8.14/3.65	YES
9.95/4.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.95/4.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.95/4.17	
9.95/4.17	
9.95/4.17	H-Termination with start terms of the given HASKELL could be proven:
9.95/4.17	
9.95/4.17	(0) HASKELL
9.95/4.17	(1) BR [EQUIVALENT, 0 ms]
9.95/4.17	(2) HASKELL
9.95/4.17	(3) COR [EQUIVALENT, 0 ms]
9.95/4.17	(4) HASKELL
9.95/4.17	(5) NumRed [SOUND, 0 ms]
9.95/4.17	(6) HASKELL
9.95/4.17	(7) Narrow [SOUND, 0 ms]
9.95/4.17	(8) AND
9.95/4.17	    (9) QDP
9.95/4.17	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.95/4.17	        (11) YES
9.95/4.17	    (12) QDP
9.95/4.17	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.95/4.17	        (14) YES
9.95/4.17	
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(0)
9.95/4.17	Obligation:
9.95/4.17	mainModule Main 
9.95/4.17	module Main where {
9.95/4.17	import qualified Prelude;
9.95/4.17	}
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(1) BR (EQUIVALENT)
9.95/4.17	Replaced joker patterns by fresh variables and removed binding patterns.
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(2)
9.95/4.17	Obligation:
9.95/4.17	mainModule Main 
9.95/4.17	module Main where {
9.95/4.17	import qualified Prelude;
9.95/4.17	}
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(3) COR (EQUIVALENT)
9.95/4.17	Cond Reductions:
9.95/4.17	The following Function with conditions
9.95/4.17	"undefined |Falseundefined;
9.95/4.17	"
9.95/4.17	is transformed to
9.95/4.17	"undefined  = undefined1;
9.95/4.17	"
9.95/4.17	"undefined0 True = undefined;
9.95/4.17	"
9.95/4.17	"undefined1  = undefined0 False;
9.95/4.17	"
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(4)
9.95/4.17	Obligation:
9.95/4.17	mainModule Main 
9.95/4.17	module Main where {
9.95/4.17	import qualified Prelude;
9.95/4.17	}
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(5) NumRed (SOUND)
9.95/4.17	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(6)
9.95/4.17	Obligation:
9.95/4.17	mainModule Main 
9.95/4.17	module Main where {
9.95/4.17	import qualified Prelude;
9.95/4.17	}
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(7) Narrow (SOUND)
9.95/4.17	Haskell To QDPs
9.95/4.17	
9.95/4.17	digraph dp_graph {
9.95/4.17	node [outthreshold=100, inthreshold=100];1[label="pi",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
9.95/4.17	3[label="fromInt (Pos (Succ (Succ (Succ (Succ Zero))))) * atan (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];3 -> 4[label="",style="solid", color="black", weight=3];
9.95/4.17	4[label="primMulFloat (fromInt (Pos (Succ (Succ (Succ (Succ Zero)))))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.95/4.17	5[label="primMulFloat (primIntToFloat (Pos (Succ (Succ (Succ (Succ Zero)))))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.95/4.17	6 -> 10[label="",style="dashed", color="red", weight=0];
9.95/4.17	6[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];6 -> 11[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	11[label="atan (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.95/4.17	10[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="triangle"];197[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];10 -> 197[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	197 -> 16[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	15[label="primAtanFloat (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
9.95/4.17	16[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
9.95/4.17	18 -> 21[label="",style="dashed", color="red", weight=0];
9.95/4.17	18[label="terminator (fromInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];18 -> 22[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	19[label="Float (Pos (Succ (Succ (Succ (Succ Zero)))) * vx30) (Pos (Succ Zero) * vx31)",fontsize=16,color="green",shape="box"];19 -> 23[label="",style="dashed", color="green", weight=3];
9.95/4.17	19 -> 24[label="",style="dashed", color="green", weight=3];
9.95/4.17	22[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
9.95/4.17	21[label="terminator vx4",fontsize=16,color="black",shape="triangle"];21 -> 26[label="",style="solid", color="black", weight=3];
9.95/4.17	23[label="Pos (Succ (Succ (Succ (Succ Zero)))) * vx30",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
9.95/4.17	24[label="Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
9.95/4.17	25[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
9.95/4.17	26[label="ter1m vx4",fontsize=16,color="green",shape="box"];26 -> 30[label="",style="dashed", color="green", weight=3];
9.95/4.17	27[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) vx30",fontsize=16,color="burlywood",shape="box"];198[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];27 -> 198[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	198 -> 31[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	199[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];27 -> 199[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	199 -> 32[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	28[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];200[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];28 -> 200[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	200 -> 33[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	201[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];28 -> 201[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	201 -> 34[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	29[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];30[label="vx4",fontsize=16,color="green",shape="box"];31[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos vx300)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
9.95/4.17	32[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) (Neg vx300)",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
9.95/4.17	33[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
9.95/4.17	34[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
9.95/4.17	35[label="Pos (primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300)",fontsize=16,color="green",shape="box"];35 -> 39[label="",style="dashed", color="green", weight=3];
9.95/4.17	36[label="Neg (primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300)",fontsize=16,color="green",shape="box"];36 -> 40[label="",style="dashed", color="green", weight=3];
9.95/4.17	37[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];37 -> 41[label="",style="dashed", color="green", weight=3];
9.95/4.17	38[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];38 -> 42[label="",style="dashed", color="green", weight=3];
9.95/4.17	39[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300",fontsize=16,color="burlywood",shape="triangle"];202[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];39 -> 202[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	202 -> 43[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	203[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 203[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	203 -> 44[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	40 -> 39[label="",style="dashed", color="red", weight=0];
9.95/4.17	40[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300",fontsize=16,color="magenta"];40 -> 45[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	41[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];204[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];41 -> 204[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	204 -> 46[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	205[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 205[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	205 -> 47[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	42 -> 41[label="",style="dashed", color="red", weight=0];
9.95/4.17	42[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];42 -> 48[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	43[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ vx3000)",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
9.95/4.17	44[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) Zero",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
9.95/4.17	45[label="vx300",fontsize=16,color="green",shape="box"];46[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
9.95/4.17	47[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
9.95/4.17	48[label="vx310",fontsize=16,color="green",shape="box"];49[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
9.95/4.17	50[label="Zero",fontsize=16,color="green",shape="box"];51[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
9.95/4.17	52[label="Zero",fontsize=16,color="green",shape="box"];53[label="primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];53 -> 55[label="",style="solid", color="black", weight=3];
9.95/4.17	54[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];54 -> 56[label="",style="solid", color="black", weight=3];
9.95/4.17	55 -> 57[label="",style="dashed", color="red", weight=0];
9.95/4.17	55[label="primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="magenta"];55 -> 58[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	56[label="Succ vx3100",fontsize=16,color="green",shape="box"];58 -> 41[label="",style="dashed", color="red", weight=0];
9.95/4.17	58[label="primMulNat (Succ Zero) (Succ vx3000)",fontsize=16,color="magenta"];58 -> 59[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	57[label="primPlusNat (primPlusNat (primPlusNat vx5 (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="burlywood",shape="triangle"];206[label="vx5/Succ vx50",fontsize=10,color="white",style="solid",shape="box"];57 -> 206[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	206 -> 60[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	207[label="vx5/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 207[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	207 -> 61[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	59[label="Succ vx3000",fontsize=16,color="green",shape="box"];60[label="primPlusNat (primPlusNat (primPlusNat (Succ vx50) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
9.95/4.17	61[label="primPlusNat (primPlusNat (primPlusNat Zero (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
9.95/4.17	62[label="primPlusNat (primPlusNat (Succ (Succ (primPlusNat vx50 vx3000))) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];62 -> 64[label="",style="solid", color="black", weight=3];
9.95/4.17	63[label="primPlusNat (primPlusNat (Succ vx3000) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];63 -> 65[label="",style="solid", color="black", weight=3];
9.95/4.17	64 -> 140[label="",style="dashed", color="red", weight=0];
9.95/4.17	64[label="primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000))) (Succ vx3000)",fontsize=16,color="magenta"];64 -> 141[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	64 -> 142[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	65 -> 140[label="",style="dashed", color="red", weight=0];
9.95/4.17	65[label="primPlusNat (Succ (Succ (primPlusNat vx3000 vx3000))) (Succ vx3000)",fontsize=16,color="magenta"];65 -> 143[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	65 -> 144[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	141[label="Succ vx3000",fontsize=16,color="green",shape="box"];142[label="Succ (primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000)",fontsize=16,color="green",shape="box"];142 -> 167[label="",style="dashed", color="green", weight=3];
9.95/4.17	140[label="primPlusNat (Succ vx7) vx8",fontsize=16,color="burlywood",shape="triangle"];208[label="vx8/Succ vx80",fontsize=10,color="white",style="solid",shape="box"];140 -> 208[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	208 -> 168[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	209[label="vx8/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 209[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	209 -> 169[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	143[label="Succ vx3000",fontsize=16,color="green",shape="box"];144[label="Succ (primPlusNat vx3000 vx3000)",fontsize=16,color="green",shape="box"];144 -> 170[label="",style="dashed", color="green", weight=3];
9.95/4.17	167 -> 140[label="",style="dashed", color="red", weight=0];
9.95/4.17	167[label="primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000",fontsize=16,color="magenta"];167 -> 171[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	167 -> 172[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	168[label="primPlusNat (Succ vx7) (Succ vx80)",fontsize=16,color="black",shape="box"];168 -> 173[label="",style="solid", color="black", weight=3];
9.95/4.17	169[label="primPlusNat (Succ vx7) Zero",fontsize=16,color="black",shape="box"];169 -> 174[label="",style="solid", color="black", weight=3];
9.95/4.17	170[label="primPlusNat vx3000 vx3000",fontsize=16,color="burlywood",shape="triangle"];210[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];170 -> 210[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	210 -> 175[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	211[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];170 -> 211[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	211 -> 176[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	171[label="vx3000",fontsize=16,color="green",shape="box"];172[label="primPlusNat vx50 vx3000",fontsize=16,color="burlywood",shape="triangle"];212[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];172 -> 212[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	212 -> 177[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	213[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];172 -> 213[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	213 -> 178[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	173[label="Succ (Succ (primPlusNat vx7 vx80))",fontsize=16,color="green",shape="box"];173 -> 179[label="",style="dashed", color="green", weight=3];
9.95/4.17	174[label="Succ vx7",fontsize=16,color="green",shape="box"];175[label="primPlusNat (Succ vx30000) (Succ vx30000)",fontsize=16,color="black",shape="box"];175 -> 180[label="",style="solid", color="black", weight=3];
9.95/4.17	176[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];176 -> 181[label="",style="solid", color="black", weight=3];
9.95/4.17	177[label="primPlusNat (Succ vx500) vx3000",fontsize=16,color="burlywood",shape="box"];214[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];177 -> 214[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	214 -> 182[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	215[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];177 -> 215[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	215 -> 183[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	178[label="primPlusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];216[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];178 -> 216[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	216 -> 184[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	217[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];178 -> 217[label="",style="solid", color="burlywood", weight=9];
9.95/4.17	217 -> 185[label="",style="solid", color="burlywood", weight=3];
9.95/4.17	179 -> 172[label="",style="dashed", color="red", weight=0];
9.95/4.17	179[label="primPlusNat vx7 vx80",fontsize=16,color="magenta"];179 -> 186[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	179 -> 187[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	180[label="Succ (Succ (primPlusNat vx30000 vx30000))",fontsize=16,color="green",shape="box"];180 -> 188[label="",style="dashed", color="green", weight=3];
9.95/4.17	181[label="Zero",fontsize=16,color="green",shape="box"];182[label="primPlusNat (Succ vx500) (Succ vx30000)",fontsize=16,color="black",shape="box"];182 -> 189[label="",style="solid", color="black", weight=3];
9.95/4.17	183[label="primPlusNat (Succ vx500) Zero",fontsize=16,color="black",shape="box"];183 -> 190[label="",style="solid", color="black", weight=3];
9.95/4.17	184[label="primPlusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];184 -> 191[label="",style="solid", color="black", weight=3];
9.95/4.17	185[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];185 -> 192[label="",style="solid", color="black", weight=3];
9.95/4.17	186[label="vx80",fontsize=16,color="green",shape="box"];187[label="vx7",fontsize=16,color="green",shape="box"];188 -> 170[label="",style="dashed", color="red", weight=0];
9.95/4.17	188[label="primPlusNat vx30000 vx30000",fontsize=16,color="magenta"];188 -> 193[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	189[label="Succ (Succ (primPlusNat vx500 vx30000))",fontsize=16,color="green",shape="box"];189 -> 194[label="",style="dashed", color="green", weight=3];
9.95/4.17	190[label="Succ vx500",fontsize=16,color="green",shape="box"];191[label="Succ vx30000",fontsize=16,color="green",shape="box"];192[label="Zero",fontsize=16,color="green",shape="box"];193[label="vx30000",fontsize=16,color="green",shape="box"];194 -> 172[label="",style="dashed", color="red", weight=0];
9.95/4.17	194[label="primPlusNat vx500 vx30000",fontsize=16,color="magenta"];194 -> 195[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	194 -> 196[label="",style="dashed", color="magenta", weight=3];
9.95/4.17	195[label="vx30000",fontsize=16,color="green",shape="box"];196[label="vx500",fontsize=16,color="green",shape="box"];}
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(8)
9.95/4.17	Complex Obligation (AND)
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(9)
9.95/4.17	Obligation:
9.95/4.17	Q DP problem:
9.95/4.17	The TRS P consists of the following rules:
9.95/4.17	
9.95/4.17	   new_primPlusNat(Succ(vx30000)) -> new_primPlusNat(vx30000)
9.95/4.17	
9.95/4.17	R is empty.
9.95/4.17	Q is empty.
9.95/4.17	We have to consider all minimal (P,Q,R)-chains.
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(10) QDPSizeChangeProof (EQUIVALENT)
9.95/4.17	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. 
9.95/4.17	
9.95/4.17	From the DPs we obtained the following set of size-change graphs:
9.95/4.17	*new_primPlusNat(Succ(vx30000)) -> new_primPlusNat(vx30000)
9.95/4.17	The graph contains the following edges 1 > 1
9.95/4.17	
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(11)
9.95/4.17	YES
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(12)
9.95/4.17	Obligation:
9.95/4.17	Q DP problem:
9.95/4.17	The TRS P consists of the following rules:
9.95/4.17	
9.95/4.17	   new_primPlusNat0(Succ(vx500), Succ(vx30000)) -> new_primPlusNat0(vx500, vx30000)
9.95/4.17	
9.95/4.17	R is empty.
9.95/4.17	Q is empty.
9.95/4.17	We have to consider all minimal (P,Q,R)-chains.
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(13) QDPSizeChangeProof (EQUIVALENT)
9.95/4.17	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. 
9.95/4.17	
9.95/4.17	From the DPs we obtained the following set of size-change graphs:
9.95/4.17	*new_primPlusNat0(Succ(vx500), Succ(vx30000)) -> new_primPlusNat0(vx500, vx30000)
9.95/4.17	The graph contains the following edges 1 > 1, 2 > 2
9.95/4.17	
9.95/4.17	
9.95/4.17	----------------------------------------
9.95/4.17	
9.95/4.17	(14)
9.95/4.17	YES
10.11/4.21	EOF