7.94/3.67	YES
9.71/4.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.71/4.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.71/4.21	
9.71/4.21	
9.71/4.21	H-Termination with start terms of the given HASKELL could be proven:
9.71/4.21	
9.71/4.21	(0) HASKELL
9.71/4.21	(1) BR [EQUIVALENT, 0 ms]
9.71/4.21	(2) HASKELL
9.71/4.21	(3) COR [EQUIVALENT, 0 ms]
9.71/4.21	(4) HASKELL
9.71/4.21	(5) Narrow [SOUND, 0 ms]
9.71/4.21	(6) QDP
9.71/4.21	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.71/4.21	(8) YES
9.71/4.21	
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(0)
9.71/4.21	Obligation:
9.71/4.21	mainModule Main 
9.71/4.21	module Main where {
9.71/4.21	import qualified Prelude;
9.71/4.21	data MyBool = MyTrue  | MyFalse ;
9.71/4.21	
9.71/4.21	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.71/4.21	
9.71/4.21	data Main.Nat = Succ Main.Nat  | Zero ;
9.71/4.21	
9.71/4.21	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	esEsMyInt = primEqInt;
9.71/4.21	
9.71/4.21	fsEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	fsEsMyInt x y = not (esEsMyInt x y);
9.71/4.21	
9.71/4.21	not :: MyBool  ->  MyBool;
9.71/4.21	not MyTrue = MyFalse;
9.71/4.21	not MyFalse = MyTrue;
9.71/4.21	
9.71/4.21	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt vv vw = MyFalse;
9.71/4.21	
9.71/4.21	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.71/4.21	primEqNat Main.Zero Main.Zero = MyTrue;
9.71/4.21	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.71/4.21	
9.71/4.21	}
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(1) BR (EQUIVALENT)
9.71/4.21	Replaced joker patterns by fresh variables and removed binding patterns.
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(2)
9.71/4.21	Obligation:
9.71/4.21	mainModule Main 
9.71/4.21	module Main where {
9.71/4.21	import qualified Prelude;
9.71/4.21	data MyBool = MyTrue  | MyFalse ;
9.71/4.21	
9.71/4.21	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.71/4.21	
9.71/4.21	data Main.Nat = Succ Main.Nat  | Zero ;
9.71/4.21	
9.71/4.21	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	esEsMyInt = primEqInt;
9.71/4.21	
9.71/4.21	fsEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	fsEsMyInt x y = not (esEsMyInt x y);
9.71/4.21	
9.71/4.21	not :: MyBool  ->  MyBool;
9.71/4.21	not MyTrue = MyFalse;
9.71/4.21	not MyFalse = MyTrue;
9.71/4.21	
9.71/4.21	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt vv vw = MyFalse;
9.71/4.21	
9.71/4.21	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.71/4.21	primEqNat Main.Zero Main.Zero = MyTrue;
9.71/4.21	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.71/4.21	
9.71/4.21	}
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(3) COR (EQUIVALENT)
9.71/4.21	Cond Reductions:
9.71/4.21	The following Function with conditions
9.71/4.21	"undefined |Falseundefined;
9.71/4.21	"
9.71/4.21	is transformed to
9.71/4.21	"undefined  = undefined1;
9.71/4.21	"
9.71/4.21	"undefined0 True = undefined;
9.71/4.21	"
9.71/4.21	"undefined1  = undefined0 False;
9.71/4.21	"
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(4)
9.71/4.21	Obligation:
9.71/4.21	mainModule Main 
9.71/4.21	module Main where {
9.71/4.21	import qualified Prelude;
9.71/4.21	data MyBool = MyTrue  | MyFalse ;
9.71/4.21	
9.71/4.21	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.71/4.21	
9.71/4.21	data Main.Nat = Succ Main.Nat  | Zero ;
9.71/4.21	
9.71/4.21	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	esEsMyInt = primEqInt;
9.71/4.21	
9.71/4.21	fsEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	fsEsMyInt x y = not (esEsMyInt x y);
9.71/4.21	
9.71/4.21	not :: MyBool  ->  MyBool;
9.71/4.21	not MyTrue = MyFalse;
9.71/4.21	not MyFalse = MyTrue;
9.71/4.21	
9.71/4.21	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.71/4.21	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.71/4.21	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.71/4.21	primEqInt vv vw = MyFalse;
9.71/4.21	
9.71/4.21	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.71/4.21	primEqNat Main.Zero Main.Zero = MyTrue;
9.71/4.21	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.71/4.21	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.71/4.21	
9.71/4.21	}
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(5) Narrow (SOUND)
9.71/4.21	Haskell To QDPs
9.71/4.21	
9.71/4.21	digraph dp_graph {
9.71/4.21	node [outthreshold=100, inthreshold=100];1[label="fsEsMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.71/4.21	3[label="fsEsMyInt vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.71/4.21	4[label="fsEsMyInt vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.71/4.21	5[label="not (esEsMyInt vz3 vz4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.71/4.21	6[label="not (primEqInt vz3 vz4)",fontsize=16,color="burlywood",shape="box"];63[label="vz3/Pos vz30",fontsize=10,color="white",style="solid",shape="box"];6 -> 63[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	63 -> 7[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	64[label="vz3/Neg vz30",fontsize=10,color="white",style="solid",shape="box"];6 -> 64[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	64 -> 8[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	7[label="not (primEqInt (Pos vz30) vz4)",fontsize=16,color="burlywood",shape="box"];65[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];7 -> 65[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	65 -> 9[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	66[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 66[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	66 -> 10[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	8[label="not (primEqInt (Neg vz30) vz4)",fontsize=16,color="burlywood",shape="box"];67[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 67[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	67 -> 11[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	68[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 68[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	68 -> 12[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	9[label="not (primEqInt (Pos (Succ vz300)) vz4)",fontsize=16,color="burlywood",shape="box"];69[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];9 -> 69[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	69 -> 13[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	70[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];9 -> 70[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	70 -> 14[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	10[label="not (primEqInt (Pos Zero) vz4)",fontsize=16,color="burlywood",shape="box"];71[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];10 -> 71[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	71 -> 15[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	72[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];10 -> 72[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	72 -> 16[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	11[label="not (primEqInt (Neg (Succ vz300)) vz4)",fontsize=16,color="burlywood",shape="box"];73[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];11 -> 73[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	73 -> 17[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	74[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];11 -> 74[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	74 -> 18[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	12[label="not (primEqInt (Neg Zero) vz4)",fontsize=16,color="burlywood",shape="box"];75[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];12 -> 75[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	75 -> 19[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	76[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];12 -> 76[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	76 -> 20[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	13[label="not (primEqInt (Pos (Succ vz300)) (Pos vz40))",fontsize=16,color="burlywood",shape="box"];77[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 77[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	77 -> 21[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	78[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 78[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	78 -> 22[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	14[label="not (primEqInt (Pos (Succ vz300)) (Neg vz40))",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.71/4.21	15[label="not (primEqInt (Pos Zero) (Pos vz40))",fontsize=16,color="burlywood",shape="box"];79[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];15 -> 79[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	79 -> 24[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	80[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 80[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	80 -> 25[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	16[label="not (primEqInt (Pos Zero) (Neg vz40))",fontsize=16,color="burlywood",shape="box"];81[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];16 -> 81[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	81 -> 26[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	82[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 82[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	82 -> 27[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	17[label="not (primEqInt (Neg (Succ vz300)) (Pos vz40))",fontsize=16,color="black",shape="box"];17 -> 28[label="",style="solid", color="black", weight=3];
9.71/4.21	18[label="not (primEqInt (Neg (Succ vz300)) (Neg vz40))",fontsize=16,color="burlywood",shape="box"];83[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];18 -> 83[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	83 -> 29[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	84[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 84[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	84 -> 30[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	19[label="not (primEqInt (Neg Zero) (Pos vz40))",fontsize=16,color="burlywood",shape="box"];85[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];19 -> 85[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	85 -> 31[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	86[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 86[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	86 -> 32[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	20[label="not (primEqInt (Neg Zero) (Neg vz40))",fontsize=16,color="burlywood",shape="box"];87[label="vz40/Succ vz400",fontsize=10,color="white",style="solid",shape="box"];20 -> 87[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	87 -> 33[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	88[label="vz40/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 88[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	88 -> 34[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	21[label="not (primEqInt (Pos (Succ vz300)) (Pos (Succ vz400)))",fontsize=16,color="black",shape="box"];21 -> 35[label="",style="solid", color="black", weight=3];
9.71/4.21	22[label="not (primEqInt (Pos (Succ vz300)) (Pos Zero))",fontsize=16,color="black",shape="box"];22 -> 36[label="",style="solid", color="black", weight=3];
9.71/4.21	23[label="not MyFalse",fontsize=16,color="black",shape="triangle"];23 -> 37[label="",style="solid", color="black", weight=3];
9.71/4.21	24[label="not (primEqInt (Pos Zero) (Pos (Succ vz400)))",fontsize=16,color="black",shape="box"];24 -> 38[label="",style="solid", color="black", weight=3];
9.71/4.21	25[label="not (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];25 -> 39[label="",style="solid", color="black", weight=3];
9.71/4.21	26[label="not (primEqInt (Pos Zero) (Neg (Succ vz400)))",fontsize=16,color="black",shape="box"];26 -> 40[label="",style="solid", color="black", weight=3];
9.71/4.21	27[label="not (primEqInt (Pos Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
9.71/4.21	28 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	28[label="not MyFalse",fontsize=16,color="magenta"];29[label="not (primEqInt (Neg (Succ vz300)) (Neg (Succ vz400)))",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
9.71/4.21	30[label="not (primEqInt (Neg (Succ vz300)) (Neg Zero))",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
9.71/4.21	31[label="not (primEqInt (Neg Zero) (Pos (Succ vz400)))",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
9.71/4.21	32[label="not (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
9.71/4.21	33[label="not (primEqInt (Neg Zero) (Neg (Succ vz400)))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
9.71/4.21	34[label="not (primEqInt (Neg Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3];
9.71/4.21	35[label="not (primEqNat vz300 vz400)",fontsize=16,color="burlywood",shape="triangle"];89[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];35 -> 89[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	89 -> 48[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	90[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 90[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	90 -> 49[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	36 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	36[label="not MyFalse",fontsize=16,color="magenta"];37[label="MyTrue",fontsize=16,color="green",shape="box"];38 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	38[label="not MyFalse",fontsize=16,color="magenta"];39[label="not MyTrue",fontsize=16,color="black",shape="triangle"];39 -> 50[label="",style="solid", color="black", weight=3];
9.71/4.21	40 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	40[label="not MyFalse",fontsize=16,color="magenta"];41 -> 39[label="",style="dashed", color="red", weight=0];
9.71/4.21	41[label="not MyTrue",fontsize=16,color="magenta"];42 -> 35[label="",style="dashed", color="red", weight=0];
9.71/4.21	42[label="not (primEqNat vz300 vz400)",fontsize=16,color="magenta"];42 -> 51[label="",style="dashed", color="magenta", weight=3];
9.71/4.21	42 -> 52[label="",style="dashed", color="magenta", weight=3];
9.71/4.21	43 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	43[label="not MyFalse",fontsize=16,color="magenta"];44 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	44[label="not MyFalse",fontsize=16,color="magenta"];45 -> 39[label="",style="dashed", color="red", weight=0];
9.71/4.21	45[label="not MyTrue",fontsize=16,color="magenta"];46 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	46[label="not MyFalse",fontsize=16,color="magenta"];47 -> 39[label="",style="dashed", color="red", weight=0];
9.71/4.21	47[label="not MyTrue",fontsize=16,color="magenta"];48[label="not (primEqNat (Succ vz3000) vz400)",fontsize=16,color="burlywood",shape="box"];91[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];48 -> 91[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	91 -> 53[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	92[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 92[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	92 -> 54[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	49[label="not (primEqNat Zero vz400)",fontsize=16,color="burlywood",shape="box"];93[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];49 -> 93[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	93 -> 55[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	94[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 94[label="",style="solid", color="burlywood", weight=9];
9.71/4.21	94 -> 56[label="",style="solid", color="burlywood", weight=3];
9.71/4.21	50[label="MyFalse",fontsize=16,color="green",shape="box"];51[label="vz300",fontsize=16,color="green",shape="box"];52[label="vz400",fontsize=16,color="green",shape="box"];53[label="not (primEqNat (Succ vz3000) (Succ vz4000))",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
9.71/4.21	54[label="not (primEqNat (Succ vz3000) Zero)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
9.71/4.21	55[label="not (primEqNat Zero (Succ vz4000))",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
9.71/4.21	56[label="not (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
9.71/4.21	57 -> 35[label="",style="dashed", color="red", weight=0];
9.71/4.21	57[label="not (primEqNat vz3000 vz4000)",fontsize=16,color="magenta"];57 -> 61[label="",style="dashed", color="magenta", weight=3];
9.71/4.21	57 -> 62[label="",style="dashed", color="magenta", weight=3];
9.71/4.21	58 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	58[label="not MyFalse",fontsize=16,color="magenta"];59 -> 23[label="",style="dashed", color="red", weight=0];
9.71/4.21	59[label="not MyFalse",fontsize=16,color="magenta"];60 -> 39[label="",style="dashed", color="red", weight=0];
9.71/4.21	60[label="not MyTrue",fontsize=16,color="magenta"];61[label="vz3000",fontsize=16,color="green",shape="box"];62[label="vz4000",fontsize=16,color="green",shape="box"];}
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(6)
9.71/4.21	Obligation:
9.71/4.21	Q DP problem:
9.71/4.21	The TRS P consists of the following rules:
9.71/4.21	
9.71/4.21	   new_not(Main.Succ(vz3000), Main.Succ(vz4000)) -> new_not(vz3000, vz4000)
9.71/4.21	
9.71/4.21	R is empty.
9.71/4.21	Q is empty.
9.71/4.21	We have to consider all minimal (P,Q,R)-chains.
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(7) QDPSizeChangeProof (EQUIVALENT)
9.71/4.21	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. 
9.71/4.21	
9.71/4.21	From the DPs we obtained the following set of size-change graphs:
9.71/4.21	*new_not(Main.Succ(vz3000), Main.Succ(vz4000)) -> new_not(vz3000, vz4000)
9.71/4.21	The graph contains the following edges 1 > 1, 2 > 2
9.71/4.21	
9.71/4.21	
9.71/4.21	----------------------------------------
9.71/4.21	
9.71/4.21	(8)
9.71/4.21	YES
9.96/4.29	EOF