8.43/3.62	YES
10.10/4.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.10/4.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.10/4.11	
10.10/4.11	
10.10/4.11	H-Termination with start terms of the given HASKELL could be proven:
10.10/4.11	
10.10/4.11	(0) HASKELL
10.10/4.11	(1) BR [EQUIVALENT, 0 ms]
10.10/4.11	(2) HASKELL
10.10/4.11	(3) COR [EQUIVALENT, 0 ms]
10.10/4.11	(4) HASKELL
10.10/4.11	(5) Narrow [SOUND, 0 ms]
10.10/4.11	(6) AND
10.10/4.11	    (7) QDP
10.10/4.11	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.10/4.11	        (9) YES
10.10/4.11	    (10) QDP
10.10/4.11	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.10/4.11	        (12) YES
10.10/4.11	    (13) QDP
10.10/4.11	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.10/4.11	        (15) YES
10.10/4.11	
10.10/4.11	
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(0)
10.10/4.11	Obligation:
10.10/4.11	mainModule Main 
10.10/4.11	module Main where {
10.10/4.11	import qualified Prelude;
10.10/4.11	data List a = Cons a (List a)  | Nil ;
10.10/4.11	
10.10/4.11	data MyBool = MyTrue  | MyFalse ;
10.10/4.11	
10.10/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.10/4.11	
10.10/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.10/4.11	
10.10/4.11	data Ratio a = CnPc a a ;
10.10/4.11	
10.10/4.11	any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
10.10/4.11	any p = pt or (map p);
10.10/4.11	
10.10/4.11	asAs :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	asAs MyFalse x = MyFalse;
10.10/4.11	asAs MyTrue x = x;
10.10/4.11	
10.10/4.11	elemRatio :: Ratio MyInt  ->  List (Ratio MyInt)  ->  MyBool;
10.10/4.11	elemRatio = pt any esEsRatio;
10.10/4.11	
10.10/4.11	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	esEsMyInt = primEqInt;
10.10/4.11	
10.10/4.11	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
10.10/4.11	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
10.10/4.11	
10.10/4.11	foldr :: (b  ->  a  ->  a)  ->  a  ->  List b  ->  a;
10.10/4.11	foldr f z Nil = z;
10.10/4.11	foldr f z (Cons x xs) = f x (foldr f z xs);
10.10/4.11	
10.10/4.11	map :: (b  ->  a)  ->  List b  ->  List a;
10.10/4.11	map f Nil = Nil;
10.10/4.11	map f (Cons x xs) = Cons (f x) (map f xs);
10.10/4.11	
10.10/4.11	or :: List MyBool  ->  MyBool;
10.10/4.11	or = foldr pePe MyFalse;
10.10/4.11	
10.10/4.11	pePe :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	pePe MyFalse x = x;
10.10/4.11	pePe MyTrue x = MyTrue;
10.10/4.11	
10.10/4.11	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt vv vw = MyFalse;
10.10/4.11	
10.10/4.11	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.10/4.11	primEqNat Main.Zero Main.Zero = MyTrue;
10.10/4.11	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.10/4.11	
10.10/4.11	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
10.10/4.11	pt f g x = f (g x);
10.10/4.11	
10.10/4.11	}
10.10/4.11	
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(1) BR (EQUIVALENT)
10.10/4.11	Replaced joker patterns by fresh variables and removed binding patterns.
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(2)
10.10/4.11	Obligation:
10.10/4.11	mainModule Main 
10.10/4.11	module Main where {
10.10/4.11	import qualified Prelude;
10.10/4.11	data List a = Cons a (List a)  | Nil ;
10.10/4.11	
10.10/4.11	data MyBool = MyTrue  | MyFalse ;
10.10/4.11	
10.10/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.10/4.11	
10.10/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.10/4.11	
10.10/4.11	data Ratio a = CnPc a a ;
10.10/4.11	
10.10/4.11	any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
10.10/4.11	any p = pt or (map p);
10.10/4.11	
10.10/4.11	asAs :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	asAs MyFalse x = MyFalse;
10.10/4.11	asAs MyTrue x = x;
10.10/4.11	
10.10/4.11	elemRatio :: Ratio MyInt  ->  List (Ratio MyInt)  ->  MyBool;
10.10/4.11	elemRatio = pt any esEsRatio;
10.10/4.11	
10.10/4.11	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	esEsMyInt = primEqInt;
10.10/4.11	
10.10/4.11	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
10.10/4.11	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
10.10/4.11	
10.10/4.11	foldr :: (a  ->  b  ->  b)  ->  b  ->  List a  ->  b;
10.10/4.11	foldr f z Nil = z;
10.10/4.11	foldr f z (Cons x xs) = f x (foldr f z xs);
10.10/4.11	
10.10/4.11	map :: (b  ->  a)  ->  List b  ->  List a;
10.10/4.11	map f Nil = Nil;
10.10/4.11	map f (Cons x xs) = Cons (f x) (map f xs);
10.10/4.11	
10.10/4.11	or :: List MyBool  ->  MyBool;
10.10/4.11	or = foldr pePe MyFalse;
10.10/4.11	
10.10/4.11	pePe :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	pePe MyFalse x = x;
10.10/4.11	pePe MyTrue x = MyTrue;
10.10/4.11	
10.10/4.11	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt vv vw = MyFalse;
10.10/4.11	
10.10/4.11	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.10/4.11	primEqNat Main.Zero Main.Zero = MyTrue;
10.10/4.11	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.10/4.11	
10.10/4.11	pt :: (a  ->  c)  ->  (b  ->  a)  ->  b  ->  c;
10.10/4.11	pt f g x = f (g x);
10.10/4.11	
10.10/4.11	}
10.10/4.11	
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(3) COR (EQUIVALENT)
10.10/4.11	Cond Reductions:
10.10/4.11	The following Function with conditions
10.10/4.11	"undefined |Falseundefined;
10.10/4.11	"
10.10/4.11	is transformed to
10.10/4.11	"undefined  = undefined1;
10.10/4.11	"
10.10/4.11	"undefined0 True = undefined;
10.10/4.11	"
10.10/4.11	"undefined1  = undefined0 False;
10.10/4.11	"
10.10/4.11	
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(4)
10.10/4.11	Obligation:
10.10/4.11	mainModule Main 
10.10/4.11	module Main where {
10.10/4.11	import qualified Prelude;
10.10/4.11	data List a = Cons a (List a)  | Nil ;
10.10/4.11	
10.10/4.11	data MyBool = MyTrue  | MyFalse ;
10.10/4.11	
10.10/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.10/4.11	
10.10/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.10/4.11	
10.10/4.11	data Ratio a = CnPc a a ;
10.10/4.11	
10.10/4.11	any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
10.10/4.11	any p = pt or (map p);
10.10/4.11	
10.10/4.11	asAs :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	asAs MyFalse x = MyFalse;
10.10/4.11	asAs MyTrue x = x;
10.10/4.11	
10.10/4.11	elemRatio :: Ratio MyInt  ->  List (Ratio MyInt)  ->  MyBool;
10.10/4.11	elemRatio = pt any esEsRatio;
10.10/4.11	
10.10/4.11	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	esEsMyInt = primEqInt;
10.10/4.11	
10.10/4.11	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
10.10/4.11	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
10.10/4.11	
10.10/4.11	foldr :: (b  ->  a  ->  a)  ->  a  ->  List b  ->  a;
10.10/4.11	foldr f z Nil = z;
10.10/4.11	foldr f z (Cons x xs) = f x (foldr f z xs);
10.10/4.11	
10.10/4.11	map :: (b  ->  a)  ->  List b  ->  List a;
10.10/4.11	map f Nil = Nil;
10.10/4.11	map f (Cons x xs) = Cons (f x) (map f xs);
10.10/4.11	
10.10/4.11	or :: List MyBool  ->  MyBool;
10.10/4.11	or = foldr pePe MyFalse;
10.10/4.11	
10.10/4.11	pePe :: MyBool  ->  MyBool  ->  MyBool;
10.10/4.11	pePe MyFalse x = x;
10.10/4.11	pePe MyTrue x = MyTrue;
10.10/4.11	
10.10/4.11	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
10.10/4.11	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
10.10/4.11	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
10.10/4.11	primEqInt vv vw = MyFalse;
10.10/4.11	
10.10/4.11	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
10.10/4.11	primEqNat Main.Zero Main.Zero = MyTrue;
10.10/4.11	primEqNat Main.Zero (Main.Succ y) = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) Main.Zero = MyFalse;
10.10/4.11	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
10.10/4.11	
10.10/4.11	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
10.10/4.11	pt f g x = f (g x);
10.10/4.11	
10.10/4.11	}
10.10/4.11	
10.10/4.11	----------------------------------------
10.10/4.11	
10.10/4.11	(5) Narrow (SOUND)
10.10/4.11	Haskell To QDPs
10.10/4.11	
10.10/4.11	digraph dp_graph {
10.10/4.11	node [outthreshold=100, inthreshold=100];1[label="elemRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.10/4.11	3[label="elemRatio vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.10/4.11	4[label="elemRatio vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.10/4.12	5[label="pt any esEsRatio vz3 vz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.10/4.12	6[label="any (esEsRatio vz3) vz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.10/4.12	7[label="pt or (map (esEsRatio vz3)) vz4",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.10/4.12	8[label="or (map (esEsRatio vz3) vz4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
10.10/4.12	9[label="foldr pePe MyFalse (map (esEsRatio vz3) vz4)",fontsize=16,color="burlywood",shape="triangle"];136[label="vz4/Cons vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];9 -> 136[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	136 -> 10[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	137[label="vz4/Nil",fontsize=10,color="white",style="solid",shape="box"];9 -> 137[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	137 -> 11[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	10[label="foldr pePe MyFalse (map (esEsRatio vz3) (Cons vz40 vz41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
10.10/4.12	11[label="foldr pePe MyFalse (map (esEsRatio vz3) Nil)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
10.10/4.12	12[label="foldr pePe MyFalse (Cons (esEsRatio vz3 vz40) (map (esEsRatio vz3) vz41))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
10.10/4.12	13[label="foldr pePe MyFalse Nil",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
10.10/4.12	14 -> 16[label="",style="dashed", color="red", weight=0];
10.10/4.12	14[label="pePe (esEsRatio vz3 vz40) (foldr pePe MyFalse (map (esEsRatio vz3) vz41))",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	15[label="MyFalse",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
10.10/4.12	17[label="foldr pePe MyFalse (map (esEsRatio vz3) vz41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	16[label="pePe (esEsRatio vz3 vz40) vz5",fontsize=16,color="burlywood",shape="triangle"];138[label="vz3/CnPc vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];16 -> 138[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	138 -> 19[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	18[label="vz41",fontsize=16,color="green",shape="box"];19[label="pePe (esEsRatio (CnPc vz30 vz31) vz40) vz5",fontsize=16,color="burlywood",shape="box"];139[label="vz40/CnPc vz400 vz401",fontsize=10,color="white",style="solid",shape="box"];19 -> 139[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	139 -> 20[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	20[label="pePe (esEsRatio (CnPc vz30 vz31) (CnPc vz400 vz401)) vz5",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
10.10/4.12	21[label="pePe (asAs (esEsMyInt vz30 vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
10.10/4.12	22[label="pePe (asAs (primEqInt vz30 vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];140[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 140[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	140 -> 23[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	141[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 141[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	141 -> 24[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	23[label="pePe (asAs (primEqInt (Pos vz300) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];142[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];23 -> 142[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	142 -> 25[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	143[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 143[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	143 -> 26[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	24[label="pePe (asAs (primEqInt (Neg vz300) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];144[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];24 -> 144[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	144 -> 27[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	145[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 145[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	145 -> 28[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	25[label="pePe (asAs (primEqInt (Pos (Succ vz3000)) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];146[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 146[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	146 -> 29[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	147[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 147[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	147 -> 30[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	26[label="pePe (asAs (primEqInt (Pos Zero) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];148[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 148[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	148 -> 31[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	149[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 149[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	149 -> 32[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	27[label="pePe (asAs (primEqInt (Neg (Succ vz3000)) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];150[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 150[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	150 -> 33[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	151[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 151[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	151 -> 34[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	28[label="pePe (asAs (primEqInt (Neg Zero) vz400) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];152[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 152[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	152 -> 35[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	153[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 153[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	153 -> 36[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	29[label="pePe (asAs (primEqInt (Pos (Succ vz3000)) (Pos vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];154[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];29 -> 154[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	154 -> 37[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	155[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 155[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	155 -> 38[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	30[label="pePe (asAs (primEqInt (Pos (Succ vz3000)) (Neg vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
10.10/4.12	31[label="pePe (asAs (primEqInt (Pos Zero) (Pos vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];156[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];31 -> 156[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	156 -> 40[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	157[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];31 -> 157[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	157 -> 41[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	32[label="pePe (asAs (primEqInt (Pos Zero) (Neg vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];158[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];32 -> 158[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	158 -> 42[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	159[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 159[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	159 -> 43[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	33[label="pePe (asAs (primEqInt (Neg (Succ vz3000)) (Pos vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3];
10.10/4.12	34[label="pePe (asAs (primEqInt (Neg (Succ vz3000)) (Neg vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];160[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];34 -> 160[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	160 -> 45[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	161[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 161[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	161 -> 46[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	35[label="pePe (asAs (primEqInt (Neg Zero) (Pos vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];162[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];35 -> 162[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	162 -> 47[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	163[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 163[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	163 -> 48[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	36[label="pePe (asAs (primEqInt (Neg Zero) (Neg vz4000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];164[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];36 -> 164[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	164 -> 49[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	165[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 165[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	165 -> 50[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	37[label="pePe (asAs (primEqInt (Pos (Succ vz3000)) (Pos (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
10.10/4.12	38[label="pePe (asAs (primEqInt (Pos (Succ vz3000)) (Pos Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
10.10/4.12	39[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="triangle"];39 -> 53[label="",style="solid", color="black", weight=3];
10.10/4.12	40[label="pePe (asAs (primEqInt (Pos Zero) (Pos (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
10.10/4.12	41[label="pePe (asAs (primEqInt (Pos Zero) (Pos Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
10.10/4.12	42[label="pePe (asAs (primEqInt (Pos Zero) (Neg (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
10.10/4.12	43[label="pePe (asAs (primEqInt (Pos Zero) (Neg Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
10.10/4.12	44 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	44[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];45[label="pePe (asAs (primEqInt (Neg (Succ vz3000)) (Neg (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];45 -> 58[label="",style="solid", color="black", weight=3];
10.10/4.12	46[label="pePe (asAs (primEqInt (Neg (Succ vz3000)) (Neg Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];46 -> 59[label="",style="solid", color="black", weight=3];
10.10/4.12	47[label="pePe (asAs (primEqInt (Neg Zero) (Pos (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];47 -> 60[label="",style="solid", color="black", weight=3];
10.10/4.12	48[label="pePe (asAs (primEqInt (Neg Zero) (Pos Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];48 -> 61[label="",style="solid", color="black", weight=3];
10.10/4.12	49[label="pePe (asAs (primEqInt (Neg Zero) (Neg (Succ vz40000))) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];49 -> 62[label="",style="solid", color="black", weight=3];
10.10/4.12	50[label="pePe (asAs (primEqInt (Neg Zero) (Neg Zero)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];50 -> 63[label="",style="solid", color="black", weight=3];
10.10/4.12	51[label="pePe (asAs (primEqNat vz3000 vz40000) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="triangle"];166[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];51 -> 166[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	166 -> 64[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	167[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 167[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	167 -> 65[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	52 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	52[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];53[label="pePe MyFalse vz5",fontsize=16,color="black",shape="triangle"];53 -> 66[label="",style="solid", color="black", weight=3];
10.10/4.12	54 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	54[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];55[label="pePe (asAs MyTrue (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="triangle"];55 -> 67[label="",style="solid", color="black", weight=3];
10.10/4.12	56 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	56[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];57 -> 55[label="",style="dashed", color="red", weight=0];
10.10/4.12	57[label="pePe (asAs MyTrue (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];58 -> 51[label="",style="dashed", color="red", weight=0];
10.10/4.12	58[label="pePe (asAs (primEqNat vz3000 vz40000) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];58 -> 68[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	58 -> 69[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	59 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	59[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];60 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	60[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];61 -> 55[label="",style="dashed", color="red", weight=0];
10.10/4.12	61[label="pePe (asAs MyTrue (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];62 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	62[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];63 -> 55[label="",style="dashed", color="red", weight=0];
10.10/4.12	63[label="pePe (asAs MyTrue (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];64[label="pePe (asAs (primEqNat (Succ vz30000) vz40000) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];168[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];64 -> 168[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	168 -> 70[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	169[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 169[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	169 -> 71[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	65[label="pePe (asAs (primEqNat Zero vz40000) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];170[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];65 -> 170[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	170 -> 72[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	171[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 171[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	171 -> 73[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	66[label="vz5",fontsize=16,color="green",shape="box"];67[label="pePe (esEsMyInt vz31 vz401) vz5",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
10.10/4.12	68[label="vz3000",fontsize=16,color="green",shape="box"];69[label="vz40000",fontsize=16,color="green",shape="box"];70[label="pePe (asAs (primEqNat (Succ vz30000) (Succ vz400000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];70 -> 75[label="",style="solid", color="black", weight=3];
10.10/4.12	71[label="pePe (asAs (primEqNat (Succ vz30000) Zero) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];71 -> 76[label="",style="solid", color="black", weight=3];
10.10/4.12	72[label="pePe (asAs (primEqNat Zero (Succ vz400000)) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];72 -> 77[label="",style="solid", color="black", weight=3];
10.10/4.12	73[label="pePe (asAs (primEqNat Zero Zero) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];73 -> 78[label="",style="solid", color="black", weight=3];
10.10/4.12	74[label="pePe (primEqInt vz31 vz401) vz5",fontsize=16,color="burlywood",shape="box"];172[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];74 -> 172[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	172 -> 79[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	173[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];74 -> 173[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	173 -> 80[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	75 -> 51[label="",style="dashed", color="red", weight=0];
10.10/4.12	75[label="pePe (asAs (primEqNat vz30000 vz400000) (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];75 -> 81[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	75 -> 82[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	76 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	76[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];77 -> 39[label="",style="dashed", color="red", weight=0];
10.10/4.12	77[label="pePe (asAs MyFalse (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];78 -> 55[label="",style="dashed", color="red", weight=0];
10.10/4.12	78[label="pePe (asAs MyTrue (esEsMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];79[label="pePe (primEqInt (Pos vz310) vz401) vz5",fontsize=16,color="burlywood",shape="box"];174[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];79 -> 174[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	174 -> 83[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	175[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 175[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	175 -> 84[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	80[label="pePe (primEqInt (Neg vz310) vz401) vz5",fontsize=16,color="burlywood",shape="box"];176[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];80 -> 176[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	176 -> 85[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	177[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];80 -> 177[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	177 -> 86[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	81[label="vz30000",fontsize=16,color="green",shape="box"];82[label="vz400000",fontsize=16,color="green",shape="box"];83[label="pePe (primEqInt (Pos (Succ vz3100)) vz401) vz5",fontsize=16,color="burlywood",shape="box"];178[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];83 -> 178[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	178 -> 87[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	179[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];83 -> 179[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	179 -> 88[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	84[label="pePe (primEqInt (Pos Zero) vz401) vz5",fontsize=16,color="burlywood",shape="box"];180[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];84 -> 180[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	180 -> 89[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	181[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];84 -> 181[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	181 -> 90[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	85[label="pePe (primEqInt (Neg (Succ vz3100)) vz401) vz5",fontsize=16,color="burlywood",shape="box"];182[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 182[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	182 -> 91[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	183[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 183[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	183 -> 92[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	86[label="pePe (primEqInt (Neg Zero) vz401) vz5",fontsize=16,color="burlywood",shape="box"];184[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 184[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	184 -> 93[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	185[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 185[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	185 -> 94[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	87[label="pePe (primEqInt (Pos (Succ vz3100)) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];186[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];87 -> 186[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	186 -> 95[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	187[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 187[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	187 -> 96[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	88[label="pePe (primEqInt (Pos (Succ vz3100)) (Neg vz4010)) vz5",fontsize=16,color="black",shape="box"];88 -> 97[label="",style="solid", color="black", weight=3];
10.10/4.12	89[label="pePe (primEqInt (Pos Zero) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];188[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];89 -> 188[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	188 -> 98[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	189[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 189[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	189 -> 99[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	90[label="pePe (primEqInt (Pos Zero) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];190[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];90 -> 190[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	190 -> 100[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	191[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];90 -> 191[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	191 -> 101[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	91[label="pePe (primEqInt (Neg (Succ vz3100)) (Pos vz4010)) vz5",fontsize=16,color="black",shape="box"];91 -> 102[label="",style="solid", color="black", weight=3];
10.10/4.12	92[label="pePe (primEqInt (Neg (Succ vz3100)) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];192[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];92 -> 192[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	192 -> 103[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	193[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];92 -> 193[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	193 -> 104[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	93[label="pePe (primEqInt (Neg Zero) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];194[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];93 -> 194[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	194 -> 105[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	195[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];93 -> 195[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	195 -> 106[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	94[label="pePe (primEqInt (Neg Zero) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];196[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];94 -> 196[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	196 -> 107[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	197[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 197[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	197 -> 108[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	95[label="pePe (primEqInt (Pos (Succ vz3100)) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];95 -> 109[label="",style="solid", color="black", weight=3];
10.10/4.12	96[label="pePe (primEqInt (Pos (Succ vz3100)) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];96 -> 110[label="",style="solid", color="black", weight=3];
10.10/4.12	97 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	97[label="pePe MyFalse vz5",fontsize=16,color="magenta"];98[label="pePe (primEqInt (Pos Zero) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];98 -> 111[label="",style="solid", color="black", weight=3];
10.10/4.12	99[label="pePe (primEqInt (Pos Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];99 -> 112[label="",style="solid", color="black", weight=3];
10.10/4.12	100[label="pePe (primEqInt (Pos Zero) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];100 -> 113[label="",style="solid", color="black", weight=3];
10.10/4.12	101[label="pePe (primEqInt (Pos Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];101 -> 114[label="",style="solid", color="black", weight=3];
10.10/4.12	102 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	102[label="pePe MyFalse vz5",fontsize=16,color="magenta"];103[label="pePe (primEqInt (Neg (Succ vz3100)) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];103 -> 115[label="",style="solid", color="black", weight=3];
10.10/4.12	104[label="pePe (primEqInt (Neg (Succ vz3100)) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];104 -> 116[label="",style="solid", color="black", weight=3];
10.10/4.12	105[label="pePe (primEqInt (Neg Zero) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];105 -> 117[label="",style="solid", color="black", weight=3];
10.10/4.12	106[label="pePe (primEqInt (Neg Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];106 -> 118[label="",style="solid", color="black", weight=3];
10.10/4.12	107[label="pePe (primEqInt (Neg Zero) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];107 -> 119[label="",style="solid", color="black", weight=3];
10.10/4.12	108[label="pePe (primEqInt (Neg Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];108 -> 120[label="",style="solid", color="black", weight=3];
10.10/4.12	109[label="pePe (primEqNat vz3100 vz40100) vz5",fontsize=16,color="burlywood",shape="triangle"];198[label="vz3100/Succ vz31000",fontsize=10,color="white",style="solid",shape="box"];109 -> 198[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	198 -> 121[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	199[label="vz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];109 -> 199[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	199 -> 122[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	110 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	110[label="pePe MyFalse vz5",fontsize=16,color="magenta"];111 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	111[label="pePe MyFalse vz5",fontsize=16,color="magenta"];112[label="pePe MyTrue vz5",fontsize=16,color="black",shape="triangle"];112 -> 123[label="",style="solid", color="black", weight=3];
10.10/4.12	113 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	113[label="pePe MyFalse vz5",fontsize=16,color="magenta"];114 -> 112[label="",style="dashed", color="red", weight=0];
10.10/4.12	114[label="pePe MyTrue vz5",fontsize=16,color="magenta"];115 -> 109[label="",style="dashed", color="red", weight=0];
10.10/4.12	115[label="pePe (primEqNat vz3100 vz40100) vz5",fontsize=16,color="magenta"];115 -> 124[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	115 -> 125[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	116 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	116[label="pePe MyFalse vz5",fontsize=16,color="magenta"];117 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	117[label="pePe MyFalse vz5",fontsize=16,color="magenta"];118 -> 112[label="",style="dashed", color="red", weight=0];
10.10/4.12	118[label="pePe MyTrue vz5",fontsize=16,color="magenta"];119 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	119[label="pePe MyFalse vz5",fontsize=16,color="magenta"];120 -> 112[label="",style="dashed", color="red", weight=0];
10.10/4.12	120[label="pePe MyTrue vz5",fontsize=16,color="magenta"];121[label="pePe (primEqNat (Succ vz31000) vz40100) vz5",fontsize=16,color="burlywood",shape="box"];200[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];121 -> 200[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	200 -> 126[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	201[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 201[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	201 -> 127[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	122[label="pePe (primEqNat Zero vz40100) vz5",fontsize=16,color="burlywood",shape="box"];202[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];122 -> 202[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	202 -> 128[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	203[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];122 -> 203[label="",style="solid", color="burlywood", weight=9];
10.10/4.12	203 -> 129[label="",style="solid", color="burlywood", weight=3];
10.10/4.12	123[label="MyTrue",fontsize=16,color="green",shape="box"];124[label="vz40100",fontsize=16,color="green",shape="box"];125[label="vz3100",fontsize=16,color="green",shape="box"];126[label="pePe (primEqNat (Succ vz31000) (Succ vz401000)) vz5",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
10.10/4.12	127[label="pePe (primEqNat (Succ vz31000) Zero) vz5",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3];
10.10/4.12	128[label="pePe (primEqNat Zero (Succ vz401000)) vz5",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3];
10.10/4.12	129[label="pePe (primEqNat Zero Zero) vz5",fontsize=16,color="black",shape="box"];129 -> 133[label="",style="solid", color="black", weight=3];
10.10/4.12	130 -> 109[label="",style="dashed", color="red", weight=0];
10.10/4.12	130[label="pePe (primEqNat vz31000 vz401000) vz5",fontsize=16,color="magenta"];130 -> 134[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	130 -> 135[label="",style="dashed", color="magenta", weight=3];
10.10/4.12	131 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	131[label="pePe MyFalse vz5",fontsize=16,color="magenta"];132 -> 53[label="",style="dashed", color="red", weight=0];
10.10/4.12	132[label="pePe MyFalse vz5",fontsize=16,color="magenta"];133 -> 112[label="",style="dashed", color="red", weight=0];
10.10/4.12	133[label="pePe MyTrue vz5",fontsize=16,color="magenta"];134[label="vz401000",fontsize=16,color="green",shape="box"];135[label="vz31000",fontsize=16,color="green",shape="box"];}
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(6)
10.10/4.12	Complex Obligation (AND)
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(7)
10.10/4.12	Obligation:
10.10/4.12	Q DP problem:
10.10/4.12	The TRS P consists of the following rules:
10.10/4.12	
10.10/4.12	   new_foldr(vz3, Cons(vz40, vz41)) -> new_foldr(vz3, vz41)
10.10/4.12	
10.10/4.12	R is empty.
10.10/4.12	Q is empty.
10.10/4.12	We have to consider all minimal (P,Q,R)-chains.
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(8) QDPSizeChangeProof (EQUIVALENT)
10.10/4.12	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. 
10.10/4.12	
10.10/4.12	From the DPs we obtained the following set of size-change graphs:
10.10/4.12	*new_foldr(vz3, Cons(vz40, vz41)) -> new_foldr(vz3, vz41)
10.10/4.12	The graph contains the following edges 1 >= 1, 2 > 2
10.10/4.12	
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(9)
10.10/4.12	YES
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(10)
10.10/4.12	Obligation:
10.10/4.12	Q DP problem:
10.10/4.12	The TRS P consists of the following rules:
10.10/4.12	
10.10/4.12	   new_pePe(Main.Succ(vz31000), Main.Succ(vz401000), vz5) -> new_pePe(vz31000, vz401000, vz5)
10.10/4.12	
10.10/4.12	R is empty.
10.10/4.12	Q is empty.
10.10/4.12	We have to consider all minimal (P,Q,R)-chains.
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(11) QDPSizeChangeProof (EQUIVALENT)
10.10/4.12	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. 
10.10/4.12	
10.10/4.12	From the DPs we obtained the following set of size-change graphs:
10.10/4.12	*new_pePe(Main.Succ(vz31000), Main.Succ(vz401000), vz5) -> new_pePe(vz31000, vz401000, vz5)
10.10/4.12	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
10.10/4.12	
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(12)
10.10/4.12	YES
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(13)
10.10/4.12	Obligation:
10.10/4.12	Q DP problem:
10.10/4.12	The TRS P consists of the following rules:
10.10/4.12	
10.10/4.12	   new_pePe0(Main.Succ(vz30000), Main.Succ(vz400000), vz31, vz401, vz5) -> new_pePe0(vz30000, vz400000, vz31, vz401, vz5)
10.10/4.12	
10.10/4.12	R is empty.
10.10/4.12	Q is empty.
10.10/4.12	We have to consider all minimal (P,Q,R)-chains.
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(14) QDPSizeChangeProof (EQUIVALENT)
10.10/4.12	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. 
10.10/4.12	
10.10/4.12	From the DPs we obtained the following set of size-change graphs:
10.10/4.12	*new_pePe0(Main.Succ(vz30000), Main.Succ(vz400000), vz31, vz401, vz5) -> new_pePe0(vz30000, vz400000, vz31, vz401, vz5)
10.10/4.12	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
10.10/4.12	
10.10/4.12	
10.10/4.12	----------------------------------------
10.10/4.12	
10.10/4.12	(15)
10.10/4.12	YES
10.10/4.16	EOF