8.12/3.62	YES
9.90/4.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.90/4.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.90/4.13	
9.90/4.13	
9.90/4.13	H-Termination with start terms of the given HASKELL could be proven:
9.90/4.13	
9.90/4.13	(0) HASKELL
9.90/4.13	(1) BR [EQUIVALENT, 0 ms]
9.90/4.13	(2) HASKELL
9.90/4.13	(3) COR [EQUIVALENT, 0 ms]
9.90/4.13	(4) HASKELL
9.90/4.13	(5) NumRed [SOUND, 0 ms]
9.90/4.13	(6) HASKELL
9.90/4.13	(7) Narrow [SOUND, 0 ms]
9.90/4.13	(8) AND
9.90/4.13	    (9) QDP
9.90/4.13	        (10) QDPSizeChangeProof [EQUIVALENT, 1 ms]
9.90/4.13	        (11) YES
9.90/4.13	    (12) QDP
9.90/4.13	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.90/4.13	        (14) YES
9.90/4.13	    (15) QDP
9.90/4.13	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.90/4.13	        (17) YES
9.90/4.13	
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(0)
9.90/4.13	Obligation:
9.90/4.13	mainModule Main 
9.90/4.13	module Main where {
9.90/4.13	import qualified Prelude;
9.90/4.13	}
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(1) BR (EQUIVALENT)
9.90/4.13	Replaced joker patterns by fresh variables and removed binding patterns.
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(2)
9.90/4.13	Obligation:
9.90/4.13	mainModule Main 
9.90/4.13	module Main where {
9.90/4.13	import qualified Prelude;
9.90/4.13	}
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(3) COR (EQUIVALENT)
9.90/4.13	Cond Reductions:
9.90/4.13	The following Function with conditions
9.90/4.13	"undefined |Falseundefined;
9.90/4.13	"
9.90/4.13	is transformed to
9.90/4.13	"undefined  = undefined1;
9.90/4.13	"
9.90/4.13	"undefined0 True = undefined;
9.90/4.13	"
9.90/4.13	"undefined1  = undefined0 False;
9.90/4.13	"
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(4)
9.90/4.13	Obligation:
9.90/4.13	mainModule Main 
9.90/4.13	module Main where {
9.90/4.13	import qualified Prelude;
9.90/4.13	}
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(5) NumRed (SOUND)
9.90/4.13	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(6)
9.90/4.13	Obligation:
9.90/4.13	mainModule Main 
9.90/4.13	module Main where {
9.90/4.13	import qualified Prelude;
9.90/4.13	}
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(7) Narrow (SOUND)
9.90/4.13	Haskell To QDPs
9.90/4.13	
9.90/4.13	digraph dp_graph {
9.90/4.13	node [outthreshold=100, inthreshold=100];1[label="acosh",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.90/4.13	3[label="acosh vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.90/4.13	4[label="log (vx3 + sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.90/4.13	5[label="primLogFloat (vx3 + sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.90/4.13	6[label="terminator (vx3 + sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.90/4.13	7[label="ter0m (vx3 + sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
9.90/4.13	8[label="vx3 + sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.90/4.13	9[label="primPlusFloat vx3 (sqrt (vx3 * vx3 - fromInt (Pos (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];151[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];9 -> 151[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	151 -> 10[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	10[label="primPlusFloat (Float vx30 vx31) (sqrt (Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.90/4.13	11 -> 14[label="",style="dashed", color="red", weight=0];
9.90/4.13	11[label="primPlusFloat (Float vx30 vx31) (primSqrtFloat (Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];11 -> 15[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	15[label="primSqrtFloat (Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
9.90/4.13	14[label="primPlusFloat (Float vx30 vx31) vx4",fontsize=16,color="burlywood",shape="triangle"];152[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];14 -> 152[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	152 -> 19[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	18[label="terminator (Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3];
9.90/4.13	19[label="primPlusFloat (Float vx30 vx31) (Float vx40 vx41)",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
9.90/4.13	21[label="ter2m (Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];21 -> 24[label="",style="dashed", color="green", weight=3];
9.90/4.13	22[label="Float (vx30 * vx41 + vx40 * vx31) (vx31 * vx41)",fontsize=16,color="green",shape="box"];22 -> 25[label="",style="dashed", color="green", weight=3];
9.90/4.13	22 -> 26[label="",style="dashed", color="green", weight=3];
9.90/4.13	24 -> 20[label="",style="dashed", color="red", weight=0];
9.90/4.13	24[label="Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];25[label="vx30 * vx41 + vx40 * vx31",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
9.90/4.13	26[label="vx31 * vx41",fontsize=16,color="black",shape="triangle"];26 -> 29[label="",style="solid", color="black", weight=3];
9.90/4.13	20[label="Float vx30 vx31 * Float vx30 vx31 - fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];20 -> 23[label="",style="solid", color="black", weight=3];
9.90/4.13	28 -> 31[label="",style="dashed", color="red", weight=0];
9.90/4.13	28[label="primPlusInt (vx30 * vx41) (vx40 * vx31)",fontsize=16,color="magenta"];28 -> 32[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	28 -> 33[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	29[label="primMulInt vx31 vx41",fontsize=16,color="burlywood",shape="box"];153[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];29 -> 153[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	153 -> 34[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	154[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];29 -> 154[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	154 -> 35[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	23[label="primMinusFloat (Float vx30 vx31 * Float vx30 vx31) (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
9.90/4.13	32 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	32[label="vx40 * vx31",fontsize=16,color="magenta"];32 -> 36[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	32 -> 37[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	33 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	33[label="vx30 * vx41",fontsize=16,color="magenta"];33 -> 38[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	31[label="primPlusInt vx6 vx5",fontsize=16,color="burlywood",shape="triangle"];155[label="vx6/Pos vx60",fontsize=10,color="white",style="solid",shape="box"];31 -> 155[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	155 -> 39[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	156[label="vx6/Neg vx60",fontsize=10,color="white",style="solid",shape="box"];31 -> 156[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	156 -> 40[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	34[label="primMulInt (Pos vx310) vx41",fontsize=16,color="burlywood",shape="box"];157[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];34 -> 157[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	157 -> 44[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	158[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];34 -> 158[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	158 -> 45[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	35[label="primMulInt (Neg vx310) vx41",fontsize=16,color="burlywood",shape="box"];159[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];35 -> 159[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	159 -> 46[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	160[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];35 -> 160[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	160 -> 47[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	27[label="primMinusFloat (primMulFloat (Float vx30 vx31) (Float vx30 vx31)) (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
9.90/4.13	36[label="vx40",fontsize=16,color="green",shape="box"];37[label="vx31",fontsize=16,color="green",shape="box"];38[label="vx30",fontsize=16,color="green",shape="box"];39[label="primPlusInt (Pos vx60) vx5",fontsize=16,color="burlywood",shape="box"];161[label="vx5/Pos vx50",fontsize=10,color="white",style="solid",shape="box"];39 -> 161[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	161 -> 48[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	162[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];39 -> 162[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	162 -> 49[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	40[label="primPlusInt (Neg vx60) vx5",fontsize=16,color="burlywood",shape="box"];163[label="vx5/Pos vx50",fontsize=10,color="white",style="solid",shape="box"];40 -> 163[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	163 -> 50[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	164[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];40 -> 164[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	164 -> 51[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	44[label="primMulInt (Pos vx310) (Pos vx410)",fontsize=16,color="black",shape="box"];44 -> 56[label="",style="solid", color="black", weight=3];
9.90/4.13	45[label="primMulInt (Pos vx310) (Neg vx410)",fontsize=16,color="black",shape="box"];45 -> 57[label="",style="solid", color="black", weight=3];
9.90/4.13	46[label="primMulInt (Neg vx310) (Pos vx410)",fontsize=16,color="black",shape="box"];46 -> 58[label="",style="solid", color="black", weight=3];
9.90/4.13	47[label="primMulInt (Neg vx310) (Neg vx410)",fontsize=16,color="black",shape="box"];47 -> 59[label="",style="solid", color="black", weight=3];
9.90/4.13	30 -> 41[label="",style="dashed", color="red", weight=0];
9.90/4.13	30[label="primMinusFloat (Float (vx30 * vx30) (vx31 * vx31)) (fromInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];30 -> 42[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	30 -> 43[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	48[label="primPlusInt (Pos vx60) (Pos vx50)",fontsize=16,color="black",shape="box"];48 -> 60[label="",style="solid", color="black", weight=3];
9.90/4.13	49[label="primPlusInt (Pos vx60) (Neg vx50)",fontsize=16,color="black",shape="box"];49 -> 61[label="",style="solid", color="black", weight=3];
9.90/4.13	50[label="primPlusInt (Neg vx60) (Pos vx50)",fontsize=16,color="black",shape="box"];50 -> 62[label="",style="solid", color="black", weight=3];
9.90/4.13	51[label="primPlusInt (Neg vx60) (Neg vx50)",fontsize=16,color="black",shape="box"];51 -> 63[label="",style="solid", color="black", weight=3];
9.90/4.13	56[label="Pos (primMulNat vx310 vx410)",fontsize=16,color="green",shape="box"];56 -> 65[label="",style="dashed", color="green", weight=3];
9.90/4.13	57[label="Neg (primMulNat vx310 vx410)",fontsize=16,color="green",shape="box"];57 -> 66[label="",style="dashed", color="green", weight=3];
9.90/4.13	58[label="Neg (primMulNat vx310 vx410)",fontsize=16,color="green",shape="box"];58 -> 67[label="",style="dashed", color="green", weight=3];
9.90/4.13	59[label="Pos (primMulNat vx310 vx410)",fontsize=16,color="green",shape="box"];59 -> 68[label="",style="dashed", color="green", weight=3];
9.90/4.13	42 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	42[label="vx31 * vx31",fontsize=16,color="magenta"];42 -> 52[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	43 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	43[label="vx30 * vx30",fontsize=16,color="magenta"];43 -> 53[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	43 -> 54[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	41[label="primMinusFloat (Float vx8 vx7) (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];41 -> 55[label="",style="solid", color="black", weight=3];
9.90/4.13	60[label="Pos (primPlusNat vx60 vx50)",fontsize=16,color="green",shape="box"];60 -> 69[label="",style="dashed", color="green", weight=3];
9.90/4.13	61[label="primMinusNat vx60 vx50",fontsize=16,color="burlywood",shape="triangle"];165[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];61 -> 165[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	165 -> 70[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	166[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 166[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	166 -> 71[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	62 -> 61[label="",style="dashed", color="red", weight=0];
9.90/4.13	62[label="primMinusNat vx50 vx60",fontsize=16,color="magenta"];62 -> 72[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	62 -> 73[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	63[label="Neg (primPlusNat vx60 vx50)",fontsize=16,color="green",shape="box"];63 -> 74[label="",style="dashed", color="green", weight=3];
9.90/4.13	65[label="primMulNat vx310 vx410",fontsize=16,color="burlywood",shape="triangle"];167[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];65 -> 167[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	167 -> 76[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	168[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];65 -> 168[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	168 -> 77[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	66 -> 65[label="",style="dashed", color="red", weight=0];
9.90/4.13	66[label="primMulNat vx310 vx410",fontsize=16,color="magenta"];66 -> 78[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	67 -> 65[label="",style="dashed", color="red", weight=0];
9.90/4.13	67[label="primMulNat vx310 vx410",fontsize=16,color="magenta"];67 -> 79[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	68 -> 65[label="",style="dashed", color="red", weight=0];
9.90/4.13	68[label="primMulNat vx310 vx410",fontsize=16,color="magenta"];68 -> 80[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	68 -> 81[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	52[label="vx31",fontsize=16,color="green",shape="box"];53[label="vx30",fontsize=16,color="green",shape="box"];54[label="vx30",fontsize=16,color="green",shape="box"];55[label="primMinusFloat (Float vx8 vx7) (primIntToFloat (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
9.90/4.13	69[label="primPlusNat vx60 vx50",fontsize=16,color="burlywood",shape="triangle"];169[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];69 -> 169[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	169 -> 82[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	170[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 170[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	170 -> 83[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	70[label="primMinusNat (Succ vx600) vx50",fontsize=16,color="burlywood",shape="box"];171[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];70 -> 171[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	171 -> 84[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	172[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 172[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	172 -> 85[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	71[label="primMinusNat Zero vx50",fontsize=16,color="burlywood",shape="box"];173[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];71 -> 173[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	173 -> 86[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	174[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];71 -> 174[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	174 -> 87[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	72[label="vx60",fontsize=16,color="green",shape="box"];73[label="vx50",fontsize=16,color="green",shape="box"];74 -> 69[label="",style="dashed", color="red", weight=0];
9.90/4.13	74[label="primPlusNat vx60 vx50",fontsize=16,color="magenta"];74 -> 88[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	74 -> 89[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	76[label="primMulNat (Succ vx3100) vx410",fontsize=16,color="burlywood",shape="box"];175[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];76 -> 175[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	175 -> 92[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	176[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];76 -> 176[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	176 -> 93[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	77[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];177[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];77 -> 177[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	177 -> 94[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	178[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 178[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	178 -> 95[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	78[label="vx410",fontsize=16,color="green",shape="box"];79[label="vx310",fontsize=16,color="green",shape="box"];80[label="vx410",fontsize=16,color="green",shape="box"];81[label="vx310",fontsize=16,color="green",shape="box"];64[label="primMinusFloat (Float vx8 vx7) (Float (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];64 -> 75[label="",style="solid", color="black", weight=3];
9.90/4.13	82[label="primPlusNat (Succ vx600) vx50",fontsize=16,color="burlywood",shape="box"];179[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];82 -> 179[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	179 -> 96[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	180[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];82 -> 180[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	180 -> 97[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	83[label="primPlusNat Zero vx50",fontsize=16,color="burlywood",shape="box"];181[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];83 -> 181[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	181 -> 98[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	182[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];83 -> 182[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	182 -> 99[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	84[label="primMinusNat (Succ vx600) (Succ vx500)",fontsize=16,color="black",shape="box"];84 -> 100[label="",style="solid", color="black", weight=3];
9.90/4.13	85[label="primMinusNat (Succ vx600) Zero",fontsize=16,color="black",shape="box"];85 -> 101[label="",style="solid", color="black", weight=3];
9.90/4.13	86[label="primMinusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];86 -> 102[label="",style="solid", color="black", weight=3];
9.90/4.13	87[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];87 -> 103[label="",style="solid", color="black", weight=3];
9.90/4.13	88[label="vx50",fontsize=16,color="green",shape="box"];89[label="vx60",fontsize=16,color="green",shape="box"];92[label="primMulNat (Succ vx3100) (Succ vx4100)",fontsize=16,color="black",shape="box"];92 -> 107[label="",style="solid", color="black", weight=3];
9.90/4.13	93[label="primMulNat (Succ vx3100) Zero",fontsize=16,color="black",shape="box"];93 -> 108[label="",style="solid", color="black", weight=3];
9.90/4.13	94[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];94 -> 109[label="",style="solid", color="black", weight=3];
9.90/4.13	95[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];95 -> 110[label="",style="solid", color="black", weight=3];
9.90/4.13	75[label="Float (vx8 * Pos (Succ Zero) - Pos (Succ Zero) * vx7) (vx7 * Pos (Succ Zero))",fontsize=16,color="green",shape="box"];75 -> 90[label="",style="dashed", color="green", weight=3];
9.90/4.13	75 -> 91[label="",style="dashed", color="green", weight=3];
9.90/4.13	96[label="primPlusNat (Succ vx600) (Succ vx500)",fontsize=16,color="black",shape="box"];96 -> 111[label="",style="solid", color="black", weight=3];
9.90/4.13	97[label="primPlusNat (Succ vx600) Zero",fontsize=16,color="black",shape="box"];97 -> 112[label="",style="solid", color="black", weight=3];
9.90/4.13	98[label="primPlusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];98 -> 113[label="",style="solid", color="black", weight=3];
9.90/4.13	99[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];99 -> 114[label="",style="solid", color="black", weight=3];
9.90/4.13	100 -> 61[label="",style="dashed", color="red", weight=0];
9.90/4.13	100[label="primMinusNat vx600 vx500",fontsize=16,color="magenta"];100 -> 115[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	100 -> 116[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	101[label="Pos (Succ vx600)",fontsize=16,color="green",shape="box"];102[label="Neg (Succ vx500)",fontsize=16,color="green",shape="box"];103[label="Pos Zero",fontsize=16,color="green",shape="box"];107 -> 69[label="",style="dashed", color="red", weight=0];
9.90/4.13	107[label="primPlusNat (primMulNat vx3100 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];107 -> 124[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	107 -> 125[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	108[label="Zero",fontsize=16,color="green",shape="box"];109[label="Zero",fontsize=16,color="green",shape="box"];110[label="Zero",fontsize=16,color="green",shape="box"];90 -> 104[label="",style="dashed", color="red", weight=0];
9.90/4.13	90[label="vx8 * Pos (Succ Zero) - Pos (Succ Zero) * vx7",fontsize=16,color="magenta"];90 -> 105[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	90 -> 106[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	91 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	91[label="vx7 * Pos (Succ Zero)",fontsize=16,color="magenta"];91 -> 117[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	91 -> 118[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	111[label="Succ (Succ (primPlusNat vx600 vx500))",fontsize=16,color="green",shape="box"];111 -> 126[label="",style="dashed", color="green", weight=3];
9.90/4.13	112[label="Succ vx600",fontsize=16,color="green",shape="box"];113[label="Succ vx500",fontsize=16,color="green",shape="box"];114[label="Zero",fontsize=16,color="green",shape="box"];115[label="vx500",fontsize=16,color="green",shape="box"];116[label="vx600",fontsize=16,color="green",shape="box"];124[label="Succ vx4100",fontsize=16,color="green",shape="box"];125 -> 65[label="",style="dashed", color="red", weight=0];
9.90/4.13	125[label="primMulNat vx3100 (Succ vx4100)",fontsize=16,color="magenta"];125 -> 129[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	125 -> 130[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	105 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	105[label="vx8 * Pos (Succ Zero)",fontsize=16,color="magenta"];105 -> 119[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	105 -> 120[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	106 -> 26[label="",style="dashed", color="red", weight=0];
9.90/4.13	106[label="Pos (Succ Zero) * vx7",fontsize=16,color="magenta"];106 -> 121[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	106 -> 122[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	104[label="vx10 - vx9",fontsize=16,color="black",shape="triangle"];104 -> 123[label="",style="solid", color="black", weight=3];
9.90/4.13	117[label="vx7",fontsize=16,color="green",shape="box"];118[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];126 -> 69[label="",style="dashed", color="red", weight=0];
9.90/4.13	126[label="primPlusNat vx600 vx500",fontsize=16,color="magenta"];126 -> 131[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	126 -> 132[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	129[label="Succ vx4100",fontsize=16,color="green",shape="box"];130[label="vx3100",fontsize=16,color="green",shape="box"];119[label="vx8",fontsize=16,color="green",shape="box"];120[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];121[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];122[label="vx7",fontsize=16,color="green",shape="box"];123[label="primMinusInt vx10 vx9",fontsize=16,color="burlywood",shape="box"];183[label="vx10/Pos vx100",fontsize=10,color="white",style="solid",shape="box"];123 -> 183[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	183 -> 127[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	184[label="vx10/Neg vx100",fontsize=10,color="white",style="solid",shape="box"];123 -> 184[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	184 -> 128[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	131[label="vx500",fontsize=16,color="green",shape="box"];132[label="vx600",fontsize=16,color="green",shape="box"];127[label="primMinusInt (Pos vx100) vx9",fontsize=16,color="burlywood",shape="box"];185[label="vx9/Pos vx90",fontsize=10,color="white",style="solid",shape="box"];127 -> 185[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	185 -> 133[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	186[label="vx9/Neg vx90",fontsize=10,color="white",style="solid",shape="box"];127 -> 186[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	186 -> 134[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	128[label="primMinusInt (Neg vx100) vx9",fontsize=16,color="burlywood",shape="box"];187[label="vx9/Pos vx90",fontsize=10,color="white",style="solid",shape="box"];128 -> 187[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	187 -> 135[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	188[label="vx9/Neg vx90",fontsize=10,color="white",style="solid",shape="box"];128 -> 188[label="",style="solid", color="burlywood", weight=9];
9.90/4.13	188 -> 136[label="",style="solid", color="burlywood", weight=3];
9.90/4.13	133[label="primMinusInt (Pos vx100) (Pos vx90)",fontsize=16,color="black",shape="box"];133 -> 137[label="",style="solid", color="black", weight=3];
9.90/4.13	134[label="primMinusInt (Pos vx100) (Neg vx90)",fontsize=16,color="black",shape="box"];134 -> 138[label="",style="solid", color="black", weight=3];
9.90/4.13	135[label="primMinusInt (Neg vx100) (Pos vx90)",fontsize=16,color="black",shape="box"];135 -> 139[label="",style="solid", color="black", weight=3];
9.90/4.13	136[label="primMinusInt (Neg vx100) (Neg vx90)",fontsize=16,color="black",shape="box"];136 -> 140[label="",style="solid", color="black", weight=3];
9.90/4.13	137 -> 61[label="",style="dashed", color="red", weight=0];
9.90/4.13	137[label="primMinusNat vx100 vx90",fontsize=16,color="magenta"];137 -> 141[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	137 -> 142[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	138[label="Pos (primPlusNat vx100 vx90)",fontsize=16,color="green",shape="box"];138 -> 143[label="",style="dashed", color="green", weight=3];
9.90/4.13	139[label="Neg (primPlusNat vx100 vx90)",fontsize=16,color="green",shape="box"];139 -> 144[label="",style="dashed", color="green", weight=3];
9.90/4.13	140 -> 61[label="",style="dashed", color="red", weight=0];
9.90/4.13	140[label="primMinusNat vx90 vx100",fontsize=16,color="magenta"];140 -> 145[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	140 -> 146[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	141[label="vx90",fontsize=16,color="green",shape="box"];142[label="vx100",fontsize=16,color="green",shape="box"];143 -> 69[label="",style="dashed", color="red", weight=0];
9.90/4.13	143[label="primPlusNat vx100 vx90",fontsize=16,color="magenta"];143 -> 147[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	143 -> 148[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	144 -> 69[label="",style="dashed", color="red", weight=0];
9.90/4.13	144[label="primPlusNat vx100 vx90",fontsize=16,color="magenta"];144 -> 149[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	144 -> 150[label="",style="dashed", color="magenta", weight=3];
9.90/4.13	145[label="vx100",fontsize=16,color="green",shape="box"];146[label="vx90",fontsize=16,color="green",shape="box"];147[label="vx90",fontsize=16,color="green",shape="box"];148[label="vx100",fontsize=16,color="green",shape="box"];149[label="vx90",fontsize=16,color="green",shape="box"];150[label="vx100",fontsize=16,color="green",shape="box"];}
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(8)
9.90/4.13	Complex Obligation (AND)
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(9)
9.90/4.13	Obligation:
9.90/4.13	Q DP problem:
9.90/4.13	The TRS P consists of the following rules:
9.90/4.13	
9.90/4.13	   new_primMulNat(Succ(vx3100), Succ(vx4100)) -> new_primMulNat(vx3100, Succ(vx4100))
9.90/4.13	
9.90/4.13	R is empty.
9.90/4.13	Q is empty.
9.90/4.13	We have to consider all minimal (P,Q,R)-chains.
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(10) QDPSizeChangeProof (EQUIVALENT)
9.90/4.13	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. 
9.90/4.13	
9.90/4.13	From the DPs we obtained the following set of size-change graphs:
9.90/4.13	*new_primMulNat(Succ(vx3100), Succ(vx4100)) -> new_primMulNat(vx3100, Succ(vx4100))
9.90/4.13	The graph contains the following edges 1 > 1, 2 >= 2
9.90/4.13	
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(11)
9.90/4.13	YES
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(12)
9.90/4.13	Obligation:
9.90/4.13	Q DP problem:
9.90/4.13	The TRS P consists of the following rules:
9.90/4.13	
9.90/4.13	   new_primMinusNat(Succ(vx600), Succ(vx500)) -> new_primMinusNat(vx600, vx500)
9.90/4.13	
9.90/4.13	R is empty.
9.90/4.13	Q is empty.
9.90/4.13	We have to consider all minimal (P,Q,R)-chains.
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(13) QDPSizeChangeProof (EQUIVALENT)
9.90/4.13	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. 
9.90/4.13	
9.90/4.13	From the DPs we obtained the following set of size-change graphs:
9.90/4.13	*new_primMinusNat(Succ(vx600), Succ(vx500)) -> new_primMinusNat(vx600, vx500)
9.90/4.13	The graph contains the following edges 1 > 1, 2 > 2
9.90/4.13	
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(14)
9.90/4.13	YES
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(15)
9.90/4.13	Obligation:
9.90/4.13	Q DP problem:
9.90/4.13	The TRS P consists of the following rules:
9.90/4.13	
9.90/4.13	   new_primPlusNat(Succ(vx600), Succ(vx500)) -> new_primPlusNat(vx600, vx500)
9.90/4.13	
9.90/4.13	R is empty.
9.90/4.13	Q is empty.
9.90/4.13	We have to consider all minimal (P,Q,R)-chains.
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(16) QDPSizeChangeProof (EQUIVALENT)
9.90/4.13	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. 
9.90/4.13	
9.90/4.13	From the DPs we obtained the following set of size-change graphs:
9.90/4.13	*new_primPlusNat(Succ(vx600), Succ(vx500)) -> new_primPlusNat(vx600, vx500)
9.90/4.13	The graph contains the following edges 1 > 1, 2 > 2
9.90/4.13	
9.90/4.13	
9.90/4.13	----------------------------------------
9.90/4.13	
9.90/4.13	(17)
9.90/4.13	YES
9.90/4.17	EOF