/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) - Signature: {0/1,1/1,2/1,3/1,4/1,5/1} / {} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. 0_0(1) -> 1 0_1(1) -> 63 0_1(2) -> 1 0_1(2) -> 10 0_1(2) -> 63 0_1(2) -> 96 0_1(2) -> 228 0_1(2) -> 258 0_1(2) -> 302 0_1(9) -> 264 0_1(10) -> 25 0_1(12) -> 11 0_1(14) -> 13 0_1(17) -> 16 0_1(19) -> 18 0_1(22) -> 21 0_1(30) -> 29 0_1(33) -> 32 0_1(34) -> 96 0_1(41) -> 40 0_1(42) -> 228 0_1(51) -> 50 0_1(55) -> 96 0_1(57) -> 56 0_1(59) -> 58 0_1(63) -> 258 0_1(72) -> 71 0_1(94) -> 93 0_1(96) -> 141 0_1(100) -> 99 0_1(104) -> 55 0_1(109) -> 108 0_1(121) -> 120 0_1(147) -> 146 0_1(150) -> 149 0_1(210) -> 209 0_1(211) -> 210 0_1(223) -> 222 0_1(225) -> 224 0_1(229) -> 27 0_1(241) -> 240 0_1(244) -> 243 0_1(251) -> 250 0_1(255) -> 254 0_1(264) -> 263 0_1(265) -> 264 0_2(157) -> 156 0_2(166) -> 165 0_2(175) -> 174 0_2(184) -> 183 0_2(193) -> 192 0_2(202) -> 201 0_2(217) -> 216 0_2(218) -> 217 0_2(278) -> 277 0_2(294) -> 258 0_2(303) -> 25 0_2(303) -> 63 0_2(303) -> 141 0_2(303) -> 258 0_2(310) -> 263 0_2(319) -> 141 0_2(327) -> 360 0_2(328) -> 96 0_2(337) -> 209 0_2(357) -> 356 0_2(365) -> 364 0_2(374) -> 373 0_2(383) -> 382 0_2(392) -> 391 0_2(393) -> 392 0_2(396) -> 395 0_3(346) -> 216 0_3(403) -> 391 0_3(416) -> 415 1_0(1) -> 1 1_1(1) -> 10 1_1(2) -> 10 1_1(6) -> 5 1_1(7) -> 6 1_1(9) -> 8 1_1(10) -> 103 1_1(20) -> 3 1_1(24) -> 23 1_1(34) -> 241 1_1(43) -> 26 1_1(49) -> 48 1_1(52) -> 51 1_1(54) -> 268 1_1(55) -> 1 1_1(55) -> 10 1_1(55) -> 19 1_1(55) -> 62 1_1(55) -> 103 1_1(55) -> 133 1_1(55) -> 302 1_1(58) -> 57 1_1(63) -> 62 1_1(65) -> 10 1_1(68) -> 67 1_1(70) -> 69 1_1(83) -> 284 1_1(91) -> 90 1_1(92) -> 91 1_1(99) -> 98 1_1(106) -> 105 1_1(111) -> 27 1_1(114) -> 113 1_1(118) -> 117 1_1(124) -> 123 1_1(125) -> 124 1_1(126) -> 125 1_1(145) -> 144 1_1(226) -> 225 1_1(227) -> 144 1_1(234) -> 256 1_1(235) -> 89 1_1(239) -> 238 1_1(242) -> 28 1_1(245) -> 244 1_1(257) -> 256 1_1(259) -> 10 1_1(260) -> 259 1_1(269) -> 268 1_2(1) -> 302 1_2(2) -> 221 1_2(9) -> 318 1_2(34) -> 327 1_2(55) -> 327 1_2(104) -> 336 1_2(211) -> 345 1_2(220) -> 309 1_2(265) -> 318 1_2(275) -> 274 1_2(293) -> 292 1_2(298) -> 297 1_2(299) -> 298 1_2(301) -> 300 1_2(303) -> 221 1_2(307) -> 306 1_2(308) -> 307 1_2(314) -> 313 1_2(315) -> 314 1_2(317) -> 316 1_2(323) -> 322 1_2(324) -> 323 1_2(326) -> 325 1_2(328) -> 221 1_2(332) -> 331 1_2(333) -> 332 1_2(335) -> 334 1_2(341) -> 340 1_2(342) -> 341 1_2(344) -> 343 1_2(355) -> 295 1_2(359) -> 358 1_3(218) -> 354 1_3(350) -> 349 1_3(351) -> 350 1_3(353) -> 352 1_3(393) -> 411 1_3(407) -> 406 1_3(408) -> 407 1_3(410) -> 409 2_0(1) -> 1 2_1(1) -> 19 2_1(2) -> 19 2_1(10) -> 9 2_1(11) -> 19 2_1(23) -> 22 2_1(26) -> 1 2_1(26) -> 19 2_1(26) -> 34 2_1(26) -> 42 2_1(26) -> 63 2_1(26) -> 82 2_1(26) -> 83 2_1(26) -> 95 2_1(26) -> 96 2_1(26) -> 110 2_1(26) -> 161 2_1(26) -> 179 2_1(26) -> 234 2_1(26) -> 257 2_1(26) -> 258 2_1(26) -> 369 2_1(31) -> 30 2_1(34) -> 54 2_1(37) -> 36 2_1(41) -> 152 2_1(42) -> 133 2_1(47) -> 46 2_1(54) -> 53 2_1(55) -> 19 2_1(56) -> 55 2_1(60) -> 59 2_1(62) -> 61 2_1(70) -> 245 2_1(77) -> 19 2_1(82) -> 136 2_1(83) -> 82 2_1(84) -> 3 2_1(86) -> 85 2_1(87) -> 86 2_1(95) -> 127 2_1(103) -> 102 2_1(104) -> 19 2_1(105) -> 104 2_1(115) -> 223 2_1(131) -> 130 2_1(138) -> 137 2_1(141) -> 140 2_1(148) -> 90 2_1(151) -> 150 2_1(207) -> 26 2_1(208) -> 207 2_1(231) -> 230 2_1(240) -> 239 2_1(241) -> 265 2_1(246) -> 89 2_1(248) -> 247 2_1(251) -> 269 2_1(259) -> 19 2_1(262) -> 261 2_1(268) -> 267 2_1(283) -> 282 2_1(284) -> 283 2_2(155) -> 154 2_2(158) -> 157 2_2(160) -> 159 2_2(164) -> 163 2_2(167) -> 166 2_2(169) -> 168 2_2(173) -> 172 2_2(176) -> 175 2_2(178) -> 177 2_2(182) -> 181 2_2(185) -> 184 2_2(187) -> 186 2_2(191) -> 190 2_2(194) -> 193 2_2(196) -> 195 2_2(200) -> 199 2_2(203) -> 202 2_2(205) -> 204 2_2(213) -> 76 2_2(213) -> 161 2_2(213) -> 234 2_2(213) -> 257 2_2(214) -> 213 2_2(215) -> 214 2_2(221) -> 220 2_2(270) -> 24 2_2(270) -> 83 2_2(274) -> 273 2_2(276) -> 275 2_2(291) -> 290 2_2(292) -> 291 2_2(302) -> 301 2_2(318) -> 317 2_2(327) -> 326 2_2(336) -> 335 2_2(345) -> 344 2_2(358) -> 357 2_2(363) -> 362 2_2(366) -> 365 2_2(368) -> 367 2_2(372) -> 371 2_2(375) -> 374 2_2(377) -> 376 2_2(381) -> 380 2_2(384) -> 383 2_2(386) -> 385 2_2(388) -> 257 2_2(389) -> 388 2_2(390) -> 389 2_2(397) -> 396 2_3(354) -> 353 2_3(411) -> 410 2_3(414) -> 413 2_3(417) -> 416 2_3(419) -> 418 3_0(1) -> 1 3_1(1) -> 34 3_1(8) -> 7 3_1(9) -> 60 3_1(11) -> 1 3_1(11) -> 10 3_1(11) -> 24 3_1(11) -> 34 3_1(11) -> 42 3_1(11) -> 62 3_1(11) -> 63 3_1(11) -> 83 3_1(11) -> 95 3_1(11) -> 161 3_1(11) -> 234 3_1(11) -> 257 3_1(11) -> 258 3_1(11) -> 302 3_1(11) -> 369 3_1(19) -> 70 3_1(21) -> 20 3_1(26) -> 34 3_1(27) -> 26 3_1(29) -> 28 3_1(32) -> 31 3_1(35) -> 2 3_1(36) -> 35 3_1(39) -> 38 3_1(40) -> 39 3_1(42) -> 41 3_1(46) -> 45 3_1(53) -> 52 3_1(55) -> 34 3_1(61) -> 60 3_1(63) -> 95 3_1(69) -> 68 3_1(71) -> 11 3_1(73) -> 72 3_1(76) -> 75 3_1(77) -> 55 3_1(78) -> 77 3_1(79) -> 78 3_1(82) -> 81 3_1(88) -> 87 3_1(96) -> 95 3_1(108) -> 107 3_1(113) -> 112 3_1(115) -> 114 3_1(116) -> 115 3_1(117) -> 104 3_1(128) -> 71 3_1(132) -> 131 3_1(133) -> 132 3_1(136) -> 135 3_1(142) -> 43 3_1(149) -> 148 3_1(209) -> 208 3_1(222) -> 209 3_1(224) -> 128 3_1(228) -> 251 3_1(230) -> 229 3_1(232) -> 231 3_1(243) -> 242 3_1(253) -> 252 3_1(259) -> 34 3_1(263) -> 262 3_1(279) -> 64 3_1(282) -> 281 3_2(156) -> 155 3_2(161) -> 160 3_2(165) -> 164 3_2(170) -> 169 3_2(174) -> 173 3_2(179) -> 178 3_2(183) -> 182 3_2(188) -> 187 3_2(192) -> 191 3_2(197) -> 196 3_2(201) -> 200 3_2(206) -> 205 3_2(216) -> 215 3_2(277) -> 276 3_2(285) -> 24 3_2(287) -> 286 3_2(290) -> 289 3_2(300) -> 299 3_2(309) -> 308 3_2(316) -> 315 3_2(325) -> 324 3_2(334) -> 333 3_2(343) -> 342 3_2(356) -> 355 3_2(364) -> 363 3_2(369) -> 368 3_2(373) -> 372 3_2(378) -> 377 3_2(382) -> 381 3_2(387) -> 386 3_2(391) -> 390 3_2(395) -> 216 3_2(401) -> 397 3_3(352) -> 351 3_3(409) -> 408 3_3(415) -> 414 3_3(420) -> 419 4_0(1) -> 1 4_1(1) -> 42 4_1(2) -> 42 4_1(3) -> 2 4_1(4) -> 3 4_1(9) -> 212 4_1(10) -> 147 4_1(18) -> 17 4_1(19) -> 110 4_1(25) -> 76 4_1(28) -> 27 4_1(34) -> 49 4_1(38) -> 37 4_1(42) -> 88 4_1(44) -> 43 4_1(45) -> 44 4_1(49) -> 88 4_1(50) -> 20 4_1(54) -> 126 4_1(55) -> 42 4_1(63) -> 234 4_1(64) -> 42 4_1(66) -> 65 4_1(67) -> 66 4_1(75) -> 74 4_1(80) -> 79 4_1(81) -> 80 4_1(89) -> 1 4_1(89) -> 10 4_1(89) -> 42 4_1(89) -> 49 4_1(89) -> 83 4_1(89) -> 94 4_1(89) -> 147 4_1(89) -> 170 4_1(89) -> 284 4_1(89) -> 302 4_1(89) -> 369 4_1(89) -> 378 4_1(90) -> 89 4_1(93) -> 92 4_1(95) -> 94 4_1(97) -> 26 4_1(98) -> 97 4_1(104) -> 42 4_1(107) -> 106 4_1(110) -> 109 4_1(112) -> 111 4_1(119) -> 118 4_1(123) -> 147 4_1(127) -> 126 4_1(129) -> 128 4_1(139) -> 138 4_1(140) -> 139 4_1(143) -> 142 4_1(146) -> 145 4_1(152) -> 151 4_1(212) -> 211 4_1(228) -> 227 4_1(236) -> 235 4_1(238) -> 237 4_1(247) -> 246 4_1(249) -> 248 4_1(250) -> 249 4_1(254) -> 253 4_1(256) -> 255 4_1(258) -> 257 4_1(259) -> 42 4_1(261) -> 260 4_1(266) -> 122 4_1(280) -> 279 4_1(281) -> 280 4_2(1) -> 369 4_2(2) -> 161 4_2(3) -> 278 4_2(10) -> 170 4_2(19) -> 179 4_2(42) -> 161 4_2(51) -> 188 4_2(63) -> 161 4_2(94) -> 197 4_2(104) -> 161 4_2(147) -> 206 4_2(153) -> 42 4_2(153) -> 147 4_2(153) -> 161 4_2(153) -> 170 4_2(153) -> 227 4_2(153) -> 234 4_2(153) -> 257 4_2(153) -> 369 4_2(154) -> 153 4_2(159) -> 158 4_2(162) -> 76 4_2(162) -> 234 4_2(162) -> 257 4_2(163) -> 162 4_2(168) -> 167 4_2(171) -> 17 4_2(172) -> 171 4_2(177) -> 176 4_2(180) -> 20 4_2(181) -> 180 4_2(186) -> 185 4_2(189) -> 92 4_2(190) -> 189 4_2(195) -> 194 4_2(198) -> 145 4_2(199) -> 198 4_2(204) -> 203 4_2(219) -> 218 4_2(220) -> 219 4_2(251) -> 378 4_2(255) -> 387 4_2(272) -> 271 4_2(288) -> 287 4_2(289) -> 288 4_2(294) -> 161 4_2(295) -> 294 4_2(296) -> 295 4_2(301) -> 394 4_2(303) -> 170 4_2(304) -> 303 4_2(305) -> 304 4_2(311) -> 310 4_2(312) -> 311 4_2(320) -> 319 4_2(321) -> 320 4_2(329) -> 328 4_2(330) -> 329 4_2(338) -> 337 4_2(339) -> 338 4_2(361) -> 161 4_2(361) -> 234 4_2(362) -> 361 4_2(367) -> 366 4_2(370) -> 249 4_2(371) -> 370 4_2(376) -> 375 4_2(379) -> 253 4_2(380) -> 379 4_2(385) -> 384 4_2(394) -> 393 4_3(303) -> 420 4_3(347) -> 346 4_3(348) -> 347 4_3(404) -> 403 4_3(405) -> 404 4_3(412) -> 161 4_3(413) -> 412 4_3(418) -> 417 5_0(1) -> 1 5_1(1) -> 83 5_1(5) -> 4 5_1(10) -> 116 5_1(13) -> 12 5_1(15) -> 14 5_1(16) -> 15 5_1(25) -> 24 5_1(34) -> 33 5_1(48) -> 47 5_1(63) -> 83 5_1(64) -> 11 5_1(65) -> 64 5_1(74) -> 73 5_1(85) -> 84 5_1(88) -> 121 5_1(101) -> 100 5_1(102) -> 101 5_1(120) -> 119 5_1(122) -> 26 5_1(123) -> 122 5_1(130) -> 129 5_1(134) -> 72 5_1(135) -> 134 5_1(137) -> 97 5_1(144) -> 143 5_1(147) -> 233 5_1(227) -> 226 5_1(233) -> 232 5_1(234) -> 233 5_1(237) -> 236 5_1(252) -> 89 5_1(259) -> 1 5_1(259) -> 83 5_1(267) -> 266 5_2(259) -> 293 5_2(271) -> 270 5_2(273) -> 272 5_2(286) -> 285 5_2(297) -> 296 5_2(306) -> 305 5_2(313) -> 312 5_2(322) -> 321 5_2(327) -> 401 5_2(331) -> 330 5_2(340) -> 339 5_2(360) -> 359 5_3(349) -> 348 5_3(406) -> 405 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) - Signature: {0/1,1/1,2/1,3/1,4/1,5/1} / {} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))