7.86/3.63	YES
9.63/4.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.63/4.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.63/4.14	
9.63/4.14	
9.63/4.14	H-Termination with start terms of the given HASKELL could be proven:
9.63/4.14	
9.63/4.14	(0) HASKELL
9.63/4.14	(1) BR [EQUIVALENT, 0 ms]
9.63/4.14	(2) HASKELL
9.63/4.14	(3) COR [EQUIVALENT, 0 ms]
9.63/4.14	(4) HASKELL
9.63/4.14	(5) Narrow [SOUND, 0 ms]
9.63/4.14	(6) QDP
9.63/4.14	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.63/4.14	(8) YES
9.63/4.14	
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(0)
9.63/4.14	Obligation:
9.63/4.14	mainModule Main 
9.63/4.14	module Main where {
9.63/4.14	import qualified Prelude;
9.63/4.14	data Main.Char = Char MyInt ;
9.63/4.14	
9.63/4.14	data MyBool = MyTrue  | MyFalse ;
9.63/4.14	
9.63/4.14	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.63/4.14	
9.63/4.14	data Main.Nat = Succ Main.Nat  | Zero ;
9.63/4.14	
9.63/4.14	data Ordering = LT  | EQ  | GT ;
9.63/4.14	
9.63/4.14	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	compareChar = primCmpChar;
9.63/4.14	
9.63/4.14	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	esEsOrdering LT LT = MyTrue;
9.63/4.14	esEsOrdering LT EQ = MyFalse;
9.63/4.14	esEsOrdering LT GT = MyFalse;
9.63/4.14	esEsOrdering EQ LT = MyFalse;
9.63/4.14	esEsOrdering EQ EQ = MyTrue;
9.63/4.14	esEsOrdering EQ GT = MyFalse;
9.63/4.14	esEsOrdering GT LT = MyFalse;
9.63/4.14	esEsOrdering GT EQ = MyFalse;
9.63/4.14	esEsOrdering GT GT = MyTrue;
9.63/4.14	
9.63/4.14	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	fsEsOrdering x y = not (esEsOrdering x y);
9.63/4.14	
9.63/4.14	ltEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.63/4.14	ltEsChar x y = fsEsOrdering (compareChar x y) GT;
9.63/4.14	
9.63/4.14	not :: MyBool  ->  MyBool;
9.63/4.14	not MyTrue = MyFalse;
9.63/4.14	not MyFalse = MyTrue;
9.63/4.14	
9.63/4.14	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.63/4.14	
9.63/4.14	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.63/4.14	
9.63/4.14	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.63/4.14	primCmpNat Main.Zero Main.Zero = EQ;
9.63/4.14	primCmpNat Main.Zero (Main.Succ y) = LT;
9.63/4.14	primCmpNat (Main.Succ x) Main.Zero = GT;
9.63/4.14	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.63/4.14	
9.63/4.14	}
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(1) BR (EQUIVALENT)
9.63/4.14	Replaced joker patterns by fresh variables and removed binding patterns.
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(2)
9.63/4.14	Obligation:
9.63/4.14	mainModule Main 
9.63/4.14	module Main where {
9.63/4.14	import qualified Prelude;
9.63/4.14	data Main.Char = Char MyInt ;
9.63/4.14	
9.63/4.14	data MyBool = MyTrue  | MyFalse ;
9.63/4.14	
9.63/4.14	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.63/4.14	
9.63/4.14	data Main.Nat = Succ Main.Nat  | Zero ;
9.63/4.14	
9.63/4.14	data Ordering = LT  | EQ  | GT ;
9.63/4.14	
9.63/4.14	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	compareChar = primCmpChar;
9.63/4.14	
9.63/4.14	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	esEsOrdering LT LT = MyTrue;
9.63/4.14	esEsOrdering LT EQ = MyFalse;
9.63/4.14	esEsOrdering LT GT = MyFalse;
9.63/4.14	esEsOrdering EQ LT = MyFalse;
9.63/4.14	esEsOrdering EQ EQ = MyTrue;
9.63/4.14	esEsOrdering EQ GT = MyFalse;
9.63/4.14	esEsOrdering GT LT = MyFalse;
9.63/4.14	esEsOrdering GT EQ = MyFalse;
9.63/4.14	esEsOrdering GT GT = MyTrue;
9.63/4.14	
9.63/4.14	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	fsEsOrdering x y = not (esEsOrdering x y);
9.63/4.14	
9.63/4.14	ltEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.63/4.14	ltEsChar x y = fsEsOrdering (compareChar x y) GT;
9.63/4.14	
9.63/4.14	not :: MyBool  ->  MyBool;
9.63/4.14	not MyTrue = MyFalse;
9.63/4.14	not MyFalse = MyTrue;
9.63/4.14	
9.63/4.14	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.63/4.14	
9.63/4.14	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.63/4.14	
9.63/4.14	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.63/4.14	primCmpNat Main.Zero Main.Zero = EQ;
9.63/4.14	primCmpNat Main.Zero (Main.Succ y) = LT;
9.63/4.14	primCmpNat (Main.Succ x) Main.Zero = GT;
9.63/4.14	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.63/4.14	
9.63/4.14	}
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(3) COR (EQUIVALENT)
9.63/4.14	Cond Reductions:
9.63/4.14	The following Function with conditions
9.63/4.14	"undefined |Falseundefined;
9.63/4.14	"
9.63/4.14	is transformed to
9.63/4.14	"undefined  = undefined1;
9.63/4.14	"
9.63/4.14	"undefined0 True = undefined;
9.63/4.14	"
9.63/4.14	"undefined1  = undefined0 False;
9.63/4.14	"
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(4)
9.63/4.14	Obligation:
9.63/4.14	mainModule Main 
9.63/4.14	module Main where {
9.63/4.14	import qualified Prelude;
9.63/4.14	data Main.Char = Char MyInt ;
9.63/4.14	
9.63/4.14	data MyBool = MyTrue  | MyFalse ;
9.63/4.14	
9.63/4.14	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.63/4.14	
9.63/4.14	data Main.Nat = Succ Main.Nat  | Zero ;
9.63/4.14	
9.63/4.14	data Ordering = LT  | EQ  | GT ;
9.63/4.14	
9.63/4.14	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	compareChar = primCmpChar;
9.63/4.14	
9.63/4.14	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	esEsOrdering LT LT = MyTrue;
9.63/4.14	esEsOrdering LT EQ = MyFalse;
9.63/4.14	esEsOrdering LT GT = MyFalse;
9.63/4.14	esEsOrdering EQ LT = MyFalse;
9.63/4.14	esEsOrdering EQ EQ = MyTrue;
9.63/4.14	esEsOrdering EQ GT = MyFalse;
9.63/4.14	esEsOrdering GT LT = MyFalse;
9.63/4.14	esEsOrdering GT EQ = MyFalse;
9.63/4.14	esEsOrdering GT GT = MyTrue;
9.63/4.14	
9.63/4.14	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.63/4.14	fsEsOrdering x y = not (esEsOrdering x y);
9.63/4.14	
9.63/4.14	ltEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.63/4.14	ltEsChar x y = fsEsOrdering (compareChar x y) GT;
9.63/4.14	
9.63/4.14	not :: MyBool  ->  MyBool;
9.63/4.14	not MyTrue = MyFalse;
9.63/4.14	not MyFalse = MyTrue;
9.63/4.14	
9.63/4.14	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.63/4.14	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.63/4.14	
9.63/4.14	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.63/4.14	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.63/4.14	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.63/4.14	
9.63/4.14	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.63/4.14	primCmpNat Main.Zero Main.Zero = EQ;
9.63/4.14	primCmpNat Main.Zero (Main.Succ y) = LT;
9.63/4.14	primCmpNat (Main.Succ x) Main.Zero = GT;
9.63/4.14	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.63/4.14	
9.63/4.14	}
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(5) Narrow (SOUND)
9.63/4.14	Haskell To QDPs
9.63/4.14	
9.63/4.14	digraph dp_graph {
9.63/4.14	node [outthreshold=100, inthreshold=100];1[label="ltEsChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.63/4.14	3[label="ltEsChar vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.63/4.14	4[label="ltEsChar vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.63/4.14	5[label="fsEsOrdering (compareChar vx3 vx4) GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.63/4.14	6[label="not (esEsOrdering (compareChar vx3 vx4) GT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.63/4.14	7[label="not (esEsOrdering (primCmpChar vx3 vx4) GT)",fontsize=16,color="burlywood",shape="box"];76[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];7 -> 76[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	76 -> 8[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	8[label="not (esEsOrdering (primCmpChar (Char vx30) vx4) GT)",fontsize=16,color="burlywood",shape="box"];77[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];8 -> 77[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	77 -> 9[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	9[label="not (esEsOrdering (primCmpChar (Char vx30) (Char vx40)) GT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.63/4.14	10[label="not (esEsOrdering (primCmpInt vx30 vx40) GT)",fontsize=16,color="burlywood",shape="box"];78[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 78[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	78 -> 11[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	79[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 79[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	79 -> 12[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	11[label="not (esEsOrdering (primCmpInt (Pos vx300) vx40) GT)",fontsize=16,color="burlywood",shape="box"];80[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];11 -> 80[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	80 -> 13[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	81[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 81[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	81 -> 14[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	12[label="not (esEsOrdering (primCmpInt (Neg vx300) vx40) GT)",fontsize=16,color="burlywood",shape="box"];82[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];12 -> 82[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	82 -> 15[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	83[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 83[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	83 -> 16[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	13[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) vx40) GT)",fontsize=16,color="burlywood",shape="box"];84[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 84[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	84 -> 17[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	85[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 85[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	85 -> 18[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	14[label="not (esEsOrdering (primCmpInt (Pos Zero) vx40) GT)",fontsize=16,color="burlywood",shape="box"];86[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 86[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	86 -> 19[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	87[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 87[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	87 -> 20[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	15[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) vx40) GT)",fontsize=16,color="burlywood",shape="box"];88[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 88[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	88 -> 21[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	89[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 89[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	89 -> 22[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	16[label="not (esEsOrdering (primCmpInt (Neg Zero) vx40) GT)",fontsize=16,color="burlywood",shape="box"];90[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 90[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	90 -> 23[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	91[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 91[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	91 -> 24[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	17[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Pos vx400)) GT)",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3];
9.63/4.14	18[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Neg vx400)) GT)",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3];
9.63/4.14	19[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos vx400)) GT)",fontsize=16,color="burlywood",shape="box"];92[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];19 -> 92[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	92 -> 27[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	93[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 93[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	93 -> 28[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	20[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg vx400)) GT)",fontsize=16,color="burlywood",shape="box"];94[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];20 -> 94[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	94 -> 29[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	95[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 95[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	95 -> 30[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	21[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Pos vx400)) GT)",fontsize=16,color="black",shape="box"];21 -> 31[label="",style="solid", color="black", weight=3];
9.63/4.14	22[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Neg vx400)) GT)",fontsize=16,color="black",shape="box"];22 -> 32[label="",style="solid", color="black", weight=3];
9.63/4.14	23[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos vx400)) GT)",fontsize=16,color="burlywood",shape="box"];96[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 96[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	96 -> 33[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	97[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 97[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	97 -> 34[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	24[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg vx400)) GT)",fontsize=16,color="burlywood",shape="box"];98[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];24 -> 98[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	98 -> 35[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	99[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 99[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	99 -> 36[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	25[label="not (esEsOrdering (primCmpNat (Succ vx3000) vx400) GT)",fontsize=16,color="burlywood",shape="triangle"];100[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 100[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	100 -> 37[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	101[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 101[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	101 -> 38[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	26[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="triangle"];26 -> 39[label="",style="solid", color="black", weight=3];
9.63/4.14	27[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx4000))) GT)",fontsize=16,color="black",shape="box"];27 -> 40[label="",style="solid", color="black", weight=3];
9.63/4.14	28[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) GT)",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3];
9.63/4.14	29[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vx4000))) GT)",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
9.63/4.14	30[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) GT)",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
9.63/4.14	31[label="not (esEsOrdering LT GT)",fontsize=16,color="black",shape="triangle"];31 -> 44[label="",style="solid", color="black", weight=3];
9.63/4.14	32[label="not (esEsOrdering (primCmpNat vx400 (Succ vx3000)) GT)",fontsize=16,color="burlywood",shape="triangle"];102[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];32 -> 102[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	102 -> 45[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	103[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 103[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	103 -> 46[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	33[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx4000))) GT)",fontsize=16,color="black",shape="box"];33 -> 47[label="",style="solid", color="black", weight=3];
9.63/4.14	34[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) GT)",fontsize=16,color="black",shape="box"];34 -> 48[label="",style="solid", color="black", weight=3];
9.63/4.14	35[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vx4000))) GT)",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
9.63/4.14	36[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) GT)",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
9.63/4.14	37[label="not (esEsOrdering (primCmpNat (Succ vx3000) (Succ vx4000)) GT)",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
9.63/4.14	38[label="not (esEsOrdering (primCmpNat (Succ vx3000) Zero) GT)",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
9.63/4.14	39[label="not MyTrue",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
9.63/4.14	40 -> 32[label="",style="dashed", color="red", weight=0];
9.63/4.14	40[label="not (esEsOrdering (primCmpNat Zero (Succ vx4000)) GT)",fontsize=16,color="magenta"];40 -> 54[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	40 -> 55[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	41[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="triangle"];41 -> 56[label="",style="solid", color="black", weight=3];
9.63/4.14	42 -> 26[label="",style="dashed", color="red", weight=0];
9.63/4.14	42[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];43 -> 41[label="",style="dashed", color="red", weight=0];
9.63/4.14	43[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];44[label="not MyFalse",fontsize=16,color="black",shape="triangle"];44 -> 57[label="",style="solid", color="black", weight=3];
9.63/4.14	45[label="not (esEsOrdering (primCmpNat (Succ vx4000) (Succ vx3000)) GT)",fontsize=16,color="black",shape="box"];45 -> 58[label="",style="solid", color="black", weight=3];
9.63/4.14	46[label="not (esEsOrdering (primCmpNat Zero (Succ vx3000)) GT)",fontsize=16,color="black",shape="box"];46 -> 59[label="",style="solid", color="black", weight=3];
9.63/4.14	47 -> 31[label="",style="dashed", color="red", weight=0];
9.63/4.14	47[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];48 -> 41[label="",style="dashed", color="red", weight=0];
9.63/4.14	48[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];49 -> 25[label="",style="dashed", color="red", weight=0];
9.63/4.14	49[label="not (esEsOrdering (primCmpNat (Succ vx4000) Zero) GT)",fontsize=16,color="magenta"];49 -> 60[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	49 -> 61[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	50 -> 41[label="",style="dashed", color="red", weight=0];
9.63/4.14	50[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];51[label="not (esEsOrdering (primCmpNat vx3000 vx4000) GT)",fontsize=16,color="burlywood",shape="triangle"];104[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];51 -> 104[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	104 -> 62[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	105[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 105[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	105 -> 63[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	52 -> 26[label="",style="dashed", color="red", weight=0];
9.63/4.14	52[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];53[label="MyFalse",fontsize=16,color="green",shape="box"];54[label="Zero",fontsize=16,color="green",shape="box"];55[label="vx4000",fontsize=16,color="green",shape="box"];56 -> 44[label="",style="dashed", color="red", weight=0];
9.63/4.14	56[label="not MyFalse",fontsize=16,color="magenta"];57[label="MyTrue",fontsize=16,color="green",shape="box"];58 -> 51[label="",style="dashed", color="red", weight=0];
9.63/4.14	58[label="not (esEsOrdering (primCmpNat vx4000 vx3000) GT)",fontsize=16,color="magenta"];58 -> 64[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	58 -> 65[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	59 -> 31[label="",style="dashed", color="red", weight=0];
9.63/4.14	59[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];60[label="vx4000",fontsize=16,color="green",shape="box"];61[label="Zero",fontsize=16,color="green",shape="box"];62[label="not (esEsOrdering (primCmpNat (Succ vx30000) vx4000) GT)",fontsize=16,color="burlywood",shape="box"];106[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];62 -> 106[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	106 -> 66[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	107[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 107[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	107 -> 67[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	63[label="not (esEsOrdering (primCmpNat Zero vx4000) GT)",fontsize=16,color="burlywood",shape="box"];108[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];63 -> 108[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	108 -> 68[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	109[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 109[label="",style="solid", color="burlywood", weight=9];
9.63/4.14	109 -> 69[label="",style="solid", color="burlywood", weight=3];
9.63/4.14	64[label="vx3000",fontsize=16,color="green",shape="box"];65[label="vx4000",fontsize=16,color="green",shape="box"];66[label="not (esEsOrdering (primCmpNat (Succ vx30000) (Succ vx40000)) GT)",fontsize=16,color="black",shape="box"];66 -> 70[label="",style="solid", color="black", weight=3];
9.63/4.14	67[label="not (esEsOrdering (primCmpNat (Succ vx30000) Zero) GT)",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3];
9.63/4.14	68[label="not (esEsOrdering (primCmpNat Zero (Succ vx40000)) GT)",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
9.63/4.14	69[label="not (esEsOrdering (primCmpNat Zero Zero) GT)",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
9.63/4.14	70 -> 51[label="",style="dashed", color="red", weight=0];
9.63/4.14	70[label="not (esEsOrdering (primCmpNat vx30000 vx40000) GT)",fontsize=16,color="magenta"];70 -> 74[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	70 -> 75[label="",style="dashed", color="magenta", weight=3];
9.63/4.14	71 -> 26[label="",style="dashed", color="red", weight=0];
9.63/4.14	71[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];72 -> 31[label="",style="dashed", color="red", weight=0];
9.63/4.14	72[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];73 -> 41[label="",style="dashed", color="red", weight=0];
9.63/4.14	73[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];74[label="vx40000",fontsize=16,color="green",shape="box"];75[label="vx30000",fontsize=16,color="green",shape="box"];}
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(6)
9.63/4.14	Obligation:
9.63/4.14	Q DP problem:
9.63/4.14	The TRS P consists of the following rules:
9.63/4.14	
9.63/4.14	   new_not(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_not(vx30000, vx40000)
9.63/4.14	
9.63/4.14	R is empty.
9.63/4.14	Q is empty.
9.63/4.14	We have to consider all minimal (P,Q,R)-chains.
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(7) QDPSizeChangeProof (EQUIVALENT)
9.63/4.14	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
9.63/4.14	
9.63/4.14	From the DPs we obtained the following set of size-change graphs:
9.63/4.14	*new_not(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_not(vx30000, vx40000)
9.63/4.14	The graph contains the following edges 1 > 1, 2 > 2
9.63/4.14	
9.63/4.14	
9.63/4.14	----------------------------------------
9.63/4.14	
9.63/4.14	(8)
9.63/4.14	YES
9.63/4.19	EOF