7.81/3.49	YES
9.30/4.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.30/4.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.30/4.01	
9.30/4.01	
9.30/4.01	H-Termination with start terms of the given HASKELL could be proven:
9.30/4.01	
9.30/4.01	(0) HASKELL
9.30/4.01	(1) BR [EQUIVALENT, 0 ms]
9.30/4.01	(2) HASKELL
9.30/4.01	(3) COR [EQUIVALENT, 0 ms]
9.30/4.01	(4) HASKELL
9.30/4.01	(5) Narrow [SOUND, 0 ms]
9.30/4.01	(6) QDP
9.30/4.01	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.30/4.01	(8) YES
9.30/4.01	
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(0)
9.30/4.01	Obligation:
9.30/4.01	mainModule Main 
9.30/4.01	module Main where {
9.30/4.01	import qualified Prelude;
9.30/4.01	data Main.Char = Char MyInt ;
9.30/4.01	
9.30/4.01	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.30/4.01	
9.30/4.01	data Main.Nat = Succ Main.Nat  | Zero ;
9.30/4.01	
9.30/4.01	data Ordering = LT  | EQ  | GT ;
9.30/4.01	
9.30/4.01	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	compareChar = primCmpChar;
9.30/4.01	
9.30/4.01	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.30/4.01	
9.30/4.01	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.30/4.01	
9.30/4.01	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.30/4.01	primCmpNat Main.Zero Main.Zero = EQ;
9.30/4.01	primCmpNat Main.Zero (Main.Succ y) = LT;
9.30/4.01	primCmpNat (Main.Succ x) Main.Zero = GT;
9.30/4.01	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.30/4.01	
9.30/4.01	}
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(1) BR (EQUIVALENT)
9.30/4.01	Replaced joker patterns by fresh variables and removed binding patterns.
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(2)
9.30/4.01	Obligation:
9.30/4.01	mainModule Main 
9.30/4.01	module Main where {
9.30/4.01	import qualified Prelude;
9.30/4.01	data Main.Char = Char MyInt ;
9.30/4.01	
9.30/4.01	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.30/4.01	
9.30/4.01	data Main.Nat = Succ Main.Nat  | Zero ;
9.30/4.01	
9.30/4.01	data Ordering = LT  | EQ  | GT ;
9.30/4.01	
9.30/4.01	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	compareChar = primCmpChar;
9.30/4.01	
9.30/4.01	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.30/4.01	
9.30/4.01	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.30/4.01	
9.30/4.01	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.30/4.01	primCmpNat Main.Zero Main.Zero = EQ;
9.30/4.01	primCmpNat Main.Zero (Main.Succ y) = LT;
9.30/4.01	primCmpNat (Main.Succ x) Main.Zero = GT;
9.30/4.01	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.30/4.01	
9.30/4.01	}
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(3) COR (EQUIVALENT)
9.30/4.01	Cond Reductions:
9.30/4.01	The following Function with conditions
9.30/4.01	"undefined |Falseundefined;
9.30/4.01	"
9.30/4.01	is transformed to
9.30/4.01	"undefined  = undefined1;
9.30/4.01	"
9.30/4.01	"undefined0 True = undefined;
9.30/4.01	"
9.30/4.01	"undefined1  = undefined0 False;
9.30/4.01	"
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(4)
9.30/4.01	Obligation:
9.30/4.01	mainModule Main 
9.30/4.01	module Main where {
9.30/4.01	import qualified Prelude;
9.30/4.01	data Main.Char = Char MyInt ;
9.30/4.01	
9.30/4.01	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.30/4.01	
9.30/4.01	data Main.Nat = Succ Main.Nat  | Zero ;
9.30/4.01	
9.30/4.01	data Ordering = LT  | EQ  | GT ;
9.30/4.01	
9.30/4.01	compareChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	compareChar = primCmpChar;
9.30/4.01	
9.30/4.01	primCmpChar :: Main.Char  ->  Main.Char  ->  Ordering;
9.30/4.01	primCmpChar (Main.Char x) (Main.Char y) = primCmpInt x y;
9.30/4.01	
9.30/4.01	primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
9.30/4.01	primCmpInt (Main.Pos x) (Main.Neg y) = GT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Pos y) = LT;
9.30/4.01	primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;
9.30/4.01	
9.30/4.01	primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
9.30/4.01	primCmpNat Main.Zero Main.Zero = EQ;
9.30/4.01	primCmpNat Main.Zero (Main.Succ y) = LT;
9.30/4.01	primCmpNat (Main.Succ x) Main.Zero = GT;
9.30/4.01	primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;
9.30/4.01	
9.30/4.01	}
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(5) Narrow (SOUND)
9.30/4.01	Haskell To QDPs
9.30/4.01	
9.30/4.01	digraph dp_graph {
9.30/4.01	node [outthreshold=100, inthreshold=100];1[label="compareChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.30/4.01	3[label="compareChar vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.30/4.01	4[label="compareChar vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.30/4.01	5[label="primCmpChar vx3 vx4",fontsize=16,color="burlywood",shape="box"];69[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 69[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	69 -> 6[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	6[label="primCmpChar (Char vx30) vx4",fontsize=16,color="burlywood",shape="box"];70[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 70[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	70 -> 7[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	7[label="primCmpChar (Char vx30) (Char vx40)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.30/4.01	8[label="primCmpInt vx30 vx40",fontsize=16,color="burlywood",shape="box"];71[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 71[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	71 -> 9[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	72[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 72[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	72 -> 10[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	9[label="primCmpInt (Pos vx300) vx40",fontsize=16,color="burlywood",shape="box"];73[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];9 -> 73[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	73 -> 11[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	74[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 74[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	74 -> 12[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	10[label="primCmpInt (Neg vx300) vx40",fontsize=16,color="burlywood",shape="box"];75[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];10 -> 75[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	75 -> 13[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	76[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 76[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	76 -> 14[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	11[label="primCmpInt (Pos (Succ vx3000)) vx40",fontsize=16,color="burlywood",shape="box"];77[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];11 -> 77[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	77 -> 15[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	78[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];11 -> 78[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	78 -> 16[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	12[label="primCmpInt (Pos Zero) vx40",fontsize=16,color="burlywood",shape="box"];79[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];12 -> 79[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	79 -> 17[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	80[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];12 -> 80[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	80 -> 18[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	13[label="primCmpInt (Neg (Succ vx3000)) vx40",fontsize=16,color="burlywood",shape="box"];81[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 81[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	81 -> 19[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	82[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 82[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	82 -> 20[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	14[label="primCmpInt (Neg Zero) vx40",fontsize=16,color="burlywood",shape="box"];83[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 83[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	83 -> 21[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	84[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 84[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	84 -> 22[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	15[label="primCmpInt (Pos (Succ vx3000)) (Pos vx400)",fontsize=16,color="black",shape="box"];15 -> 23[label="",style="solid", color="black", weight=3];
9.30/4.01	16[label="primCmpInt (Pos (Succ vx3000)) (Neg vx400)",fontsize=16,color="black",shape="box"];16 -> 24[label="",style="solid", color="black", weight=3];
9.30/4.01	17[label="primCmpInt (Pos Zero) (Pos vx400)",fontsize=16,color="burlywood",shape="box"];85[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 85[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	85 -> 25[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	86[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 86[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	86 -> 26[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	18[label="primCmpInt (Pos Zero) (Neg vx400)",fontsize=16,color="burlywood",shape="box"];87[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 87[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	87 -> 27[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	88[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 88[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	88 -> 28[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	19[label="primCmpInt (Neg (Succ vx3000)) (Pos vx400)",fontsize=16,color="black",shape="box"];19 -> 29[label="",style="solid", color="black", weight=3];
9.30/4.01	20[label="primCmpInt (Neg (Succ vx3000)) (Neg vx400)",fontsize=16,color="black",shape="box"];20 -> 30[label="",style="solid", color="black", weight=3];
9.30/4.01	21[label="primCmpInt (Neg Zero) (Pos vx400)",fontsize=16,color="burlywood",shape="box"];89[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 89[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	89 -> 31[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	90[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 90[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	90 -> 32[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	22[label="primCmpInt (Neg Zero) (Neg vx400)",fontsize=16,color="burlywood",shape="box"];91[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 91[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	91 -> 33[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	92[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 92[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	92 -> 34[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	23[label="primCmpNat (Succ vx3000) vx400",fontsize=16,color="burlywood",shape="triangle"];93[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 93[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	93 -> 35[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	94[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 94[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	94 -> 36[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	24[label="GT",fontsize=16,color="green",shape="box"];25[label="primCmpInt (Pos Zero) (Pos (Succ vx4000))",fontsize=16,color="black",shape="box"];25 -> 37[label="",style="solid", color="black", weight=3];
9.30/4.01	26[label="primCmpInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];26 -> 38[label="",style="solid", color="black", weight=3];
9.30/4.01	27[label="primCmpInt (Pos Zero) (Neg (Succ vx4000))",fontsize=16,color="black",shape="box"];27 -> 39[label="",style="solid", color="black", weight=3];
9.30/4.01	28[label="primCmpInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];28 -> 40[label="",style="solid", color="black", weight=3];
9.30/4.01	29[label="LT",fontsize=16,color="green",shape="box"];30[label="primCmpNat vx400 (Succ vx3000)",fontsize=16,color="burlywood",shape="triangle"];95[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];30 -> 95[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	95 -> 41[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	96[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];30 -> 96[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	96 -> 42[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	31[label="primCmpInt (Neg Zero) (Pos (Succ vx4000))",fontsize=16,color="black",shape="box"];31 -> 43[label="",style="solid", color="black", weight=3];
9.30/4.01	32[label="primCmpInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];32 -> 44[label="",style="solid", color="black", weight=3];
9.30/4.01	33[label="primCmpInt (Neg Zero) (Neg (Succ vx4000))",fontsize=16,color="black",shape="box"];33 -> 45[label="",style="solid", color="black", weight=3];
9.30/4.01	34[label="primCmpInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];34 -> 46[label="",style="solid", color="black", weight=3];
9.30/4.01	35[label="primCmpNat (Succ vx3000) (Succ vx4000)",fontsize=16,color="black",shape="box"];35 -> 47[label="",style="solid", color="black", weight=3];
9.30/4.01	36[label="primCmpNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];36 -> 48[label="",style="solid", color="black", weight=3];
9.30/4.01	37 -> 30[label="",style="dashed", color="red", weight=0];
9.30/4.01	37[label="primCmpNat Zero (Succ vx4000)",fontsize=16,color="magenta"];37 -> 49[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	37 -> 50[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	38[label="EQ",fontsize=16,color="green",shape="box"];39[label="GT",fontsize=16,color="green",shape="box"];40[label="EQ",fontsize=16,color="green",shape="box"];41[label="primCmpNat (Succ vx4000) (Succ vx3000)",fontsize=16,color="black",shape="box"];41 -> 51[label="",style="solid", color="black", weight=3];
9.30/4.01	42[label="primCmpNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];42 -> 52[label="",style="solid", color="black", weight=3];
9.30/4.01	43[label="LT",fontsize=16,color="green",shape="box"];44[label="EQ",fontsize=16,color="green",shape="box"];45 -> 23[label="",style="dashed", color="red", weight=0];
9.30/4.01	45[label="primCmpNat (Succ vx4000) Zero",fontsize=16,color="magenta"];45 -> 53[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	45 -> 54[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	46[label="EQ",fontsize=16,color="green",shape="box"];47[label="primCmpNat vx3000 vx4000",fontsize=16,color="burlywood",shape="triangle"];97[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];47 -> 97[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	97 -> 55[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	98[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 98[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	98 -> 56[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	48[label="GT",fontsize=16,color="green",shape="box"];49[label="Zero",fontsize=16,color="green",shape="box"];50[label="vx4000",fontsize=16,color="green",shape="box"];51 -> 47[label="",style="dashed", color="red", weight=0];
9.30/4.01	51[label="primCmpNat vx4000 vx3000",fontsize=16,color="magenta"];51 -> 57[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	51 -> 58[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	52[label="LT",fontsize=16,color="green",shape="box"];53[label="Zero",fontsize=16,color="green",shape="box"];54[label="vx4000",fontsize=16,color="green",shape="box"];55[label="primCmpNat (Succ vx30000) vx4000",fontsize=16,color="burlywood",shape="box"];99[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];55 -> 99[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	99 -> 59[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	100[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 100[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	100 -> 60[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	56[label="primCmpNat Zero vx4000",fontsize=16,color="burlywood",shape="box"];101[label="vx4000/Succ vx40000",fontsize=10,color="white",style="solid",shape="box"];56 -> 101[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	101 -> 61[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	102[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 102[label="",style="solid", color="burlywood", weight=9];
9.30/4.01	102 -> 62[label="",style="solid", color="burlywood", weight=3];
9.30/4.01	57[label="vx3000",fontsize=16,color="green",shape="box"];58[label="vx4000",fontsize=16,color="green",shape="box"];59[label="primCmpNat (Succ vx30000) (Succ vx40000)",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
9.30/4.01	60[label="primCmpNat (Succ vx30000) Zero",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
9.30/4.01	61[label="primCmpNat Zero (Succ vx40000)",fontsize=16,color="black",shape="box"];61 -> 65[label="",style="solid", color="black", weight=3];
9.30/4.01	62[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];62 -> 66[label="",style="solid", color="black", weight=3];
9.30/4.01	63 -> 47[label="",style="dashed", color="red", weight=0];
9.30/4.01	63[label="primCmpNat vx30000 vx40000",fontsize=16,color="magenta"];63 -> 67[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	63 -> 68[label="",style="dashed", color="magenta", weight=3];
9.30/4.01	64[label="GT",fontsize=16,color="green",shape="box"];65[label="LT",fontsize=16,color="green",shape="box"];66[label="EQ",fontsize=16,color="green",shape="box"];67[label="vx40000",fontsize=16,color="green",shape="box"];68[label="vx30000",fontsize=16,color="green",shape="box"];}
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(6)
9.30/4.01	Obligation:
9.30/4.01	Q DP problem:
9.30/4.01	The TRS P consists of the following rules:
9.30/4.01	
9.30/4.01	   new_primCmpNat(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_primCmpNat(vx30000, vx40000)
9.30/4.01	
9.30/4.01	R is empty.
9.30/4.01	Q is empty.
9.30/4.01	We have to consider all minimal (P,Q,R)-chains.
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(7) QDPSizeChangeProof (EQUIVALENT)
9.30/4.01	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. 
9.30/4.01	
9.30/4.01	From the DPs we obtained the following set of size-change graphs:
9.30/4.01	*new_primCmpNat(Main.Succ(vx30000), Main.Succ(vx40000)) -> new_primCmpNat(vx30000, vx40000)
9.30/4.01	The graph contains the following edges 1 > 1, 2 > 2
9.30/4.01	
9.30/4.01	
9.30/4.01	----------------------------------------
9.30/4.01	
9.30/4.01	(8)
9.30/4.01	YES
9.61/4.06	EOF