7.54/3.59	YES
9.21/4.09	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.21/4.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.21/4.09	
9.21/4.09	
9.21/4.09	H-Termination with start terms of the given HASKELL could be proven:
9.21/4.09	
9.21/4.09	(0) HASKELL
9.21/4.09	(1) BR [EQUIVALENT, 0 ms]
9.21/4.09	(2) HASKELL
9.21/4.09	(3) COR [EQUIVALENT, 0 ms]
9.21/4.09	(4) HASKELL
9.21/4.09	(5) Narrow [SOUND, 0 ms]
9.21/4.09	(6) AND
9.21/4.09	    (7) QDP
9.21/4.09	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.21/4.09	        (9) YES
9.21/4.09	    (10) QDP
9.21/4.09	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.21/4.09	        (12) YES
9.21/4.09	
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(0)
9.21/4.09	Obligation:
9.21/4.09	mainModule Main 
9.21/4.09	module Main where {
9.21/4.09	import qualified Prelude;
9.21/4.09	data MyBool = MyTrue  | MyFalse ;
9.21/4.09	
9.21/4.09	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.21/4.09	
9.21/4.09	data Main.Nat = Succ Main.Nat  | Zero ;
9.21/4.09	
9.21/4.09	data Ratio a = CnPc a a ;
9.21/4.09	
9.21/4.09	asAs :: MyBool  ->  MyBool  ->  MyBool;
9.21/4.09	asAs MyFalse x = MyFalse;
9.21/4.09	asAs MyTrue x = x;
9.21/4.09	
9.21/4.09	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	esEsMyInt = primEqInt;
9.21/4.09	
9.21/4.09	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
9.21/4.09	
9.21/4.09	fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	fsEsRatio x y = not (esEsRatio x y);
9.21/4.09	
9.21/4.09	not :: MyBool  ->  MyBool;
9.21/4.09	not MyTrue = MyFalse;
9.21/4.09	not MyFalse = MyTrue;
9.21/4.09	
9.21/4.09	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt vv vw = MyFalse;
9.21/4.09	
9.21/4.09	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.21/4.09	primEqNat Main.Zero Main.Zero = MyTrue;
9.21/4.09	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.21/4.09	
9.21/4.09	}
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(1) BR (EQUIVALENT)
9.21/4.09	Replaced joker patterns by fresh variables and removed binding patterns.
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(2)
9.21/4.09	Obligation:
9.21/4.09	mainModule Main 
9.21/4.09	module Main where {
9.21/4.09	import qualified Prelude;
9.21/4.09	data MyBool = MyTrue  | MyFalse ;
9.21/4.09	
9.21/4.09	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.21/4.09	
9.21/4.09	data Main.Nat = Succ Main.Nat  | Zero ;
9.21/4.09	
9.21/4.09	data Ratio a = CnPc a a ;
9.21/4.09	
9.21/4.09	asAs :: MyBool  ->  MyBool  ->  MyBool;
9.21/4.09	asAs MyFalse x = MyFalse;
9.21/4.09	asAs MyTrue x = x;
9.21/4.09	
9.21/4.09	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	esEsMyInt = primEqInt;
9.21/4.09	
9.21/4.09	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
9.21/4.09	
9.21/4.09	fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	fsEsRatio x y = not (esEsRatio x y);
9.21/4.09	
9.21/4.09	not :: MyBool  ->  MyBool;
9.21/4.09	not MyTrue = MyFalse;
9.21/4.09	not MyFalse = MyTrue;
9.21/4.09	
9.21/4.09	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt vv vw = MyFalse;
9.21/4.09	
9.21/4.09	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.21/4.09	primEqNat Main.Zero Main.Zero = MyTrue;
9.21/4.09	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.21/4.09	
9.21/4.09	}
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(3) COR (EQUIVALENT)
9.21/4.09	Cond Reductions:
9.21/4.09	The following Function with conditions
9.21/4.09	"undefined |Falseundefined;
9.21/4.09	"
9.21/4.09	is transformed to
9.21/4.09	"undefined  = undefined1;
9.21/4.09	"
9.21/4.09	"undefined0 True = undefined;
9.21/4.09	"
9.21/4.09	"undefined1  = undefined0 False;
9.21/4.09	"
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(4)
9.21/4.09	Obligation:
9.21/4.09	mainModule Main 
9.21/4.09	module Main where {
9.21/4.09	import qualified Prelude;
9.21/4.09	data MyBool = MyTrue  | MyFalse ;
9.21/4.09	
9.21/4.09	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.21/4.09	
9.21/4.09	data Main.Nat = Succ Main.Nat  | Zero ;
9.21/4.09	
9.21/4.09	data Ratio a = CnPc a a ;
9.21/4.09	
9.21/4.09	asAs :: MyBool  ->  MyBool  ->  MyBool;
9.21/4.09	asAs MyFalse x = MyFalse;
9.21/4.09	asAs MyTrue x = x;
9.21/4.09	
9.21/4.09	esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	esEsMyInt = primEqInt;
9.21/4.09	
9.21/4.09	esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);
9.21/4.09	
9.21/4.09	fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
9.21/4.09	fsEsRatio x y = not (esEsRatio x y);
9.21/4.09	
9.21/4.09	not :: MyBool  ->  MyBool;
9.21/4.09	not MyTrue = MyFalse;
9.21/4.09	not MyFalse = MyTrue;
9.21/4.09	
9.21/4.09	primEqInt :: MyInt  ->  MyInt  ->  MyBool;
9.21/4.09	primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
9.21/4.09	primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
9.21/4.09	primEqInt vv vw = MyFalse;
9.21/4.09	
9.21/4.09	primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
9.21/4.09	primEqNat Main.Zero Main.Zero = MyTrue;
9.21/4.09	primEqNat Main.Zero (Main.Succ y) = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) Main.Zero = MyFalse;
9.21/4.09	primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;
9.21/4.09	
9.21/4.09	}
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(5) Narrow (SOUND)
9.21/4.09	Haskell To QDPs
9.21/4.09	
9.21/4.09	digraph dp_graph {
9.21/4.09	node [outthreshold=100, inthreshold=100];1[label="fsEsRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.21/4.09	3[label="fsEsRatio vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.21/4.09	4[label="fsEsRatio vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.21/4.09	5[label="not (esEsRatio vz3 vz4)",fontsize=16,color="burlywood",shape="box"];123[label="vz3/CnPc vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];5 -> 123[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	123 -> 6[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	6[label="not (esEsRatio (CnPc vz30 vz31) vz4)",fontsize=16,color="burlywood",shape="box"];124[label="vz4/CnPc vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 124[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	124 -> 7[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	7[label="not (esEsRatio (CnPc vz30 vz31) (CnPc vz40 vz41))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.21/4.09	8[label="not (asAs (esEsMyInt vz30 vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.21/4.09	9[label="not (asAs (primEqInt vz30 vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];125[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];9 -> 125[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	125 -> 10[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	126[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];9 -> 126[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	126 -> 11[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	10[label="not (asAs (primEqInt (Pos vz300) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];127[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];10 -> 127[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	127 -> 12[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	128[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 128[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	128 -> 13[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	11[label="not (asAs (primEqInt (Neg vz300) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];129[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];11 -> 129[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	129 -> 14[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	130[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 130[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	130 -> 15[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	12[label="not (asAs (primEqInt (Pos (Succ vz3000)) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];131[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 131[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	131 -> 16[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	132[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 132[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	132 -> 17[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	13[label="not (asAs (primEqInt (Pos Zero) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];133[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 133[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	133 -> 18[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	134[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 134[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	134 -> 19[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	14[label="not (asAs (primEqInt (Neg (Succ vz3000)) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];135[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 135[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	135 -> 20[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	136[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 136[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	136 -> 21[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	15[label="not (asAs (primEqInt (Neg Zero) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];137[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];15 -> 137[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	137 -> 22[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	138[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];15 -> 138[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	138 -> 23[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	16[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];139[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 139[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	139 -> 24[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	140[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 140[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	140 -> 25[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	17[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.21/4.09	18[label="not (asAs (primEqInt (Pos Zero) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];141[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 141[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	141 -> 27[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	142[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 142[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	142 -> 28[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	19[label="not (asAs (primEqInt (Pos Zero) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];143[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];19 -> 143[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	143 -> 29[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	144[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 144[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	144 -> 30[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	20[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];20 -> 31[label="",style="solid", color="black", weight=3];
9.21/4.09	21[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];145[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 145[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	145 -> 32[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	146[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 146[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	146 -> 33[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	22[label="not (asAs (primEqInt (Neg Zero) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];147[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 147[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	147 -> 34[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	148[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 148[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	148 -> 35[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	23[label="not (asAs (primEqInt (Neg Zero) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];149[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 149[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	149 -> 36[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	150[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 150[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	150 -> 37[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	24[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];24 -> 38[label="",style="solid", color="black", weight=3];
9.21/4.09	25[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];25 -> 39[label="",style="solid", color="black", weight=3];
9.21/4.09	26[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="triangle"];26 -> 40[label="",style="solid", color="black", weight=3];
9.21/4.09	27[label="not (asAs (primEqInt (Pos Zero) (Pos (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
9.21/4.09	28[label="not (asAs (primEqInt (Pos Zero) (Pos Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];28 -> 42[label="",style="solid", color="black", weight=3];
9.21/4.09	29[label="not (asAs (primEqInt (Pos Zero) (Neg (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3];
9.21/4.09	30[label="not (asAs (primEqInt (Pos Zero) (Neg Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
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9.21/4.09	59[label="not (asAs (primEqNat Zero (Succ vz40000)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];59 -> 64[label="",style="solid", color="black", weight=3];
9.21/4.09	60[label="not (asAs (primEqNat Zero Zero) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];60 -> 65[label="",style="solid", color="black", weight=3];
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9.21/4.09	165 -> 76[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	166[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];71 -> 166[label="",style="solid", color="burlywood", weight=9];
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9.21/4.09	169 -> 80[label="",style="solid", color="burlywood", weight=3];
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9.21/4.09	76[label="not (primEqInt (Pos Zero) (Pos vz410))",fontsize=16,color="burlywood",shape="box"];173[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];76 -> 173[label="",style="solid", color="burlywood", weight=9];
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9.21/4.09	79[label="not (primEqInt (Neg (Succ vz3100)) (Neg vz410))",fontsize=16,color="burlywood",shape="box"];177[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];79 -> 177[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	177 -> 90[label="",style="solid", color="burlywood", weight=3];
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9.21/4.09	100 -> 40[label="",style="dashed", color="red", weight=0];
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9.21/4.09	187 -> 115[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	188[label="vz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];109 -> 188[label="",style="solid", color="burlywood", weight=9];
9.21/4.09	188 -> 116[label="",style="solid", color="burlywood", weight=3];
9.21/4.09	110[label="MyFalse",fontsize=16,color="green",shape="box"];111[label="vz3100",fontsize=16,color="green",shape="box"];112[label="vz4100",fontsize=16,color="green",shape="box"];113[label="not (primEqNat (Succ vz31000) (Succ vz41000))",fontsize=16,color="black",shape="box"];113 -> 117[label="",style="solid", color="black", weight=3];
9.21/4.09	114[label="not (primEqNat (Succ vz31000) Zero)",fontsize=16,color="black",shape="box"];114 -> 118[label="",style="solid", color="black", weight=3];
9.21/4.09	115[label="not (primEqNat Zero (Succ vz41000))",fontsize=16,color="black",shape="box"];115 -> 119[label="",style="solid", color="black", weight=3];
9.21/4.09	116[label="not (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];116 -> 120[label="",style="solid", color="black", weight=3];
9.21/4.09	117 -> 96[label="",style="dashed", color="red", weight=0];
9.21/4.09	117[label="not (primEqNat vz31000 vz41000)",fontsize=16,color="magenta"];117 -> 121[label="",style="dashed", color="magenta", weight=3];
9.21/4.09	117 -> 122[label="",style="dashed", color="magenta", weight=3];
9.21/4.09	118 -> 40[label="",style="dashed", color="red", weight=0];
9.21/4.09	118[label="not MyFalse",fontsize=16,color="magenta"];119 -> 40[label="",style="dashed", color="red", weight=0];
9.21/4.09	119[label="not MyFalse",fontsize=16,color="magenta"];120 -> 99[label="",style="dashed", color="red", weight=0];
9.21/4.09	120[label="not MyTrue",fontsize=16,color="magenta"];121[label="vz31000",fontsize=16,color="green",shape="box"];122[label="vz41000",fontsize=16,color="green",shape="box"];}
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(6)
9.21/4.09	Complex Obligation (AND)
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(7)
9.21/4.09	Obligation:
9.21/4.09	Q DP problem:
9.21/4.09	The TRS P consists of the following rules:
9.21/4.09	
9.21/4.09	   new_not0(Main.Succ(vz30000), Main.Succ(vz40000), vz31, vz41) -> new_not0(vz30000, vz40000, vz31, vz41)
9.21/4.09	
9.21/4.09	R is empty.
9.21/4.09	Q is empty.
9.21/4.09	We have to consider all minimal (P,Q,R)-chains.
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(8) QDPSizeChangeProof (EQUIVALENT)
9.21/4.09	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. 
9.21/4.09	
9.21/4.09	From the DPs we obtained the following set of size-change graphs:
9.21/4.09	*new_not0(Main.Succ(vz30000), Main.Succ(vz40000), vz31, vz41) -> new_not0(vz30000, vz40000, vz31, vz41)
9.21/4.09	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4
9.21/4.09	
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(9)
9.21/4.09	YES
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(10)
9.21/4.09	Obligation:
9.21/4.09	Q DP problem:
9.21/4.09	The TRS P consists of the following rules:
9.21/4.09	
9.21/4.09	   new_not(Main.Succ(vz31000), Main.Succ(vz41000)) -> new_not(vz31000, vz41000)
9.21/4.09	
9.21/4.09	R is empty.
9.21/4.09	Q is empty.
9.21/4.09	We have to consider all minimal (P,Q,R)-chains.
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(11) QDPSizeChangeProof (EQUIVALENT)
9.21/4.09	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. 
9.21/4.09	
9.21/4.09	From the DPs we obtained the following set of size-change graphs:
9.21/4.09	*new_not(Main.Succ(vz31000), Main.Succ(vz41000)) -> new_not(vz31000, vz41000)
9.21/4.09	The graph contains the following edges 1 > 1, 2 > 2
9.21/4.09	
9.21/4.09	
9.21/4.09	----------------------------------------
9.21/4.09	
9.21/4.09	(12)
9.21/4.09	YES
9.60/4.13	EOF