8.13/3.61	YES
9.69/4.06	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.69/4.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.69/4.06	
9.69/4.06	
9.69/4.06	H-Termination with start terms of the given HASKELL could be proven:
9.69/4.06	
9.69/4.06	(0) HASKELL
9.69/4.06	(1) BR [EQUIVALENT, 0 ms]
9.69/4.06	(2) HASKELL
9.69/4.06	(3) COR [EQUIVALENT, 0 ms]
9.69/4.06	(4) HASKELL
9.69/4.06	(5) Narrow [SOUND, 0 ms]
9.69/4.06	(6) AND
9.69/4.06	    (7) QDP
9.69/4.06	        (8) QDPSizeChangeProof [EQUIVALENT, 1 ms]
9.69/4.06	        (9) YES
9.69/4.06	    (10) QDP
9.69/4.06	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.69/4.06	        (12) YES
9.69/4.06	    (13) QDP
9.69/4.06	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.69/4.06	        (15) YES
9.69/4.06	
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(0)
9.69/4.06	Obligation:
9.69/4.06	mainModule Main 
9.69/4.06	module Main where {
9.69/4.06	import qualified Prelude;
9.69/4.06	}
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(1) BR (EQUIVALENT)
9.69/4.06	Replaced joker patterns by fresh variables and removed binding patterns.
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(2)
9.69/4.06	Obligation:
9.69/4.06	mainModule Main 
9.69/4.06	module Main where {
9.69/4.06	import qualified Prelude;
9.69/4.06	}
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(3) COR (EQUIVALENT)
9.69/4.06	Cond Reductions:
9.69/4.06	The following Function with conditions
9.69/4.06	"undefined |Falseundefined;
9.69/4.06	"
9.69/4.06	is transformed to
9.69/4.06	"undefined  = undefined1;
9.69/4.06	"
9.69/4.06	"undefined0 True = undefined;
9.69/4.06	"
9.69/4.06	"undefined1  = undefined0 False;
9.69/4.06	"
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(4)
9.69/4.06	Obligation:
9.69/4.06	mainModule Main 
9.69/4.06	module Main where {
9.69/4.06	import qualified Prelude;
9.69/4.06	}
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(5) Narrow (SOUND)
9.69/4.06	Haskell To QDPs
9.69/4.06	
9.69/4.06	digraph dp_graph {
9.69/4.06	node [outthreshold=100, inthreshold=100];1[label="notElem",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.69/4.06	3[label="notElem vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.69/4.06	4[label="notElem vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.69/4.06	5[label="all . (/=)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.69/4.06	6[label="all ((/=) vz3) vz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.69/4.06	7[label="and . map ((/=) vz3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.69/4.06	8[label="and (map ((/=) vz3) vz4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.69/4.06	9[label="foldr (&&) True (map ((/=) vz3) vz4)",fontsize=16,color="burlywood",shape="triangle"];139[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];9 -> 139[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	139 -> 10[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	140[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 140[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	140 -> 11[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	10[label="foldr (&&) True (map ((/=) vz3) (vz40 : vz41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
9.69/4.06	11[label="foldr (&&) True (map ((/=) vz3) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
9.69/4.06	12[label="foldr (&&) True (((/=) vz3 vz40) : map ((/=) vz3) vz41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
9.69/4.06	13[label="foldr (&&) True []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.69/4.06	14 -> 16[label="",style="dashed", color="red", weight=0];
9.69/4.06	14[label="(&&) (/=) vz3 vz40 foldr (&&) True (map ((/=) vz3) vz41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	15[label="True",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
9.69/4.06	17[label="foldr (&&) True (map ((/=) vz3) vz41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	16[label="(&&) (/=) vz3 vz40 vz5",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3];
9.69/4.06	18[label="vz41",fontsize=16,color="green",shape="box"];19[label="(&&) not (vz3 == vz40) vz5",fontsize=16,color="burlywood",shape="box"];141[label="vz3/vz30 :% vz31",fontsize=10,color="white",style="solid",shape="box"];19 -> 141[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	141 -> 20[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	20[label="(&&) not (vz30 :% vz31 == vz40) vz5",fontsize=16,color="burlywood",shape="box"];142[label="vz40/vz400 :% vz401",fontsize=10,color="white",style="solid",shape="box"];20 -> 142[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	142 -> 21[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	21[label="(&&) not (vz30 :% vz31 == vz400 :% vz401) vz5",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
9.69/4.06	22[label="(&&) not (vz30 == vz400 && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
9.69/4.06	23[label="(&&) not (primEqInt vz30 vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];143[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];23 -> 143[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	143 -> 24[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	144[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];23 -> 144[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	144 -> 25[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	24[label="(&&) not (primEqInt (Pos vz300) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];145[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];24 -> 145[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	145 -> 26[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	146[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 146[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	146 -> 27[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	25[label="(&&) not (primEqInt (Neg vz300) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];147[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 147[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	147 -> 28[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	148[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 148[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	148 -> 29[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	26[label="(&&) not (primEqInt (Pos (Succ vz3000)) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];149[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 149[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	149 -> 30[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	150[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 150[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	150 -> 31[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	27[label="(&&) not (primEqInt (Pos Zero) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];151[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 151[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	151 -> 32[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	152[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];27 -> 152[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	152 -> 33[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	28[label="(&&) not (primEqInt (Neg (Succ vz3000)) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];153[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 153[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	153 -> 34[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	154[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];28 -> 154[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	154 -> 35[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	29[label="(&&) not (primEqInt (Neg Zero) vz400 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];155[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];29 -> 155[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	155 -> 36[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	156[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];29 -> 156[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	156 -> 37[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	30[label="(&&) not (primEqInt (Pos (Succ vz3000)) (Pos vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];157[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];30 -> 157[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	157 -> 38[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	158[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];30 -> 158[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	158 -> 39[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	31[label="(&&) not (primEqInt (Pos (Succ vz3000)) (Neg vz4000) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
9.69/4.06	32[label="(&&) not (primEqInt (Pos Zero) (Pos vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];159[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];32 -> 159[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	159 -> 41[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	160[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 160[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	160 -> 42[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	33[label="(&&) not (primEqInt (Pos Zero) (Neg vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];161[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];33 -> 161[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	161 -> 43[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	162[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 162[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	162 -> 44[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	34[label="(&&) not (primEqInt (Neg (Succ vz3000)) (Pos vz4000) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];34 -> 45[label="",style="solid", color="black", weight=3];
9.69/4.06	35[label="(&&) not (primEqInt (Neg (Succ vz3000)) (Neg vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];163[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];35 -> 163[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	163 -> 46[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	164[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];35 -> 164[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	164 -> 47[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	36[label="(&&) not (primEqInt (Neg Zero) (Pos vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];165[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];36 -> 165[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	165 -> 48[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	166[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];36 -> 166[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	166 -> 49[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	37[label="(&&) not (primEqInt (Neg Zero) (Neg vz4000) && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];167[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];37 -> 167[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	167 -> 50[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	168[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 168[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	168 -> 51[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	38[label="(&&) not (primEqInt (Pos (Succ vz3000)) (Pos (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
9.69/4.06	39[label="(&&) not (primEqInt (Pos (Succ vz3000)) (Pos Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
9.69/4.06	40[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="black",shape="triangle"];40 -> 54[label="",style="solid", color="black", weight=3];
9.69/4.06	41[label="(&&) not (primEqInt (Pos Zero) (Pos (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
9.69/4.06	42[label="(&&) not (primEqInt (Pos Zero) (Pos Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
9.69/4.06	43[label="(&&) not (primEqInt (Pos Zero) (Neg (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
9.69/4.06	44[label="(&&) not (primEqInt (Pos Zero) (Neg Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3];
9.69/4.06	45 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	45[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];46[label="(&&) not (primEqInt (Neg (Succ vz3000)) (Neg (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];46 -> 59[label="",style="solid", color="black", weight=3];
9.69/4.06	47[label="(&&) not (primEqInt (Neg (Succ vz3000)) (Neg Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];47 -> 60[label="",style="solid", color="black", weight=3];
9.69/4.06	48[label="(&&) not (primEqInt (Neg Zero) (Pos (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];48 -> 61[label="",style="solid", color="black", weight=3];
9.69/4.06	49[label="(&&) not (primEqInt (Neg Zero) (Pos Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];49 -> 62[label="",style="solid", color="black", weight=3];
9.69/4.06	50[label="(&&) not (primEqInt (Neg Zero) (Neg (Succ vz40000)) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];50 -> 63[label="",style="solid", color="black", weight=3];
9.69/4.06	51[label="(&&) not (primEqInt (Neg Zero) (Neg Zero) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];51 -> 64[label="",style="solid", color="black", weight=3];
9.69/4.06	52[label="(&&) not (primEqNat vz3000 vz40000 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="triangle"];169[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];52 -> 169[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	169 -> 65[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	170[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 170[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	170 -> 66[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	53 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	53[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];54[label="(&&) not False vz5",fontsize=16,color="black",shape="triangle"];54 -> 67[label="",style="solid", color="black", weight=3];
9.69/4.06	55 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	55[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];56[label="(&&) not (True && vz31 == vz401) vz5",fontsize=16,color="black",shape="triangle"];56 -> 68[label="",style="solid", color="black", weight=3];
9.69/4.06	57 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	57[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];58 -> 56[label="",style="dashed", color="red", weight=0];
9.69/4.06	58[label="(&&) not (True && vz31 == vz401) vz5",fontsize=16,color="magenta"];59 -> 52[label="",style="dashed", color="red", weight=0];
9.69/4.06	59[label="(&&) not (primEqNat vz3000 vz40000 && vz31 == vz401) vz5",fontsize=16,color="magenta"];59 -> 69[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	59 -> 70[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	60 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	60[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];61 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	61[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];62 -> 56[label="",style="dashed", color="red", weight=0];
9.69/4.06	62[label="(&&) not (True && vz31 == vz401) vz5",fontsize=16,color="magenta"];63 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	63[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];64 -> 56[label="",style="dashed", color="red", weight=0];
9.69/4.06	64[label="(&&) not (True && vz31 == vz401) vz5",fontsize=16,color="magenta"];65[label="(&&) not (primEqNat (Succ vz30000) vz40000 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];171[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];65 -> 171[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	171 -> 71[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	172[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 172[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	172 -> 72[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	66[label="(&&) not (primEqNat Zero vz40000 && vz31 == vz401) vz5",fontsize=16,color="burlywood",shape="box"];173[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];66 -> 173[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	173 -> 73[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	174[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];66 -> 174[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	174 -> 74[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	67[label="(&&) True vz5",fontsize=16,color="black",shape="box"];67 -> 75[label="",style="solid", color="black", weight=3];
9.69/4.06	68[label="(&&) not (vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];68 -> 76[label="",style="solid", color="black", weight=3];
9.69/4.06	69[label="vz40000",fontsize=16,color="green",shape="box"];70[label="vz3000",fontsize=16,color="green",shape="box"];71[label="(&&) not (primEqNat (Succ vz30000) (Succ vz400000) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];71 -> 77[label="",style="solid", color="black", weight=3];
9.69/4.06	72[label="(&&) not (primEqNat (Succ vz30000) Zero && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];72 -> 78[label="",style="solid", color="black", weight=3];
9.69/4.06	73[label="(&&) not (primEqNat Zero (Succ vz400000) && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];73 -> 79[label="",style="solid", color="black", weight=3];
9.69/4.06	74[label="(&&) not (primEqNat Zero Zero && vz31 == vz401) vz5",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3];
9.69/4.06	75[label="vz5",fontsize=16,color="green",shape="box"];76[label="(&&) not (primEqInt vz31 vz401) vz5",fontsize=16,color="burlywood",shape="box"];175[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];76 -> 175[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	175 -> 81[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	176[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];76 -> 176[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	176 -> 82[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	77 -> 52[label="",style="dashed", color="red", weight=0];
9.69/4.06	77[label="(&&) not (primEqNat vz30000 vz400000 && vz31 == vz401) vz5",fontsize=16,color="magenta"];77 -> 83[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	77 -> 84[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	78 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	78[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];79 -> 40[label="",style="dashed", color="red", weight=0];
9.69/4.06	79[label="(&&) not (False && vz31 == vz401) vz5",fontsize=16,color="magenta"];80 -> 56[label="",style="dashed", color="red", weight=0];
9.69/4.06	80[label="(&&) not (True && vz31 == vz401) vz5",fontsize=16,color="magenta"];81[label="(&&) not (primEqInt (Pos vz310) vz401) vz5",fontsize=16,color="burlywood",shape="box"];177[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];81 -> 177[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	177 -> 85[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	178[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];81 -> 178[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	178 -> 86[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	82[label="(&&) not (primEqInt (Neg vz310) vz401) vz5",fontsize=16,color="burlywood",shape="box"];179[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];82 -> 179[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	179 -> 87[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	180[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];82 -> 180[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	180 -> 88[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	83[label="vz400000",fontsize=16,color="green",shape="box"];84[label="vz30000",fontsize=16,color="green",shape="box"];85[label="(&&) not (primEqInt (Pos (Succ vz3100)) vz401) vz5",fontsize=16,color="burlywood",shape="box"];181[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 181[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	181 -> 89[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	182[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];85 -> 182[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	182 -> 90[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	86[label="(&&) not (primEqInt (Pos Zero) vz401) vz5",fontsize=16,color="burlywood",shape="box"];183[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 183[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	183 -> 91[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	184[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];86 -> 184[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	184 -> 92[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	87[label="(&&) not (primEqInt (Neg (Succ vz3100)) vz401) vz5",fontsize=16,color="burlywood",shape="box"];185[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];87 -> 185[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	185 -> 93[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	186[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];87 -> 186[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	186 -> 94[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	88[label="(&&) not (primEqInt (Neg Zero) vz401) vz5",fontsize=16,color="burlywood",shape="box"];187[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];88 -> 187[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	187 -> 95[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	188[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];88 -> 188[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	188 -> 96[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	89[label="(&&) not (primEqInt (Pos (Succ vz3100)) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];189[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];89 -> 189[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	189 -> 97[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	190[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];89 -> 190[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	190 -> 98[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	90[label="(&&) not (primEqInt (Pos (Succ vz3100)) (Neg vz4010)) vz5",fontsize=16,color="black",shape="box"];90 -> 99[label="",style="solid", color="black", weight=3];
9.69/4.06	91[label="(&&) not (primEqInt (Pos Zero) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];191[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];91 -> 191[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	191 -> 100[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	192[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];91 -> 192[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	192 -> 101[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	92[label="(&&) not (primEqInt (Pos Zero) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];193[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];92 -> 193[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	193 -> 102[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	194[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];92 -> 194[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	194 -> 103[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	93[label="(&&) not (primEqInt (Neg (Succ vz3100)) (Pos vz4010)) vz5",fontsize=16,color="black",shape="box"];93 -> 104[label="",style="solid", color="black", weight=3];
9.69/4.06	94[label="(&&) not (primEqInt (Neg (Succ vz3100)) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];195[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];94 -> 195[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	195 -> 105[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	196[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 196[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	196 -> 106[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	95[label="(&&) not (primEqInt (Neg Zero) (Pos vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];197[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];95 -> 197[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	197 -> 107[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	198[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];95 -> 198[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	198 -> 108[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	96[label="(&&) not (primEqInt (Neg Zero) (Neg vz4010)) vz5",fontsize=16,color="burlywood",shape="box"];199[label="vz4010/Succ vz40100",fontsize=10,color="white",style="solid",shape="box"];96 -> 199[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	199 -> 109[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	200[label="vz4010/Zero",fontsize=10,color="white",style="solid",shape="box"];96 -> 200[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	200 -> 110[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	97[label="(&&) not (primEqInt (Pos (Succ vz3100)) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];97 -> 111[label="",style="solid", color="black", weight=3];
9.69/4.06	98[label="(&&) not (primEqInt (Pos (Succ vz3100)) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];98 -> 112[label="",style="solid", color="black", weight=3];
9.69/4.06	99 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	99[label="(&&) not False vz5",fontsize=16,color="magenta"];100[label="(&&) not (primEqInt (Pos Zero) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];100 -> 113[label="",style="solid", color="black", weight=3];
9.69/4.06	101[label="(&&) not (primEqInt (Pos Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];101 -> 114[label="",style="solid", color="black", weight=3];
9.69/4.06	102[label="(&&) not (primEqInt (Pos Zero) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];102 -> 115[label="",style="solid", color="black", weight=3];
9.69/4.06	103[label="(&&) not (primEqInt (Pos Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];103 -> 116[label="",style="solid", color="black", weight=3];
9.69/4.06	104 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	104[label="(&&) not False vz5",fontsize=16,color="magenta"];105[label="(&&) not (primEqInt (Neg (Succ vz3100)) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];105 -> 117[label="",style="solid", color="black", weight=3];
9.69/4.06	106[label="(&&) not (primEqInt (Neg (Succ vz3100)) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];106 -> 118[label="",style="solid", color="black", weight=3];
9.69/4.06	107[label="(&&) not (primEqInt (Neg Zero) (Pos (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];107 -> 119[label="",style="solid", color="black", weight=3];
9.69/4.06	108[label="(&&) not (primEqInt (Neg Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];108 -> 120[label="",style="solid", color="black", weight=3];
9.69/4.06	109[label="(&&) not (primEqInt (Neg Zero) (Neg (Succ vz40100))) vz5",fontsize=16,color="black",shape="box"];109 -> 121[label="",style="solid", color="black", weight=3];
9.69/4.06	110[label="(&&) not (primEqInt (Neg Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];110 -> 122[label="",style="solid", color="black", weight=3];
9.69/4.06	111[label="(&&) not (primEqNat vz3100 vz40100) vz5",fontsize=16,color="burlywood",shape="triangle"];201[label="vz3100/Succ vz31000",fontsize=10,color="white",style="solid",shape="box"];111 -> 201[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	201 -> 123[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	202[label="vz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];111 -> 202[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	202 -> 124[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	112 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	112[label="(&&) not False vz5",fontsize=16,color="magenta"];113 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	113[label="(&&) not False vz5",fontsize=16,color="magenta"];114[label="(&&) not True vz5",fontsize=16,color="black",shape="triangle"];114 -> 125[label="",style="solid", color="black", weight=3];
9.69/4.06	115 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	115[label="(&&) not False vz5",fontsize=16,color="magenta"];116 -> 114[label="",style="dashed", color="red", weight=0];
9.69/4.06	116[label="(&&) not True vz5",fontsize=16,color="magenta"];117 -> 111[label="",style="dashed", color="red", weight=0];
9.69/4.06	117[label="(&&) not (primEqNat vz3100 vz40100) vz5",fontsize=16,color="magenta"];117 -> 126[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	117 -> 127[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	118 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	118[label="(&&) not False vz5",fontsize=16,color="magenta"];119 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	119[label="(&&) not False vz5",fontsize=16,color="magenta"];120 -> 114[label="",style="dashed", color="red", weight=0];
9.69/4.06	120[label="(&&) not True vz5",fontsize=16,color="magenta"];121 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	121[label="(&&) not False vz5",fontsize=16,color="magenta"];122 -> 114[label="",style="dashed", color="red", weight=0];
9.69/4.06	122[label="(&&) not True vz5",fontsize=16,color="magenta"];123[label="(&&) not (primEqNat (Succ vz31000) vz40100) vz5",fontsize=16,color="burlywood",shape="box"];203[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];123 -> 203[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	203 -> 128[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	204[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];123 -> 204[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	204 -> 129[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	124[label="(&&) not (primEqNat Zero vz40100) vz5",fontsize=16,color="burlywood",shape="box"];205[label="vz40100/Succ vz401000",fontsize=10,color="white",style="solid",shape="box"];124 -> 205[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	205 -> 130[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	206[label="vz40100/Zero",fontsize=10,color="white",style="solid",shape="box"];124 -> 206[label="",style="solid", color="burlywood", weight=9];
9.69/4.06	206 -> 131[label="",style="solid", color="burlywood", weight=3];
9.69/4.06	125[label="(&&) False vz5",fontsize=16,color="black",shape="box"];125 -> 132[label="",style="solid", color="black", weight=3];
9.69/4.06	126[label="vz3100",fontsize=16,color="green",shape="box"];127[label="vz40100",fontsize=16,color="green",shape="box"];128[label="(&&) not (primEqNat (Succ vz31000) (Succ vz401000)) vz5",fontsize=16,color="black",shape="box"];128 -> 133[label="",style="solid", color="black", weight=3];
9.69/4.06	129[label="(&&) not (primEqNat (Succ vz31000) Zero) vz5",fontsize=16,color="black",shape="box"];129 -> 134[label="",style="solid", color="black", weight=3];
9.69/4.06	130[label="(&&) not (primEqNat Zero (Succ vz401000)) vz5",fontsize=16,color="black",shape="box"];130 -> 135[label="",style="solid", color="black", weight=3];
9.69/4.06	131[label="(&&) not (primEqNat Zero Zero) vz5",fontsize=16,color="black",shape="box"];131 -> 136[label="",style="solid", color="black", weight=3];
9.69/4.06	132[label="False",fontsize=16,color="green",shape="box"];133 -> 111[label="",style="dashed", color="red", weight=0];
9.69/4.06	133[label="(&&) not (primEqNat vz31000 vz401000) vz5",fontsize=16,color="magenta"];133 -> 137[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	133 -> 138[label="",style="dashed", color="magenta", weight=3];
9.69/4.06	134 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	134[label="(&&) not False vz5",fontsize=16,color="magenta"];135 -> 54[label="",style="dashed", color="red", weight=0];
9.69/4.06	135[label="(&&) not False vz5",fontsize=16,color="magenta"];136 -> 114[label="",style="dashed", color="red", weight=0];
9.69/4.06	136[label="(&&) not True vz5",fontsize=16,color="magenta"];137[label="vz31000",fontsize=16,color="green",shape="box"];138[label="vz401000",fontsize=16,color="green",shape="box"];}
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(6)
9.69/4.06	Complex Obligation (AND)
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(7)
9.69/4.06	Obligation:
9.69/4.06	Q DP problem:
9.69/4.06	The TRS P consists of the following rules:
9.69/4.06	
9.69/4.06	   new_asAs0(Succ(vz30000), Succ(vz400000), vz31, vz401, vz5) -> new_asAs0(vz30000, vz400000, vz31, vz401, vz5)
9.69/4.06	
9.69/4.06	R is empty.
9.69/4.06	Q is empty.
9.69/4.06	We have to consider all minimal (P,Q,R)-chains.
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(8) QDPSizeChangeProof (EQUIVALENT)
9.69/4.06	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. 
9.69/4.06	
9.69/4.06	From the DPs we obtained the following set of size-change graphs:
9.69/4.06	*new_asAs0(Succ(vz30000), Succ(vz400000), vz31, vz401, vz5) -> new_asAs0(vz30000, vz400000, vz31, vz401, vz5)
9.69/4.06	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
9.69/4.06	
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(9)
9.69/4.06	YES
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(10)
9.69/4.06	Obligation:
9.69/4.06	Q DP problem:
9.69/4.06	The TRS P consists of the following rules:
9.69/4.06	
9.69/4.06	   new_foldr(vz3, :(vz40, vz41)) -> new_foldr(vz3, vz41)
9.69/4.06	
9.69/4.06	R is empty.
9.69/4.06	Q is empty.
9.69/4.06	We have to consider all minimal (P,Q,R)-chains.
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(11) QDPSizeChangeProof (EQUIVALENT)
9.69/4.06	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. 
9.69/4.06	
9.69/4.06	From the DPs we obtained the following set of size-change graphs:
9.69/4.06	*new_foldr(vz3, :(vz40, vz41)) -> new_foldr(vz3, vz41)
9.69/4.06	The graph contains the following edges 1 >= 1, 2 > 2
9.69/4.06	
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(12)
9.69/4.06	YES
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(13)
9.69/4.06	Obligation:
9.69/4.06	Q DP problem:
9.69/4.06	The TRS P consists of the following rules:
9.69/4.06	
9.69/4.06	   new_asAs(Succ(vz31000), Succ(vz401000), vz5) -> new_asAs(vz31000, vz401000, vz5)
9.69/4.06	
9.69/4.06	R is empty.
9.69/4.06	Q is empty.
9.69/4.06	We have to consider all minimal (P,Q,R)-chains.
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(14) QDPSizeChangeProof (EQUIVALENT)
9.69/4.06	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. 
9.69/4.06	
9.69/4.06	From the DPs we obtained the following set of size-change graphs:
9.69/4.06	*new_asAs(Succ(vz31000), Succ(vz401000), vz5) -> new_asAs(vz31000, vz401000, vz5)
9.69/4.06	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
9.69/4.06	
9.69/4.06	
9.69/4.06	----------------------------------------
9.69/4.06	
9.69/4.06	(15)
9.69/4.06	YES
9.69/4.10	EOF