8.50/3.72	YES
10.61/4.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.61/4.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.61/4.30	
10.61/4.30	
10.61/4.30	H-Termination with start terms of the given HASKELL could be proven:
10.61/4.30	
10.61/4.30	(0) HASKELL
10.61/4.30	(1) BR [EQUIVALENT, 0 ms]
10.61/4.30	(2) HASKELL
10.61/4.30	(3) COR [EQUIVALENT, 0 ms]
10.61/4.30	(4) HASKELL
10.61/4.30	(5) Narrow [SOUND, 0 ms]
10.61/4.30	(6) QDP
10.61/4.30	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
10.61/4.30	(8) AND
10.61/4.30	    (9) QDP
10.61/4.30	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.61/4.30	        (11) YES
10.61/4.30	    (12) QDP
10.61/4.30	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.61/4.30	        (14) YES
10.61/4.30	    (15) QDP
10.61/4.30	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.61/4.30	        (17) YES
10.61/4.30	    (18) QDP
10.61/4.30	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.61/4.30	        (20) YES
10.61/4.30	
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(0)
10.61/4.30	Obligation:
10.61/4.30	mainModule Main 
10.61/4.30	module Main where {
10.61/4.30	import qualified Prelude;
10.61/4.30	data List a = Cons a (List a)  | Nil ;
10.61/4.30	
10.61/4.30	data Main.Maybe a = Nothing  | Just a ;
10.61/4.30	
10.61/4.30	data MyBool = MyTrue  | MyFalse ;
10.61/4.30	
10.61/4.30	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.61/4.30	
10.61/4.30	data Main.Nat = Succ Main.Nat  | Zero ;
10.61/4.30	
10.61/4.30	data Tup2 b a = Tup2 b a ;
10.61/4.30	
10.61/4.30	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	esEsMyInt = primEqInt;
10.61/4.30	
10.61/4.30	lookup k Nil = lookup3 k Nil;
10.61/4.30	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
10.61/4.30	
10.61/4.30	lookup0 k x y xys MyTrue = lookup k xys;
10.61/4.30	
10.61/4.30	lookup1 k x y xys MyTrue = Main.Just y;
10.61/4.30	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
10.61/4.30	
10.61/4.30	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsMyInt k x);
10.61/4.30	
10.61/4.30	lookup3 k Nil = Main.Nothing;
10.61/4.30	lookup3 wu wv = lookup2 wu wv;
10.61/4.30	
10.61/4.30	otherwise :: MyBool;
10.61/4.30	otherwise = MyTrue;
10.61/4.30	
10.61/4.30	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt vv vw = MyFalse;
10.61/4.30	
10.61/4.30	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.61/4.30	primEqNat Main.Zero Main.Zero = MyTrue;
10.61/4.30	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.61/4.30	
10.61/4.30	}
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(1) BR (EQUIVALENT)
10.61/4.30	Replaced joker patterns by fresh variables and removed binding patterns.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(2)
10.61/4.30	Obligation:
10.61/4.30	mainModule Main 
10.61/4.30	module Main where {
10.61/4.30	import qualified Prelude;
10.61/4.30	data List a = Cons a (List a)  | Nil ;
10.61/4.30	
10.61/4.30	data Main.Maybe a = Nothing  | Just a ;
10.61/4.30	
10.61/4.30	data MyBool = MyTrue  | MyFalse ;
10.61/4.30	
10.61/4.30	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.61/4.30	
10.61/4.30	data Main.Nat = Succ Main.Nat  | Zero ;
10.61/4.30	
10.61/4.30	data Tup2 b a = Tup2 b a ;
10.61/4.30	
10.61/4.30	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	esEsMyInt = primEqInt;
10.61/4.30	
10.61/4.30	lookup k Nil = lookup3 k Nil;
10.61/4.30	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
10.61/4.30	
10.61/4.30	lookup0 k x y xys MyTrue = lookup k xys;
10.61/4.30	
10.61/4.30	lookup1 k x y xys MyTrue = Main.Just y;
10.61/4.30	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
10.61/4.30	
10.61/4.30	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsMyInt k x);
10.61/4.30	
10.61/4.30	lookup3 k Nil = Main.Nothing;
10.61/4.30	lookup3 wu wv = lookup2 wu wv;
10.61/4.30	
10.61/4.30	otherwise :: MyBool;
10.61/4.30	otherwise = MyTrue;
10.61/4.30	
10.61/4.30	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt vv vw = MyFalse;
10.61/4.30	
10.61/4.30	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.61/4.30	primEqNat Main.Zero Main.Zero = MyTrue;
10.61/4.30	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.61/4.30	
10.61/4.30	}
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(3) COR (EQUIVALENT)
10.61/4.30	Cond Reductions:
10.61/4.30	The following Function with conditions
10.61/4.30	"undefined |Falseundefined;
10.61/4.30	"
10.61/4.30	is transformed to
10.61/4.30	"undefined  = undefined1;
10.61/4.30	"
10.61/4.30	"undefined0 True = undefined;
10.61/4.30	"
10.61/4.30	"undefined1  = undefined0 False;
10.61/4.30	"
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(4)
10.61/4.30	Obligation:
10.61/4.30	mainModule Main 
10.61/4.30	module Main where {
10.61/4.30	import qualified Prelude;
10.61/4.30	data List a = Cons a (List a)  | Nil ;
10.61/4.30	
10.61/4.30	data Main.Maybe a = Nothing  | Just a ;
10.61/4.30	
10.61/4.30	data MyBool = MyTrue  | MyFalse ;
10.61/4.30	
10.61/4.30	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.61/4.30	
10.61/4.30	data Main.Nat = Succ Main.Nat  | Zero ;
10.61/4.30	
10.61/4.30	data Tup2 b a = Tup2 b a ;
10.61/4.30	
10.61/4.30	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	esEsMyInt = primEqInt;
10.61/4.30	
10.61/4.30	lookup k Nil = lookup3 k Nil;
10.61/4.30	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
10.61/4.30	
10.61/4.30	lookup0 k x y xys MyTrue = lookup k xys;
10.61/4.30	
10.61/4.30	lookup1 k x y xys MyTrue = Main.Just y;
10.61/4.30	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
10.61/4.30	
10.61/4.30	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsMyInt k x);
10.61/4.30	
10.61/4.30	lookup3 k Nil = Main.Nothing;
10.61/4.30	lookup3 wu wv = lookup2 wu wv;
10.61/4.30	
10.61/4.30	otherwise :: MyBool;
10.61/4.30	otherwise = MyTrue;
10.61/4.30	
10.61/4.30	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.61/4.30	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.61/4.30	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.61/4.30	primEqInt vv vw = MyFalse;
10.61/4.30	
10.61/4.30	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.61/4.30	primEqNat Main.Zero Main.Zero = MyTrue;
10.61/4.30	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.61/4.30	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.61/4.30	
10.61/4.30	}
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(5) Narrow (SOUND)
10.61/4.30	Haskell To QDPs
10.61/4.30	
10.61/4.30	digraph dp_graph {
10.61/4.30	node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.61/4.30	3[label="lookup vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.61/4.30	4[label="lookup vz3 vz4",fontsize=16,color="burlywood",shape="triangle"];778[label="vz4/Cons vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];4 -> 778[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	778 -> 5[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	779[label="vz4/Nil",fontsize=10,color="white",style="solid",shape="box"];4 -> 779[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	779 -> 6[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	5[label="lookup vz3 (Cons vz40 vz41)",fontsize=16,color="burlywood",shape="box"];780[label="vz40/Tup2 vz400 vz401",fontsize=10,color="white",style="solid",shape="box"];5 -> 780[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	780 -> 7[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	6[label="lookup vz3 Nil",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.61/4.30	7[label="lookup vz3 (Cons (Tup2 vz400 vz401) vz41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.61/4.30	8[label="lookup3 vz3 Nil",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
10.61/4.30	9[label="lookup2 vz3 (Cons (Tup2 vz400 vz401) vz41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10.61/4.30	10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 vz3 vz400 vz401 vz41 (esEsMyInt vz3 vz400)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
10.61/4.30	12[label="lookup1 vz3 vz400 vz401 vz41 (primEqInt vz3 vz400)",fontsize=16,color="burlywood",shape="box"];781[label="vz3/Pos vz30",fontsize=10,color="white",style="solid",shape="box"];12 -> 781[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	781 -> 13[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	782[label="vz3/Neg vz30",fontsize=10,color="white",style="solid",shape="box"];12 -> 782[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	782 -> 14[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	13[label="lookup1 (Pos vz30) vz400 vz401 vz41 (primEqInt (Pos vz30) vz400)",fontsize=16,color="burlywood",shape="box"];783[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];13 -> 783[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	783 -> 15[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	784[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 784[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	784 -> 16[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	14[label="lookup1 (Neg vz30) vz400 vz401 vz41 (primEqInt (Neg vz30) vz400)",fontsize=16,color="burlywood",shape="box"];785[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];14 -> 785[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	785 -> 17[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	786[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 786[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	786 -> 18[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	15[label="lookup1 (Pos (Succ vz300)) vz400 vz401 vz41 (primEqInt (Pos (Succ vz300)) vz400)",fontsize=16,color="burlywood",shape="box"];787[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 787[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	787 -> 19[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	788[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 788[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	788 -> 20[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	16[label="lookup1 (Pos Zero) vz400 vz401 vz41 (primEqInt (Pos Zero) vz400)",fontsize=16,color="burlywood",shape="box"];789[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 789[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	789 -> 21[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	790[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 790[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	790 -> 22[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	17[label="lookup1 (Neg (Succ vz300)) vz400 vz401 vz41 (primEqInt (Neg (Succ vz300)) vz400)",fontsize=16,color="burlywood",shape="box"];791[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 791[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	791 -> 23[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	792[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 792[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	792 -> 24[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	18[label="lookup1 (Neg Zero) vz400 vz401 vz41 (primEqInt (Neg Zero) vz400)",fontsize=16,color="burlywood",shape="box"];793[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 793[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	793 -> 25[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	794[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 794[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	794 -> 26[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	19[label="lookup1 (Pos (Succ vz300)) (Pos vz4000) vz401 vz41 (primEqInt (Pos (Succ vz300)) (Pos vz4000))",fontsize=16,color="burlywood",shape="box"];795[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];19 -> 795[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	795 -> 27[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	796[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 796[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	796 -> 28[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	20[label="lookup1 (Pos (Succ vz300)) (Neg vz4000) vz401 vz41 (primEqInt (Pos (Succ vz300)) (Neg vz4000))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
10.61/4.30	21[label="lookup1 (Pos Zero) (Pos vz4000) vz401 vz41 (primEqInt (Pos Zero) (Pos vz4000))",fontsize=16,color="burlywood",shape="box"];797[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];21 -> 797[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	797 -> 30[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	798[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 798[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	798 -> 31[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	22[label="lookup1 (Pos Zero) (Neg vz4000) vz401 vz41 (primEqInt (Pos Zero) (Neg vz4000))",fontsize=16,color="burlywood",shape="box"];799[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];22 -> 799[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	799 -> 32[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	800[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 800[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	800 -> 33[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	23[label="lookup1 (Neg (Succ vz300)) (Pos vz4000) vz401 vz41 (primEqInt (Neg (Succ vz300)) (Pos vz4000))",fontsize=16,color="black",shape="box"];23 -> 34[label="",style="solid", color="black", weight=3];
10.61/4.30	24[label="lookup1 (Neg (Succ vz300)) (Neg vz4000) vz401 vz41 (primEqInt (Neg (Succ vz300)) (Neg vz4000))",fontsize=16,color="burlywood",shape="box"];801[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];24 -> 801[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	801 -> 35[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	802[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 802[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	802 -> 36[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	25[label="lookup1 (Neg Zero) (Pos vz4000) vz401 vz41 (primEqInt (Neg Zero) (Pos vz4000))",fontsize=16,color="burlywood",shape="box"];803[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];25 -> 803[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	803 -> 37[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	804[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 804[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	804 -> 38[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	26[label="lookup1 (Neg Zero) (Neg vz4000) vz401 vz41 (primEqInt (Neg Zero) (Neg vz4000))",fontsize=16,color="burlywood",shape="box"];805[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];26 -> 805[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	805 -> 39[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	806[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 806[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	806 -> 40[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	27[label="lookup1 (Pos (Succ vz300)) (Pos (Succ vz40000)) vz401 vz41 (primEqInt (Pos (Succ vz300)) (Pos (Succ vz40000)))",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
10.61/4.30	28[label="lookup1 (Pos (Succ vz300)) (Pos Zero) vz401 vz41 (primEqInt (Pos (Succ vz300)) (Pos Zero))",fontsize=16,color="black",shape="box"];28 -> 42[label="",style="solid", color="black", weight=3];
10.61/4.30	29[label="lookup1 (Pos (Succ vz300)) (Neg vz4000) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3];
10.61/4.30	30[label="lookup1 (Pos Zero) (Pos (Succ vz40000)) vz401 vz41 (primEqInt (Pos Zero) (Pos (Succ vz40000)))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
10.61/4.30	31[label="lookup1 (Pos Zero) (Pos Zero) vz401 vz41 (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];31 -> 45[label="",style="solid", color="black", weight=3];
10.61/4.30	32[label="lookup1 (Pos Zero) (Neg (Succ vz40000)) vz401 vz41 (primEqInt (Pos Zero) (Neg (Succ vz40000)))",fontsize=16,color="black",shape="box"];32 -> 46[label="",style="solid", color="black", weight=3];
10.61/4.30	33[label="lookup1 (Pos Zero) (Neg Zero) vz401 vz41 (primEqInt (Pos Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];33 -> 47[label="",style="solid", color="black", weight=3];
10.61/4.30	34[label="lookup1 (Neg (Succ vz300)) (Pos vz4000) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];34 -> 48[label="",style="solid", color="black", weight=3];
10.61/4.30	35[label="lookup1 (Neg (Succ vz300)) (Neg (Succ vz40000)) vz401 vz41 (primEqInt (Neg (Succ vz300)) (Neg (Succ vz40000)))",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
10.61/4.30	36[label="lookup1 (Neg (Succ vz300)) (Neg Zero) vz401 vz41 (primEqInt (Neg (Succ vz300)) (Neg Zero))",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
10.61/4.30	37[label="lookup1 (Neg Zero) (Pos (Succ vz40000)) vz401 vz41 (primEqInt (Neg Zero) (Pos (Succ vz40000)))",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
10.61/4.30	38[label="lookup1 (Neg Zero) (Pos Zero) vz401 vz41 (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
10.61/4.30	39[label="lookup1 (Neg Zero) (Neg (Succ vz40000)) vz401 vz41 (primEqInt (Neg Zero) (Neg (Succ vz40000)))",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
10.61/4.30	40[label="lookup1 (Neg Zero) (Neg Zero) vz401 vz41 (primEqInt (Neg Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
10.61/4.30	41 -> 620[label="",style="dashed", color="red", weight=0];
10.61/4.30	41[label="lookup1 (Pos (Succ vz300)) (Pos (Succ vz40000)) vz401 vz41 (primEqNat vz300 vz40000)",fontsize=16,color="magenta"];41 -> 621[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	41 -> 622[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	41 -> 623[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	41 -> 624[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	41 -> 625[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	41 -> 626[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	42[label="lookup1 (Pos (Succ vz300)) (Pos Zero) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];42 -> 57[label="",style="solid", color="black", weight=3];
10.61/4.30	43[label="lookup0 (Pos (Succ vz300)) (Neg vz4000) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];43 -> 58[label="",style="solid", color="black", weight=3];
10.61/4.30	44[label="lookup1 (Pos Zero) (Pos (Succ vz40000)) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];44 -> 59[label="",style="solid", color="black", weight=3];
10.61/4.30	45[label="lookup1 (Pos Zero) (Pos Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];45 -> 60[label="",style="solid", color="black", weight=3];
10.61/4.30	46[label="lookup1 (Pos Zero) (Neg (Succ vz40000)) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];46 -> 61[label="",style="solid", color="black", weight=3];
10.61/4.30	47[label="lookup1 (Pos Zero) (Neg Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];47 -> 62[label="",style="solid", color="black", weight=3];
10.61/4.30	48[label="lookup0 (Neg (Succ vz300)) (Pos vz4000) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];48 -> 63[label="",style="solid", color="black", weight=3];
10.61/4.30	49 -> 683[label="",style="dashed", color="red", weight=0];
10.61/4.30	49[label="lookup1 (Neg (Succ vz300)) (Neg (Succ vz40000)) vz401 vz41 (primEqNat vz300 vz40000)",fontsize=16,color="magenta"];49 -> 684[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	49 -> 685[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	49 -> 686[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	49 -> 687[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	49 -> 688[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	49 -> 689[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	50[label="lookup1 (Neg (Succ vz300)) (Neg Zero) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];50 -> 66[label="",style="solid", color="black", weight=3];
10.61/4.30	51[label="lookup1 (Neg Zero) (Pos (Succ vz40000)) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];51 -> 67[label="",style="solid", color="black", weight=3];
10.61/4.30	52[label="lookup1 (Neg Zero) (Pos Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];52 -> 68[label="",style="solid", color="black", weight=3];
10.61/4.30	53[label="lookup1 (Neg Zero) (Neg (Succ vz40000)) vz401 vz41 MyFalse",fontsize=16,color="black",shape="box"];53 -> 69[label="",style="solid", color="black", weight=3];
10.61/4.30	54[label="lookup1 (Neg Zero) (Neg Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];54 -> 70[label="",style="solid", color="black", weight=3];
10.61/4.30	621[label="vz300",fontsize=16,color="green",shape="box"];622[label="vz300",fontsize=16,color="green",shape="box"];623[label="vz41",fontsize=16,color="green",shape="box"];624[label="vz40000",fontsize=16,color="green",shape="box"];625[label="vz40000",fontsize=16,color="green",shape="box"];626[label="vz401",fontsize=16,color="green",shape="box"];620[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat vz78 vz79)",fontsize=16,color="burlywood",shape="triangle"];807[label="vz78/Succ vz780",fontsize=10,color="white",style="solid",shape="box"];620 -> 807[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	807 -> 681[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	808[label="vz78/Zero",fontsize=10,color="white",style="solid",shape="box"];620 -> 808[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	808 -> 682[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	57[label="lookup0 (Pos (Succ vz300)) (Pos Zero) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3];
10.61/4.30	58[label="lookup0 (Pos (Succ vz300)) (Neg vz4000) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3];
10.61/4.30	59[label="lookup0 (Pos Zero) (Pos (Succ vz40000)) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3];
10.61/4.30	60[label="Just vz401",fontsize=16,color="green",shape="box"];61[label="lookup0 (Pos Zero) (Neg (Succ vz40000)) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];61 -> 78[label="",style="solid", color="black", weight=3];
10.61/4.30	62[label="Just vz401",fontsize=16,color="green",shape="box"];63[label="lookup0 (Neg (Succ vz300)) (Pos vz4000) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];63 -> 79[label="",style="solid", color="black", weight=3];
10.61/4.30	684[label="vz300",fontsize=16,color="green",shape="box"];685[label="vz300",fontsize=16,color="green",shape="box"];686[label="vz40000",fontsize=16,color="green",shape="box"];687[label="vz401",fontsize=16,color="green",shape="box"];688[label="vz41",fontsize=16,color="green",shape="box"];689[label="vz40000",fontsize=16,color="green",shape="box"];683[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat vz85 vz86)",fontsize=16,color="burlywood",shape="triangle"];809[label="vz85/Succ vz850",fontsize=10,color="white",style="solid",shape="box"];683 -> 809[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	809 -> 744[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	810[label="vz85/Zero",fontsize=10,color="white",style="solid",shape="box"];683 -> 810[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	810 -> 745[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	66[label="lookup0 (Neg (Succ vz300)) (Neg Zero) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];66 -> 84[label="",style="solid", color="black", weight=3];
10.61/4.30	67[label="lookup0 (Neg Zero) (Pos (Succ vz40000)) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];67 -> 85[label="",style="solid", color="black", weight=3];
10.61/4.30	68[label="Just vz401",fontsize=16,color="green",shape="box"];69[label="lookup0 (Neg Zero) (Neg (Succ vz40000)) vz401 vz41 otherwise",fontsize=16,color="black",shape="box"];69 -> 86[label="",style="solid", color="black", weight=3];
10.61/4.30	70[label="Just vz401",fontsize=16,color="green",shape="box"];681[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat (Succ vz780) vz79)",fontsize=16,color="burlywood",shape="box"];811[label="vz79/Succ vz790",fontsize=10,color="white",style="solid",shape="box"];681 -> 811[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	811 -> 746[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	812[label="vz79/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 812[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	812 -> 747[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	682[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat Zero vz79)",fontsize=16,color="burlywood",shape="box"];813[label="vz79/Succ vz790",fontsize=10,color="white",style="solid",shape="box"];682 -> 813[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	813 -> 748[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	814[label="vz79/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 814[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	814 -> 749[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	75[label="lookup0 (Pos (Succ vz300)) (Pos Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];75 -> 91[label="",style="solid", color="black", weight=3];
10.61/4.30	76 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	76[label="lookup (Pos (Succ vz300)) vz41",fontsize=16,color="magenta"];76 -> 92[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	76 -> 93[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	77[label="lookup0 (Pos Zero) (Pos (Succ vz40000)) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];77 -> 94[label="",style="solid", color="black", weight=3];
10.61/4.30	78[label="lookup0 (Pos Zero) (Neg (Succ vz40000)) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];78 -> 95[label="",style="solid", color="black", weight=3];
10.61/4.30	79 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	79[label="lookup (Neg (Succ vz300)) vz41",fontsize=16,color="magenta"];79 -> 96[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	79 -> 97[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	744[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat (Succ vz850) vz86)",fontsize=16,color="burlywood",shape="box"];815[label="vz86/Succ vz860",fontsize=10,color="white",style="solid",shape="box"];744 -> 815[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	815 -> 750[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	816[label="vz86/Zero",fontsize=10,color="white",style="solid",shape="box"];744 -> 816[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	816 -> 751[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	745[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat Zero vz86)",fontsize=16,color="burlywood",shape="box"];817[label="vz86/Succ vz860",fontsize=10,color="white",style="solid",shape="box"];745 -> 817[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	817 -> 752[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	818[label="vz86/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 818[label="",style="solid", color="burlywood", weight=9];
10.61/4.30	818 -> 753[label="",style="solid", color="burlywood", weight=3];
10.61/4.30	84[label="lookup0 (Neg (Succ vz300)) (Neg Zero) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];84 -> 102[label="",style="solid", color="black", weight=3];
10.61/4.30	85[label="lookup0 (Neg Zero) (Pos (Succ vz40000)) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];85 -> 103[label="",style="solid", color="black", weight=3];
10.61/4.30	86[label="lookup0 (Neg Zero) (Neg (Succ vz40000)) vz401 vz41 MyTrue",fontsize=16,color="black",shape="box"];86 -> 104[label="",style="solid", color="black", weight=3];
10.61/4.30	746[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat (Succ vz780) (Succ vz790))",fontsize=16,color="black",shape="box"];746 -> 754[label="",style="solid", color="black", weight=3];
10.61/4.30	747[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat (Succ vz780) Zero)",fontsize=16,color="black",shape="box"];747 -> 755[label="",style="solid", color="black", weight=3];
10.61/4.30	748[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat Zero (Succ vz790))",fontsize=16,color="black",shape="box"];748 -> 756[label="",style="solid", color="black", weight=3];
10.61/4.30	749[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];749 -> 757[label="",style="solid", color="black", weight=3];
10.61/4.30	91 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	91[label="lookup (Pos (Succ vz300)) vz41",fontsize=16,color="magenta"];91 -> 110[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	91 -> 111[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	92[label="vz41",fontsize=16,color="green",shape="box"];93[label="Pos (Succ vz300)",fontsize=16,color="green",shape="box"];94 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	94[label="lookup (Pos Zero) vz41",fontsize=16,color="magenta"];94 -> 112[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	94 -> 113[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	95 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	95[label="lookup (Pos Zero) vz41",fontsize=16,color="magenta"];95 -> 114[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	95 -> 115[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	96[label="vz41",fontsize=16,color="green",shape="box"];97[label="Neg (Succ vz300)",fontsize=16,color="green",shape="box"];750[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat (Succ vz850) (Succ vz860))",fontsize=16,color="black",shape="box"];750 -> 758[label="",style="solid", color="black", weight=3];
10.61/4.30	751[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat (Succ vz850) Zero)",fontsize=16,color="black",shape="box"];751 -> 759[label="",style="solid", color="black", weight=3];
10.61/4.30	752[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat Zero (Succ vz860))",fontsize=16,color="black",shape="box"];752 -> 760[label="",style="solid", color="black", weight=3];
10.61/4.30	753[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];753 -> 761[label="",style="solid", color="black", weight=3];
10.61/4.30	102 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	102[label="lookup (Neg (Succ vz300)) vz41",fontsize=16,color="magenta"];102 -> 121[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	102 -> 122[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	103 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	103[label="lookup (Neg Zero) vz41",fontsize=16,color="magenta"];103 -> 123[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	103 -> 124[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	104 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	104[label="lookup (Neg Zero) vz41",fontsize=16,color="magenta"];104 -> 125[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	104 -> 126[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	754 -> 620[label="",style="dashed", color="red", weight=0];
10.61/4.30	754[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 (primEqNat vz780 vz790)",fontsize=16,color="magenta"];754 -> 762[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	754 -> 763[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	755[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 MyFalse",fontsize=16,color="black",shape="triangle"];755 -> 764[label="",style="solid", color="black", weight=3];
10.61/4.30	756 -> 755[label="",style="dashed", color="red", weight=0];
10.61/4.30	756[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 MyFalse",fontsize=16,color="magenta"];757[label="lookup1 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 MyTrue",fontsize=16,color="black",shape="box"];757 -> 765[label="",style="solid", color="black", weight=3];
10.61/4.30	110[label="vz41",fontsize=16,color="green",shape="box"];111[label="Pos (Succ vz300)",fontsize=16,color="green",shape="box"];112[label="vz41",fontsize=16,color="green",shape="box"];113[label="Pos Zero",fontsize=16,color="green",shape="box"];114[label="vz41",fontsize=16,color="green",shape="box"];115[label="Pos Zero",fontsize=16,color="green",shape="box"];758 -> 683[label="",style="dashed", color="red", weight=0];
10.61/4.30	758[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 (primEqNat vz850 vz860)",fontsize=16,color="magenta"];758 -> 766[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	758 -> 767[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	759[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 MyFalse",fontsize=16,color="black",shape="triangle"];759 -> 768[label="",style="solid", color="black", weight=3];
10.61/4.30	760 -> 759[label="",style="dashed", color="red", weight=0];
10.61/4.30	760[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 MyFalse",fontsize=16,color="magenta"];761[label="lookup1 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 MyTrue",fontsize=16,color="black",shape="box"];761 -> 769[label="",style="solid", color="black", weight=3];
10.61/4.30	121[label="vz41",fontsize=16,color="green",shape="box"];122[label="Neg (Succ vz300)",fontsize=16,color="green",shape="box"];123[label="vz41",fontsize=16,color="green",shape="box"];124[label="Neg Zero",fontsize=16,color="green",shape="box"];125[label="vz41",fontsize=16,color="green",shape="box"];126[label="Neg Zero",fontsize=16,color="green",shape="box"];762[label="vz780",fontsize=16,color="green",shape="box"];763[label="vz790",fontsize=16,color="green",shape="box"];764[label="lookup0 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 otherwise",fontsize=16,color="black",shape="box"];764 -> 770[label="",style="solid", color="black", weight=3];
10.61/4.30	765[label="Just vz76",fontsize=16,color="green",shape="box"];766[label="vz850",fontsize=16,color="green",shape="box"];767[label="vz860",fontsize=16,color="green",shape="box"];768[label="lookup0 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 otherwise",fontsize=16,color="black",shape="box"];768 -> 771[label="",style="solid", color="black", weight=3];
10.61/4.30	769[label="Just vz83",fontsize=16,color="green",shape="box"];770[label="lookup0 (Pos (Succ vz74)) (Pos (Succ vz75)) vz76 vz77 MyTrue",fontsize=16,color="black",shape="box"];770 -> 772[label="",style="solid", color="black", weight=3];
10.61/4.30	771[label="lookup0 (Neg (Succ vz81)) (Neg (Succ vz82)) vz83 vz84 MyTrue",fontsize=16,color="black",shape="box"];771 -> 773[label="",style="solid", color="black", weight=3];
10.61/4.30	772 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	772[label="lookup (Pos (Succ vz74)) vz77",fontsize=16,color="magenta"];772 -> 774[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	772 -> 775[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	773 -> 4[label="",style="dashed", color="red", weight=0];
10.61/4.30	773[label="lookup (Neg (Succ vz81)) vz84",fontsize=16,color="magenta"];773 -> 776[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	773 -> 777[label="",style="dashed", color="magenta", weight=3];
10.61/4.30	774[label="vz77",fontsize=16,color="green",shape="box"];775[label="Pos (Succ vz74)",fontsize=16,color="green",shape="box"];776[label="vz84",fontsize=16,color="green",shape="box"];777[label="Neg (Succ vz81)",fontsize=16,color="green",shape="box"];}
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(6)
10.61/4.30	Obligation:
10.61/4.30	Q DP problem:
10.61/4.30	The TRS P consists of the following rules:
10.61/4.30	
10.61/4.30	   new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Succ(vz790), h) -> new_lookup1(vz74, vz75, vz76, vz77, vz780, vz790, h)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup11(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Zero, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	   new_lookup12(vz81, vz82, vz83, vz84, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	   new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Neg(vz4000), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Zero, Main.Succ(vz790), h) -> new_lookup10(vz74, vz75, vz76, vz77, h)
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Pos(vz4000), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup1(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Zero, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	   new_lookup10(vz74, vz75, vz76, vz77, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	   new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Succ(vz860), bb) -> new_lookup11(vz81, vz82, vz83, vz84, vz850, vz860, bb)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Zero, Main.Succ(vz860), bb) -> new_lookup12(vz81, vz82, vz83, vz84, bb)
10.61/4.30	
10.61/4.30	R is empty.
10.61/4.30	Q is empty.
10.61/4.30	We have to consider all minimal (P,Q,R)-chains.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(7) DependencyGraphProof (EQUIVALENT)
10.61/4.30	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(8)
10.61/4.30	Complex Obligation (AND)
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(9)
10.61/4.30	Obligation:
10.61/4.30	Q DP problem:
10.61/4.30	The TRS P consists of the following rules:
10.61/4.30	
10.61/4.30	   new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	
10.61/4.30	R is empty.
10.61/4.30	Q is empty.
10.61/4.30	We have to consider all minimal (P,Q,R)-chains.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(10) QDPSizeChangeProof (EQUIVALENT)
10.61/4.30	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. 
10.61/4.30	
10.61/4.30	From the DPs we obtained the following set of size-change graphs:
10.61/4.30	*new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Neg(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Zero), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(11)
10.61/4.30	YES
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(12)
10.61/4.30	Obligation:
10.61/4.30	Q DP problem:
10.61/4.30	The TRS P consists of the following rules:
10.61/4.30	
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Zero, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Neg(vz4000), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup1(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Succ(vz790), h) -> new_lookup1(vz74, vz75, vz76, vz77, vz780, vz790, h)
10.61/4.30	   new_lookup1(vz74, vz75, vz76, vz77, Main.Zero, Main.Succ(vz790), h) -> new_lookup10(vz74, vz75, vz76, vz77, h)
10.61/4.30	   new_lookup10(vz74, vz75, vz76, vz77, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	
10.61/4.30	R is empty.
10.61/4.30	Q is empty.
10.61/4.30	We have to consider all minimal (P,Q,R)-chains.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(13) QDPSizeChangeProof (EQUIVALENT)
10.61/4.30	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. 
10.61/4.30	
10.61/4.30	From the DPs we obtained the following set of size-change graphs:
10.61/4.30	*new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup1(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 1 > 5, 2 > 6, 3 >= 7
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Succ(vz790), h) -> new_lookup1(vz74, vz75, vz76, vz77, vz780, vz790, h)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup1(vz74, vz75, vz76, vz77, Main.Zero, Main.Succ(vz790), h) -> new_lookup10(vz74, vz75, vz76, vz77, h)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup1(vz74, vz75, vz76, vz77, Main.Succ(vz780), Main.Zero, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	The graph contains the following edges 4 >= 2, 7 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup10(vz74, vz75, vz76, vz77, h) -> new_lookup(Main.Pos(Main.Succ(vz74)), vz77, h)
10.61/4.30	The graph contains the following edges 4 >= 2, 5 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Pos(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Pos(Main.Succ(vz300)), Cons(Tup2(Main.Neg(vz4000), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Succ(vz300)), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(14)
10.61/4.30	YES
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(15)
10.61/4.30	Obligation:
10.61/4.30	Q DP problem:
10.61/4.30	The TRS P consists of the following rules:
10.61/4.30	
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup11(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Zero, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Pos(vz4000), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Succ(vz860), bb) -> new_lookup11(vz81, vz82, vz83, vz84, vz850, vz860, bb)
10.61/4.30	   new_lookup11(vz81, vz82, vz83, vz84, Main.Zero, Main.Succ(vz860), bb) -> new_lookup12(vz81, vz82, vz83, vz84, bb)
10.61/4.30	   new_lookup12(vz81, vz82, vz83, vz84, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	
10.61/4.30	R is empty.
10.61/4.30	Q is empty.
10.61/4.30	We have to consider all minimal (P,Q,R)-chains.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(16) QDPSizeChangeProof (EQUIVALENT)
10.61/4.30	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. 
10.61/4.30	
10.61/4.30	From the DPs we obtained the following set of size-change graphs:
10.61/4.30	*new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Zero, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	The graph contains the following edges 4 >= 2, 7 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup11(vz300, vz40000, vz401, vz41, vz300, vz40000, ba)
10.61/4.30	The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 1 > 5, 2 > 6, 3 >= 7
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup11(vz81, vz82, vz83, vz84, Main.Succ(vz850), Main.Succ(vz860), bb) -> new_lookup11(vz81, vz82, vz83, vz84, vz850, vz860, bb)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup11(vz81, vz82, vz83, vz84, Main.Zero, Main.Succ(vz860), bb) -> new_lookup12(vz81, vz82, vz83, vz84, bb)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup12(vz81, vz82, vz83, vz84, bb) -> new_lookup(Main.Neg(Main.Succ(vz81)), vz84, bb)
10.61/4.30	The graph contains the following edges 4 >= 2, 5 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Neg(Main.Zero), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Neg(Main.Succ(vz300)), Cons(Tup2(Main.Pos(vz4000), vz401), vz41), ba) -> new_lookup(Main.Neg(Main.Succ(vz300)), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(17)
10.61/4.30	YES
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(18)
10.61/4.30	Obligation:
10.61/4.30	Q DP problem:
10.61/4.30	The TRS P consists of the following rules:
10.61/4.30	
10.61/4.30	   new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	   new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	
10.61/4.30	R is empty.
10.61/4.30	Q is empty.
10.61/4.30	We have to consider all minimal (P,Q,R)-chains.
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(19) QDPSizeChangeProof (EQUIVALENT)
10.61/4.30	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. 
10.61/4.30	
10.61/4.30	From the DPs we obtained the following set of size-change graphs:
10.61/4.30	*new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Neg(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	*new_lookup(Main.Pos(Main.Zero), Cons(Tup2(Main.Pos(Main.Succ(vz40000)), vz401), vz41), ba) -> new_lookup(Main.Pos(Main.Zero), vz41, ba)
10.61/4.30	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
10.61/4.30	
10.61/4.30	
10.61/4.30	----------------------------------------
10.61/4.30	
10.61/4.30	(20)
10.61/4.30	YES
10.61/4.34	EOF