13.2 Without Preprocessing

Table 4: Maximal number of cosets defined - Prefix-Strategies

Example	Felsch	HLT	NONE	P-ALL	P-G	P-R
$E_1 \vert E$	98	695	584	648	648	1660
$(2, 5, 7; 2) \vert E$	216	224	205	188	187	228
$G^{3, 7, 17} \vert <ab, c>$	724	1381	1153	1857	2528	1321
$PSL_2(11) \vert E$	660	661	660	715	702	660
$(2, 3, 7; 7) \vert E$	1221	2286	1534	1883	1579	1249
$M_{11}^{(1)} \vert <a>$	720	721	720	2070	1057	1130
$(8, 7 \vert 2, 3) \vert <a^2, a^{-1}b>$	824	1241	1298	1742	1609	2139
$Neu \vert <a, c>$	2650	4553	4358	15137	8240	6386
$Cam(3) \vert E$	653	2189	1222	1207	4809	3238
$G^{3,7,16}\vert E$	21504	69990	75162	67023	67080	67918
$G(2,4) \vert E$	3188	2973	3556	1871	8550	5087
$G(2,6) \vert E$	7889	4194	10593	18795	9826	16685
$G(3,3)\vert E$	25481	29007	70627	150972	88335	126650

Table 5: Total number of cosets defined - Prefix-Strategies

Example	Felsch	HLT	NONE	P-ALL	P-G	P-R
$E_1 \vert E$	104	758	584	648	648	1680
$(2, 5, 7; 2) \vert E$	216	227	205	196	200	265
$G^{3, 7, 17} \vert <ab, c>$	761	2315	1153	2235	3473	1515
$PSL_2(11) \vert E$	743	824	684	826	921	879
$(2, 3, 7; 7) \vert E$	1310	2880	1602	1951	1977	1917
$M_{11}^{(1)} \vert <a>$	724	1349	801	2448	1524	1612
$(8, 7 \vert 2, 3) \vert <a^2, a^{-1}b>$	840	1422	1300	1817	1741	2294
$Neu \vert <a, c>$	2750	7158	4403	15584	8488	6668
$Cam(3) \vert E$	660	2206	1222	1238	4823	3247
$G^{3,7,16}\vert E$	23702	161805	75705	82283	82351	84529
$G(2,4) \vert E$	3193	3255	3560	1893	8691	5248
$G(2,6) \vert E$	7893	4582	10597	19154	9947	17221
$G(3,3)\vert E$	25496	31993	70859	154763	89951	129594

Table 6: Maximal number of cosets defined - Inverse-Strategies

Example	Felsch	HLT	NONE	I-ALL	I-R	I-R-P
$E_1 \vert E$	98	695	584	746	730	890
$(2, 5, 7; 2) \vert E$	216	224	205	211	150	193
$G^{3, 7, 17} \vert <ab, c>$	724	1381	1153	1153	1153	1857
$PSL_2(11) \vert E$	660	661	660	660	660	660
$(2, 3, 7; 7) \vert E$	1221	2286	1534	1743	1534	1898
$M_{11}^{(1)} \vert <a>$	720	721	720	1114	720	2174
$(8, 7 \vert 2, 3) \vert <a^2, a^{-1}b>$	824	1241	1298	1581	1147	1744
$Neu \vert <a, c>$	2650	4553	4358	21975	7027	15184
$Cam(3) \vert E$	653	2189	1222	1161	2140	1960
$G^{3,7,16}\vert E$	21504	69990	75162	62613	78813	66887
$G(2,4) \vert E$	3188	2973	3556	12663	2274	2851
$G(2,6) \vert E$	7889	4194	10593	19571	7147	3647
$G(3,3)\vert E$	25481	29007	70627	111249	120529	28141

Table 7: Total number of cosets defined - Inverse-Strategies

Example	Felsch	HLT	NONE	I-ALL	I-R	I-R-P
$E_1 \vert E$	104	758	584	746	735	893
$(2, 5, 7; 2) \vert E$	216	227	205	215	151	198
$G^{3, 7, 17} \vert <ab, c>$	761	2315	1153	1155	1153	2235
$PSL_2(11) \vert E$	743	824	684	987	713	742
$(2, 3, 7; 7) \vert E$	1310	2880	1602	1872	1604	1960
$M_{11}^{(1)} \vert <a>$	724	1349	801	1479	955	2550
$(8, 7 \vert 2, 3) \vert <a^2, a^{-1}b>$	840	1422	1300	1742	1162	1822
$Neu \vert <a, c>$	2750	7158	4403	23401	7217	15639
$Cam(3) \vert E$	660	2206	1222	1168	2171	1971
$G^{3,7,16}\vert E$	23702	161805	75705	90200	81280	82004
$G(2,4) \vert E$	3193	3255	3560	12835	2283	2880
$G(2,6) \vert E$	7893	4582	10597	19754	7199	3674
$G(3,3)\vert E$	25496	31993	70859	112412	121480	28503