7.79/3.52	YES
9.82/4.04	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.82/4.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.82/4.04	
9.82/4.04	
9.82/4.04	H-Termination with start terms of the given HASKELL could be proven:
9.82/4.04	
9.82/4.04	(0) HASKELL
9.82/4.04	(1) BR [EQUIVALENT, 0 ms]
9.82/4.04	(2) HASKELL
9.82/4.04	(3) COR [EQUIVALENT, 0 ms]
9.82/4.04	(4) HASKELL
9.82/4.04	(5) Narrow [SOUND, 0 ms]
9.82/4.04	(6) QDP
9.82/4.04	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.82/4.04	(8) YES
9.82/4.04	
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(0)
9.82/4.04	Obligation:
9.82/4.04	mainModule Main 
9.82/4.04	module Main where {
9.82/4.04	import qualified Prelude;
9.82/4.04	data Main.Char = Char MyInt ;
9.82/4.04	
9.82/4.04	data MyBool = MyTrue  | MyFalse ;
9.82/4.04	
9.82/4.04	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.82/4.04	
9.82/4.04	data Main.Nat = Succ Main.Nat  | Zero ;
9.82/4.04	
9.82/4.04	data Ordering = LT  | EQ  | GT ;
9.82/4.04	
9.82/4.04	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	compareChar = primCmpChar;
9.82/4.04	
9.82/4.04	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	esEsOrdering LT LT = MyTrue;
9.82/4.04	esEsOrdering LT EQ = MyFalse;
9.82/4.04	esEsOrdering LT GT = MyFalse;
9.82/4.04	esEsOrdering EQ LT = MyFalse;
9.82/4.04	esEsOrdering EQ EQ = MyTrue;
9.82/4.04	esEsOrdering EQ GT = MyFalse;
9.82/4.04	esEsOrdering GT LT = MyFalse;
9.82/4.04	esEsOrdering GT EQ = MyFalse;
9.82/4.04	esEsOrdering GT GT = MyTrue;
9.82/4.04	
9.82/4.04	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	fsEsOrdering x y = not (esEsOrdering x y);
9.82/4.04	
9.82/4.04	gtEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.82/4.04	gtEsChar x y = fsEsOrdering (compareChar x y) LT;
9.82/4.04	
9.82/4.04	not :: MyBool  ->  MyBool;
9.82/4.04	not MyTrue = MyFalse;
9.82/4.04	not MyFalse = MyTrue;
9.82/4.04	
9.82/4.04	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.82/4.04	
9.82/4.04	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.82/4.04	
9.82/4.04	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.82/4.04	primCmpNat Main.Zero Main.Zero = EQ;
9.82/4.04	primCmpNat Main.Zero (Main.Succ y) = LT;
9.82/4.04	primCmpNat (Main.Succ x) Main.Zero = GT;
9.82/4.04	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.82/4.04	
9.82/4.04	}
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(1) BR (EQUIVALENT)
9.82/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(2)
9.82/4.04	Obligation:
9.82/4.04	mainModule Main 
9.82/4.04	module Main where {
9.82/4.04	import qualified Prelude;
9.82/4.04	data Main.Char = Char MyInt ;
9.82/4.04	
9.82/4.04	data MyBool = MyTrue  | MyFalse ;
9.82/4.04	
9.82/4.04	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.82/4.04	
9.82/4.04	data Main.Nat = Succ Main.Nat  | Zero ;
9.82/4.04	
9.82/4.04	data Ordering = LT  | EQ  | GT ;
9.82/4.04	
9.82/4.04	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	compareChar = primCmpChar;
9.82/4.04	
9.82/4.04	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	esEsOrdering LT LT = MyTrue;
9.82/4.04	esEsOrdering LT EQ = MyFalse;
9.82/4.04	esEsOrdering LT GT = MyFalse;
9.82/4.04	esEsOrdering EQ LT = MyFalse;
9.82/4.04	esEsOrdering EQ EQ = MyTrue;
9.82/4.04	esEsOrdering EQ GT = MyFalse;
9.82/4.04	esEsOrdering GT LT = MyFalse;
9.82/4.04	esEsOrdering GT EQ = MyFalse;
9.82/4.04	esEsOrdering GT GT = MyTrue;
9.82/4.04	
9.82/4.04	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	fsEsOrdering x y = not (esEsOrdering x y);
9.82/4.04	
9.82/4.04	gtEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.82/4.04	gtEsChar x y = fsEsOrdering (compareChar x y) LT;
9.82/4.04	
9.82/4.04	not :: MyBool  ->  MyBool;
9.82/4.04	not MyTrue = MyFalse;
9.82/4.04	not MyFalse = MyTrue;
9.82/4.04	
9.82/4.04	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.82/4.04	
9.82/4.04	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.82/4.04	
9.82/4.04	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.82/4.04	primCmpNat Main.Zero Main.Zero = EQ;
9.82/4.04	primCmpNat Main.Zero (Main.Succ y) = LT;
9.82/4.04	primCmpNat (Main.Succ x) Main.Zero = GT;
9.82/4.04	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.82/4.04	
9.82/4.04	}
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(3) COR (EQUIVALENT)
9.82/4.04	Cond Reductions:
9.82/4.04	The following Function with conditions
9.82/4.04	"undefined |Falseundefined;
9.82/4.04	"
9.82/4.04	is transformed to
9.82/4.04	"undefined  = undefined1;
9.82/4.04	"
9.82/4.04	"undefined0 True = undefined;
9.82/4.04	"
9.82/4.04	"undefined1  = undefined0 False;
9.82/4.04	"
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(4)
9.82/4.04	Obligation:
9.82/4.04	mainModule Main 
9.82/4.04	module Main where {
9.82/4.04	import qualified Prelude;
9.82/4.04	data Main.Char = Char MyInt ;
9.82/4.04	
9.82/4.04	data MyBool = MyTrue  | MyFalse ;
9.82/4.04	
9.82/4.04	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.82/4.04	
9.82/4.04	data Main.Nat = Succ Main.Nat  | Zero ;
9.82/4.04	
9.82/4.04	data Ordering = LT  | EQ  | GT ;
9.82/4.04	
9.82/4.04	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	compareChar = primCmpChar;
9.82/4.04	
9.82/4.04	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	esEsOrdering LT LT = MyTrue;
9.82/4.04	esEsOrdering LT EQ = MyFalse;
9.82/4.04	esEsOrdering LT GT = MyFalse;
9.82/4.04	esEsOrdering EQ LT = MyFalse;
9.82/4.04	esEsOrdering EQ EQ = MyTrue;
9.82/4.04	esEsOrdering EQ GT = MyFalse;
9.82/4.04	esEsOrdering GT LT = MyFalse;
9.82/4.04	esEsOrdering GT EQ = MyFalse;
9.82/4.04	esEsOrdering GT GT = MyTrue;
9.82/4.04	
9.82/4.04	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.82/4.04	fsEsOrdering x y = not (esEsOrdering x y);
9.82/4.04	
9.82/4.04	gtEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.82/4.04	gtEsChar x y = fsEsOrdering (compareChar x y) LT;
9.82/4.04	
9.82/4.04	not :: MyBool  ->  MyBool;
9.82/4.04	not MyTrue = MyFalse;
9.82/4.04	not MyFalse = MyTrue;
9.82/4.04	
9.82/4.04	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.82/4.04	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.82/4.04	
9.82/4.04	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.82/4.04	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.82/4.04	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.82/4.04	
9.82/4.04	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.82/4.04	primCmpNat Main.Zero Main.Zero = EQ;
9.82/4.04	primCmpNat Main.Zero (Main.Succ y) = LT;
9.82/4.04	primCmpNat (Main.Succ x) Main.Zero = GT;
9.82/4.04	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.82/4.04	
9.82/4.04	}
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(5) Narrow (SOUND)
9.82/4.04	Haskell To QDPs
9.82/4.04	
9.82/4.04	digraph dp_graph {
9.82/4.04	node [outthreshold=100, inthreshold=100];1[label="gtEsChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.82/4.04	3[label="gtEsChar vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.82/4.04	4[label="gtEsChar vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.82/4.04	5[label="fsEsOrdering (compareChar vx3 vx4) LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.82/4.04	6[label="not (esEsOrdering (compareChar vx3 vx4) LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.82/4.04	7[label="not (esEsOrdering (primCmpChar vx3 vx4) LT)",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];
9.82/4.04	76 -> 8[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	8[label="not (esEsOrdering (primCmpChar (Char vx30) vx4) LT)",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];
9.82/4.04	77 -> 9[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	9[label="not (esEsOrdering (primCmpChar (Char vx30) (Char vx40)) LT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.82/4.04	10[label="not (esEsOrdering (primCmpInt vx30 vx40) LT)",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];
9.82/4.04	78 -> 11[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	79[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 79[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	79 -> 12[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	11[label="not (esEsOrdering (primCmpInt (Pos vx300) vx40) LT)",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];
9.82/4.04	80 -> 13[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	81[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 81[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	81 -> 14[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	12[label="not (esEsOrdering (primCmpInt (Neg vx300) vx40) LT)",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];
9.82/4.04	82 -> 15[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	83[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 83[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	83 -> 16[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	13[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) vx40) LT)",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];
9.82/4.04	84 -> 17[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	85[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 85[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	85 -> 18[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	14[label="not (esEsOrdering (primCmpInt (Pos Zero) vx40) LT)",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];
9.82/4.04	86 -> 19[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	87[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 87[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	87 -> 20[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	15[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) vx40) LT)",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];
9.82/4.04	88 -> 21[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	89[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];15 -> 89[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	89 -> 22[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	16[label="not (esEsOrdering (primCmpInt (Neg Zero) vx40) LT)",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];
9.82/4.04	90 -> 23[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	91[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];16 -> 91[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	91 -> 24[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	17[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Pos vx400)) LT)",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3];
9.82/4.04	18[label="not (esEsOrdering (primCmpInt (Pos (Succ vx3000)) (Neg vx400)) LT)",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3];
9.82/4.04	19[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos vx400)) LT)",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];
9.82/4.04	92 -> 27[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	93[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 93[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	93 -> 28[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	20[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg vx400)) LT)",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];
9.82/4.04	94 -> 29[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	95[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 95[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	95 -> 30[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	21[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Pos vx400)) LT)",fontsize=16,color="black",shape="box"];21 -> 31[label="",style="solid", color="black", weight=3];
9.82/4.04	22[label="not (esEsOrdering (primCmpInt (Neg (Succ vx3000)) (Neg vx400)) LT)",fontsize=16,color="black",shape="box"];22 -> 32[label="",style="solid", color="black", weight=3];
9.82/4.04	23[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos vx400)) LT)",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];
9.82/4.04	96 -> 33[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	97[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 97[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	97 -> 34[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	24[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg vx400)) LT)",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];
9.82/4.04	98 -> 35[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	99[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 99[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	99 -> 36[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	25[label="not (esEsOrdering (primCmpNat (Succ vx3000) vx400) LT)",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];
9.82/4.04	100 -> 37[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	101[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 101[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	101 -> 38[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	26[label="not (esEsOrdering GT LT)",fontsize=16,color="black",shape="triangle"];26 -> 39[label="",style="solid", color="black", weight=3];
9.82/4.04	27[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vx4000))) LT)",fontsize=16,color="black",shape="box"];27 -> 40[label="",style="solid", color="black", weight=3];
9.82/4.04	28[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3];
9.82/4.04	29[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vx4000))) LT)",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
9.82/4.04	30[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
9.82/4.04	31[label="not (esEsOrdering LT LT)",fontsize=16,color="black",shape="triangle"];31 -> 44[label="",style="solid", color="black", weight=3];
9.82/4.04	32[label="not (esEsOrdering (primCmpNat vx400 (Succ vx3000)) LT)",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];
9.82/4.04	102 -> 45[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	103[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 103[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	103 -> 46[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	33[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vx4000))) LT)",fontsize=16,color="black",shape="box"];33 -> 47[label="",style="solid", color="black", weight=3];
9.82/4.04	34[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];34 -> 48[label="",style="solid", color="black", weight=3];
9.82/4.04	35[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vx4000))) LT)",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
9.82/4.04	36[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
9.82/4.04	37[label="not (esEsOrdering (primCmpNat (Succ vx3000) (Succ vx4000)) LT)",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
9.82/4.04	38[label="not (esEsOrdering (primCmpNat (Succ vx3000) Zero) LT)",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
9.82/4.04	39[label="not MyFalse",fontsize=16,color="black",shape="triangle"];39 -> 53[label="",style="solid", color="black", weight=3];
9.82/4.04	40 -> 32[label="",style="dashed", color="red", weight=0];
9.82/4.04	40[label="not (esEsOrdering (primCmpNat Zero (Succ vx4000)) LT)",fontsize=16,color="magenta"];40 -> 54[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	40 -> 55[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	41[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="triangle"];41 -> 56[label="",style="solid", color="black", weight=3];
9.82/4.04	42 -> 26[label="",style="dashed", color="red", weight=0];
9.82/4.04	42[label="not (esEsOrdering GT LT)",fontsize=16,color="magenta"];43 -> 41[label="",style="dashed", color="red", weight=0];
9.82/4.04	43[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];44[label="not MyTrue",fontsize=16,color="black",shape="box"];44 -> 57[label="",style="solid", color="black", weight=3];
9.82/4.04	45[label="not (esEsOrdering (primCmpNat (Succ vx4000) (Succ vx3000)) LT)",fontsize=16,color="black",shape="box"];45 -> 58[label="",style="solid", color="black", weight=3];
9.82/4.04	46[label="not (esEsOrdering (primCmpNat Zero (Succ vx3000)) LT)",fontsize=16,color="black",shape="box"];46 -> 59[label="",style="solid", color="black", weight=3];
9.82/4.04	47 -> 31[label="",style="dashed", color="red", weight=0];
9.82/4.04	47[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];48 -> 41[label="",style="dashed", color="red", weight=0];
9.82/4.04	48[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];49 -> 25[label="",style="dashed", color="red", weight=0];
9.82/4.04	49[label="not (esEsOrdering (primCmpNat (Succ vx4000) Zero) LT)",fontsize=16,color="magenta"];49 -> 60[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	49 -> 61[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	50 -> 41[label="",style="dashed", color="red", weight=0];
9.82/4.04	50[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];51[label="not (esEsOrdering (primCmpNat vx3000 vx4000) LT)",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];
9.82/4.04	104 -> 62[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	105[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 105[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	105 -> 63[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	52 -> 26[label="",style="dashed", color="red", weight=0];
9.82/4.04	52[label="not (esEsOrdering GT LT)",fontsize=16,color="magenta"];53[label="MyTrue",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 -> 39[label="",style="dashed", color="red", weight=0];
9.82/4.04	56[label="not MyFalse",fontsize=16,color="magenta"];57[label="MyFalse",fontsize=16,color="green",shape="box"];58 -> 51[label="",style="dashed", color="red", weight=0];
9.82/4.04	58[label="not (esEsOrdering (primCmpNat vx4000 vx3000) LT)",fontsize=16,color="magenta"];58 -> 64[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	58 -> 65[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	59 -> 31[label="",style="dashed", color="red", weight=0];
9.82/4.04	59[label="not (esEsOrdering LT LT)",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) LT)",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];
9.82/4.04	106 -> 66[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	107[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 107[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	107 -> 67[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	63[label="not (esEsOrdering (primCmpNat Zero vx4000) LT)",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];
9.82/4.04	108 -> 68[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	109[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];63 -> 109[label="",style="solid", color="burlywood", weight=9];
9.82/4.04	109 -> 69[label="",style="solid", color="burlywood", weight=3];
9.82/4.04	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)) LT)",fontsize=16,color="black",shape="box"];66 -> 70[label="",style="solid", color="black", weight=3];
9.82/4.04	67[label="not (esEsOrdering (primCmpNat (Succ vx30000) Zero) LT)",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3];
9.82/4.04	68[label="not (esEsOrdering (primCmpNat Zero (Succ vx40000)) LT)",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
9.82/4.04	69[label="not (esEsOrdering (primCmpNat Zero Zero) LT)",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
9.82/4.04	70 -> 51[label="",style="dashed", color="red", weight=0];
9.82/4.04	70[label="not (esEsOrdering (primCmpNat vx30000 vx40000) LT)",fontsize=16,color="magenta"];70 -> 74[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	70 -> 75[label="",style="dashed", color="magenta", weight=3];
9.82/4.04	71 -> 26[label="",style="dashed", color="red", weight=0];
9.82/4.04	71[label="not (esEsOrdering GT LT)",fontsize=16,color="magenta"];72 -> 31[label="",style="dashed", color="red", weight=0];
9.82/4.04	72[label="not (esEsOrdering LT LT)",fontsize=16,color="magenta"];73 -> 41[label="",style="dashed", color="red", weight=0];
9.82/4.04	73[label="not (esEsOrdering EQ LT)",fontsize=16,color="magenta"];74[label="vx40000",fontsize=16,color="green",shape="box"];75[label="vx30000",fontsize=16,color="green",shape="box"];}
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(6)
9.82/4.04	Obligation:
9.82/4.04	Q DP problem:
9.82/4.04	The TRS P consists of the following rules:
9.82/4.04	
9.82/4.04	   new_not(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_not(vx30000, vx40000)
9.82/4.04	
9.82/4.04	R is empty.
9.82/4.04	Q is empty.
9.82/4.04	We have to consider all minimal (P,Q,R)-chains.
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(7) QDPSizeChangeProof (EQUIVALENT)
9.82/4.04	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. 
9.82/4.04	
9.82/4.04	From the DPs we obtained the following set of size-change graphs:
9.82/4.04	*new_not(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_not(vx30000, vx40000)
9.82/4.04	The graph contains the following edges 1 > 1, 2 > 2
9.82/4.04	
9.82/4.04	
9.82/4.04	----------------------------------------
9.82/4.04	
9.82/4.04	(8)
9.82/4.04	YES
9.82/4.08	EOF