7.97/3.65	YES
9.51/4.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.51/4.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.51/4.17	
9.51/4.17	
9.51/4.17	H-Termination with start terms of the given HASKELL could be proven:
9.51/4.17	
9.51/4.17	(0) HASKELL
9.51/4.17	(1) BR [EQUIVALENT, 0 ms]
9.51/4.17	(2) HASKELL
9.51/4.17	(3) COR [EQUIVALENT, 0 ms]
9.51/4.17	(4) HASKELL
9.51/4.17	(5) Narrow [SOUND, 0 ms]
9.51/4.17	(6) QDP
9.51/4.17	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.51/4.17	(8) YES
9.51/4.17	
9.51/4.17	
9.51/4.17	----------------------------------------
9.51/4.17	
9.51/4.17	(0)
9.51/4.17	Obligation:
9.51/4.17	mainModule Main 
9.51/4.17	module Main where {
9.51/4.17	import qualified Prelude;
9.51/4.17	data Main.Char = Char MyInt ;
9.51/4.17	
9.51/4.17	data MyBool = MyTrue  | MyFalse ;
9.51/4.17	
9.51/4.17	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.51/4.17	
9.51/4.17	data Main.Nat = Succ Main.Nat  | Zero ;
9.51/4.17	
9.51/4.17	esEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.17	esEsChar = primEqChar;
9.51/4.17	
9.51/4.17	primEqChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.17	primEqChar (Main.Char x) (Main.Char y) = primEqInt x y;
9.51/4.17	
9.51/4.17	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.51/4.17	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.51/4.17	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt vv vw = MyFalse;
9.51/4.18	
9.51/4.18	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.51/4.18	primEqNat Main.Zero Main.Zero = MyTrue;
9.51/4.18	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.51/4.18	
9.51/4.18	}
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(1) BR (EQUIVALENT)
9.51/4.18	Replaced joker patterns by fresh variables and removed binding patterns.
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(2)
9.51/4.18	Obligation:
9.51/4.18	mainModule Main 
9.51/4.18	module Main where {
9.51/4.18	import qualified Prelude;
9.51/4.18	data Main.Char = Char MyInt ;
9.51/4.18	
9.51/4.18	data MyBool = MyTrue  | MyFalse ;
9.51/4.18	
9.51/4.18	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.51/4.18	
9.51/4.18	data Main.Nat = Succ Main.Nat  | Zero ;
9.51/4.18	
9.51/4.18	esEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.18	esEsChar = primEqChar;
9.51/4.18	
9.51/4.18	primEqChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.18	primEqChar (Main.Char x) (Main.Char y) = primEqInt x y;
9.51/4.18	
9.51/4.18	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.51/4.18	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.51/4.18	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt vv vw = MyFalse;
9.51/4.18	
9.51/4.18	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.51/4.18	primEqNat Main.Zero Main.Zero = MyTrue;
9.51/4.18	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.51/4.18	
9.51/4.18	}
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(3) COR (EQUIVALENT)
9.51/4.18	Cond Reductions:
9.51/4.18	The following Function with conditions
9.51/4.18	"undefined |Falseundefined;
9.51/4.18	"
9.51/4.18	is transformed to
9.51/4.18	"undefined  = undefined1;
9.51/4.18	"
9.51/4.18	"undefined0 True = undefined;
9.51/4.18	"
9.51/4.18	"undefined1  = undefined0 False;
9.51/4.18	"
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(4)
9.51/4.18	Obligation:
9.51/4.18	mainModule Main 
9.51/4.18	module Main where {
9.51/4.18	import qualified Prelude;
9.51/4.18	data Main.Char = Char MyInt ;
9.51/4.18	
9.51/4.18	data MyBool = MyTrue  | MyFalse ;
9.51/4.18	
9.51/4.18	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.51/4.18	
9.51/4.18	data Main.Nat = Succ Main.Nat  | Zero ;
9.51/4.18	
9.51/4.18	esEsChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.18	esEsChar = primEqChar;
9.51/4.18	
9.51/4.18	primEqChar :: Main.Char  ->  Main.Char  ->  MyBool;
9.51/4.18	primEqChar (Main.Char x) (Main.Char y) = primEqInt x y;
9.51/4.18	
9.51/4.18	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.51/4.18	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.51/4.18	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.51/4.18	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.51/4.18	primEqInt vv vw = MyFalse;
9.51/4.18	
9.51/4.18	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.51/4.18	primEqNat Main.Zero Main.Zero = MyTrue;
9.51/4.18	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.51/4.18	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.51/4.18	
9.51/4.18	}
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(5) Narrow (SOUND)
9.51/4.18	Haskell To QDPs
9.51/4.18	
9.51/4.18	digraph dp_graph {
9.51/4.18	node [outthreshold=100, inthreshold=100];1[label="esEsChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.51/4.18	3[label="esEsChar vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.51/4.18	4[label="esEsChar vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.51/4.18	5[label="primEqChar vz3 vz4",fontsize=16,color="burlywood",shape="box"];63[label="vz3/Char vz30",fontsize=10,color="white",style="solid",shape="box"];5 -> 63[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	63 -> 6[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	6[label="primEqChar (Char vz30) vz4",fontsize=16,color="burlywood",shape="box"];64[label="vz4/Char vz40",fontsize=10,color="white",style="solid",shape="box"];6 -> 64[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	64 -> 7[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	7[label="primEqChar (Char vz30) (Char vz40)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.51/4.18	8[label="primEqInt vz30 vz40",fontsize=16,color="burlywood",shape="box"];65[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 65[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	65 -> 9[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	66[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 66[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	66 -> 10[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	9[label="primEqInt (Pos vz300) vz40",fontsize=16,color="burlywood",shape="box"];67[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	67 -> 11[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	68[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 68[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	68 -> 12[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	10[label="primEqInt (Neg vz300) vz40",fontsize=16,color="burlywood",shape="box"];69[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	69 -> 13[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	70[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	70 -> 14[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	11[label="primEqInt (Pos (Succ vz3000)) vz40",fontsize=16,color="burlywood",shape="box"];71[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 71[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	71 -> 15[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	72[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 72[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	72 -> 16[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	12[label="primEqInt (Pos Zero) vz40",fontsize=16,color="burlywood",shape="box"];73[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 73[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	73 -> 17[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	74[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 74[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	74 -> 18[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	13[label="primEqInt (Neg (Succ vz3000)) vz40",fontsize=16,color="burlywood",shape="box"];75[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 75[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	75 -> 19[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	76[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 76[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	76 -> 20[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	14[label="primEqInt (Neg Zero) vz40",fontsize=16,color="burlywood",shape="box"];77[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 77[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	77 -> 21[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	78[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 78[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	78 -> 22[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	15[label="primEqInt (Pos (Succ vz3000)) (Pos vz400)",fontsize=16,color="burlywood",shape="box"];79[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 79[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	79 -> 23[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	80[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 80[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	80 -> 24[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	16[label="primEqInt (Pos (Succ vz3000)) (Neg vz400)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.51/4.18	17[label="primEqInt (Pos Zero) (Pos vz400)",fontsize=16,color="burlywood",shape="box"];81[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 81[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	81 -> 26[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	82[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 82[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	82 -> 27[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	18[label="primEqInt (Pos Zero) (Neg vz400)",fontsize=16,color="burlywood",shape="box"];83[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 83[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	83 -> 28[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	84[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 84[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	84 -> 29[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	19[label="primEqInt (Neg (Succ vz3000)) (Pos vz400)",fontsize=16,color="black",shape="box"];19 -> 30[label="",style="solid", color="black", weight=3];
9.51/4.18	20[label="primEqInt (Neg (Succ vz3000)) (Neg vz400)",fontsize=16,color="burlywood",shape="box"];85[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];20 -> 85[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	85 -> 31[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	86[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 86[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	86 -> 32[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	21[label="primEqInt (Neg Zero) (Pos vz400)",fontsize=16,color="burlywood",shape="box"];87[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 87[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	87 -> 33[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	88[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 88[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	88 -> 34[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	22[label="primEqInt (Neg Zero) (Neg vz400)",fontsize=16,color="burlywood",shape="box"];89[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 89[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	89 -> 35[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	90[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 90[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	90 -> 36[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	23[label="primEqInt (Pos (Succ vz3000)) (Pos (Succ vz4000))",fontsize=16,color="black",shape="box"];23 -> 37[label="",style="solid", color="black", weight=3];
9.51/4.18	24[label="primEqInt (Pos (Succ vz3000)) (Pos Zero)",fontsize=16,color="black",shape="box"];24 -> 38[label="",style="solid", color="black", weight=3];
9.51/4.18	25[label="MyFalse",fontsize=16,color="green",shape="box"];26[label="primEqInt (Pos Zero) (Pos (Succ vz4000))",fontsize=16,color="black",shape="box"];26 -> 39[label="",style="solid", color="black", weight=3];
9.51/4.18	27[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];27 -> 40[label="",style="solid", color="black", weight=3];
9.51/4.18	28[label="primEqInt (Pos Zero) (Neg (Succ vz4000))",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3];
9.51/4.18	29[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
9.51/4.18	30[label="MyFalse",fontsize=16,color="green",shape="box"];31[label="primEqInt (Neg (Succ vz3000)) (Neg (Succ vz4000))",fontsize=16,color="black",shape="box"];31 -> 43[label="",style="solid", color="black", weight=3];
9.51/4.18	32[label="primEqInt (Neg (Succ vz3000)) (Neg Zero)",fontsize=16,color="black",shape="box"];32 -> 44[label="",style="solid", color="black", weight=3];
9.51/4.18	33[label="primEqInt (Neg Zero) (Pos (Succ vz4000))",fontsize=16,color="black",shape="box"];33 -> 45[label="",style="solid", color="black", weight=3];
9.51/4.18	34[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];34 -> 46[label="",style="solid", color="black", weight=3];
9.51/4.18	35[label="primEqInt (Neg Zero) (Neg (Succ vz4000))",fontsize=16,color="black",shape="box"];35 -> 47[label="",style="solid", color="black", weight=3];
9.51/4.18	36[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];36 -> 48[label="",style="solid", color="black", weight=3];
9.51/4.18	37[label="primEqNat vz3000 vz4000",fontsize=16,color="burlywood",shape="triangle"];91[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];37 -> 91[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	91 -> 49[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	92[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 92[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	92 -> 50[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	38[label="MyFalse",fontsize=16,color="green",shape="box"];39[label="MyFalse",fontsize=16,color="green",shape="box"];40[label="MyTrue",fontsize=16,color="green",shape="box"];41[label="MyFalse",fontsize=16,color="green",shape="box"];42[label="MyTrue",fontsize=16,color="green",shape="box"];43 -> 37[label="",style="dashed", color="red", weight=0];
9.51/4.18	43[label="primEqNat vz3000 vz4000",fontsize=16,color="magenta"];43 -> 51[label="",style="dashed", color="magenta", weight=3];
9.51/4.18	43 -> 52[label="",style="dashed", color="magenta", weight=3];
9.51/4.18	44[label="MyFalse",fontsize=16,color="green",shape="box"];45[label="MyFalse",fontsize=16,color="green",shape="box"];46[label="MyTrue",fontsize=16,color="green",shape="box"];47[label="MyFalse",fontsize=16,color="green",shape="box"];48[label="MyTrue",fontsize=16,color="green",shape="box"];49[label="primEqNat (Succ vz30000) vz4000",fontsize=16,color="burlywood",shape="box"];93[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];49 -> 93[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	93 -> 53[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	94[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 94[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	94 -> 54[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	50[label="primEqNat Zero vz4000",fontsize=16,color="burlywood",shape="box"];95[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];50 -> 95[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	95 -> 55[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	96[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 96[label="",style="solid", color="burlywood", weight=9];
9.51/4.18	96 -> 56[label="",style="solid", color="burlywood", weight=3];
9.51/4.18	51[label="vz4000",fontsize=16,color="green",shape="box"];52[label="vz3000",fontsize=16,color="green",shape="box"];53[label="primEqNat (Succ vz30000) (Succ vz40000)",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
9.51/4.18	54[label="primEqNat (Succ vz30000) Zero",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
9.51/4.18	55[label="primEqNat Zero (Succ vz40000)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
9.51/4.18	56[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
9.51/4.18	57 -> 37[label="",style="dashed", color="red", weight=0];
9.51/4.18	57[label="primEqNat vz30000 vz40000",fontsize=16,color="magenta"];57 -> 61[label="",style="dashed", color="magenta", weight=3];
9.51/4.18	57 -> 62[label="",style="dashed", color="magenta", weight=3];
9.51/4.18	58[label="MyFalse",fontsize=16,color="green",shape="box"];59[label="MyFalse",fontsize=16,color="green",shape="box"];60[label="MyTrue",fontsize=16,color="green",shape="box"];61[label="vz40000",fontsize=16,color="green",shape="box"];62[label="vz30000",fontsize=16,color="green",shape="box"];}
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(6)
9.51/4.18	Obligation:
9.51/4.18	Q DP problem:
9.51/4.18	The TRS P consists of the following rules:
9.51/4.18	
9.51/4.18	   new_primEqNat(Main.Succ(vz30000), Main.Succ(vz40000)) -> new_primEqNat(vz30000, vz40000)
9.51/4.18	
9.51/4.18	R is empty.
9.51/4.18	Q is empty.
9.51/4.18	We have to consider all minimal (P,Q,R)-chains.
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(7) QDPSizeChangeProof (EQUIVALENT)
9.51/4.18	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. 
9.51/4.18	
9.51/4.18	From the DPs we obtained the following set of size-change graphs:
9.51/4.18	*new_primEqNat(Main.Succ(vz30000), Main.Succ(vz40000)) -> new_primEqNat(vz30000, vz40000)
9.51/4.18	The graph contains the following edges 1 > 1, 2 > 2
9.51/4.18	
9.51/4.18	
9.51/4.18	----------------------------------------
9.51/4.18	
9.51/4.18	(8)
9.51/4.18	YES
9.51/4.23	EOF