	(1) BR [EQUIVALENT, 0 ms]
10.95/4.55	(2) HASKELL
10.95/4.55	(3) COR [EQUIVALENT, 0 ms]
10.95/4.55	(4) HASKELL
10.95/4.55	(5) Narrow [SOUND, 0 ms]
10.95/4.55	(6) AND
10.95/4.55	    (7) QDP
10.95/4.55	        (8) MNOCProof [EQUIVALENT, 0 ms]
10.95/4.55	        (9) QDP
10.95/4.55	        (10) NonTerminationLoopProof [COMPLETE, 0 ms]
10.95/4.55	        (11) NO
10.95/4.55	    (12) QDP
10.95/4.55	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.95/4.55	        (14) YES
10.95/4.55	    (15) QDP
10.95/4.55	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.95/4.55	        (17) YES
10.95/4.55	    (18) QDP
10.95/4.55	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.95/4.55	        (20) YES
10.95/4.55	(21) Narrow [COMPLETE, 0 ms]
10.95/4.55	(22) TRUE
10.95/4.55	
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(0)
10.95/4.55	Obligation:
10.95/4.55	mainModule Main 
10.95/4.55	module Main where {
10.95/4.55	import qualified Prelude;
10.95/4.55	data List a = Cons a (List a)  | Nil ;
10.95/4.55	
10.95/4.55	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.95/4.55	
10.95/4.55	data Main.Nat = Succ Main.Nat  | Zero ;
10.95/4.55	
10.95/4.55	enumFromThenMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.95/4.55	enumFromThenMyInt = numericEnumFromThen;
10.95/4.55	
10.95/4.55	iterate :: (a  ->  a)  ->  a  ->  List a;
10.95/4.55	iterate f x = Cons x (iterate f (f x));
10.95/4.55	
10.95/4.55	msMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	msMyInt = primMinusInt;
10.95/4.55	
10.95/4.55	numericEnumFromThen n m = iterate (psMyInt (msMyInt m n)) n;
10.95/4.55	
10.95/4.55	primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.95/4.55	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.95/4.55	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.95/4.55	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.95/4.55	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.95/4.55	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.95/4.55	
10.95/4.55	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.95/4.55	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.95/4.55	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.95/4.55	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.95/4.55	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.95/4.55	
10.95/4.55	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	psMyInt = primPlusInt;
10.95/4.55	
10.95/4.55	}
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(1) BR (EQUIVALENT)
10.95/4.55	Replaced joker patterns by fresh variables and removed binding patterns.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(2)
10.95/4.55	Obligation:
10.95/4.55	mainModule Main 
10.95/4.55	module Main where {
10.95/4.55	import qualified Prelude;
10.95/4.55	data List a = Cons a (List a)  | Nil ;
10.95/4.55	
10.95/4.55	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.95/4.55	
10.95/4.55	data Main.Nat = Succ Main.Nat  | Zero ;
10.95/4.55	
10.95/4.55	enumFromThenMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.95/4.55	enumFromThenMyInt = numericEnumFromThen;
10.95/4.55	
10.95/4.55	iterate :: (a  ->  a)  ->  a  ->  List a;
10.95/4.55	iterate f x = Cons x (iterate f (f x));
10.95/4.55	
10.95/4.55	msMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	msMyInt = primMinusInt;
10.95/4.55	
10.95/4.55	numericEnumFromThen n m = iterate (psMyInt (msMyInt m n)) n;
10.95/4.55	
10.95/4.55	primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.95/4.55	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.95/4.55	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.95/4.55	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.95/4.55	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.95/4.55	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.95/4.55	
10.95/4.55	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.95/4.55	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.95/4.55	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.95/4.55	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.95/4.55	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.95/4.55	
10.95/4.55	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	psMyInt = primPlusInt;
10.95/4.55	
10.95/4.55	}
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(3) COR (EQUIVALENT)
10.95/4.55	Cond Reductions:
10.95/4.55	The following Function with conditions
10.95/4.55	"undefined |Falseundefined;
10.95/4.55	"
10.95/4.55	is transformed to
10.95/4.55	"undefined  = undefined1;
10.95/4.55	"
10.95/4.55	"undefined0 True = undefined;
10.95/4.55	"
10.95/4.55	"undefined1  = undefined0 False;
10.95/4.55	"
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(4)
10.95/4.55	Obligation:
10.95/4.55	mainModule Main 
10.95/4.55	module Main where {
10.95/4.55	import qualified Prelude;
10.95/4.55	data List a = Cons a (List a)  | Nil ;
10.95/4.55	
10.95/4.55	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.95/4.55	
10.95/4.55	data Main.Nat = Succ Main.Nat  | Zero ;
10.95/4.55	
10.95/4.55	enumFromThenMyInt :: MyInt  ->  MyInt  ->  List MyInt;
10.95/4.55	enumFromThenMyInt = numericEnumFromThen;
10.95/4.55	
10.95/4.55	iterate :: (a  ->  a)  ->  a  ->  List a;
10.95/4.55	iterate f x = Cons x (iterate f (f x));
10.95/4.55	
10.95/4.55	msMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	msMyInt = primMinusInt;
10.95/4.55	
10.95/4.55	numericEnumFromThen n m = iterate (psMyInt (msMyInt m n)) n;
10.95/4.55	
10.95/4.55	primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
10.95/4.55	primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
10.95/4.55	primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
10.95/4.55	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
10.95/4.55	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
10.95/4.55	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
10.95/4.55	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
10.95/4.55	
10.95/4.55	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
10.95/4.55	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
10.95/4.55	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
10.95/4.55	
10.95/4.55	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
10.95/4.55	primPlusNat Main.Zero Main.Zero = Main.Zero;
10.95/4.55	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
10.95/4.55	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
10.95/4.55	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
10.95/4.55	
10.95/4.55	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
10.95/4.55	psMyInt = primPlusInt;
10.95/4.55	
10.95/4.55	}
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(5) Narrow (SOUND)
10.95/4.55	Haskell To QDPs
10.95/4.55	
10.95/4.55	digraph dp_graph {
10.95/4.55	node [outthreshold=100, inthreshold=100];1[label="enumFromThenMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.95/4.55	3[label="enumFromThenMyInt vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.95/4.55	4[label="enumFromThenMyInt vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.95/4.55	5[label="numericEnumFromThen vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.95/4.55	6[label="iterate (psMyInt (msMyInt vx4 vx3)) vx3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.95/4.55	7[label="Cons vx3 (iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx3))",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
10.95/4.55	8 -> 13[label="",style="dashed", color="red", weight=0];
10.95/4.55	8[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	14[label="vx3",fontsize=16,color="green",shape="box"];13[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx5)",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
10.95/4.55	16[label="Cons (psMyInt (msMyInt vx4 vx3) vx5) (iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) (psMyInt (msMyInt vx4 vx3) vx5)))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3];
10.95/4.55	16 -> 18[label="",style="dashed", color="green", weight=3];
10.95/4.55	17[label="psMyInt (msMyInt vx4 vx3) vx5",fontsize=16,color="black",shape="triangle"];17 -> 19[label="",style="solid", color="black", weight=3];
10.95/4.55	18 -> 13[label="",style="dashed", color="red", weight=0];
10.95/4.55	18[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) (psMyInt (msMyInt vx4 vx3) vx5))",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	19[label="primPlusInt (msMyInt vx4 vx3) vx5",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
10.95/4.55	20 -> 17[label="",style="dashed", color="red", weight=0];
10.95/4.55	20[label="psMyInt (msMyInt vx4 vx3) vx5",fontsize=16,color="magenta"];21[label="primPlusInt (primMinusInt vx4 vx3) vx5",fontsize=16,color="burlywood",shape="box"];192[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];21 -> 192[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	192 -> 22[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	193[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];21 -> 193[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	193 -> 23[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	22[label="primPlusInt (primMinusInt (Pos vx40) vx3) vx5",fontsize=16,color="burlywood",shape="box"];194[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];22 -> 194[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	194 -> 24[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	195[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];22 -> 195[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	195 -> 25[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	23[label="primPlusInt (primMinusInt (Neg vx40) vx3) vx5",fontsize=16,color="burlywood",shape="box"];196[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];23 -> 196[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	196 -> 26[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	197[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];23 -> 197[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	197 -> 27[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	24[label="primPlusInt (primMinusInt (Pos vx40) (Pos vx30)) vx5",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
10.95/4.55	25[label="primPlusInt (primMinusInt (Pos vx40) (Neg vx30)) vx5",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
10.95/4.55	26[label="primPlusInt (primMinusInt (Neg vx40) (Pos vx30)) vx5",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
10.95/4.55	27[label="primPlusInt (primMinusInt (Neg vx40) (Neg vx30)) vx5",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
10.95/4.55	28[label="primPlusInt (primMinusNat vx40 vx30) vx5",fontsize=16,color="burlywood",shape="triangle"];198[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];28 -> 198[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	198 -> 32[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	199[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 199[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	199 -> 33[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	29[label="primPlusInt (Pos (primPlusNat vx40 vx30)) vx5",fontsize=16,color="burlywood",shape="box"];200[label="vx5/Pos vx50",fontsize=10,color="white",style="solid",shape="box"];29 -> 200[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	200 -> 34[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	201[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];29 -> 201[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	201 -> 35[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	30[label="primPlusInt (Neg (primPlusNat vx40 vx30)) vx5",fontsize=16,color="burlywood",shape="box"];202[label="vx5/Pos vx50",fontsize=10,color="white",style="solid",shape="box"];30 -> 202[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	202 -> 36[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	203[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];30 -> 203[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	203 -> 37[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	31 -> 28[label="",style="dashed", color="red", weight=0];
10.95/4.55	31[label="primPlusInt (primMinusNat vx30 vx40) vx5",fontsize=16,color="magenta"];31 -> 38[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	31 -> 39[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	32[label="primPlusInt (primMinusNat (Succ vx400) vx30) vx5",fontsize=16,color="burlywood",shape="box"];204[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];32 -> 204[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	204 -> 40[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	205[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 205[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	205 -> 41[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	33[label="primPlusInt (primMinusNat Zero vx30) vx5",fontsize=16,color="burlywood",shape="box"];206[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];33 -> 206[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	206 -> 42[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	207[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 207[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	207 -> 43[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	34[label="primPlusInt (Pos (primPlusNat vx40 vx30)) (Pos vx50)",fontsize=16,color="black",shape="box"];34 -> 44[label="",style="solid", color="black", weight=3];
10.95/4.55	35[label="primPlusInt (Pos (primPlusNat vx40 vx30)) (Neg vx50)",fontsize=16,color="black",shape="box"];35 -> 45[label="",style="solid", color="black", weight=3];
10.95/4.55	36[label="primPlusInt (Neg (primPlusNat vx40 vx30)) (Pos vx50)",fontsize=16,color="black",shape="box"];36 -> 46[label="",style="solid", color="black", weight=3];
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10.95/4.55	113 -> 107[label="",style="dashed", color="red", weight=0];
10.95/4.55	113[label="primPlusNat Zero vx50",fontsize=16,color="magenta"];114[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];114 -> 138[label="",style="dashed", color="green", weight=3];
10.95/4.55	115[label="vx300",fontsize=16,color="green",shape="box"];116 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	116[label="primMinusNat (Succ vx500) (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];116 -> 139[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	116 -> 140[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	117 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	117[label="primMinusNat (Succ vx500) (Succ vx400)",fontsize=16,color="magenta"];117 -> 141[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	117 -> 142[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	118 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	118[label="primMinusNat (Succ vx500) (Succ vx300)",fontsize=16,color="magenta"];118 -> 143[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	119 -> 80[label="",style="dashed", color="red", weight=0];
10.95/4.55	119[label="primMinusNat (Succ vx500) Zero",fontsize=16,color="magenta"];119 -> 144[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	119 -> 145[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	120 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	120[label="primMinusNat Zero (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];120 -> 146[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	120 -> 147[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	121 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	121[label="primMinusNat Zero (Succ vx400)",fontsize=16,color="magenta"];121 -> 148[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	121 -> 149[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	122 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	122[label="primMinusNat Zero (Succ vx300)",fontsize=16,color="magenta"];122 -> 150[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	123 -> 84[label="",style="dashed", color="red", weight=0];
10.95/4.55	123[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];123 -> 151[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	124[label="primPlusNat (Succ vx400) (Succ vx500)",fontsize=16,color="black",shape="box"];124 -> 152[label="",style="solid", color="black", weight=3];
10.95/4.55	125[label="primPlusNat (Succ vx400) Zero",fontsize=16,color="black",shape="box"];125 -> 153[label="",style="solid", color="black", weight=3];
10.95/4.55	126[label="primMinusNat vx400 vx500",fontsize=16,color="burlywood",shape="triangle"];250[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];126 -> 250[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	250 -> 154[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	251[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];126 -> 251[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	251 -> 155[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	127[label="Pos (Succ vx400)",fontsize=16,color="green",shape="box"];128 -> 126[label="",style="dashed", color="red", weight=0];
10.95/4.55	128[label="primMinusNat vx500 vx300",fontsize=16,color="magenta"];128 -> 156[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	128 -> 157[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	129[label="Neg (Succ vx300)",fontsize=16,color="green",shape="box"];130[label="vx300",fontsize=16,color="green",shape="box"];131[label="vx50",fontsize=16,color="green",shape="box"];132[label="primPlusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];132 -> 158[label="",style="solid", color="black", weight=3];
10.95/4.55	133[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];133 -> 159[label="",style="solid", color="black", weight=3];
10.95/4.55	134[label="Neg (Succ vx500)",fontsize=16,color="green",shape="box"];135[label="Pos Zero",fontsize=16,color="green",shape="box"];136[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];136 -> 160[label="",style="dashed", color="green", weight=3];
10.95/4.55	137[label="vx300",fontsize=16,color="green",shape="box"];138[label="primPlusNat vx400 vx300",fontsize=16,color="burlywood",shape="triangle"];252[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];138 -> 252[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	252 -> 161[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	253[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 253[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	253 -> 162[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	139[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];139 -> 163[label="",style="dashed", color="green", weight=3];
10.95/4.55	140[label="Succ vx500",fontsize=16,color="green",shape="box"];141[label="vx400",fontsize=16,color="green",shape="box"];142[label="Succ vx500",fontsize=16,color="green",shape="box"];143[label="Succ vx500",fontsize=16,color="green",shape="box"];144[label="Zero",fontsize=16,color="green",shape="box"];145[label="vx500",fontsize=16,color="green",shape="box"];146[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];146 -> 164[label="",style="dashed", color="green", weight=3];
10.95/4.55	147[label="Zero",fontsize=16,color="green",shape="box"];148[label="vx400",fontsize=16,color="green",shape="box"];149[label="Zero",fontsize=16,color="green",shape="box"];150[label="Zero",fontsize=16,color="green",shape="box"];151[label="Zero",fontsize=16,color="green",shape="box"];152[label="Succ (Succ (primPlusNat vx400 vx500))",fontsize=16,color="green",shape="box"];152 -> 165[label="",style="dashed", color="green", weight=3];
10.95/4.55	153[label="Succ vx400",fontsize=16,color="green",shape="box"];154[label="primMinusNat (Succ vx4000) vx500",fontsize=16,color="burlywood",shape="box"];254[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];154 -> 254[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	254 -> 166[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	255[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];154 -> 255[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	255 -> 167[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	155[label="primMinusNat Zero vx500",fontsize=16,color="burlywood",shape="box"];256[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];155 -> 256[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	256 -> 168[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	257[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];155 -> 257[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	257 -> 169[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	156[label="vx500",fontsize=16,color="green",shape="box"];157[label="vx300",fontsize=16,color="green",shape="box"];158[label="Succ vx500",fontsize=16,color="green",shape="box"];159[label="Zero",fontsize=16,color="green",shape="box"];160 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	160[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];161[label="primPlusNat (Succ vx4000) vx300",fontsize=16,color="burlywood",shape="box"];258[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];161 -> 258[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	258 -> 170[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	259[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];161 -> 259[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	259 -> 171[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	162[label="primPlusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];260[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];162 -> 260[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	260 -> 172[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	261[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];162 -> 261[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	261 -> 173[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	163 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	163[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];163 -> 174[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	163 -> 175[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	164 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	164[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];164 -> 176[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	164 -> 177[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	165 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	165[label="primPlusNat vx400 vx500",fontsize=16,color="magenta"];165 -> 178[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	166[label="primMinusNat (Succ vx4000) (Succ vx5000)",fontsize=16,color="black",shape="box"];166 -> 179[label="",style="solid", color="black", weight=3];
10.95/4.55	167[label="primMinusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];167 -> 180[label="",style="solid", color="black", weight=3];
10.95/4.55	168[label="primMinusNat Zero (Succ vx5000)",fontsize=16,color="black",shape="box"];168 -> 181[label="",style="solid", color="black", weight=3];
10.95/4.55	169[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];169 -> 182[label="",style="solid", color="black", weight=3];
10.95/4.55	170[label="primPlusNat (Succ vx4000) (Succ vx3000)",fontsize=16,color="black",shape="box"];170 -> 183[label="",style="solid", color="black", weight=3];
10.95/4.55	171[label="primPlusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];171 -> 184[label="",style="solid", color="black", weight=3];
10.95/4.55	172[label="primPlusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];172 -> 185[label="",style="solid", color="black", weight=3];
10.95/4.55	173[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];173 -> 186[label="",style="solid", color="black", weight=3];
10.95/4.55	174[label="vx300",fontsize=16,color="green",shape="box"];175[label="vx400",fontsize=16,color="green",shape="box"];176[label="vx300",fontsize=16,color="green",shape="box"];177[label="vx400",fontsize=16,color="green",shape="box"];178[label="vx500",fontsize=16,color="green",shape="box"];179 -> 126[label="",style="dashed", color="red", weight=0];
10.95/4.55	179[label="primMinusNat vx4000 vx5000",fontsize=16,color="magenta"];179 -> 187[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	179 -> 188[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	180[label="Pos (Succ vx4000)",fontsize=16,color="green",shape="box"];181[label="Neg (Succ vx5000)",fontsize=16,color="green",shape="box"];182[label="Pos Zero",fontsize=16,color="green",shape="box"];183[label="Succ (Succ (primPlusNat vx4000 vx3000))",fontsize=16,color="green",shape="box"];183 -> 189[label="",style="dashed", color="green", weight=3];
10.95/4.55	184[label="Succ vx4000",fontsize=16,color="green",shape="box"];185[label="Succ vx3000",fontsize=16,color="green",shape="box"];186[label="Zero",fontsize=16,color="green",shape="box"];187[label="vx4000",fontsize=16,color="green",shape="box"];188[label="vx5000",fontsize=16,color="green",shape="box"];189 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	189[label="primPlusNat vx4000 vx3000",fontsize=16,color="magenta"];189 -> 190[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	189 -> 191[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	190[label="vx3000",fontsize=16,color="green",shape="box"];191[label="vx4000",fontsize=16,color="green",shape="box"];}
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(6)
10.95/4.55	Complex Obligation (AND)
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(7)
10.95/4.55	Obligation:
10.95/4.55	Q DP problem:
10.95/4.55	The TRS P consists of the following rules:
10.95/4.55	
10.95/4.55	   new_iterate(vx4, vx3, vx5) -> new_iterate(vx4, vx3, new_psMyInt(vx4, vx3, vx5))
10.95/4.55	
10.95/4.55	The TRS R consists of the following rules:
10.95/4.55	
10.95/4.55	   new_primMinusNat0(vx400, Main.Succ(vx500)) -> new_primMinusNat1(vx400, vx500)
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(vx300), Main.Pos(vx50)) -> new_primMinusNat3(vx50, vx300)
10.95/4.55	   new_primPlusNat1(Main.Succ(vx4000), Main.Zero) -> Main.Succ(vx4000)
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Succ(vx3000)) -> Main.Succ(vx3000)
10.95/4.55	   new_primMinusNat2(Main.Zero) -> Main.Pos(Main.Zero)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Zero)) -> new_primMinusNat2(Main.Zero)
10.95/4.55	   new_primMinusNat3(Main.Succ(vx500), vx300) -> new_primMinusNat1(vx500, vx300)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), Main.Succ(new_primPlusNat1(vx400, vx300)))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Pos(vx50)) -> Main.Pos(new_primPlusNat3(vx50))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Neg(vx50)) -> new_primMinusNat2(vx50)
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Zero) -> Main.Zero
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Zero, Main.Neg(vx50)) -> new_primMinusNat0(vx400, vx50)
10.95/4.55	   new_primPlusNat2(Main.Succ(vx400), Main.Succ(vx300), vx50) -> new_primPlusNat0(Main.Succ(new_primPlusNat1(vx400, vx300)), vx50)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat0(vx500, Main.Zero)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(vx400)), Main.Neg(Main.Zero), Main.Neg(vx50)) -> new_primMinusNat0(vx400, vx50)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Succ(vx300)), Main.Neg(vx50)) -> new_primMinusNat0(vx300, vx50)
10.95/4.55	   new_primPlusNat1(Main.Succ(vx4000), Main.Succ(vx3000)) -> Main.Succ(Main.Succ(new_primPlusNat1(vx4000, vx3000)))
10.95/4.55	   new_psMyInt(Main.Neg(vx40), Main.Neg(vx30), vx5) -> new_primPlusInt0(vx30, vx40, vx5)
10.95/4.55	   new_primPlusNat3(Main.Succ(vx500)) -> Main.Succ(vx500)
10.95/4.55	   new_primMinusNat0(vx400, Main.Zero) -> Main.Pos(Main.Succ(vx400))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Zero), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), vx300)
10.95/4.55	   new_primPlusNat0(vx400, Main.Succ(vx500)) -> Main.Succ(Main.Succ(new_primPlusNat1(vx400, vx500)))
10.95/4.55	   new_primPlusNat3(Main.Zero) -> Main.Zero
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Zero, vx50) -> new_primPlusNat3(vx50)
10.95/4.55	   new_primMinusNat1(Main.Succ(vx4000), Main.Zero) -> Main.Pos(Main.Succ(vx4000))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(vx300), Main.Neg(vx50)) -> Main.Neg(new_primPlusNat0(vx300, vx50))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Zero), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, vx300)
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Succ(vx300), vx5) -> new_primPlusInt0(vx400, vx300, vx5)
10.95/4.55	   new_psMyInt(Main.Pos(vx40), Main.Neg(vx30), Main.Pos(vx50)) -> Main.Pos(new_primPlusNat2(vx40, vx30, vx50))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Succ(vx5000)) -> Main.Neg(Main.Succ(vx5000))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Zero) -> Main.Pos(Main.Zero)
10.95/4.55	   new_primMinusNat1(Main.Succ(vx4000), Main.Succ(vx5000)) -> new_primMinusNat1(vx4000, vx5000)
10.95/4.55	   new_primPlusNat2(Main.Succ(vx400), Main.Zero, vx50) -> new_primPlusNat0(vx400, vx50)
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Succ(vx300), vx50) -> new_primPlusNat0(vx300, vx50)
10.95/4.55	   new_primMinusNat3(Main.Zero, vx300) -> Main.Neg(Main.Succ(vx300))
10.95/4.55	   new_psMyInt(Main.Neg(vx40), Main.Pos(vx30), Main.Neg(vx50)) -> Main.Neg(new_primPlusNat2(vx40, vx30, vx50))
10.95/4.55	   new_primPlusNat0(vx400, Main.Zero) -> Main.Succ(vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, Main.Succ(new_primPlusNat1(vx400, vx300)))
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Zero, Main.Pos(vx50)) -> Main.Pos(new_primPlusNat0(vx400, vx50))
10.95/4.55	   new_psMyInt(Main.Pos(vx40), Main.Pos(vx30), vx5) -> new_primPlusInt0(vx40, vx30, vx5)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Zero), Main.Neg(vx50)) -> new_primMinusNat2(vx50)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(vx400)), Main.Neg(Main.Succ(vx300)), Main.Neg(vx50)) -> new_primMinusNat0(Main.Succ(new_primPlusNat1(vx400, vx300)), vx50)
10.95/4.55	   new_primMinusNat2(Main.Succ(vx500)) -> Main.Neg(Main.Succ(vx500))
10.95/4.55	
10.95/4.55	The set Q consists of the following terms:
10.95/4.55	
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(x0)), Main.Pos(Main.Zero))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(x0)), Main.Pos(Main.Succ(x1)), Main.Pos(Main.Succ(x2)))
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Succ(x0), x1)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Succ(x0)))
10.95/4.55	   new_primPlusNat3(Main.Succ(x0))
10.95/4.55	   new_primMinusNat1(Main.Succ(x0), Main.Zero)
10.95/4.55	   new_primPlusNat3(Main.Zero)
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(x0), Main.Pos(x1))
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(x0)), Main.Neg(Main.Zero), Main.Neg(x1))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(x0), Main.Neg(x1))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(x0)), Main.Pos(Main.Succ(x1)))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(x0)), Main.Pos(Main.Zero), Main.Pos(Main.Succ(x1)))
10.95/4.55	   new_primPlusInt0(Main.Succ(x0), Main.Succ(x1), x2)
10.95/4.55	   new_psMyInt(Main.Neg(x0), Main.Neg(x1), x2)
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Zero)
10.95/4.55	   new_psMyInt(Main.Pos(x0), Main.Pos(x1), x2)
10.95/4.55	   new_psMyInt(Main.Neg(x0), Main.Pos(x1), Main.Neg(x2))
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Zero), Main.Neg(x0))
10.95/4.55	   new_primPlusInt0(Main.Succ(x0), Main.Zero, Main.Pos(x1))
10.95/4.55	   new_primMinusNat0(x0, Main.Succ(x1))
10.95/4.55	   new_psMyInt(Main.Pos(x0), Main.Neg(x1), Main.Pos(x2))
10.95/4.55	   new_primMinusNat3(Main.Zero, x0)
10.95/4.55	   new_primMinusNat2(Main.Succ(x0))
10.95/4.55	   new_primMinusNat3(Main.Succ(x0), x1)
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Neg(x0))
10.95/4.55	   new_primPlusNat0(x0, Main.Succ(x1))
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Succ(x0))
10.95/4.55	   new_primMinusNat2(Main.Zero)
10.95/4.55	   new_primMinusNat1(Main.Succ(x0), Main.Succ(x1))
10.95/4.55	   new_primPlusNat0(x0, Main.Zero)
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Zero, x0)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(x0)), Main.Neg(Main.Succ(x1)), Main.Neg(x2))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Zero)
10.95/4.55	   new_primPlusNat1(Main.Succ(x0), Main.Succ(x1))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(x0)), Main.Pos(Main.Zero), Main.Pos(Main.Zero))
10.95/4.55	   new_primPlusNat1(Main.Succ(x0), Main.Zero)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(x0)), Main.Pos(Main.Succ(x1)), Main.Pos(Main.Zero))
10.95/4.55	   new_primPlusNat2(Main.Succ(x0), Main.Succ(x1), x2)
10.95/4.55	   new_primPlusNat2(Main.Succ(x0), Main.Zero, x1)
10.95/4.55	   new_primMinusNat0(x0, Main.Zero)
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Pos(x0))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Succ(x0))
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Succ(x0)), Main.Neg(x1))
10.95/4.55	   new_primPlusInt0(Main.Succ(x0), Main.Zero, Main.Neg(x1))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Zero))
10.95/4.55	
10.95/4.55	We have to consider all minimal (P,Q,R)-chains.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(8) MNOCProof (EQUIVALENT)
10.95/4.55	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(9)
10.95/4.55	Obligation:
10.95/4.55	Q DP problem:
10.95/4.55	The TRS P consists of the following rules:
10.95/4.55	
10.95/4.55	   new_iterate(vx4, vx3, vx5) -> new_iterate(vx4, vx3, new_psMyInt(vx4, vx3, vx5))
10.95/4.55	
10.95/4.55	The TRS R consists of the following rules:
10.95/4.55	
10.95/4.55	   new_primMinusNat0(vx400, Main.Succ(vx500)) -> new_primMinusNat1(vx400, vx500)
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(vx300), Main.Pos(vx50)) -> new_primMinusNat3(vx50, vx300)
10.95/4.55	   new_primPlusNat1(Main.Succ(vx4000), Main.Zero) -> Main.Succ(vx4000)
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Succ(vx3000)) -> Main.Succ(vx3000)
10.95/4.55	   new_primMinusNat2(Main.Zero) -> Main.Pos(Main.Zero)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Zero)) -> new_primMinusNat2(Main.Zero)
10.95/4.55	   new_primMinusNat3(Main.Succ(vx500), vx300) -> new_primMinusNat1(vx500, vx300)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), Main.Succ(new_primPlusNat1(vx400, vx300)))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Pos(vx50)) -> Main.Pos(new_primPlusNat3(vx50))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Zero, Main.Neg(vx50)) -> new_primMinusNat2(vx50)
10.95/4.55	   new_primPlusNat1(Main.Zero, Main.Zero) -> Main.Zero
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Zero, Main.Neg(vx50)) -> new_primMinusNat0(vx400, vx50)
10.95/4.55	   new_primPlusNat2(Main.Succ(vx400), Main.Succ(vx300), vx50) -> new_primPlusNat0(Main.Succ(new_primPlusNat1(vx400, vx300)), vx50)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Zero), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat0(vx500, Main.Zero)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(vx400)), Main.Neg(Main.Zero), Main.Neg(vx50)) -> new_primMinusNat0(vx400, vx50)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Succ(vx300)), Main.Neg(vx50)) -> new_primMinusNat0(vx300, vx50)
10.95/4.55	   new_primPlusNat1(Main.Succ(vx4000), Main.Succ(vx3000)) -> Main.Succ(Main.Succ(new_primPlusNat1(vx4000, vx3000)))
10.95/4.55	   new_psMyInt(Main.Neg(vx40), Main.Neg(vx30), vx5) -> new_primPlusInt0(vx30, vx40, vx5)
10.95/4.55	   new_primPlusNat3(Main.Succ(vx500)) -> Main.Succ(vx500)
10.95/4.55	   new_primMinusNat0(vx400, Main.Zero) -> Main.Pos(Main.Succ(vx400))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Zero), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Succ(vx500))) -> new_primMinusNat3(Main.Succ(vx500), vx300)
10.95/4.55	   new_primPlusNat0(vx400, Main.Succ(vx500)) -> Main.Succ(Main.Succ(new_primPlusNat1(vx400, vx500)))
10.95/4.55	   new_primPlusNat3(Main.Zero) -> Main.Zero
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Zero, vx50) -> new_primPlusNat3(vx50)
10.95/4.55	   new_primMinusNat1(Main.Succ(vx4000), Main.Zero) -> Main.Pos(Main.Succ(vx4000))
10.95/4.55	   new_primPlusInt0(Main.Zero, Main.Succ(vx300), Main.Neg(vx50)) -> Main.Neg(new_primPlusNat0(vx300, vx50))
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Zero), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Zero), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, vx300)
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Succ(vx300), vx5) -> new_primPlusInt0(vx400, vx300, vx5)
10.95/4.55	   new_psMyInt(Main.Pos(vx40), Main.Neg(vx30), Main.Pos(vx50)) -> Main.Pos(new_primPlusNat2(vx40, vx30, vx50))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Succ(vx5000)) -> Main.Neg(Main.Succ(vx5000))
10.95/4.55	   new_primMinusNat1(Main.Zero, Main.Zero) -> Main.Pos(Main.Zero)
10.95/4.55	   new_primMinusNat1(Main.Succ(vx4000), Main.Succ(vx5000)) -> new_primMinusNat1(vx4000, vx5000)
10.95/4.55	   new_primPlusNat2(Main.Succ(vx400), Main.Zero, vx50) -> new_primPlusNat0(vx400, vx50)
10.95/4.55	   new_primPlusNat2(Main.Zero, Main.Succ(vx300), vx50) -> new_primPlusNat0(vx300, vx50)
10.95/4.55	   new_primMinusNat3(Main.Zero, vx300) -> Main.Neg(Main.Succ(vx300))
10.95/4.55	   new_psMyInt(Main.Neg(vx40), Main.Pos(vx30), Main.Neg(vx50)) -> Main.Neg(new_primPlusNat2(vx40, vx30, vx50))
10.95/4.55	   new_primPlusNat0(vx400, Main.Zero) -> Main.Succ(vx400)
10.95/4.55	   new_psMyInt(Main.Neg(Main.Succ(vx400)), Main.Pos(Main.Succ(vx300)), Main.Pos(Main.Zero)) -> new_primMinusNat3(Main.Zero, Main.Succ(new_primPlusNat1(vx400, vx300)))
10.95/4.55	   new_primPlusInt0(Main.Succ(vx400), Main.Zero, Main.Pos(vx50)) -> Main.Pos(new_primPlusNat0(vx400, vx50))
10.95/4.55	   new_psMyInt(Main.Pos(vx40), Main.Pos(vx30), vx5) -> new_primPlusInt0(vx40, vx30, vx5)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Zero), Main.Neg(Main.Zero), Main.Neg(vx50)) -> new_primMinusNat2(vx50)
10.95/4.55	   new_psMyInt(Main.Pos(Main.Succ(vx400)), Main.Neg(Main.Succ(vx300)), Main.Neg(vx50)) -> new_primMinusNat0(Main.Succ(new_primPlusNat1(vx400, vx300)), vx50)
10.95/4.55	   new_primMinusNat2(Main.Succ(vx500)) -> Main.Neg(Main.Succ(vx500))
10.95/4.55	
10.95/4.55	Q is empty.
10.95/4.55	We have to consider all (P,Q,R)-chains.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(10) NonTerminationLoopProof (COMPLETE)
10.95/4.55	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
10.95/4.55	Found a loop by semiunifying a rule from P directly.
10.95/4.55	
10.95/4.55	s = new_iterate(vx4, vx3, vx5) evaluates to  t =new_iterate(vx4, vx3, new_psMyInt(vx4, vx3, vx5))
10.95/4.55	
10.95/4.55	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
10.95/4.55	* Matcher: [vx5 / new_psMyInt(vx4, vx3, vx5)]
10.95/4.55	* Semiunifier: [ ]
10.95/4.55	
10.95/4.55	--------------------------------------------------------------------------------
10.95/4.55	Rewriting sequence
10.95/4.55	
10.95/4.55	The DP semiunifies directly so there is only one rewrite step from new_iterate(vx4, vx3, vx5) to new_iterate(vx4, vx3, new_psMyInt(vx4, vx3, vx5)).
10.95/4.55	
10.95/4.55	
10.95/4.55	
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(11)
10.95/4.55	NO
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(12)
10.95/4.55	Obligation:
10.95/4.55	Q DP problem:
10.95/4.55	The TRS P consists of the following rules:
10.95/4.55	
10.95/4.55	   new_primPlusInt(Main.Succ(vx400), Main.Succ(vx300), vx5) -> new_primPlusInt(vx400, vx300, vx5)
10.95/4.55	
10.95/4.55	R is empty.
10.95/4.55	Q is empty.
10.95/4.55	We have to consider all minimal (P,Q,R)-chains.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(13) QDPSizeChangeProof (EQUIVALENT)
10.95/4.55	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. 
10.95/4.55	
10.95/4.55	From the DPs we obtained the following set of size-change graphs:
10.95/4.55	*new_primPlusInt(Main.Succ(vx400), Main.Succ(vx300), vx5) -> new_primPlusInt(vx400, vx300, vx5)
10.95/4.55	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
10.95/4.55	
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(14)
10.95/4.55	YES
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(15)
10.95/4.55	Obligation:
10.95/4.55	Q DP problem:
10.95/4.55	The TRS P consists of the following rules:
10.95/4.55	
10.95/4.55	   new_primMinusNat(Main.Succ(vx4000), Main.Succ(vx5000)) -> new_primMinusNat(vx4000, vx5000)
10.95/4.55	
10.95/4.55	R is empty.
10.95/4.55	Q is empty.
10.95/4.55	We have to consider all minimal (P,Q,R)-chains.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(16) QDPSizeChangeProof (EQUIVALENT)
10.95/4.55	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. 
10.95/4.55	
10.95/4.55	From the DPs we obtained the following set of size-change graphs:
10.95/4.55	*new_primMinusNat(Main.Succ(vx4000), Main.Succ(vx5000)) -> new_primMinusNat(vx4000, vx5000)
10.95/4.55	The graph contains the following edges 1 > 1, 2 > 2
10.95/4.55	
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(17)
10.95/4.55	YES
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(18)
10.95/4.55	Obligation:
10.95/4.55	Q DP problem:
10.95/4.55	The TRS P consists of the following rules:
10.95/4.55	
10.95/4.55	   new_primPlusNat(Main.Succ(vx4000), Main.Succ(vx3000)) -> new_primPlusNat(vx4000, vx3000)
10.95/4.55	
10.95/4.55	R is empty.
10.95/4.55	Q is empty.
10.95/4.55	We have to consider all minimal (P,Q,R)-chains.
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(19) QDPSizeChangeProof (EQUIVALENT)
10.95/4.55	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. 
10.95/4.55	
10.95/4.55	From the DPs we obtained the following set of size-change graphs:
10.95/4.55	*new_primPlusNat(Main.Succ(vx4000), Main.Succ(vx3000)) -> new_primPlusNat(vx4000, vx3000)
10.95/4.55	The graph contains the following edges 1 > 1, 2 > 2
10.95/4.55	
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(20)
10.95/4.55	YES
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(21) Narrow (COMPLETE)
10.95/4.55	Haskell To QDPs
10.95/4.55	
10.95/4.55	digraph dp_graph {
10.95/4.55	node [outthreshold=100, inthreshold=100];1[label="enumFromThenMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.95/4.55	3[label="enumFromThenMyInt vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.95/4.55	4[label="enumFromThenMyInt vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.95/4.55	5[label="numericEnumFromThen vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.95/4.55	6[label="iterate (psMyInt (msMyInt vx4 vx3)) vx3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.95/4.55	7[label="Cons vx3 (iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx3))",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
10.95/4.55	8 -> 13[label="",style="dashed", color="red", weight=0];
10.95/4.55	8[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	14[label="vx3",fontsize=16,color="green",shape="box"];13[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) vx5)",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
10.95/4.55	16[label="Cons (psMyInt (msMyInt vx4 vx3) vx5) (iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) (psMyInt (msMyInt vx4 vx3) vx5)))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3];
10.95/4.55	16 -> 18[label="",style="dashed", color="green", weight=3];
10.95/4.55	17[label="psMyInt (msMyInt vx4 vx3) vx5",fontsize=16,color="black",shape="triangle"];17 -> 19[label="",style="solid", color="black", weight=3];
10.95/4.55	18 -> 13[label="",style="dashed", color="red", weight=0];
10.95/4.55	18[label="iterate (psMyInt (msMyInt vx4 vx3)) (psMyInt (msMyInt vx4 vx3) (psMyInt (msMyInt vx4 vx3) vx5))",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	19[label="primPlusInt (msMyInt vx4 vx3) vx5",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
10.95/4.55	20 -> 17[label="",style="dashed", color="red", weight=0];
10.95/4.55	20[label="psMyInt (msMyInt vx4 vx3) vx5",fontsize=16,color="magenta"];21[label="primPlusInt (primMinusInt vx4 vx3) vx5",fontsize=16,color="burlywood",shape="box"];192[label="vx4/Pos vx40",fontsize=10,color="white",style="solid",shape="box"];21 -> 192[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	192 -> 22[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	193[label="vx4/Neg vx40",fontsize=10,color="white",style="solid",shape="box"];21 -> 193[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	193 -> 23[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	22[label="primPlusInt (primMinusInt (Pos vx40) vx3) vx5",fontsize=16,color="burlywood",shape="box"];194[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];22 -> 194[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	194 -> 24[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	195[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];22 -> 195[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	195 -> 25[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	23[label="primPlusInt (primMinusInt (Neg vx40) vx3) vx5",fontsize=16,color="burlywood",shape="box"];196[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];23 -> 196[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	196 -> 26[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	197[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];23 -> 197[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	197 -> 27[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	24[label="primPlusInt (primMinusInt (Pos vx40) (Pos vx30)) vx5",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
10.95/4.55	25[label="primPlusInt (primMinusInt (Pos vx40) (Neg vx30)) vx5",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
10.95/4.55	26[label="primPlusInt (primMinusInt (Neg vx40) (Pos vx30)) vx5",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
10.95/4.55	27[label="primPlusInt (primMinusInt (Neg vx40) (Neg vx30)) vx5",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
10.95/4.55	28[label="primPlusInt (primMinusNat vx40 vx30) vx5",fontsize=16,color="burlywood",shape="triangle"];198[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];28 -> 198[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	198 -> 32[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	199[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 199[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	199 -> 33[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	29[label="primPlusInt (Pos (primPlusNat vx40 vx30)) vx5",fontsize=16,color="burlywood",shape="box"];200[label="vx5/Pos vx50",fontsize=10,color="white",style="solid",shape="box"];29 -> 200[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	200 -> 34[label="",style="solid", color="burlywood", weight=3];
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10.95/4.55	201 -> 35[label="",style="solid", color="burlywood", weight=3];
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10.95/4.55	247 -> 125[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	102[label="primMinusNat (Succ vx400) (Succ vx500)",fontsize=16,color="black",shape="box"];102 -> 126[label="",style="solid", color="black", weight=3];
10.95/4.55	103[label="primMinusNat (Succ vx400) Zero",fontsize=16,color="black",shape="box"];103 -> 127[label="",style="solid", color="black", weight=3];
10.95/4.55	104[label="primMinusNat (Succ vx500) (Succ vx300)",fontsize=16,color="black",shape="box"];104 -> 128[label="",style="solid", color="black", weight=3];
10.95/4.55	105[label="primMinusNat Zero (Succ vx300)",fontsize=16,color="black",shape="box"];105 -> 129[label="",style="solid", color="black", weight=3];
10.95/4.55	106 -> 101[label="",style="dashed", color="red", weight=0];
10.95/4.55	106[label="primPlusNat (Succ vx300) vx50",fontsize=16,color="magenta"];106 -> 130[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	106 -> 131[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	107[label="primPlusNat Zero vx50",fontsize=16,color="burlywood",shape="triangle"];248[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];107 -> 248[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	248 -> 132[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	249[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 249[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	249 -> 133[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	108[label="primMinusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];108 -> 134[label="",style="solid", color="black", weight=3];
10.95/4.55	109[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];109 -> 135[label="",style="solid", color="black", weight=3];
10.95/4.55	110 -> 101[label="",style="dashed", color="red", weight=0];
10.95/4.55	110[label="primPlusNat (Succ (Succ (primPlusNat vx400 vx300))) vx50",fontsize=16,color="magenta"];110 -> 136[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	111 -> 101[label="",style="dashed", color="red", weight=0];
10.95/4.55	111[label="primPlusNat (Succ vx400) vx50",fontsize=16,color="magenta"];112 -> 101[label="",style="dashed", color="red", weight=0];
10.95/4.55	112[label="primPlusNat (Succ vx300) vx50",fontsize=16,color="magenta"];112 -> 137[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	113 -> 107[label="",style="dashed", color="red", weight=0];
10.95/4.55	113[label="primPlusNat Zero vx50",fontsize=16,color="magenta"];114[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];114 -> 138[label="",style="dashed", color="green", weight=3];
10.95/4.55	115[label="vx300",fontsize=16,color="green",shape="box"];116 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	116[label="primMinusNat (Succ vx500) (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];116 -> 139[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	116 -> 140[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	117 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	117[label="primMinusNat (Succ vx500) (Succ vx400)",fontsize=16,color="magenta"];117 -> 141[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	117 -> 142[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	118 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	118[label="primMinusNat (Succ vx500) (Succ vx300)",fontsize=16,color="magenta"];118 -> 143[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	119 -> 80[label="",style="dashed", color="red", weight=0];
10.95/4.55	119[label="primMinusNat (Succ vx500) Zero",fontsize=16,color="magenta"];119 -> 144[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	119 -> 145[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	120 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	120[label="primMinusNat Zero (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];120 -> 146[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	120 -> 147[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	121 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	121[label="primMinusNat Zero (Succ vx400)",fontsize=16,color="magenta"];121 -> 148[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	121 -> 149[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	122 -> 81[label="",style="dashed", color="red", weight=0];
10.95/4.55	122[label="primMinusNat Zero (Succ vx300)",fontsize=16,color="magenta"];122 -> 150[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	123 -> 84[label="",style="dashed", color="red", weight=0];
10.95/4.55	123[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];123 -> 151[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	124[label="primPlusNat (Succ vx400) (Succ vx500)",fontsize=16,color="black",shape="box"];124 -> 152[label="",style="solid", color="black", weight=3];
10.95/4.55	125[label="primPlusNat (Succ vx400) Zero",fontsize=16,color="black",shape="box"];125 -> 153[label="",style="solid", color="black", weight=3];
10.95/4.55	126[label="primMinusNat vx400 vx500",fontsize=16,color="burlywood",shape="triangle"];250[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];126 -> 250[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	250 -> 154[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	251[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];126 -> 251[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	251 -> 155[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	127[label="Pos (Succ vx400)",fontsize=16,color="green",shape="box"];128 -> 126[label="",style="dashed", color="red", weight=0];
10.95/4.55	128[label="primMinusNat vx500 vx300",fontsize=16,color="magenta"];128 -> 156[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	128 -> 157[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	129[label="Neg (Succ vx300)",fontsize=16,color="green",shape="box"];130[label="vx300",fontsize=16,color="green",shape="box"];131[label="vx50",fontsize=16,color="green",shape="box"];132[label="primPlusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];132 -> 158[label="",style="solid", color="black", weight=3];
10.95/4.55	133[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];133 -> 159[label="",style="solid", color="black", weight=3];
10.95/4.55	134[label="Neg (Succ vx500)",fontsize=16,color="green",shape="box"];135[label="Pos Zero",fontsize=16,color="green",shape="box"];136[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];136 -> 160[label="",style="dashed", color="green", weight=3];
10.95/4.55	137[label="vx300",fontsize=16,color="green",shape="box"];138[label="primPlusNat vx400 vx300",fontsize=16,color="burlywood",shape="triangle"];252[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];138 -> 252[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	252 -> 161[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	253[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 253[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	253 -> 162[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	139[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];139 -> 163[label="",style="dashed", color="green", weight=3];
10.95/4.55	140[label="Succ vx500",fontsize=16,color="green",shape="box"];141[label="vx400",fontsize=16,color="green",shape="box"];142[label="Succ vx500",fontsize=16,color="green",shape="box"];143[label="Succ vx500",fontsize=16,color="green",shape="box"];144[label="Zero",fontsize=16,color="green",shape="box"];145[label="vx500",fontsize=16,color="green",shape="box"];146[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];146 -> 164[label="",style="dashed", color="green", weight=3];
10.95/4.55	147[label="Zero",fontsize=16,color="green",shape="box"];148[label="vx400",fontsize=16,color="green",shape="box"];149[label="Zero",fontsize=16,color="green",shape="box"];150[label="Zero",fontsize=16,color="green",shape="box"];151[label="Zero",fontsize=16,color="green",shape="box"];152[label="Succ (Succ (primPlusNat vx400 vx500))",fontsize=16,color="green",shape="box"];152 -> 165[label="",style="dashed", color="green", weight=3];
10.95/4.55	153[label="Succ vx400",fontsize=16,color="green",shape="box"];154[label="primMinusNat (Succ vx4000) vx500",fontsize=16,color="burlywood",shape="box"];254[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];154 -> 254[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	254 -> 166[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	255[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];154 -> 255[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	255 -> 167[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	155[label="primMinusNat Zero vx500",fontsize=16,color="burlywood",shape="box"];256[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];155 -> 256[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	256 -> 168[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	257[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];155 -> 257[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	257 -> 169[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	156[label="vx500",fontsize=16,color="green",shape="box"];157[label="vx300",fontsize=16,color="green",shape="box"];158[label="Succ vx500",fontsize=16,color="green",shape="box"];159[label="Zero",fontsize=16,color="green",shape="box"];160 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	160[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];161[label="primPlusNat (Succ vx4000) vx300",fontsize=16,color="burlywood",shape="box"];258[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];161 -> 258[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	258 -> 170[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	259[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];161 -> 259[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	259 -> 171[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	162[label="primPlusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];260[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];162 -> 260[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	260 -> 172[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	261[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];162 -> 261[label="",style="solid", color="burlywood", weight=9];
10.95/4.55	261 -> 173[label="",style="solid", color="burlywood", weight=3];
10.95/4.55	163 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	163[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];163 -> 174[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	163 -> 175[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	164 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	164[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];164 -> 176[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	164 -> 177[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	165 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	165[label="primPlusNat vx400 vx500",fontsize=16,color="magenta"];165 -> 178[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	166[label="primMinusNat (Succ vx4000) (Succ vx5000)",fontsize=16,color="black",shape="box"];166 -> 179[label="",style="solid", color="black", weight=3];
10.95/4.55	167[label="primMinusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];167 -> 180[label="",style="solid", color="black", weight=3];
10.95/4.55	168[label="primMinusNat Zero (Succ vx5000)",fontsize=16,color="black",shape="box"];168 -> 181[label="",style="solid", color="black", weight=3];
10.95/4.55	169[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];169 -> 182[label="",style="solid", color="black", weight=3];
10.95/4.55	170[label="primPlusNat (Succ vx4000) (Succ vx3000)",fontsize=16,color="black",shape="box"];170 -> 183[label="",style="solid", color="black", weight=3];
10.95/4.55	171[label="primPlusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];171 -> 184[label="",style="solid", color="black", weight=3];
10.95/4.55	172[label="primPlusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];172 -> 185[label="",style="solid", color="black", weight=3];
10.95/4.55	173[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];173 -> 186[label="",style="solid", color="black", weight=3];
10.95/4.55	174[label="vx300",fontsize=16,color="green",shape="box"];175[label="vx400",fontsize=16,color="green",shape="box"];176[label="vx300",fontsize=16,color="green",shape="box"];177[label="vx400",fontsize=16,color="green",shape="box"];178[label="vx500",fontsize=16,color="green",shape="box"];179 -> 126[label="",style="dashed", color="red", weight=0];
10.95/4.55	179[label="primMinusNat vx4000 vx5000",fontsize=16,color="magenta"];179 -> 187[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	179 -> 188[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	180[label="Pos (Succ vx4000)",fontsize=16,color="green",shape="box"];181[label="Neg (Succ vx5000)",fontsize=16,color="green",shape="box"];182[label="Pos Zero",fontsize=16,color="green",shape="box"];183[label="Succ (Succ (primPlusNat vx4000 vx3000))",fontsize=16,color="green",shape="box"];183 -> 189[label="",style="dashed", color="green", weight=3];
10.95/4.55	184[label="Succ vx4000",fontsize=16,color="green",shape="box"];185[label="Succ vx3000",fontsize=16,color="green",shape="box"];186[label="Zero",fontsize=16,color="green",shape="box"];187[label="vx4000",fontsize=16,color="green",shape="box"];188[label="vx5000",fontsize=16,color="green",shape="box"];189 -> 138[label="",style="dashed", color="red", weight=0];
10.95/4.55	189[label="primPlusNat vx4000 vx3000",fontsize=16,color="magenta"];189 -> 190[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	189 -> 191[label="",style="dashed", color="magenta", weight=3];
10.95/4.55	190[label="vx3000",fontsize=16,color="green",shape="box"];191[label="vx4000",fontsize=16,color="green",shape="box"];}
10.95/4.55	
10.95/4.55	----------------------------------------
10.95/4.55	
10.95/4.55	(22)
10.95/4.55	TRUE
11.03/4.60	EOF