PB'12 competition: satisfaction and optimization track: solvers results per benchmarks

Result page for benchmark
normalized-PB06/OPT-SMALLINT/submitted-PB06/liu/
vtxcov/normalized-vtxcov_v2000_e4000_36.opb.PB06.opb

Jump to solvers results

General information on the benchmark

Namenormalized-PB06/OPT-SMALLINT/submitted-PB06/liu/
vtxcov/normalized-vtxcov_v2000_e4000_36.opb.PB06.opb
MD5SUM77b4ba393aa7b9b6b0fcb1b4220a12a4
Bench CategoryOPT-SMALLINT (optimisation, small integers)
Best result obtained on this benchmarkSAT
Best value of the objective obtained on this benchmark1038
Best CPU time to get the best result obtained on this benchmark1796.75
Has Objective FunctionYES
SatisfiableYES
(Un)Satisfiability was provedYES
Best value of the objective function 1036
Optimality of the best value was proved NO
Number of variables1969
Total number of constraints4000
Number of constraints which are clauses4000
Number of constraints which are cardinality constraints (but not clauses)0
Number of constraints which are nor clauses,nor cardinality constraints0
Minimum length of a constraint2
Maximum length of a constraint2
Number of terms in the objective function 1969
Biggest coefficient in the objective function 1
Number of bits for the biggest coefficient in the objective function 1
Sum of the numbers in the objective function 1969
Number of bits of the sum of numbers in the objective function 11
Biggest number in a constraint 1
Number of bits of the biggest number in a constraint 1
Biggest sum of numbers in a constraint 1969
Number of bits of the biggest sum of numbers11
Number of products (including duplicates)0
Sum of products size (including duplicates)0
Number of different products0
Sum of products size0

Results of the different solvers on this benchmark

Solver NameTraceIDAnswerobjective functionCPU timeWall clock time
SCIP spx SCIP 2.1.1.4. with SoPlex 1.6.0.3 fixed (complete)3690906SAT1038 1796.75 1797.05
SCIP spx E SCIP 2.1.1.4. Exp with SoPlex 1.6.0.3 fixed (complete)3692072SAT1038 1796.77 1797.06
SCIP spx standard SCIP 2.1.1.4. with SoPlex 1.6.0.3 standard fixed (complete)3693238SAT1039 1796.73 1797.05
PB11: SCIP spx E_2 2011-06-10 (fixed) (complete)3731832SAT1043 1796.75 1797.04
PB10: SCIPspx SCIP 1.2.1.3 with SoPlex 1.4.2 (CVS Version 30.5.2010) as LP solver (complete)3731830SAT1045 1789.73 1790.03
PB09: SCIPspx SCIP 1.1.0.7 with SoPLEX 1.4.1(24.4.2009) (complete)3731826SAT1046 1797.74 1798.03
PB07: bsolo 3.0.17 (complete)3731823SAT (TO)1054 1800.01 1800.31
bsolo 3.2 (complete)3707908SAT1064 1798.03 1798.32
PB09: bsolo 3.1 (complete)3731825SAT1069 1798.01 1798.3
PB11: Sat4j Res//CP 2.3.0 (complete)3731831SAT (TO)1157 1800.04 978.65
clasp 2.0.6-R5325 (opt) (complete)3709074SAT (TO)1170 1800.01 1800.31
PB07: PB-clasp 2007-04-10 (complete)3731822SAT (TO)1170 1800.13 1800.42
pwbo 2.02 (complete)3725896SAT (TO)1171 1800.14 900.339
pwbo 2.0 (complete)3703595SAT (TO)1171 1800.44 900.335
PB07: Pueblo 1.4 (incomplete)3720016SAT1175 1783.01 1783.3
PB07: minisat+ 1.14 (complete)3721186SAT (TO)1175 1800.04 1800.51
PB10: SAT4J PB RES // CP 2.2.0 2010-05-31 (complete)3731828SAT (TO)1177 1800.16 966.345
SAT 4j PB RES // CP 2.3.2 Snapshot (complete)3687646SAT (TO)1178 1800.14 1001.06
SAT4J PB specific settings 2.3.2 snapshot (complete)3710670SAT (TO)1184 1800.51 1787.77
PB09: SAT4J Pseudo Resolution 2.1.1 (complete)3731827SAT (TO)1188 1800.05 1797.77
PB12: minisatp 1.0-2-g022594c (complete)3723519SAT (TO)1203 1800.08 1800.72
Sat 4j PB Resolution 2.3.2 Snapshot (complete)3687647SAT (TO)1204 1800.06 1781.18
wbo 1.7 (complete)3705116? 1799.47 1800.02
wbo 1.72 (complete)3727417? 1799.79 1800.02
toysat 2012-06-01 (complete)3725115? (TO) 1800.02 1800.41
PB10: pb_cplex 2010-06-29 (complete)3731829? (TO) 1800.02 509.017
npSolver inc-topdown-quickBound (fixed) (complete)3751971? (TO) 1800.04 1800.41
npSolver inc-topdown-quickBound (complete)3702814? (TO) 1800.06 1800.41
npSolver inc-topDown (fixed) (complete)3747183? (TO) 1800.06 1800.41
npSolver inc-topDown (complete)3698026? (TO) 1800.07 1800.41
npSolver inc (fixed) (complete)3748779? (TO) 1800.08 1800.41
npSolver 1.0 (complete)3701218? (TO) 1800.1 1800.41
toysat 2012-05-17 (complete)3706742? (TO) 1800.11 1800.51
npSolver inc (complete)3699622? (TO) 1800.11 1800.41
npSolver 1.0 (fixed) (complete)3750375? (TO) 1800.12 1800.41
pb2sat 2012-05-19 (complete)3696430? (TO) 1800.13 1800.51
pb2satCp2 2012-05-19 (complete)3694834? (TO) 1800.14 1800.51
PB07: SAT4JPseudoResolution 2007-03-23 (complete)3731824No Cert. 256.465 252.77

Additionnal information

This section presents information obtained from the best job displayed in the list (i.e. solvers whose names are not hidden).

objective function: 1038
Solution found:
-x1969 -x1968 x1967 x1966 -x1965 -x1964 x1963 -x1962 x1961 -x1960 x1959 x1958 -x1957 x1956 x1955 x1954 x1953 x1952 x1951 x1950 x1949 -x1948
-x1947 -x1946 x1945 -x1944 x1943 -x1942 -x1941 x1940 -x1939 x1938 x1937 x1936 x1935 x1934 x1933 x1932 -x1931 -x1930 -x1929 x1928 -x1927
-x1926 x1925 x1924 x1923 -x1922 x1921 x1920 x1919 -x1918 -x1917 -x1916 x1915 x1914 x1913 x1912 x1911 -x1910 -x1909 x1908 -x1907 x1906 -x1905
x1904 -x1903 -x1902 -x1901 x1900 -x1899 x1898 x1897 -x1896 x1895 x1894 x1893 x1892 x1891 x1890 x1889 x1888 -x1887 x1886 -x1885 -x1884 x1883
x1882 x1881 x1880 x1879 x1878 -x1877 x1876 -x1875 x1874 -x1873 x1872 x1871 -x1870 x1869 -x1868 x1867 x1866 -x1865 x1864 x1863 -x1862 x1861
-x1860 x1859 -x1858 -x1857 x1856 -x1855 x1854 -x1853 -x1852 x1851 x1850 x1849 x1848 x1847 -x1846 x1845 x1844 -x1843 -x1842 x1841 -x1840
-x1839 -x1838 x1837 -x1836 -x1835 -x1834 x1833 -x1832 -x1831 -x1830 -x1829 x1828 x1827 x1826 x1825 -x1824 x1823 x1822 x1821 -x1820 x1819
-x1818 -x1817 x1816 -x1815 -x1814 -x1813 x1812 x1811 x1810 -x1809 x1808 x1807 -x1806 -x1805 x1804 -x1803 -x1802 x1801 -x1800 -x1799 -x1798
-x1797 -x1796 -x1795 -x1794 x1793 -x1792 -x1791 -x1790 -x1789 x1788 -x1787 x1786 x1785 -x1784 x1783 -x1782 -x1781 -x1780 x1779 x1778 x1777
-x1776 -x1775 x1774 -x1773 -x1772 -x1771 -x1770 -x1769 x1768 x1767 -x1766 x1765 -x1764 x1763 -x1762 x1761 -x1760 -x1759 x1758 -x1757 -x1756
-x1755 -x1754 -x1753 -x1752 -x1751 x1750 -x1749 x1748 -x1747 x1746 -x1745 -x1744 x1743 x1742 x1741 -x1740 x1739 x1738 x1737 x1736 -x1735
x1734 -x1733 x1732 -x1731 -x1730 -x1729 -x1728 -x1727 x1726 -x1725 x1724 x1723 -x1722 x1721 -x1720 x1719 -x1718 x1717 -x1716 x1715 -x1714
-x1713 -x1712 -x1711 x1710 -x1709 x1708 x1707 -x1706 -x1705 x1704 x1703 x1702 x1701 x1700 x1699 x1698 -x1697 x1696 x1695 x1694 x1693 x1692
x1691 x1690 x1689 x1688 -x1687 -x1686 x1685 x1684 x1683 -x1682 x1681 -x1680 -x1679 -x1678 -x1677 x1676 x1675 -x1674 -x1673 x1672 x1671 x1670
x1669 x1668 -x1667 x1666 x1665 x1664 x1663 -x1662 -x1661 x1660 -x1659 -x1658 -x1657 x1656 x1655 -x1654 x1653 x1652 x1651 x1650 -x1649 -x1648
x1647 -x1646 x1645 -x1644 x1643 -x1642 x1641 x1640 x1639 -x1638 -x1637 x1636 -x1635 x1634 x1633 x1632 x1631 x1630 -x1629 -x1628 -x1627 x1626
x1625 x1624 x1623 -x1622 -x1621 x1620 x1619 -x1618 x1617 -x1616 -x1615 -x1614 -x1613 -x1612 x1611 -x1610 x1609 x1608 -x1607 -x1606 x1605
-x1604 -x1603 -x1602 x1601 x1600 -x1599 -x1598 x1597 -x1596 x1595 x1594 x1593 -x1592 x1591 -x1590 x1589 -x1588 -x1587 x1586 -x1585 x1584
-x1583 -x1582 -x1581 -x1580 -x1579 -x1578 x1577 x1576 -x1575 -x1574 -x1573 x1572 x1571 x1570 x1569 -x1568 -x1567 x1566 -x1565 -x1564 -x1563
-x1562 -x1561 x1560 x1559 x1558 -x1557 -x1556 x1555 -x1554 -x1553 -x1552 x1551 -x1550 x1549 x1548 -x1547 x1546 -x1545 x1544 x1543 x1542
-x1541 -x1540 -x1539 x1538 x1537 -x1536 x1535 x1534 -x1533 x1532 x1531 -x1530 x1529 -x1528 x1527 -x1526 -x1525 -x1524 x1523 x1522 x1521
x1520 -x1519 x1518 x1517 x1516 -x1515 -x1514 -x1513 -x1512 -x1511 -x1510 x1509 x1508 x1507 x1506 -x1505 -x1504 -x1503 x1502 -x1501 -x1500
x1499 x1498 -x1497 x1496 -x1495 -x1494 x1493 -x1492 -x1491 x1490 -x1489 -x1488 x1487 -x1486 x1485 x1484 x1483 -x1482 x1481 -x1480 -x1479
x1478 -x1477 x1476 -x1475 x1474 x1473 -x1472 -x1471 x1470 x1469 -x1468 x1467 -x1466 x1465 x1464 x1463 x1462 -x1461 -x1460 -x1459 x1458 x1457
-x1456 -x1455 -x1454 -x1453 -x1452 x1451 x1450 x1449 x1448 -x1447 -x1446 x1445 x1444 x1443 -x1442 -x1441 x1440 -x1439 -x1438 x1437 -x1436
x1435 -x1434 x1433 -x1432 -x1431 -x1430 x1429 x1428 x1427 -x1426 -x1425 -x1424 -x1423 x1422 -x1421 -x1420 x1419 x1418 -x1417 x1416 -x1415
x1414 x1413 x1412 -x1411 x1410 -x1409 x1408 x1407 x1406 -x1405 -x1404 -x1403 x1402 -x1401 -x1400 -x1399 -x1398 x1397 -x1396 x1395 -x1394
x1393 -x1392 -x1391 -x1390 x1389 x1388 -x1387 -x1386 x1385 x1384 x1383 x1382 -x1381 x1380 -x1379 x1378 -x1377 x1376 x1375 x1374 x1373 -x1372
-x1371 x1370 -x1369 x1368 x1367 -x1366 -x1365 x1364 x1363 -x1362 x1361 x1360 -x1359 -x1358 -x1357 x1356 x1355 x1354 x1353 x1352 x1351 x1350
x1349 -x1348 x1347 -x1346 -x1345 x1344 -x1343 x1342 x1341 x1340 x1339 -x1338 x1337 x1336 x1335 -x1334 x1333 x1332 -x1331 -x1330 x1329 x1328
-x1327 x1326 -x1325 -x1324 -x1323 -x1322 -x1321 x1320 -x1319 x1318 -x1317 x1316 x1315 x1314 x1313 x1312 x1311 -x1310 x1309 x1308 x1307
-x1306 -x1305 x1304 -x1303 x1302 x1301 -x1300 -x1299 x1298 x1297 -x1296 -x1295 x1294 x1293 x1292 x1291 -x1290 x1289 -x1288 -x1287 -x1286
-x1285 x1284 x1283 -x1282 -x1281 x1280 -x1279 -x1278 x1277 x1276 -x1275 -x1274 -x1273 x1272 x1271 x1270 x1269 -x1268 x1267 x1266 -x1265
x1264 -x1263 -x1262 x1261 x1260 x1259 x1258 -x1257 -x1256 -x1255 x1254 -x1253 -x1252 x1251 -x1250 -x1249 -x1248 x1247 x1246 -x1245 -x1244
-x1243 x1242 x1241 x1240 x1239 -x1238 x1237 -x1236 x1235 -x1234 -x1233 -x1232 x1231 x1230 x1229 -x1228 -x1227 x1226 -x1225 x1224 x1223
-x1222 -x1221 -x1220 x1219 -x1218 x1217 -x1216 x1215 x1214 x1213 x1212 -x1211 -x1210 x1209 -x1208 -x1207 -x1206 x1205 x1204 -x1203 x1202
-x1201 -x1200 x1199 -x1198 x1197 x1196 x1195 x1194 x1193 x1192 x1191 x1190 -x1189 x1188 x1187 -x1186 x1185 -x1184 x1183 x1182 x1181 x1180
x1179 -x1178 -x1177 -x1176 x1175 -x1174 x1173 x1172 x1171 x1170 -x1169 -x1168 x1167 -x1166 -x1165 x1164 -x1163 -x1162 -x1161 x1160 x1159
-x1158 x1157 -x1156 x1155 -x1154 -x1153 x1152 -x1151 -x1150 -x1149 x1148 -x1147 x1146 -x1145 -x1144 x1143 x1142 x1141 -x1140 x1139 x1138
x1137 x1136 x1135 x1134 x1133 x1132 x1131 -x1130 x1129 x1128 x1127 -x1126 x1125 x1124 -x1123 x1122 x1121 x1120 -x1119 x1118 x1117 x1116
-x1115 -x1114 -x1113 x1112 -x1111 -x1110 -x1109 x1108 x1107 -x1106 -x1105 -x1104 x1103 x1102 -x1101 x1100 x1099 x1098 x1097 -x1096 x1095
-x1094 x1093 -x1092 -x1091 x1090 x1089 -x1088 x1087 -x1086 x1085 -x1084 -x1083 -x1082 -x1081 -x1080 x1079 -x1078 x1077 x1076 x1075 -x1074
x1073 -x1072 -x1071 x1070 x1069 x1068 -x1067 x1066 x1065 -x1064 x1063 -x1062 -x1061 x1060 x1059 -x1058 -x1057 x1056 -x1055 -x1054 x1053
-x1052 x1051 x1050 -x1049 -x1048 -x1047 x1046 -x1045 x1044 -x1043 -x1042 -x1041 x1040 x1039 x1038 x1037 x1036 -x1035 x1034 -x1033 x1032
-x1031 x1030 x1029 x1028 x1027 x1026 x1025 -x1024 x1023 -x1022 -x1021 -x1020 -x1019 x1018 -x1017 x1016 -x1015 x1014 -x1013 -x1012 x1011
-x1010 x1009 x1008 -x1007 -x1006 x1005 x1004 -x1003 -x1002 -x1001 x1000 x999 -x998 -x997 x996 -x995 x994 x993 -x992 -x991 x990 -x989 x988
x987 x986 -x985 x984 x983 -x982 x981 x980 -x979 -x978 x977 -x976 x975 x974 x973 x972 -x971 x970 x969 -x968 -x967 -x966 -x965 x964 x963 x962
x961 -x960 -x959 x958 x957 -x956 x955 x954 -x953 x952 x951 -x950 -x949 -x948 -x947 x946 x945 x944 -x943 x942 x941 x940 x939 x938 x937 x936
x935 -x934 -x933 -x932 -x931 -x930 x929 x928 -x927 x926 x925 -x924 -x923 -x922 x921 x920 -x919 x918 -x917 x916 -x915 x914 x913 -x912 -x911
x910 x909 x908 x907 -x906 -x905 x904 x903 -x902 x901 x900 -x899 -x898 -x897 x896 -x895 -x894 -x893 x892 -x891 x890 -x889 -x888 x887 x886
-x885 x884 -x883 -x882 x881 x880 x879 x878 x877 x876 -x875 -x874 -x873 -x872 x871 -x870 -x869 -x868 x867 -x866 -x865 -x864 -x863 -x862 -x861
x860 x859 x858 -x857 x856 -x855 x854 x853 -x852 x851 x850 -x849 -x848 x847 -x846 x845 -x844 -x843 -x842 -x841 -x840 x839 -x838 -x837 x836
x835 -x834 x833 x832 -x831 -x830 x829 x828 -x827 -x826 -x825 -x824 x823 -x822 -x821 x820 x819 x818 -x817 x816 -x815 x814 x813 x812 x811 x810
-x809 x808 -x807 x806 x805 x804 x803 x802 -x801 -x800 x799 -x798 x797 -x796 x795 x794 x793 x792 x791 -x790 -x789 -x788 x787 x786 -x785 x784
x783 x782 x781 -x780 x779 -x778 x777 x776 x775 x774 x773 -x772 -x771 x770 x769 x768 x767 -x766 x765 x764 x763 x762 x761 -x760 x759 -x758
x757 x756 -x755 x754 x753 -x752 -x751 -x750 -x749 -x748 -x747 x746 -x745 x744 -x743 -x742 x741 -x740 x739 x738 -x737 -x736 x735 -x734 x733
x732 x731 x730 x729 x728 -x727 -x726 -x725 x724 -x723 -x722 x721 x720 -x719 -x718 x717 -x716 -x715 x714 -x713 -x712 -x711 x710 -x709 -x708
x707 -x706 x705 -x704 -x703 -x702 -x701 x700 x699 x698 -x697 -x696 -x695 -x694 x693 -x692 -x691 x690 -x689 -x688 x687 x686 -x685 x684 -x683
-x682 x681 -x680 -x679 x678 x677 -x676 -x675 -x674 -x673 x672 -x671 x670 x669 x668 x667 -x666 x665 -x664 x663 -x662 -x661 -x660 x659 x658
-x657 -x656 x655 x654 x653 -x652 -x651 x650 -x649 x648 x647 x646 x645 x644 x643 -x642 x641 x640 -x639 -x638 -x637 x636 x635 -x634 x633 -x632
x631 x630 x629 -x628 -x627 x626 x625 -x624 x623 x622 -x621 x620 -x619 -x618 x617 x616 -x615 -x614 x613 -x612 -x611 -x610 -x609 x608 x607
x606 x605 x604 -x603 -x602 -x601 -x600 -x599 x598 -x597 -x596 x595 -x594 -x593 x592 x591 -x590 -x589 x588 x587 -x586 x585 x584 -x583 -x582
x581 x580 -x579 x578 x577 -x576 x575 x574 x573 -x572 -x571 -x570 -x569 x568 -x567 -x566 x565 x564 -x563 -x562 x561 x560 -x559 x558 x557
-x556 -x555 -x554 x553 -x552 x551 x550 -x549 x548 x547 -x546 -x545 x544 x543 x542 x541 -x540 -x539 -x538 x537 -x536 -x535 -x534 -x533 x532
-x531 x530 -x529 x528 x527 -x526 -x525 -x524 -x523 -x522 x521 x520 -x519 -x518 x517 x516 x515 x514 -x513 -x512 -x511 x510 x509 x508 -x507
x506 x505 x504 x503 x502 -x501 -x500 x499 x498 x497 -x496 -x495 -x494 -x493 x492 x491 -x490 x489 x488 -x487 -x486 -x485 x484 x483 -x482 x481
x480 x479 x478 x477 x476 -x475 -x474 x473 x472 -x471 -x470 x469 -x468 -x467 -x466 x465 x464 -x463 x462 -x461 -x460 x459 x458 -x457 x456 x455
-x454 -x453 x452 x451 -x450 x449 -x448 -x447 x446 x445 x444 x443 -x442 x441 -x440 x439 -x438 -x437 -x436 x435 -x434 -x433 x432 -x431 x430
x429 x428 -x427 x426 x425 -x424 x423 x422 x421 x420 x419 x418 x417 -x416 -x415 x414 x413 -x412 x411 -x410 x409 -x408 -x407 -x406 x405 x404
-x403 -x402 -x401 -x400 -x399 x398 x397 x396 x395 x394 x393 -x392 -x391 -x390 x389 -x388 x387 -x386 -x385 -x384 x383 x382 -x381 -x380 -x379
-x378 x377 x376 -x375 x374 x373 -x372 -x371 x370 -x369 x368 x367 -x366 x365 -x364 -x363 x362 -x361 -x360 -x359 x358 -x357 -x356 x355 x354
x353 x352 -x351 x350 x349 -x348 -x347 -x346 x345 x344 x343 x342 -x341 x340 x339 -x338 x337 x336 -x335 x334 -x333 x332 -x331 -x330 x329 -x328
-x327 -x326 -x325 x324 x323 x322 -x321 x320 x319 x318 x317 -x316 x315 -x314 -x313 -x312 -x311 -x310 -x309 x308 -x307 x306 -x305 x304 x303
x302 x301 x300 -x299 -x298 -x297 -x296 x295 -x294 -x293 -x292 x291 x290 x289 x288 x287 x286 x285 -x284 x283 -x282 x281 -x280 x279 -x278 x277
-x276 x275 x274 -x273 x272 x271 x270 x269 -x268 x267 x266 -x265 -x264 x263 -x262 x261 x260 -x259 -x258 -x257 x256 x255 x254 x253 -x252 x251
x250 -x249 x248 -x247 -x246 x245 x244 x243 -x242 -x241 x240 x239 x238 x237 -x236 -x235 x234 -x233 x232 -x231 -x230 x229 x228 -x227 x226 x225
x224 -x223 x222 x221 x220 x219 -x218 x217 x216 x215 -x214 -x213 -x212 -x211 x210 x209 -x208 x207 -x206 x205 x204 x203 x202 x201 x200 -x199
-x198 -x197 -x196 -x195 -x194 -x193 -x192 x191 -x190 -x189 x188 -x187 x186 x185 -x184 x183 x182 -x181 -x180 -x179 x178 x177 x176 x175 x174
x173 -x172 x171 -x170 -x169 -x168 x167 x166 -x165 -x164 -x163 -x162 x161 -x160 x159 x158 -x157 x156 x155 -x154 x153 x152 -x151 x150 -x149
x148 -x147 -x146 -x145 x144 -x143 -x142 -x141 -x140 -x139 x138 -x137 -x136 x135 -x134 -x133 x132 -x131 x130 x129 x128 x127 x126 x125 x124
x123 -x122 -x121 -x120 -x119 -x118 x117 x116 x115 x114 x113 -x112 x111 x110 x109 x108 -x107 -x106 -x105 x104 -x103 -x102 x101 -x100 x99 x98
-x97 x96 x95 -x94 -x93 -x92 -x91 x90 x89 -x88 x87 x86 x85 -x84 x83 x82 x81 x80 x79 -x78 x77 x76 x75 x74 x73 -x72 x71 x70 x69 x68 -x67 x66
-x65 x64 x63 -x62 -x61 x60 -x59 x58 -x57 x56 x55 -x54 -x53 -x52 x51 -x50 -x49 x48 x47 -x46 -x45 -x44 -x43 -x42 x41 x40 -x39 -x38 -x37 -x36
-x35 x34 x33 -x32 -x31 x30 -x29 x28 x27 x26 -x25 x24 -x23 x22 -x21 x20 x19 x18 x17 x16 x15 x14 x13 x12 -x11 x10 -x9 -x8 x7 x6 -x5 -x4 x3 -x2
x1