8.27/3.61	YES
9.94/4.06	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.94/4.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.94/4.06	
9.94/4.06	
9.94/4.06	H-Termination with start terms of the given HASKELL could be proven:
9.94/4.06	
9.94/4.06	(0) HASKELL
9.94/4.06	(1) BR [EQUIVALENT, 0 ms]
9.94/4.06	(2) HASKELL
9.94/4.06	(3) COR [EQUIVALENT, 0 ms]
9.94/4.06	(4) HASKELL
9.94/4.06	(5) Narrow [SOUND, 0 ms]
9.94/4.06	(6) AND
9.94/4.06	    (7) QDP
9.94/4.06	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.94/4.06	        (9) YES
9.94/4.06	    (10) QDP
9.94/4.06	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.94/4.06	        (12) YES
9.94/4.06	    (13) QDP
9.94/4.06	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.94/4.06	        (15) YES
9.94/4.06	
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(0)
9.94/4.06	Obligation:
9.94/4.06	mainModule Main 
9.94/4.06	module Main where {
9.94/4.06	import qualified Prelude;
9.94/4.06	}
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(1) BR (EQUIVALENT)
9.94/4.06	Replaced joker patterns by fresh variables and removed binding patterns.
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(2)
9.94/4.06	Obligation:
9.94/4.06	mainModule Main 
9.94/4.06	module Main where {
9.94/4.06	import qualified Prelude;
9.94/4.06	}
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(3) COR (EQUIVALENT)
9.94/4.06	Cond Reductions:
9.94/4.06	The following Function with conditions
9.94/4.06	"undefined |Falseundefined;
9.94/4.06	"
9.94/4.06	is transformed to
9.94/4.06	"undefined  = undefined1;
9.94/4.06	"
9.94/4.06	"undefined0 True = undefined;
9.94/4.06	"
9.94/4.06	"undefined1  = undefined0 False;
9.94/4.06	"
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(4)
9.94/4.06	Obligation:
9.94/4.06	mainModule Main 
9.94/4.06	module Main where {
9.94/4.06	import qualified Prelude;
9.94/4.06	}
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(5) Narrow (SOUND)
9.94/4.06	Haskell To QDPs
9.94/4.06	
9.94/4.06	digraph dp_graph {
9.94/4.06	node [outthreshold=100, inthreshold=100];1[label="elem",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.94/4.06	3[label="elem vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.94/4.06	4[label="elem vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.94/4.06	5[label="any . (==)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.94/4.06	6[label="any ((==) vz3) vz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.94/4.06	7[label="or . map ((==) vz3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.94/4.06	8[label="or (map ((==) vz3) vz4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.94/4.06	9[label="foldr (||) False (map ((==) vz3) vz4)",fontsize=16,color="burlywood",shape="triangle"];136[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];9 -> 136[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	136 -> 10[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	137[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 137[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	137 -> 11[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	10[label="foldr (||) False (map ((==) vz3) (vz40 : vz41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
9.94/4.06	11[label="foldr (||) False (map ((==) vz3) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
9.94/4.06	12[label="foldr (||) False (((==) vz3 vz40) : map ((==) vz3) vz41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
9.94/4.06	13[label="foldr (||) False []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.94/4.06	14 -> 16[label="",style="dashed", color="red", weight=0];
9.94/4.06	14[label="(||) (==) vz3 vz40 foldr (||) False (map ((==) vz3) vz41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	15[label="False",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
9.94/4.06	17[label="foldr (||) False (map ((==) vz3) vz41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	16[label="(||) (==) vz3 vz40 vz5",fontsize=16,color="burlywood",shape="triangle"];138[label="vz3/vz30 :% vz31",fontsize=10,color="white",style="solid",shape="box"];16 -> 138[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	138 -> 19[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	18[label="vz41",fontsize=16,color="green",shape="box"];19[label="(||) (==) vz30 :% vz31 vz40 vz5",fontsize=16,color="burlywood",shape="box"];139[label="vz40/vz400 :% vz401",fontsize=10,color="white",style="solid",shape="box"];19 -> 139[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	139 -> 20[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	20[label="(||) (==) vz30 :% vz31 vz400 :% vz401 vz5",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
9.94/4.06	21[label="(||) vz30 == vz400 && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
9.94/4.06	22[label="(||) primEqInt vz30 vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];140[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 140[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	140 -> 23[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	141[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 141[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	141 -> 24[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	23[label="(||) primEqInt (Pos vz300) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];142[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];23 -> 142[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	142 -> 25[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	143[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 143[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	143 -> 26[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	24[label="(||) primEqInt (Neg vz300) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];144[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];24 -> 144[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	144 -> 27[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	145[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 145[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	145 -> 28[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	25[label="(||) primEqInt (Pos (Succ vz3000)) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];146[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 146[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	146 -> 29[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	147[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 147[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	147 -> 30[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	26[label="(||) primEqInt (Pos Zero) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];148[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 148[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	148 -> 31[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	149[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 149[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	149 -> 32[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	27[label="(||) primEqInt (Neg (Succ vz3000)) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];150[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 150[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	150 -> 33[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	151[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 151[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	151 -> 34[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	28[label="(||) primEqInt (Neg Zero) vz400 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];152[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 152[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	152 -> 35[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	153[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 153[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	153 -> 36[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	29[label="(||) primEqInt (Pos (Succ vz3000)) (Pos vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];154[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];29 -> 154[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	154 -> 37[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	155[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 155[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	155 -> 38[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	30[label="(||) primEqInt (Pos (Succ vz3000)) (Neg vz4000) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
9.94/4.06	31[label="(||) primEqInt (Pos Zero) (Pos vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];156[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];31 -> 156[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	156 -> 40[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	157[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];31 -> 157[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	157 -> 41[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	32[label="(||) primEqInt (Pos Zero) (Neg vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];158[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];32 -> 158[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	158 -> 42[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	159[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 159[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	159 -> 43[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	33[label="(||) primEqInt (Neg (Succ vz3000)) (Pos vz4000) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3];
9.94/4.06	34[label="(||) primEqInt (Neg (Succ vz3000)) (Neg vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];160[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];34 -> 160[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	160 -> 45[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	161[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 161[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	161 -> 46[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	35[label="(||) primEqInt (Neg Zero) (Pos vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];162[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];35 -> 162[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	162 -> 47[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	163[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 163[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	163 -> 48[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	36[label="(||) primEqInt (Neg Zero) (Neg vz4000) && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];164[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];36 -> 164[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	164 -> 49[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	165[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 165[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	165 -> 50[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	37[label="(||) primEqInt (Pos (Succ vz3000)) (Pos (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
9.94/4.06	38[label="(||) primEqInt (Pos (Succ vz3000)) (Pos Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
9.94/4.06	39[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="black",shape="triangle"];39 -> 53[label="",style="solid", color="black", weight=3];
9.94/4.06	40[label="(||) primEqInt (Pos Zero) (Pos (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
9.94/4.06	41[label="(||) primEqInt (Pos Zero) (Pos Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
9.94/4.06	42[label="(||) primEqInt (Pos Zero) (Neg (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
9.94/4.06	43[label="(||) primEqInt (Pos Zero) (Neg Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
9.94/4.06	44 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	44[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];45[label="(||) primEqInt (Neg (Succ vz3000)) (Neg (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];45 -> 58[label="",style="solid", color="black", weight=3];
9.94/4.06	46[label="(||) primEqInt (Neg (Succ vz3000)) (Neg Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];46 -> 59[label="",style="solid", color="black", weight=3];
9.94/4.06	47[label="(||) primEqInt (Neg Zero) (Pos (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];47 -> 60[label="",style="solid", color="black", weight=3];
9.94/4.06	48[label="(||) primEqInt (Neg Zero) (Pos Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];48 -> 61[label="",style="solid", color="black", weight=3];
9.94/4.06	49[label="(||) primEqInt (Neg Zero) (Neg (Succ vz40000)) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];49 -> 62[label="",style="solid", color="black", weight=3];
9.94/4.06	50[label="(||) primEqInt (Neg Zero) (Neg Zero) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];50 -> 63[label="",style="solid", color="black", weight=3];
9.94/4.06	51[label="(||) primEqNat vz3000 vz40000 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="triangle"];166[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];51 -> 166[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	166 -> 64[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	167[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 167[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	167 -> 65[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	52 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	52[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];53[label="(||) False vz5",fontsize=16,color="black",shape="triangle"];53 -> 66[label="",style="solid", color="black", weight=3];
9.94/4.06	54 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	54[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];55[label="(||) True && vz31 == vz401 vz5",fontsize=16,color="black",shape="triangle"];55 -> 67[label="",style="solid", color="black", weight=3];
9.94/4.06	56 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	56[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];57 -> 55[label="",style="dashed", color="red", weight=0];
9.94/4.06	57[label="(||) True && vz31 == vz401 vz5",fontsize=16,color="magenta"];58 -> 51[label="",style="dashed", color="red", weight=0];
9.94/4.06	58[label="(||) primEqNat vz3000 vz40000 && vz31 == vz401 vz5",fontsize=16,color="magenta"];58 -> 68[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	58 -> 69[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	59 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	59[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];60 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	60[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];61 -> 55[label="",style="dashed", color="red", weight=0];
9.94/4.06	61[label="(||) True && vz31 == vz401 vz5",fontsize=16,color="magenta"];62 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	62[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];63 -> 55[label="",style="dashed", color="red", weight=0];
9.94/4.06	63[label="(||) True && vz31 == vz401 vz5",fontsize=16,color="magenta"];64[label="(||) primEqNat (Succ vz30000) vz40000 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];168[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];64 -> 168[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	168 -> 70[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	169[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 169[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	169 -> 71[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	65[label="(||) primEqNat Zero vz40000 && vz31 == vz401 vz5",fontsize=16,color="burlywood",shape="box"];170[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];65 -> 170[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	170 -> 72[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	171[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 171[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	171 -> 73[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	66[label="vz5",fontsize=16,color="green",shape="box"];67[label="(||) vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
9.94/4.06	68[label="vz40000",fontsize=16,color="green",shape="box"];69[label="vz3000",fontsize=16,color="green",shape="box"];70[label="(||) primEqNat (Succ vz30000) (Succ vz400000) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];70 -> 75[label="",style="solid", color="black", weight=3];
9.94/4.06	71[label="(||) primEqNat (Succ vz30000) Zero && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];71 -> 76[label="",style="solid", color="black", weight=3];
9.94/4.06	72[label="(||) primEqNat Zero (Succ vz400000) && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];72 -> 77[label="",style="solid", color="black", weight=3];
9.94/4.06	73[label="(||) primEqNat Zero Zero && vz31 == vz401 vz5",fontsize=16,color="black",shape="box"];73 -> 78[label="",style="solid", color="black", weight=3];
9.94/4.06	74[label="(||) primEqInt vz31 vz401 vz5",fontsize=16,color="burlywood",shape="box"];172[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];74 -> 172[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	172 -> 79[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	173[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];74 -> 173[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	173 -> 80[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	75 -> 51[label="",style="dashed", color="red", weight=0];
9.94/4.06	75[label="(||) primEqNat vz30000 vz400000 && vz31 == vz401 vz5",fontsize=16,color="magenta"];75 -> 81[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	75 -> 82[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	76 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	76[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];77 -> 39[label="",style="dashed", color="red", weight=0];
9.94/4.06	77[label="(||) False && vz31 == vz401 vz5",fontsize=16,color="magenta"];78 -> 55[label="",style="dashed", color="red", weight=0];
9.94/4.06	78[label="(||) True && vz31 == vz401 vz5",fontsize=16,color="magenta"];79[label="(||) primEqInt (Pos vz310) vz401 vz5",fontsize=16,color="burlywood",shape="box"];174[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];79 -> 174[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	174 -> 83[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	175[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 175[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	175 -> 84[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	80[label="(||) primEqInt (Neg vz310) vz401 vz5",fontsize=16,color="burlywood",shape="box"];176[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];80 -> 176[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	176 -> 85[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	177[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];80 -> 177[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	177 -> 86[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	81[label="vz400000",fontsize=16,color="green",shape="box"];82[label="vz30000",fontsize=16,color="green",shape="box"];83[label="(||) primEqInt (Pos (Succ vz3100)) vz401 vz5",fontsize=16,color="burlywood",shape="box"];178[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];83 -> 178[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	178 -> 87[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	179[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];83 -> 179[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	179 -> 88[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	84[label="(||) primEqInt (Pos Zero) vz401 vz5",fontsize=16,color="burlywood",shape="box"];180[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];84 -> 180[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	180 -> 89[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	181[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];84 -> 181[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	181 -> 90[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	85[label="(||) primEqInt (Neg (Succ vz3100)) vz401 vz5",fontsize=16,color="burlywood",shape="box"];182[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 182[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	182 -> 91[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	183[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 183[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	183 -> 92[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	86[label="(||) primEqInt (Neg Zero) vz401 vz5",fontsize=16,color="burlywood",shape="box"];184[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 184[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	184 -> 93[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	185[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 185[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	185 -> 94[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	87[label="(||) primEqInt (Pos (Succ vz3100)) (Pos vz4010) vz5",fontsize=16,color="burlywood",shape="box"];186[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];87 -> 186[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	186 -> 95[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	187[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 187[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	187 -> 96[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	88[label="(||) primEqInt (Pos (Succ vz3100)) (Neg vz4010) vz5",fontsize=16,color="black",shape="box"];88 -> 97[label="",style="solid", color="black", weight=3];
9.94/4.06	89[label="(||) primEqInt (Pos Zero) (Pos vz4010) vz5",fontsize=16,color="burlywood",shape="box"];188[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];89 -> 188[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	188 -> 98[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	189[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 189[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	189 -> 99[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	90[label="(||) primEqInt (Pos Zero) (Neg vz4010) vz5",fontsize=16,color="burlywood",shape="box"];190[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];90 -> 190[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	190 -> 100[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	191[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];90 -> 191[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	191 -> 101[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	91[label="(||) primEqInt (Neg (Succ vz3100)) (Pos vz4010) vz5",fontsize=16,color="black",shape="box"];91 -> 102[label="",style="solid", color="black", weight=3];
9.94/4.06	92[label="(||) primEqInt (Neg (Succ vz3100)) (Neg vz4010) vz5",fontsize=16,color="burlywood",shape="box"];192[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];92 -> 192[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	192 -> 103[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	193[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];92 -> 193[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	193 -> 104[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	93[label="(||) primEqInt (Neg Zero) (Pos vz4010) vz5",fontsize=16,color="burlywood",shape="box"];194[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];93 -> 194[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	194 -> 105[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	195[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];93 -> 195[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	195 -> 106[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	94[label="(||) primEqInt (Neg Zero) (Neg vz4010) vz5",fontsize=16,color="burlywood",shape="box"];196[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];94 -> 196[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	196 -> 107[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	197[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 197[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	197 -> 108[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	95[label="(||) primEqInt (Pos (Succ vz3100)) (Pos (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];95 -> 109[label="",style="solid", color="black", weight=3];
9.94/4.06	96[label="(||) primEqInt (Pos (Succ vz3100)) (Pos Zero) vz5",fontsize=16,color="black",shape="box"];96 -> 110[label="",style="solid", color="black", weight=3];
9.94/4.06	97 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	97[label="(||) False vz5",fontsize=16,color="magenta"];98[label="(||) primEqInt (Pos Zero) (Pos (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];98 -> 111[label="",style="solid", color="black", weight=3];
9.94/4.06	99[label="(||) primEqInt (Pos Zero) (Pos Zero) vz5",fontsize=16,color="black",shape="box"];99 -> 112[label="",style="solid", color="black", weight=3];
9.94/4.06	100[label="(||) primEqInt (Pos Zero) (Neg (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];100 -> 113[label="",style="solid", color="black", weight=3];
9.94/4.06	101[label="(||) primEqInt (Pos Zero) (Neg Zero) vz5",fontsize=16,color="black",shape="box"];101 -> 114[label="",style="solid", color="black", weight=3];
9.94/4.06	102 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	102[label="(||) False vz5",fontsize=16,color="magenta"];103[label="(||) primEqInt (Neg (Succ vz3100)) (Neg (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];103 -> 115[label="",style="solid", color="black", weight=3];
9.94/4.06	104[label="(||) primEqInt (Neg (Succ vz3100)) (Neg Zero) vz5",fontsize=16,color="black",shape="box"];104 -> 116[label="",style="solid", color="black", weight=3];
9.94/4.06	105[label="(||) primEqInt (Neg Zero) (Pos (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];105 -> 117[label="",style="solid", color="black", weight=3];
9.94/4.06	106[label="(||) primEqInt (Neg Zero) (Pos Zero) vz5",fontsize=16,color="black",shape="box"];106 -> 118[label="",style="solid", color="black", weight=3];
9.94/4.06	107[label="(||) primEqInt (Neg Zero) (Neg (Succ vz40100)) vz5",fontsize=16,color="black",shape="box"];107 -> 119[label="",style="solid", color="black", weight=3];
9.94/4.06	108[label="(||) primEqInt (Neg Zero) (Neg Zero) vz5",fontsize=16,color="black",shape="box"];108 -> 120[label="",style="solid", color="black", weight=3];
9.94/4.06	109[label="(||) primEqNat vz3100 vz40100 vz5",fontsize=16,color="burlywood",shape="triangle"];198[label="vz3100/Succ vz31000",fontsize=10,color="white",style="solid",shape="box"];109 -> 198[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	198 -> 121[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	199[label="vz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];109 -> 199[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	199 -> 122[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	110 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	110[label="(||) False vz5",fontsize=16,color="magenta"];111 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	111[label="(||) False vz5",fontsize=16,color="magenta"];112[label="(||) True vz5",fontsize=16,color="black",shape="triangle"];112 -> 123[label="",style="solid", color="black", weight=3];
9.94/4.06	113 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	113[label="(||) False vz5",fontsize=16,color="magenta"];114 -> 112[label="",style="dashed", color="red", weight=0];
9.94/4.06	114[label="(||) True vz5",fontsize=16,color="magenta"];115 -> 109[label="",style="dashed", color="red", weight=0];
9.94/4.06	115[label="(||) primEqNat vz3100 vz40100 vz5",fontsize=16,color="magenta"];115 -> 124[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	115 -> 125[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	116 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	116[label="(||) False vz5",fontsize=16,color="magenta"];117 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	117[label="(||) False vz5",fontsize=16,color="magenta"];118 -> 112[label="",style="dashed", color="red", weight=0];
9.94/4.06	118[label="(||) True vz5",fontsize=16,color="magenta"];119 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	119[label="(||) False vz5",fontsize=16,color="magenta"];120 -> 112[label="",style="dashed", color="red", weight=0];
9.94/4.06	120[label="(||) True vz5",fontsize=16,color="magenta"];121[label="(||) primEqNat (Succ vz31000) vz40100 vz5",fontsize=16,color="burlywood",shape="box"];200[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];121 -> 200[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	200 -> 126[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	201[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 201[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	201 -> 127[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	122[label="(||) primEqNat Zero vz40100 vz5",fontsize=16,color="burlywood",shape="box"];202[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];122 -> 202[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	202 -> 128[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	203[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];122 -> 203[label="",style="solid", color="burlywood", weight=9];
9.94/4.06	203 -> 129[label="",style="solid", color="burlywood", weight=3];
9.94/4.06	123[label="True",fontsize=16,color="green",shape="box"];124[label="vz3100",fontsize=16,color="green",shape="box"];125[label="vz40100",fontsize=16,color="green",shape="box"];126[label="(||) primEqNat (Succ vz31000) (Succ vz401000) vz5",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
9.94/4.06	127[label="(||) primEqNat (Succ vz31000) Zero vz5",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3];
9.94/4.06	128[label="(||) primEqNat Zero (Succ vz401000) vz5",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3];
9.94/4.06	129[label="(||) primEqNat Zero Zero vz5",fontsize=16,color="black",shape="box"];129 -> 133[label="",style="solid", color="black", weight=3];
9.94/4.06	130 -> 109[label="",style="dashed", color="red", weight=0];
9.94/4.06	130[label="(||) primEqNat vz31000 vz401000 vz5",fontsize=16,color="magenta"];130 -> 134[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	130 -> 135[label="",style="dashed", color="magenta", weight=3];
9.94/4.06	131 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	131[label="(||) False vz5",fontsize=16,color="magenta"];132 -> 53[label="",style="dashed", color="red", weight=0];
9.94/4.06	132[label="(||) False vz5",fontsize=16,color="magenta"];133 -> 112[label="",style="dashed", color="red", weight=0];
9.94/4.06	133[label="(||) True vz5",fontsize=16,color="magenta"];134[label="vz31000",fontsize=16,color="green",shape="box"];135[label="vz401000",fontsize=16,color="green",shape="box"];}
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(6)
9.94/4.06	Complex Obligation (AND)
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(7)
9.94/4.06	Obligation:
9.94/4.06	Q DP problem:
9.94/4.06	The TRS P consists of the following rules:
9.94/4.06	
9.94/4.06	   new_foldr(vz3, :(vz40, vz41)) -> new_foldr(vz3, vz41)
9.94/4.06	
9.94/4.06	R is empty.
9.94/4.06	Q is empty.
9.94/4.06	We have to consider all minimal (P,Q,R)-chains.
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(8) QDPSizeChangeProof (EQUIVALENT)
9.94/4.06	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. 
9.94/4.06	
9.94/4.06	From the DPs we obtained the following set of size-change graphs:
9.94/4.06	*new_foldr(vz3, :(vz40, vz41)) -> new_foldr(vz3, vz41)
9.94/4.06	The graph contains the following edges 1 >= 1, 2 > 2
9.94/4.06	
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(9)
9.94/4.06	YES
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(10)
9.94/4.06	Obligation:
9.94/4.06	Q DP problem:
9.94/4.06	The TRS P consists of the following rules:
9.94/4.06	
9.94/4.06	   new_pePe(Succ(vz31000), Succ(vz401000), vz5) -> new_pePe(vz31000, vz401000, vz5)
9.94/4.06	
9.94/4.06	R is empty.
9.94/4.06	Q is empty.
9.94/4.06	We have to consider all minimal (P,Q,R)-chains.
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(11) QDPSizeChangeProof (EQUIVALENT)
9.94/4.06	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. 
9.94/4.06	
9.94/4.06	From the DPs we obtained the following set of size-change graphs:
9.94/4.06	*new_pePe(Succ(vz31000), Succ(vz401000), vz5) -> new_pePe(vz31000, vz401000, vz5)
9.94/4.06	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
9.94/4.06	
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(12)
9.94/4.06	YES
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(13)
9.94/4.06	Obligation:
9.94/4.06	Q DP problem:
9.94/4.06	The TRS P consists of the following rules:
9.94/4.06	
9.94/4.06	   new_pePe0(Succ(vz30000), Succ(vz400000), vz31, vz401, vz5) -> new_pePe0(vz30000, vz400000, vz31, vz401, vz5)
9.94/4.06	
9.94/4.06	R is empty.
9.94/4.06	Q is empty.
9.94/4.06	We have to consider all minimal (P,Q,R)-chains.
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(14) QDPSizeChangeProof (EQUIVALENT)
9.94/4.06	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. 
9.94/4.06	
9.94/4.06	From the DPs we obtained the following set of size-change graphs:
9.94/4.06	*new_pePe0(Succ(vz30000), Succ(vz400000), vz31, vz401, vz5) -> new_pePe0(vz30000, vz400000, vz31, vz401, vz5)
9.94/4.06	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
9.94/4.06	
9.94/4.06	
9.94/4.06	----------------------------------------
9.94/4.06	
9.94/4.06	(15)
9.94/4.06	YES
9.94/4.12	EOF