8.20/3.62	YES
9.67/4.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.67/4.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.67/4.05	
9.67/4.05	
9.67/4.05	H-Termination with start terms of the given HASKELL could be proven:
9.67/4.05	
9.67/4.05	(0) HASKELL
9.67/4.05	(1) BR [EQUIVALENT, 0 ms]
9.67/4.05	(2) HASKELL
9.67/4.05	(3) COR [EQUIVALENT, 0 ms]
9.67/4.05	(4) HASKELL
9.67/4.05	(5) Narrow [SOUND, 0 ms]
9.67/4.05	(6) AND
9.67/4.05	    (7) QDP
9.67/4.05	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.67/4.05	        (9) YES
9.67/4.05	    (10) QDP
9.67/4.05	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.67/4.05	        (12) YES
9.67/4.05	
9.67/4.05	
9.67/4.05	----------------------------------------
9.67/4.05	
9.67/4.05	(0)
9.67/4.05	Obligation:
9.67/4.05	mainModule Main 
9.67/4.05	module Main where {
9.67/4.05	import qualified Prelude;
9.67/4.05	}
9.67/4.05	
9.67/4.05	----------------------------------------
9.67/4.05	
9.67/4.05	(1) BR (EQUIVALENT)
9.67/4.05	Replaced joker patterns by fresh variables and removed binding patterns.
9.67/4.05	----------------------------------------
9.67/4.05	
9.67/4.05	(2)
9.67/4.05	Obligation:
9.67/4.05	mainModule Main 
9.67/4.05	module Main where {
9.67/4.05	import qualified Prelude;
9.67/4.05	}
9.67/4.05	
9.67/4.05	----------------------------------------
9.67/4.05	
9.67/4.05	(3) COR (EQUIVALENT)
9.67/4.05	Cond Reductions:
9.67/4.05	The following Function with conditions
9.67/4.05	"undefined |Falseundefined;
9.67/4.06	"
9.67/4.06	is transformed to
9.67/4.06	"undefined  = undefined1;
9.67/4.06	"
9.67/4.06	"undefined0 True = undefined;
9.67/4.06	"
9.67/4.06	"undefined1  = undefined0 False;
9.67/4.06	"
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(4)
9.67/4.06	Obligation:
9.67/4.06	mainModule Main 
9.67/4.06	module Main where {
9.67/4.06	import qualified Prelude;
9.67/4.06	}
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(5) Narrow (SOUND)
9.67/4.06	Haskell To QDPs
9.67/4.06	
9.67/4.06	digraph dp_graph {
9.67/4.06	node [outthreshold=100, inthreshold=100];1[label="(==)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.67/4.06	3[label="(==) vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.67/4.06	4[label="(==) vz3 vz4",fontsize=16,color="burlywood",shape="triangle"];120[label="vz3/vz30 :% vz31",fontsize=10,color="white",style="solid",shape="box"];4 -> 120[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	120 -> 5[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	5[label="(==) vz30 :% vz31 vz4",fontsize=16,color="burlywood",shape="box"];121[label="vz4/vz40 :% vz41",fontsize=10,color="white",style="solid",shape="box"];5 -> 121[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	121 -> 6[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	6[label="(==) vz30 :% vz31 vz40 :% vz41",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.67/4.06	7[label="vz30 == vz40 && vz31 == vz41",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.67/4.06	8[label="primEqInt vz30 vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];122[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 122[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	122 -> 9[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	123[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 123[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	123 -> 10[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	9[label="primEqInt (Pos vz300) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];124[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];9 -> 124[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	124 -> 11[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	125[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 125[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	125 -> 12[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	10[label="primEqInt (Neg vz300) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];126[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];10 -> 126[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	126 -> 13[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	127[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 127[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	127 -> 14[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	11[label="primEqInt (Pos (Succ vz3000)) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];128[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 128[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	128 -> 15[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	129[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];11 -> 129[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	129 -> 16[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	12[label="primEqInt (Pos Zero) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];130[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 130[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	130 -> 17[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	131[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 131[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	131 -> 18[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	13[label="primEqInt (Neg (Succ vz3000)) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];132[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 132[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	132 -> 19[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	133[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 133[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	133 -> 20[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	14[label="primEqInt (Neg Zero) vz40 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];134[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 134[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	134 -> 21[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	135[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 135[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	135 -> 22[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	15[label="primEqInt (Pos (Succ vz3000)) (Pos vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];136[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 136[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	136 -> 23[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	137[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];15 -> 137[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	137 -> 24[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	16[label="primEqInt (Pos (Succ vz3000)) (Neg vz400) && vz31 == vz41",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.67/4.06	17[label="primEqInt (Pos Zero) (Pos vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];138[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 138[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	138 -> 26[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	139[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 139[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	139 -> 27[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	18[label="primEqInt (Pos Zero) (Neg vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];140[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 140[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	140 -> 28[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	141[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 141[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	141 -> 29[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	19[label="primEqInt (Neg (Succ vz3000)) (Pos vz400) && vz31 == vz41",fontsize=16,color="black",shape="box"];19 -> 30[label="",style="solid", color="black", weight=3];
9.67/4.06	20[label="primEqInt (Neg (Succ vz3000)) (Neg vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];142[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];20 -> 142[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	142 -> 31[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	143[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];20 -> 143[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	143 -> 32[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	21[label="primEqInt (Neg Zero) (Pos vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];144[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 144[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	144 -> 33[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	145[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 145[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	145 -> 34[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	22[label="primEqInt (Neg Zero) (Neg vz400) && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];146[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 146[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	146 -> 35[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	147[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 147[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	147 -> 36[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	23[label="primEqInt (Pos (Succ vz3000)) (Pos (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];23 -> 37[label="",style="solid", color="black", weight=3];
9.67/4.06	24[label="primEqInt (Pos (Succ vz3000)) (Pos Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];24 -> 38[label="",style="solid", color="black", weight=3];
9.67/4.06	25[label="False && vz31 == vz41",fontsize=16,color="black",shape="triangle"];25 -> 39[label="",style="solid", color="black", weight=3];
9.67/4.06	26[label="primEqInt (Pos Zero) (Pos (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];26 -> 40[label="",style="solid", color="black", weight=3];
9.67/4.06	27[label="primEqInt (Pos Zero) (Pos Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
9.67/4.06	28[label="primEqInt (Pos Zero) (Neg (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];28 -> 42[label="",style="solid", color="black", weight=3];
9.67/4.06	29[label="primEqInt (Pos Zero) (Neg Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3];
9.67/4.06	30 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	30[label="False && vz31 == vz41",fontsize=16,color="magenta"];31[label="primEqInt (Neg (Succ vz3000)) (Neg (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
9.67/4.06	32[label="primEqInt (Neg (Succ vz3000)) (Neg Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
9.67/4.06	33[label="primEqInt (Neg Zero) (Pos (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
9.67/4.06	34[label="primEqInt (Neg Zero) (Pos Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3];
9.67/4.06	35[label="primEqInt (Neg Zero) (Neg (Succ vz4000)) && vz31 == vz41",fontsize=16,color="black",shape="box"];35 -> 48[label="",style="solid", color="black", weight=3];
9.67/4.06	36[label="primEqInt (Neg Zero) (Neg Zero) && vz31 == vz41",fontsize=16,color="black",shape="box"];36 -> 49[label="",style="solid", color="black", weight=3];
9.67/4.06	37[label="primEqNat vz3000 vz4000 && vz31 == vz41",fontsize=16,color="burlywood",shape="triangle"];148[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];37 -> 148[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	148 -> 50[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	149[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 149[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	149 -> 51[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	38 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	38[label="False && vz31 == vz41",fontsize=16,color="magenta"];39[label="False",fontsize=16,color="green",shape="box"];40 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	40[label="False && vz31 == vz41",fontsize=16,color="magenta"];41[label="True && vz31 == vz41",fontsize=16,color="black",shape="triangle"];41 -> 52[label="",style="solid", color="black", weight=3];
9.67/4.06	42 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	42[label="False && vz31 == vz41",fontsize=16,color="magenta"];43 -> 41[label="",style="dashed", color="red", weight=0];
9.67/4.06	43[label="True && vz31 == vz41",fontsize=16,color="magenta"];44 -> 37[label="",style="dashed", color="red", weight=0];
9.67/4.06	44[label="primEqNat vz3000 vz4000 && vz31 == vz41",fontsize=16,color="magenta"];44 -> 53[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	44 -> 54[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	45 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	45[label="False && vz31 == vz41",fontsize=16,color="magenta"];46 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	46[label="False && vz31 == vz41",fontsize=16,color="magenta"];47 -> 41[label="",style="dashed", color="red", weight=0];
9.67/4.06	47[label="True && vz31 == vz41",fontsize=16,color="magenta"];48 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	48[label="False && vz31 == vz41",fontsize=16,color="magenta"];49 -> 41[label="",style="dashed", color="red", weight=0];
9.67/4.06	49[label="True && vz31 == vz41",fontsize=16,color="magenta"];50[label="primEqNat (Succ vz30000) vz4000 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];150[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];50 -> 150[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	150 -> 55[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	151[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 151[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	151 -> 56[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	51[label="primEqNat Zero vz4000 && vz31 == vz41",fontsize=16,color="burlywood",shape="box"];152[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];51 -> 152[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	152 -> 57[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	153[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 153[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	153 -> 58[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	52[label="vz31 == vz41",fontsize=16,color="black",shape="box"];52 -> 59[label="",style="solid", color="black", weight=3];
9.67/4.06	53[label="vz3000",fontsize=16,color="green",shape="box"];54[label="vz4000",fontsize=16,color="green",shape="box"];55[label="primEqNat (Succ vz30000) (Succ vz40000) && vz31 == vz41",fontsize=16,color="black",shape="box"];55 -> 60[label="",style="solid", color="black", weight=3];
9.67/4.06	56[label="primEqNat (Succ vz30000) Zero && vz31 == vz41",fontsize=16,color="black",shape="box"];56 -> 61[label="",style="solid", color="black", weight=3];
9.67/4.06	57[label="primEqNat Zero (Succ vz40000) && vz31 == vz41",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3];
9.67/4.06	58[label="primEqNat Zero Zero && vz31 == vz41",fontsize=16,color="black",shape="box"];58 -> 63[label="",style="solid", color="black", weight=3];
9.67/4.06	59[label="primEqInt vz31 vz41",fontsize=16,color="burlywood",shape="box"];154[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];59 -> 154[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	154 -> 64[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	155[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];59 -> 155[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	155 -> 65[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	60 -> 37[label="",style="dashed", color="red", weight=0];
9.67/4.06	60[label="primEqNat vz30000 vz40000 && vz31 == vz41",fontsize=16,color="magenta"];60 -> 66[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	60 -> 67[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	61 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	61[label="False && vz31 == vz41",fontsize=16,color="magenta"];62 -> 25[label="",style="dashed", color="red", weight=0];
9.67/4.06	62[label="False && vz31 == vz41",fontsize=16,color="magenta"];63 -> 41[label="",style="dashed", color="red", weight=0];
9.67/4.06	63[label="True && vz31 == vz41",fontsize=16,color="magenta"];64[label="primEqInt (Pos vz310) vz41",fontsize=16,color="burlywood",shape="box"];156[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];64 -> 156[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	156 -> 68[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	157[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 157[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	157 -> 69[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	65[label="primEqInt (Neg vz310) vz41",fontsize=16,color="burlywood",shape="box"];158[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];65 -> 158[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	158 -> 70[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	159[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 159[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	159 -> 71[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	66[label="vz30000",fontsize=16,color="green",shape="box"];67[label="vz40000",fontsize=16,color="green",shape="box"];68[label="primEqInt (Pos (Succ vz3100)) vz41",fontsize=16,color="burlywood",shape="box"];160[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];68 -> 160[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	160 -> 72[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	161[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];68 -> 161[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	161 -> 73[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	69[label="primEqInt (Pos Zero) vz41",fontsize=16,color="burlywood",shape="box"];162[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];69 -> 162[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	162 -> 74[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	163[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];69 -> 163[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	163 -> 75[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	70[label="primEqInt (Neg (Succ vz3100)) vz41",fontsize=16,color="burlywood",shape="box"];164[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];70 -> 164[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	164 -> 76[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	165[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];70 -> 165[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	165 -> 77[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	71[label="primEqInt (Neg Zero) vz41",fontsize=16,color="burlywood",shape="box"];166[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];71 -> 166[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	166 -> 78[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	167[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];71 -> 167[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	167 -> 79[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	72[label="primEqInt (Pos (Succ vz3100)) (Pos vz410)",fontsize=16,color="burlywood",shape="box"];168[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];72 -> 168[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	168 -> 80[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	169[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 169[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	169 -> 81[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	73[label="primEqInt (Pos (Succ vz3100)) (Neg vz410)",fontsize=16,color="black",shape="box"];73 -> 82[label="",style="solid", color="black", weight=3];
9.67/4.06	74[label="primEqInt (Pos Zero) (Pos vz410)",fontsize=16,color="burlywood",shape="box"];170[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];74 -> 170[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	170 -> 83[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	171[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];74 -> 171[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	171 -> 84[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	75[label="primEqInt (Pos Zero) (Neg vz410)",fontsize=16,color="burlywood",shape="box"];172[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];75 -> 172[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	172 -> 85[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	173[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];75 -> 173[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	173 -> 86[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	76[label="primEqInt (Neg (Succ vz3100)) (Pos vz410)",fontsize=16,color="black",shape="box"];76 -> 87[label="",style="solid", color="black", weight=3];
9.67/4.06	77[label="primEqInt (Neg (Succ vz3100)) (Neg vz410)",fontsize=16,color="burlywood",shape="box"];174[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];77 -> 174[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	174 -> 88[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	175[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 175[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	175 -> 89[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	78[label="primEqInt (Neg Zero) (Pos vz410)",fontsize=16,color="burlywood",shape="box"];176[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];78 -> 176[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	176 -> 90[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	177[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];78 -> 177[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	177 -> 91[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	79[label="primEqInt (Neg Zero) (Neg vz410)",fontsize=16,color="burlywood",shape="box"];178[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];79 -> 178[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	178 -> 92[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	179[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 179[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	179 -> 93[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	80[label="primEqInt (Pos (Succ vz3100)) (Pos (Succ vz4100))",fontsize=16,color="black",shape="box"];80 -> 94[label="",style="solid", color="black", weight=3];
9.67/4.06	81[label="primEqInt (Pos (Succ vz3100)) (Pos Zero)",fontsize=16,color="black",shape="box"];81 -> 95[label="",style="solid", color="black", weight=3];
9.67/4.06	82[label="False",fontsize=16,color="green",shape="box"];83[label="primEqInt (Pos Zero) (Pos (Succ vz4100))",fontsize=16,color="black",shape="box"];83 -> 96[label="",style="solid", color="black", weight=3];
9.67/4.06	84[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];84 -> 97[label="",style="solid", color="black", weight=3];
9.67/4.06	85[label="primEqInt (Pos Zero) (Neg (Succ vz4100))",fontsize=16,color="black",shape="box"];85 -> 98[label="",style="solid", color="black", weight=3];
9.67/4.06	86[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];86 -> 99[label="",style="solid", color="black", weight=3];
9.67/4.06	87[label="False",fontsize=16,color="green",shape="box"];88[label="primEqInt (Neg (Succ vz3100)) (Neg (Succ vz4100))",fontsize=16,color="black",shape="box"];88 -> 100[label="",style="solid", color="black", weight=3];
9.67/4.06	89[label="primEqInt (Neg (Succ vz3100)) (Neg Zero)",fontsize=16,color="black",shape="box"];89 -> 101[label="",style="solid", color="black", weight=3];
9.67/4.06	90[label="primEqInt (Neg Zero) (Pos (Succ vz4100))",fontsize=16,color="black",shape="box"];90 -> 102[label="",style="solid", color="black", weight=3];
9.67/4.06	91[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];91 -> 103[label="",style="solid", color="black", weight=3];
9.67/4.06	92[label="primEqInt (Neg Zero) (Neg (Succ vz4100))",fontsize=16,color="black",shape="box"];92 -> 104[label="",style="solid", color="black", weight=3];
9.67/4.06	93[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];93 -> 105[label="",style="solid", color="black", weight=3];
9.67/4.06	94[label="primEqNat vz3100 vz4100",fontsize=16,color="burlywood",shape="triangle"];180[label="vz3100/Succ vz31000",fontsize=10,color="white",style="solid",shape="box"];94 -> 180[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	180 -> 106[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	181[label="vz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 181[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	181 -> 107[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	95[label="False",fontsize=16,color="green",shape="box"];96[label="False",fontsize=16,color="green",shape="box"];97[label="True",fontsize=16,color="green",shape="box"];98[label="False",fontsize=16,color="green",shape="box"];99[label="True",fontsize=16,color="green",shape="box"];100 -> 94[label="",style="dashed", color="red", weight=0];
9.67/4.06	100[label="primEqNat vz3100 vz4100",fontsize=16,color="magenta"];100 -> 108[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	100 -> 109[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	101[label="False",fontsize=16,color="green",shape="box"];102[label="False",fontsize=16,color="green",shape="box"];103[label="True",fontsize=16,color="green",shape="box"];104[label="False",fontsize=16,color="green",shape="box"];105[label="True",fontsize=16,color="green",shape="box"];106[label="primEqNat (Succ vz31000) vz4100",fontsize=16,color="burlywood",shape="box"];182[label="vz4100/Succ vz41000",fontsize=10,color="white",style="solid",shape="box"];106 -> 182[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	182 -> 110[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	183[label="vz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];106 -> 183[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	183 -> 111[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	107[label="primEqNat Zero vz4100",fontsize=16,color="burlywood",shape="box"];184[label="vz4100/Succ vz41000",fontsize=10,color="white",style="solid",shape="box"];107 -> 184[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	184 -> 112[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	185[label="vz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 185[label="",style="solid", color="burlywood", weight=9];
9.67/4.06	185 -> 113[label="",style="solid", color="burlywood", weight=3];
9.67/4.06	108[label="vz4100",fontsize=16,color="green",shape="box"];109[label="vz3100",fontsize=16,color="green",shape="box"];110[label="primEqNat (Succ vz31000) (Succ vz41000)",fontsize=16,color="black",shape="box"];110 -> 114[label="",style="solid", color="black", weight=3];
9.67/4.06	111[label="primEqNat (Succ vz31000) Zero",fontsize=16,color="black",shape="box"];111 -> 115[label="",style="solid", color="black", weight=3];
9.67/4.06	112[label="primEqNat Zero (Succ vz41000)",fontsize=16,color="black",shape="box"];112 -> 116[label="",style="solid", color="black", weight=3];
9.67/4.06	113[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];113 -> 117[label="",style="solid", color="black", weight=3];
9.67/4.06	114 -> 94[label="",style="dashed", color="red", weight=0];
9.67/4.06	114[label="primEqNat vz31000 vz41000",fontsize=16,color="magenta"];114 -> 118[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	114 -> 119[label="",style="dashed", color="magenta", weight=3];
9.67/4.06	115[label="False",fontsize=16,color="green",shape="box"];116[label="False",fontsize=16,color="green",shape="box"];117[label="True",fontsize=16,color="green",shape="box"];118[label="vz41000",fontsize=16,color="green",shape="box"];119[label="vz31000",fontsize=16,color="green",shape="box"];}
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(6)
9.67/4.06	Complex Obligation (AND)
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(7)
9.67/4.06	Obligation:
9.67/4.06	Q DP problem:
9.67/4.06	The TRS P consists of the following rules:
9.67/4.06	
9.67/4.06	   new_asAs(Succ(vz30000), Succ(vz40000), vz31, vz41) -> new_asAs(vz30000, vz40000, vz31, vz41)
9.67/4.06	
9.67/4.06	R is empty.
9.67/4.06	Q is empty.
9.67/4.06	We have to consider all minimal (P,Q,R)-chains.
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(8) QDPSizeChangeProof (EQUIVALENT)
9.67/4.06	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. 
9.67/4.06	
9.67/4.06	From the DPs we obtained the following set of size-change graphs:
9.67/4.06	*new_asAs(Succ(vz30000), Succ(vz40000), vz31, vz41) -> new_asAs(vz30000, vz40000, vz31, vz41)
9.67/4.06	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4
9.67/4.06	
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(9)
9.67/4.06	YES
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(10)
9.67/4.06	Obligation:
9.67/4.06	Q DP problem:
9.67/4.06	The TRS P consists of the following rules:
9.67/4.06	
9.67/4.06	   new_primEqNat(Succ(vz31000), Succ(vz41000)) -> new_primEqNat(vz31000, vz41000)
9.67/4.06	
9.67/4.06	R is empty.
9.67/4.06	Q is empty.
9.67/4.06	We have to consider all minimal (P,Q,R)-chains.
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(11) QDPSizeChangeProof (EQUIVALENT)
9.67/4.06	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. 
9.67/4.06	
9.67/4.06	From the DPs we obtained the following set of size-change graphs:
9.67/4.06	*new_primEqNat(Succ(vz31000), Succ(vz41000)) -> new_primEqNat(vz31000, vz41000)
9.67/4.06	The graph contains the following edges 1 > 1, 2 > 2
9.67/4.06	
9.67/4.06	
9.67/4.06	----------------------------------------
9.67/4.06	
9.67/4.06	(12)
9.67/4.06	YES
9.91/4.09	EOF