Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(2(2(1(0(0(5(x1))))))) -> 5(1(5(4(5(5(3(0(1(4(x1))))))))))
, 5(1(5(0(5(3(5(x1))))))) -> 5(4(3(0(5(4(4(2(0(5(x1))))))))))
, 4(0(5(5(5(0(5(x1))))))) -> 1(3(0(2(3(1(2(0(2(2(x1))))))))))
, 4(0(5(2(0(5(0(x1))))))) -> 4(3(4(5(4(0(5(2(3(0(x1))))))))))
, 3(3(0(1(2(0(3(x1))))))) -> 5(4(4(2(3(5(2(4(0(3(x1))))))))))
, 3(2(0(5(4(1(5(x1))))))) -> 3(5(1(4(2(0(4(3(2(4(x1))))))))))
, 2(2(4(1(0(5(5(x1))))))) -> 4(4(3(3(0(0(2(4(4(2(x1))))))))))
, 2(0(3(0(4(1(5(x1))))))) -> 2(0(1(2(4(3(5(5(3(0(x1))))))))))
, 2(0(0(0(5(2(1(x1))))))) -> 2(2(5(4(1(3(1(4(3(1(x1))))))))))
, 1(0(4(5(5(1(5(x1))))))) -> 1(5(0(4(1(4(4(4(0(4(x1))))))))))
, 0(5(1(2(1(2(4(x1))))))) -> 0(3(5(0(5(4(2(2(3(5(x1))))))))))
, 0(0(0(5(5(1(5(x1))))))) -> 0(4(4(5(3(2(1(2(0(1(x1))))))))))
, 0(0(0(5(4(2(1(x1))))))) -> 5(3(0(2(5(2(1(4(3(2(x1))))))))))
, 5(5(0(5(5(1(x1)))))) -> 5(5(5(2(1(2(3(5(4(0(x1))))))))))
, 4(1(0(5(0(4(x1)))))) -> 4(1(2(1(4(3(0(1(0(4(x1))))))))))
, 2(1(0(5(0(5(x1)))))) -> 3(4(2(1(0(1(2(4(4(5(x1))))))))))
, 2(0(3(0(1(2(x1)))))) -> 1(5(1(4(0(3(2(4(0(4(x1))))))))))
, 2(0(0(5(0(5(x1)))))) -> 4(4(1(5(5(2(5(5(3(5(x1))))))))))
, 1(3(2(2(2(1(x1)))))) -> 0(1(2(5(0(4(2(5(5(0(x1))))))))))
, 1(0(5(0(2(0(x1)))))) -> 0(5(0(2(5(1(3(0(3(4(x1))))))))))
, 1(0(2(2(1(2(x1)))))) -> 1(5(0(2(4(0(4(4(1(2(x1))))))))))
, 1(0(0(5(5(2(x1)))))) -> 4(5(1(0(2(2(5(3(5(5(x1))))))))))
, 0(5(0(0(0(5(x1)))))) -> 5(5(0(2(4(4(1(1(3(5(x1))))))))))
, 0(0(5(3(2(0(x1)))))) -> 0(3(0(4(3(3(0(1(3(0(x1))))))))))
, 0(0(3(5(0(5(x1)))))) -> 0(4(1(5(2(0(4(2(4(3(x1))))))))))
, 5(1(3(0(5(x1))))) -> 0(4(0(3(2(5(4(5(3(0(x1))))))))))
, 4(0(0(5(1(x1))))) -> 1(0(2(4(0(4(2(0(3(0(x1))))))))))
, 2(1(2(1(2(x1))))) -> 2(3(2(4(2(2(5(3(4(3(x1))))))))))
, 2(0(5(1(4(x1))))) -> 4(5(5(4(4(5(3(2(2(3(x1))))))))))
, 1(0(5(1(0(x1))))) -> 0(2(1(3(1(1(4(0(1(0(x1))))))))))
, 0(5(5(0(5(x1))))) -> 5(3(5(1(4(0(2(5(4(4(x1))))))))))
, 0(5(2(1(5(x1))))) -> 5(4(0(3(5(4(4(2(2(4(x1))))))))))
, 0(5(2(0(3(x1))))) -> 3(0(0(1(1(0(4(5(1(3(x1))))))))))
, 4(1(0(5(x1)))) -> 4(0(2(1(3(1(4(5(3(1(x1))))))))))
, 2(0(5(5(x1)))) -> 3(5(4(3(3(4(3(3(4(2(x1))))))))))
, 1(5(0(5(x1)))) -> 1(3(5(4(2(2(4(5(0(1(x1))))))))))
, 0(5(1(4(x1)))) -> 5(3(1(4(4(4(3(4(5(4(x1))))))))))
, 0(5(0(5(x1)))) -> 4(4(1(3(0(4(3(4(2(4(x1))))))))))
, 0(0(5(3(x1)))) -> 5(4(4(3(3(3(4(3(3(3(x1))))))))))
, 1(5(2(x1))) -> 1(1(2(3(3(3(4(4(4(4(x1))))))))))
, 1(0(5(x1))) -> 1(1(1(4(4(4(5(5(0(4(x1))))))))))
, 0(5(x1)) -> 5(1(3(2(4(0(4(1(4(5(x1))))))))))
, 0(5(x1)) -> 3(3(4(2(4(4(3(5(0(2(x1))))))))))
, 0(5(x1)) -> 2(4(5(0(4(2(5(2(3(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ 5_0(1) -> 1
, 5_1(1) -> 18
, 5_1(2) -> 1
, 5_1(2) -> 17
, 5_1(2) -> 18
, 5_1(2) -> 42
, 5_1(2) -> 136
, 5_1(2) -> 156
, 5_1(2) -> 294
, 5_1(2) -> 353
, 5_1(2) -> 404
, 5_1(2) -> 455
, 5_1(4) -> 3
, 5_1(6) -> 5
, 5_1(7) -> 6
, 5_1(10) -> 267
, 5_1(14) -> 13
, 5_1(17) -> 137
, 5_1(18) -> 156
, 5_1(28) -> 18
, 5_1(31) -> 30
, 5_1(34) -> 33
, 5_1(35) -> 64
, 5_1(39) -> 38
, 5_1(42) -> 130
, 5_1(44) -> 43
, 5_1(50) -> 38
, 5_1(58) -> 18
, 5_1(64) -> 63
, 5_1(66) -> 65
, 5_1(71) -> 242
, 5_1(73) -> 19
, 5_1(79) -> 323
, 5_1(82) -> 81
, 5_1(84) -> 83
, 5_1(87) -> 130
, 5_1(90) -> 89
, 5_1(94) -> 261
, 5_1(98) -> 97
, 5_1(102) -> 2
, 5_1(103) -> 102
, 5_1(108) -> 107
, 5_1(127) -> 126
, 5_1(128) -> 127
, 5_1(130) -> 129
, 5_1(133) -> 132
, 5_1(137) -> 136
, 5_1(138) -> 80
, 5_1(141) -> 140
, 5_1(150) -> 28
, 5_1(155) -> 154
, 5_1(168) -> 167
, 5_1(184) -> 183
, 5_1(196) -> 195
, 5_1(197) -> 150
, 5_1(200) -> 199
, 5_1(202) -> 33
, 5_1(219) -> 95
, 5_1(224) -> 223
, 5_1(227) -> 226
, 5_1(236) -> 235
, 5_1(257) -> 20
, 5_1(323) -> 322
, 5_1(381) -> 1
, 5_1(396) -> 395
, 5_1(442) -> 18
, 5_1(443) -> 442
, 5_1(447) -> 446
, 5_1(480) -> 2
, 5_1(481) -> 18
, 5_1(482) -> 2
, 5_2(1) -> 353
, 5_2(2) -> 353
, 5_2(4) -> 353
, 5_2(14) -> 362
, 5_2(28) -> 353
, 5_2(34) -> 371
, 5_2(44) -> 353
, 5_2(58) -> 353
, 5_2(73) -> 353
, 5_2(84) -> 380
, 5_2(102) -> 353
, 5_2(138) -> 389
, 5_2(175) -> 174
, 5_2(202) -> 371
, 5_2(204) -> 203
, 5_2(205) -> 204
, 5_2(208) -> 207
, 5_2(219) -> 353
, 5_2(249) -> 248
, 5_2(268) -> 17
, 5_2(268) -> 41
, 5_2(268) -> 94
, 5_2(268) -> 217
, 5_2(268) -> 404
, 5_2(268) -> 530
, 5_2(276) -> 275
, 5_2(330) -> 329
, 5_2(331) -> 330
, 5_2(339) -> 338
, 5_2(340) -> 339
, 5_2(354) -> 12
, 5_2(363) -> 32
, 5_2(372) -> 82
, 5_2(381) -> 1
, 5_2(381) -> 17
, 5_2(381) -> 18
, 5_2(381) -> 72
, 5_2(381) -> 218
, 5_2(381) -> 235
, 5_2(381) -> 236
, 5_2(381) -> 353
, 5_2(381) -> 404
, 5_2(404) -> 403
, 5_2(413) -> 412
, 5_2(422) -> 421
, 5_2(431) -> 430
, 5_2(440) -> 439
, 5_2(442) -> 353
, 5_2(450) -> 449
, 5_2(454) -> 453
, 5_2(458) -> 457
, 5_2(462) -> 461
, 5_2(466) -> 465
, 5_2(470) -> 469
, 5_2(474) -> 473
, 5_2(478) -> 477
, 5_2(480) -> 353
, 5_2(481) -> 353
, 5_2(482) -> 481
, 5_2(486) -> 485
, 5_2(511) -> 510
, 5_2(512) -> 511
, 5_2(522) -> 136
, 5_2(523) -> 522
, 5_2(524) -> 523
, 5_2(529) -> 528
, 5_2(532) -> 531
, 5_2(554) -> 553
, 5_2(556) -> 555
, 5_2(574) -> 573
, 5_3(381) -> 614
, 5_3(599) -> 598
, 5_3(603) -> 602
, 5_3(606) -> 404
, 5_3(622) -> 621
, 0_0(1) -> 1
, 0_1(1) -> 17
, 0_1(2) -> 17
, 0_1(3) -> 17
, 0_1(9) -> 8
, 0_1(10) -> 79
, 0_1(13) -> 12
, 0_1(18) -> 17
, 0_1(19) -> 17
, 0_1(21) -> 20
, 0_1(26) -> 25
, 0_1(27) -> 396
, 0_1(33) -> 32
, 0_1(35) -> 190
, 0_1(42) -> 41
, 0_1(43) -> 17
, 0_1(48) -> 47
, 0_1(54) -> 53
, 0_1(55) -> 54
, 0_1(59) -> 58
, 0_1(72) -> 94
, 0_1(73) -> 17
, 0_1(74) -> 73
, 0_1(80) -> 1
, 0_1(80) -> 17
, 0_1(80) -> 18
, 0_1(80) -> 72
, 0_1(80) -> 218
, 0_1(80) -> 235
, 0_1(80) -> 236
, 0_1(80) -> 353
, 0_1(80) -> 404
, 0_1(83) -> 82
, 0_1(95) -> 17
, 0_1(96) -> 95
, 0_1(114) -> 113
, 0_1(118) -> 117
, 0_1(124) -> 123
, 0_1(134) -> 133
, 0_1(138) -> 17
, 0_1(139) -> 138
, 0_1(144) -> 143
, 0_1(147) -> 146
, 0_1(152) -> 151
, 0_1(157) -> 102
, 0_1(162) -> 81
, 0_1(166) -> 165
, 0_1(168) -> 17
, 0_1(170) -> 169
, 0_1(181) -> 88
, 0_1(185) -> 19
, 0_1(188) -> 187
, 0_1(218) -> 217
, 0_1(222) -> 221
, 0_1(225) -> 11
, 0_1(230) -> 43
, 0_1(231) -> 230
, 0_1(234) -> 233
, 0_1(237) -> 28
, 0_1(278) -> 277
, 0_1(344) -> 343
, 0_1(381) -> 17
, 0_1(382) -> 17
, 0_1(444) -> 443
, 0_1(483) -> 17
, 0_2(1) -> 404
, 0_2(3) -> 530
, 0_2(72) -> 404
, 0_2(138) -> 557
, 0_2(151) -> 530
, 0_2(168) -> 513
, 0_2(172) -> 17
, 0_2(172) -> 94
, 0_2(172) -> 217
, 0_2(172) -> 404
, 0_2(175) -> 513
, 0_2(177) -> 176
, 0_2(185) -> 566
, 0_2(256) -> 404
, 0_2(285) -> 284
, 0_2(289) -> 340
, 0_2(332) -> 331
, 0_2(350) -> 349
, 0_2(359) -> 358
, 0_2(368) -> 367
, 0_2(377) -> 376
, 0_2(382) -> 530
, 0_2(386) -> 385
, 0_2(405) -> 404
, 0_2(414) -> 413
, 0_2(423) -> 422
, 0_2(432) -> 431
, 0_2(441) -> 440
, 0_2(451) -> 450
, 0_2(459) -> 458
, 0_2(467) -> 466
, 0_2(475) -> 474
, 0_2(480) -> 331
, 0_2(483) -> 482
, 0_2(506) -> 505
, 0_2(535) -> 534
, 0_2(539) -> 538
, 0_2(549) -> 235
, 0_2(551) -> 550
, 0_2(558) -> 218
, 0_2(565) -> 564
, 0_2(568) -> 567
, 0_3(600) -> 599
, 0_3(605) -> 622
, 0_3(611) -> 610
, 2_0(1) -> 1
, 2_1(1) -> 27
, 2_1(2) -> 27
, 2_1(10) -> 50
, 2_1(17) -> 16
, 2_1(19) -> 27
, 2_1(22) -> 21
, 2_1(25) -> 24
, 2_1(27) -> 26
, 2_1(35) -> 34
, 2_1(37) -> 36
, 2_1(40) -> 39
, 2_1(42) -> 202
, 2_1(47) -> 46
, 2_1(50) -> 229
, 2_1(56) -> 55
, 2_1(58) -> 1
, 2_1(58) -> 16
, 2_1(58) -> 17
, 2_1(58) -> 27
, 2_1(58) -> 189
, 2_1(58) -> 404
, 2_1(58) -> 405
, 2_1(61) -> 60
, 2_1(65) -> 58
, 2_1(70) -> 171
, 2_1(78) -> 125
, 2_1(86) -> 85
, 2_1(87) -> 86
, 2_1(92) -> 91
, 2_1(94) -> 93
, 2_1(97) -> 96
, 2_1(99) -> 98
, 2_1(101) -> 447
, 2_1(102) -> 27
, 2_1(104) -> 103
, 2_1(106) -> 105
, 2_1(110) -> 109
, 2_1(116) -> 115
, 2_1(120) -> 119
, 2_1(129) -> 128
, 2_1(132) -> 131
, 2_1(136) -> 135
, 2_1(138) -> 27
, 2_1(140) -> 139
, 2_1(145) -> 74
, 2_1(153) -> 152
, 2_1(154) -> 153
, 2_1(158) -> 157
, 2_1(169) -> 168
, 2_1(183) -> 182
, 2_1(186) -> 185
, 2_1(190) -> 189
, 2_1(192) -> 191
, 2_1(194) -> 193
, 2_1(195) -> 194
, 2_1(202) -> 201
, 2_1(212) -> 80
, 2_1(223) -> 222
, 2_1(224) -> 119
, 2_1(238) -> 237
, 2_1(259) -> 258
, 2_1(260) -> 259
, 2_1(296) -> 295
, 2_1(342) -> 341
, 2_1(381) -> 27
, 2_1(392) -> 391
, 2_1(446) -> 445
, 2_1(480) -> 27
, 2_1(482) -> 27
, 2_2(1) -> 405
, 2_2(2) -> 256
, 2_2(4) -> 256
, 2_2(14) -> 414
, 2_2(28) -> 256
, 2_2(34) -> 423
, 2_2(44) -> 256
, 2_2(58) -> 256
, 2_2(73) -> 256
, 2_2(84) -> 432
, 2_2(102) -> 256
, 2_2(103) -> 256
, 2_2(138) -> 441
, 2_2(150) -> 256
, 2_2(176) -> 175
, 2_2(179) -> 178
, 2_2(202) -> 423
, 2_2(210) -> 209
, 2_2(211) -> 210
, 2_2(219) -> 256
, 2_2(289) -> 288
, 2_2(303) -> 302
, 2_2(348) -> 347
, 2_2(357) -> 356
, 2_2(366) -> 365
, 2_2(375) -> 374
, 2_2(381) -> 256
, 2_2(384) -> 383
, 2_2(400) -> 399
, 2_2(409) -> 408
, 2_2(418) -> 417
, 2_2(427) -> 426
, 2_2(436) -> 435
, 2_2(442) -> 256
, 2_2(443) -> 256
, 2_2(448) -> 17
, 2_2(448) -> 41
, 2_2(448) -> 94
, 2_2(448) -> 217
, 2_2(448) -> 404
, 2_2(448) -> 530
, 2_2(453) -> 452
, 2_2(455) -> 454
, 2_2(456) -> 12
, 2_2(461) -> 460
, 2_2(463) -> 462
, 2_2(464) -> 32
, 2_2(469) -> 468
, 2_2(471) -> 470
, 2_2(472) -> 82
, 2_2(477) -> 476
, 2_2(479) -> 478
, 2_2(480) -> 1
, 2_2(480) -> 17
, 2_2(480) -> 18
, 2_2(480) -> 72
, 2_2(480) -> 218
, 2_2(480) -> 235
, 2_2(480) -> 236
, 2_2(480) -> 353
, 2_2(480) -> 404
, 2_2(481) -> 72
, 2_2(482) -> 1
, 2_2(485) -> 484
, 2_2(487) -> 486
, 2_2(505) -> 189
, 2_2(508) -> 507
, 2_2(525) -> 524
, 2_2(527) -> 526
, 2_2(537) -> 536
, 2_2(553) -> 552
, 2_2(559) -> 558
, 2_2(569) -> 568
, 2_3(312) -> 311
, 2_3(381) -> 605
, 2_3(597) -> 404
, 2_3(602) -> 601
, 2_3(604) -> 603
, 2_3(609) -> 608
, 2_3(618) -> 617
, 3_0(1) -> 1
, 3_1(1) -> 42
, 3_1(2) -> 42
, 3_1(8) -> 7
, 3_1(10) -> 144
, 3_1(12) -> 11
, 3_1(17) -> 35
, 3_1(18) -> 87
, 3_1(20) -> 19
, 3_1(23) -> 22
, 3_1(27) -> 101
, 3_1(28) -> 42
, 3_1(29) -> 28
, 3_1(38) -> 37
, 3_1(42) -> 294
, 3_1(43) -> 1
, 3_1(43) -> 16
, 3_1(43) -> 17
, 3_1(43) -> 27
, 3_1(43) -> 42
, 3_1(43) -> 101
, 3_1(43) -> 404
, 3_1(43) -> 405
, 3_1(43) -> 455
, 3_1(50) -> 49
, 3_1(52) -> 51
, 3_1(53) -> 52
, 3_1(57) -> 247
, 3_1(58) -> 35
, 3_1(63) -> 62
, 3_1(69) -> 68
, 3_1(70) -> 196
, 3_1(72) -> 71
, 3_1(80) -> 87
, 3_1(81) -> 80
, 3_1(84) -> 42
, 3_1(91) -> 90
, 3_1(94) -> 112
, 3_1(95) -> 2
, 3_1(107) -> 106
, 3_1(113) -> 112
, 3_1(125) -> 124
, 3_1(138) -> 42
, 3_1(143) -> 142
, 3_1(156) -> 155
, 3_1(164) -> 163
, 3_1(165) -> 164
, 3_1(182) -> 181
, 3_1(191) -> 58
, 3_1(201) -> 200
, 3_1(214) -> 213
, 3_1(226) -> 225
, 3_1(240) -> 239
, 3_1(244) -> 243
, 3_1(245) -> 244
, 3_1(247) -> 246
, 3_1(266) -> 265
, 3_1(277) -> 126
, 3_1(280) -> 279
, 3_1(290) -> 36
, 3_1(291) -> 290
, 3_1(292) -> 291
, 3_1(294) -> 293
, 3_1(297) -> 296
, 3_1(298) -> 297
, 3_1(299) -> 298
, 3_1(341) -> 3
, 3_1(381) -> 35
, 3_1(390) -> 43
, 3_1(395) -> 394
, 3_1(433) -> 42
, 3_1(480) -> 35
, 3_1(482) -> 35
, 3_2(1) -> 455
, 3_2(46) -> 211
, 3_2(72) -> 455
, 3_2(84) -> 180
, 3_2(123) -> 211
, 3_2(209) -> 208
, 3_2(221) -> 211
, 3_2(248) -> 16
, 3_2(251) -> 250
, 3_2(252) -> 251
, 3_2(254) -> 253
, 3_2(255) -> 254
, 3_2(256) -> 455
, 3_2(269) -> 268
, 3_2(274) -> 273
, 3_2(284) -> 283
, 3_2(287) -> 286
, 3_2(304) -> 303
, 3_2(305) -> 304
, 3_2(306) -> 305
, 3_2(332) -> 254
, 3_2(347) -> 346
, 3_2(353) -> 455
, 3_2(356) -> 355
, 3_2(365) -> 364
, 3_2(374) -> 373
, 3_2(383) -> 382
, 3_2(397) -> 17
, 3_2(397) -> 41
, 3_2(397) -> 94
, 3_2(397) -> 217
, 3_2(397) -> 404
, 3_2(397) -> 530
, 3_2(398) -> 397
, 3_2(403) -> 402
, 3_2(405) -> 455
, 3_2(406) -> 12
, 3_2(407) -> 406
, 3_2(412) -> 411
, 3_2(414) -> 463
, 3_2(415) -> 32
, 3_2(416) -> 415
, 3_2(421) -> 420
, 3_2(423) -> 471
, 3_2(424) -> 82
, 3_2(425) -> 424
, 3_2(430) -> 429
, 3_2(432) -> 479
, 3_2(433) -> 1
, 3_2(433) -> 17
, 3_2(433) -> 18
, 3_2(433) -> 72
, 3_2(433) -> 218
, 3_2(433) -> 235
, 3_2(433) -> 236
, 3_2(433) -> 353
, 3_2(433) -> 404
, 3_2(434) -> 433
, 3_2(439) -> 438
, 3_2(441) -> 487
, 3_2(510) -> 509
, 3_2(513) -> 512
, 3_2(528) -> 527
, 3_2(536) -> 535
, 3_2(552) -> 551
, 3_2(557) -> 556
, 3_2(561) -> 560
, 3_2(571) -> 570
, 3_2(575) -> 574
, 3_3(313) -> 312
, 3_3(314) -> 313
, 3_3(315) -> 314
, 3_3(605) -> 604
, 3_3(608) -> 607
, 3_3(615) -> 404
, 3_3(616) -> 615
, 3_3(621) -> 620
, 4_0(1) -> 1
, 4_1(1) -> 10
, 4_1(2) -> 10
, 4_1(4) -> 10
, 4_1(5) -> 4
, 4_1(9) -> 344
, 4_1(10) -> 224
, 4_1(11) -> 2
, 4_1(15) -> 14
, 4_1(16) -> 15
, 4_1(17) -> 108
, 4_1(18) -> 121
, 4_1(27) -> 57
, 4_1(28) -> 1
, 4_1(28) -> 10
, 4_1(28) -> 16
, 4_1(28) -> 17
, 4_1(28) -> 26
, 4_1(28) -> 27
, 4_1(28) -> 72
, 4_1(28) -> 108
, 4_1(28) -> 218
, 4_1(28) -> 229
, 4_1(28) -> 332
, 4_1(28) -> 404
, 4_1(28) -> 405
, 4_1(30) -> 29
, 4_1(32) -> 31
, 4_1(35) -> 70
, 4_1(36) -> 11
, 4_1(41) -> 40
, 4_1(42) -> 70
, 4_1(46) -> 45
, 4_1(49) -> 48
, 4_1(50) -> 280
, 4_1(51) -> 28
, 4_1(57) -> 56
, 4_1(58) -> 10
, 4_1(59) -> 10
, 4_1(62) -> 61
, 4_1(64) -> 184
, 4_1(67) -> 66
, 4_1(71) -> 70
, 4_1(73) -> 10
, 4_1(75) -> 74
, 4_1(77) -> 76
, 4_1(78) -> 77
, 4_1(79) -> 78
, 4_1(80) -> 10
, 4_1(85) -> 84
, 4_1(88) -> 80
, 4_1(89) -> 88
, 4_1(101) -> 100
, 4_1(112) -> 111
, 4_1(115) -> 43
, 4_1(121) -> 120
, 4_1(123) -> 122
, 4_1(132) -> 10
, 4_1(135) -> 134
, 4_1(138) -> 10
, 4_1(146) -> 145
, 4_1(148) -> 147
, 4_1(149) -> 148
, 4_1(159) -> 158
, 4_1(160) -> 159
, 4_1(163) -> 162
, 4_1(171) -> 170
, 4_1(187) -> 186
, 4_1(189) -> 188
, 4_1(193) -> 192
, 4_1(198) -> 197
, 4_1(199) -> 198
, 4_1(217) -> 216
, 4_1(221) -> 220
, 4_1(224) -> 300
, 4_1(228) -> 227
, 4_1(229) -> 228
, 4_1(235) -> 234
, 4_1(242) -> 241
, 4_1(243) -> 44
, 4_1(246) -> 245
, 4_1(258) -> 257
, 4_1(261) -> 260
, 4_1(263) -> 262
, 4_1(264) -> 263
, 4_1(265) -> 264
, 4_1(267) -> 266
, 4_1(279) -> 278
, 4_1(293) -> 292
, 4_1(294) -> 292
, 4_1(300) -> 299
, 4_1(320) -> 319
, 4_1(321) -> 320
, 4_1(322) -> 321
, 4_1(343) -> 342
, 4_1(345) -> 344
, 4_1(381) -> 10
, 4_1(391) -> 390
, 4_1(393) -> 392
, 4_1(394) -> 393
, 4_1(442) -> 58
, 4_1(445) -> 444
, 4_1(480) -> 10
, 4_1(482) -> 10
, 4_1(483) -> 10
, 4_2(1) -> 332
, 4_2(2) -> 332
, 4_2(4) -> 332
, 4_2(28) -> 332
, 4_2(44) -> 289
, 4_2(46) -> 276
, 4_2(58) -> 332
, 4_2(61) -> 539
, 4_2(73) -> 332
, 4_2(102) -> 332
, 4_2(123) -> 276
, 4_2(132) -> 539
, 4_2(138) -> 289
, 4_2(169) -> 309
, 4_2(173) -> 172
, 4_2(178) -> 177
, 4_2(180) -> 179
, 4_2(203) -> 16
, 4_2(206) -> 205
, 4_2(207) -> 206
, 4_2(219) -> 289
, 4_2(221) -> 276
, 4_2(250) -> 249
, 4_2(253) -> 252
, 4_2(256) -> 255
, 4_2(271) -> 270
, 4_2(272) -> 271
, 4_2(273) -> 272
, 4_2(275) -> 274
, 4_2(281) -> 17
, 4_2(282) -> 281
, 4_2(286) -> 285
, 4_2(288) -> 287
, 4_2(296) -> 539
, 4_2(307) -> 306
, 4_2(308) -> 307
, 4_2(309) -> 308
, 4_2(327) -> 326
, 4_2(328) -> 327
, 4_2(329) -> 328
, 4_2(336) -> 335
, 4_2(337) -> 336
, 4_2(338) -> 337
, 4_2(349) -> 348
, 4_2(351) -> 350
, 4_2(353) -> 352
, 4_2(358) -> 357
, 4_2(360) -> 359
, 4_2(362) -> 361
, 4_2(367) -> 366
, 4_2(369) -> 368
, 4_2(371) -> 370
, 4_2(376) -> 375
, 4_2(378) -> 377
, 4_2(380) -> 379
, 4_2(381) -> 289
, 4_2(385) -> 384
, 4_2(387) -> 386
, 4_2(389) -> 388
, 4_2(399) -> 398
, 4_2(401) -> 400
, 4_2(402) -> 401
, 4_2(408) -> 407
, 4_2(410) -> 409
, 4_2(411) -> 410
, 4_2(417) -> 416
, 4_2(419) -> 418
, 4_2(420) -> 419
, 4_2(426) -> 425
, 4_2(428) -> 427
, 4_2(429) -> 428
, 4_2(435) -> 434
, 4_2(437) -> 436
, 4_2(438) -> 437
, 4_2(442) -> 289
, 4_2(449) -> 448
, 4_2(452) -> 451
, 4_2(457) -> 456
, 4_2(460) -> 459
, 4_2(465) -> 464
, 4_2(468) -> 467
, 4_2(473) -> 472
, 4_2(476) -> 475
, 4_2(480) -> 289
, 4_2(481) -> 480
, 4_2(482) -> 289
, 4_2(484) -> 483
, 4_2(509) -> 508
, 4_2(530) -> 529
, 4_2(534) -> 533
, 4_2(538) -> 537
, 4_2(550) -> 549
, 4_2(555) -> 554
, 4_2(564) -> 563
, 4_2(567) -> 159
, 4_2(573) -> 572
, 4_3(176) -> 318
, 4_3(316) -> 315
, 4_3(317) -> 316
, 4_3(318) -> 317
, 4_3(598) -> 597
, 4_3(601) -> 600
, 4_3(610) -> 609
, 4_3(612) -> 611
, 4_3(614) -> 613
, 4_3(617) -> 616
, 4_3(619) -> 618
, 4_3(620) -> 619
, 1_0(1) -> 1
, 1_1(1) -> 72
, 1_1(2) -> 72
, 1_1(3) -> 2
, 1_1(4) -> 72
, 1_1(10) -> 9
, 1_1(17) -> 218
, 1_1(19) -> 1
, 1_1(19) -> 10
, 1_1(19) -> 16
, 1_1(19) -> 27
, 1_1(19) -> 72
, 1_1(19) -> 108
, 1_1(19) -> 114
, 1_1(19) -> 189
, 1_1(19) -> 218
, 1_1(19) -> 332
, 1_1(19) -> 405
, 1_1(24) -> 23
, 1_1(27) -> 149
, 1_1(35) -> 166
, 1_1(42) -> 236
, 1_1(45) -> 44
, 1_1(60) -> 59
, 1_1(68) -> 67
, 1_1(70) -> 69
, 1_1(73) -> 72
, 1_1(76) -> 75
, 1_1(79) -> 114
, 1_1(80) -> 236
, 1_1(87) -> 161
, 1_1(93) -> 92
, 1_1(100) -> 99
, 1_1(105) -> 104
, 1_1(108) -> 215
, 1_1(109) -> 28
, 1_1(111) -> 110
, 1_1(117) -> 116
, 1_1(119) -> 118
, 1_1(121) -> 345
, 1_1(122) -> 73
, 1_1(126) -> 51
, 1_1(131) -> 80
, 1_1(138) -> 72
, 1_1(142) -> 141
, 1_1(151) -> 150
, 1_1(161) -> 160
, 1_1(167) -> 88
, 1_1(213) -> 212
, 1_1(215) -> 214
, 1_1(216) -> 215
, 1_1(220) -> 219
, 1_1(232) -> 231
, 1_1(233) -> 232
, 1_1(236) -> 160
, 1_1(239) -> 238
, 1_1(241) -> 240
, 1_1(262) -> 95
, 1_1(295) -> 19
, 1_1(319) -> 295
, 1_1(381) -> 72
, 1_2(138) -> 575
, 1_2(174) -> 173
, 1_2(270) -> 269
, 1_2(283) -> 282
, 1_2(301) -> 88
, 1_2(302) -> 301
, 1_2(324) -> 218
, 1_2(325) -> 324
, 1_2(326) -> 325
, 1_2(333) -> 72
, 1_2(333) -> 160
, 1_2(333) -> 218
, 1_2(334) -> 333
, 1_2(335) -> 334
, 1_2(346) -> 268
, 1_2(352) -> 351
, 1_2(355) -> 354
, 1_2(361) -> 360
, 1_2(364) -> 363
, 1_2(370) -> 369
, 1_2(373) -> 372
, 1_2(379) -> 378
, 1_2(382) -> 381
, 1_2(388) -> 387
, 1_2(480) -> 351
, 1_2(507) -> 506
, 1_2(526) -> 525
, 1_2(531) -> 189
, 1_2(533) -> 532
, 1_2(560) -> 559
, 1_2(562) -> 561
, 1_2(563) -> 562
, 1_2(566) -> 565
, 1_2(570) -> 569
, 1_2(572) -> 571
, 1_3(310) -> 173
, 1_3(311) -> 310
, 1_3(607) -> 606
, 1_3(613) -> 612}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 5(2(2(1(0(0(5(x1))))))) -> 5(1(5(4(5(5(3(0(1(4(x1))))))))))
, 5(1(5(0(5(3(5(x1))))))) -> 5(4(3(0(5(4(4(2(0(5(x1))))))))))
, 4(0(5(5(5(0(5(x1))))))) -> 1(3(0(2(3(1(2(0(2(2(x1))))))))))
, 4(0(5(2(0(5(0(x1))))))) -> 4(3(4(5(4(0(5(2(3(0(x1))))))))))
, 3(3(0(1(2(0(3(x1))))))) -> 5(4(4(2(3(5(2(4(0(3(x1))))))))))
, 3(2(0(5(4(1(5(x1))))))) -> 3(5(1(4(2(0(4(3(2(4(x1))))))))))
, 2(2(4(1(0(5(5(x1))))))) -> 4(4(3(3(0(0(2(4(4(2(x1))))))))))
, 2(0(3(0(4(1(5(x1))))))) -> 2(0(1(2(4(3(5(5(3(0(x1))))))))))
, 2(0(0(0(5(2(1(x1))))))) -> 2(2(5(4(1(3(1(4(3(1(x1))))))))))
, 1(0(4(5(5(1(5(x1))))))) -> 1(5(0(4(1(4(4(4(0(4(x1))))))))))
, 0(5(1(2(1(2(4(x1))))))) -> 0(3(5(0(5(4(2(2(3(5(x1))))))))))
, 0(0(0(5(5(1(5(x1))))))) -> 0(4(4(5(3(2(1(2(0(1(x1))))))))))
, 0(0(0(5(4(2(1(x1))))))) -> 5(3(0(2(5(2(1(4(3(2(x1))))))))))
, 5(5(0(5(5(1(x1)))))) -> 5(5(5(2(1(2(3(5(4(0(x1))))))))))
, 4(1(0(5(0(4(x1)))))) -> 4(1(2(1(4(3(0(1(0(4(x1))))))))))
, 2(1(0(5(0(5(x1)))))) -> 3(4(2(1(0(1(2(4(4(5(x1))))))))))
, 2(0(3(0(1(2(x1)))))) -> 1(5(1(4(0(3(2(4(0(4(x1))))))))))
, 2(0(0(5(0(5(x1)))))) -> 4(4(1(5(5(2(5(5(3(5(x1))))))))))
, 1(3(2(2(2(1(x1)))))) -> 0(1(2(5(0(4(2(5(5(0(x1))))))))))
, 1(0(5(0(2(0(x1)))))) -> 0(5(0(2(5(1(3(0(3(4(x1))))))))))
, 1(0(2(2(1(2(x1)))))) -> 1(5(0(2(4(0(4(4(1(2(x1))))))))))
, 1(0(0(5(5(2(x1)))))) -> 4(5(1(0(2(2(5(3(5(5(x1))))))))))
, 0(5(0(0(0(5(x1)))))) -> 5(5(0(2(4(4(1(1(3(5(x1))))))))))
, 0(0(5(3(2(0(x1)))))) -> 0(3(0(4(3(3(0(1(3(0(x1))))))))))
, 0(0(3(5(0(5(x1)))))) -> 0(4(1(5(2(0(4(2(4(3(x1))))))))))
, 5(1(3(0(5(x1))))) -> 0(4(0(3(2(5(4(5(3(0(x1))))))))))
, 4(0(0(5(1(x1))))) -> 1(0(2(4(0(4(2(0(3(0(x1))))))))))
, 2(1(2(1(2(x1))))) -> 2(3(2(4(2(2(5(3(4(3(x1))))))))))
, 2(0(5(1(4(x1))))) -> 4(5(5(4(4(5(3(2(2(3(x1))))))))))
, 1(0(5(1(0(x1))))) -> 0(2(1(3(1(1(4(0(1(0(x1))))))))))
, 0(5(5(0(5(x1))))) -> 5(3(5(1(4(0(2(5(4(4(x1))))))))))
, 0(5(2(1(5(x1))))) -> 5(4(0(3(5(4(4(2(2(4(x1))))))))))
, 0(5(2(0(3(x1))))) -> 3(0(0(1(1(0(4(5(1(3(x1))))))))))
, 4(1(0(5(x1)))) -> 4(0(2(1(3(1(4(5(3(1(x1))))))))))
, 2(0(5(5(x1)))) -> 3(5(4(3(3(4(3(3(4(2(x1))))))))))
, 1(5(0(5(x1)))) -> 1(3(5(4(2(2(4(5(0(1(x1))))))))))
, 0(5(1(4(x1)))) -> 5(3(1(4(4(4(3(4(5(4(x1))))))))))
, 0(5(0(5(x1)))) -> 4(4(1(3(0(4(3(4(2(4(x1))))))))))
, 0(0(5(3(x1)))) -> 5(4(4(3(3(3(4(3(3(3(x1))))))))))
, 1(5(2(x1))) -> 1(1(2(3(3(3(4(4(4(4(x1))))))))))
, 1(0(5(x1))) -> 1(1(1(4(4(4(5(5(0(4(x1))))))))))
, 0(5(x1)) -> 5(1(3(2(4(0(4(1(4(5(x1))))))))))
, 0(5(x1)) -> 3(3(4(2(4(4(3(5(0(2(x1))))))))))
, 0(5(x1)) -> 2(4(5(0(4(2(5(2(3(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool IDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 5(2(2(1(0(0(5(x1))))))) -> 5(1(5(4(5(5(3(0(1(4(x1))))))))))
, 5(1(5(0(5(3(5(x1))))))) -> 5(4(3(0(5(4(4(2(0(5(x1))))))))))
, 4(0(5(5(5(0(5(x1))))))) -> 1(3(0(2(3(1(2(0(2(2(x1))))))))))
, 4(0(5(2(0(5(0(x1))))))) -> 4(3(4(5(4(0(5(2(3(0(x1))))))))))
, 3(3(0(1(2(0(3(x1))))))) -> 5(4(4(2(3(5(2(4(0(3(x1))))))))))
, 3(2(0(5(4(1(5(x1))))))) -> 3(5(1(4(2(0(4(3(2(4(x1))))))))))
, 2(2(4(1(0(5(5(x1))))))) -> 4(4(3(3(0(0(2(4(4(2(x1))))))))))
, 2(0(3(0(4(1(5(x1))))))) -> 2(0(1(2(4(3(5(5(3(0(x1))))))))))
, 2(0(0(0(5(2(1(x1))))))) -> 2(2(5(4(1(3(1(4(3(1(x1))))))))))
, 1(0(4(5(5(1(5(x1))))))) -> 1(5(0(4(1(4(4(4(0(4(x1))))))))))
, 0(5(1(2(1(2(4(x1))))))) -> 0(3(5(0(5(4(2(2(3(5(x1))))))))))
, 0(0(0(5(5(1(5(x1))))))) -> 0(4(4(5(3(2(1(2(0(1(x1))))))))))
, 0(0(0(5(4(2(1(x1))))))) -> 5(3(0(2(5(2(1(4(3(2(x1))))))))))
, 5(5(0(5(5(1(x1)))))) -> 5(5(5(2(1(2(3(5(4(0(x1))))))))))
, 4(1(0(5(0(4(x1)))))) -> 4(1(2(1(4(3(0(1(0(4(x1))))))))))
, 2(1(0(5(0(5(x1)))))) -> 3(4(2(1(0(1(2(4(4(5(x1))))))))))
, 2(0(3(0(1(2(x1)))))) -> 1(5(1(4(0(3(2(4(0(4(x1))))))))))
, 2(0(0(5(0(5(x1)))))) -> 4(4(1(5(5(2(5(5(3(5(x1))))))))))
, 1(3(2(2(2(1(x1)))))) -> 0(1(2(5(0(4(2(5(5(0(x1))))))))))
, 1(0(5(0(2(0(x1)))))) -> 0(5(0(2(5(1(3(0(3(4(x1))))))))))
, 1(0(2(2(1(2(x1)))))) -> 1(5(0(2(4(0(4(4(1(2(x1))))))))))
, 1(0(0(5(5(2(x1)))))) -> 4(5(1(0(2(2(5(3(5(5(x1))))))))))
, 0(5(0(0(0(5(x1)))))) -> 5(5(0(2(4(4(1(1(3(5(x1))))))))))
, 0(0(5(3(2(0(x1)))))) -> 0(3(0(4(3(3(0(1(3(0(x1))))))))))
, 0(0(3(5(0(5(x1)))))) -> 0(4(1(5(2(0(4(2(4(3(x1))))))))))
, 5(1(3(0(5(x1))))) -> 0(4(0(3(2(5(4(5(3(0(x1))))))))))
, 4(0(0(5(1(x1))))) -> 1(0(2(4(0(4(2(0(3(0(x1))))))))))
, 2(1(2(1(2(x1))))) -> 2(3(2(4(2(2(5(3(4(3(x1))))))))))
, 2(0(5(1(4(x1))))) -> 4(5(5(4(4(5(3(2(2(3(x1))))))))))
, 1(0(5(1(0(x1))))) -> 0(2(1(3(1(1(4(0(1(0(x1))))))))))
, 0(5(5(0(5(x1))))) -> 5(3(5(1(4(0(2(5(4(4(x1))))))))))
, 0(5(2(1(5(x1))))) -> 5(4(0(3(5(4(4(2(2(4(x1))))))))))
, 0(5(2(0(3(x1))))) -> 3(0(0(1(1(0(4(5(1(3(x1))))))))))
, 4(1(0(5(x1)))) -> 4(0(2(1(3(1(4(5(3(1(x1))))))))))
, 2(0(5(5(x1)))) -> 3(5(4(3(3(4(3(3(4(2(x1))))))))))
, 1(5(0(5(x1)))) -> 1(3(5(4(2(2(4(5(0(1(x1))))))))))
, 0(5(1(4(x1)))) -> 5(3(1(4(4(4(3(4(5(4(x1))))))))))
, 0(5(0(5(x1)))) -> 4(4(1(3(0(4(3(4(2(4(x1))))))))))
, 0(0(5(3(x1)))) -> 5(4(4(3(3(3(4(3(3(3(x1))))))))))
, 1(5(2(x1))) -> 1(1(2(3(3(3(4(4(4(4(x1))))))))))
, 1(0(5(x1))) -> 1(1(1(4(4(4(5(5(0(4(x1))))))))))
, 0(5(x1)) -> 5(1(3(2(4(0(4(1(4(5(x1))))))))))
, 0(5(x1)) -> 3(3(4(2(4(4(3(5(0(2(x1))))))))))
, 0(5(x1)) -> 2(4(5(0(4(2(5(2(3(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 5(2(2(1(0(0(5(x1))))))) -> 5(1(5(4(5(5(3(0(1(4(x1))))))))))
, 5(1(5(0(5(3(5(x1))))))) -> 5(4(3(0(5(4(4(2(0(5(x1))))))))))
, 4(0(5(5(5(0(5(x1))))))) -> 1(3(0(2(3(1(2(0(2(2(x1))))))))))
, 4(0(5(2(0(5(0(x1))))))) -> 4(3(4(5(4(0(5(2(3(0(x1))))))))))
, 3(3(0(1(2(0(3(x1))))))) -> 5(4(4(2(3(5(2(4(0(3(x1))))))))))
, 3(2(0(5(4(1(5(x1))))))) -> 3(5(1(4(2(0(4(3(2(4(x1))))))))))
, 2(2(4(1(0(5(5(x1))))))) -> 4(4(3(3(0(0(2(4(4(2(x1))))))))))
, 2(0(3(0(4(1(5(x1))))))) -> 2(0(1(2(4(3(5(5(3(0(x1))))))))))
, 2(0(0(0(5(2(1(x1))))))) -> 2(2(5(4(1(3(1(4(3(1(x1))))))))))
, 1(0(4(5(5(1(5(x1))))))) -> 1(5(0(4(1(4(4(4(0(4(x1))))))))))
, 0(5(1(2(1(2(4(x1))))))) -> 0(3(5(0(5(4(2(2(3(5(x1))))))))))
, 0(0(0(5(5(1(5(x1))))))) -> 0(4(4(5(3(2(1(2(0(1(x1))))))))))
, 0(0(0(5(4(2(1(x1))))))) -> 5(3(0(2(5(2(1(4(3(2(x1))))))))))
, 5(5(0(5(5(1(x1)))))) -> 5(5(5(2(1(2(3(5(4(0(x1))))))))))
, 4(1(0(5(0(4(x1)))))) -> 4(1(2(1(4(3(0(1(0(4(x1))))))))))
, 2(1(0(5(0(5(x1)))))) -> 3(4(2(1(0(1(2(4(4(5(x1))))))))))
, 2(0(3(0(1(2(x1)))))) -> 1(5(1(4(0(3(2(4(0(4(x1))))))))))
, 2(0(0(5(0(5(x1)))))) -> 4(4(1(5(5(2(5(5(3(5(x1))))))))))
, 1(3(2(2(2(1(x1)))))) -> 0(1(2(5(0(4(2(5(5(0(x1))))))))))
, 1(0(5(0(2(0(x1)))))) -> 0(5(0(2(5(1(3(0(3(4(x1))))))))))
, 1(0(2(2(1(2(x1)))))) -> 1(5(0(2(4(0(4(4(1(2(x1))))))))))
, 1(0(0(5(5(2(x1)))))) -> 4(5(1(0(2(2(5(3(5(5(x1))))))))))
, 0(5(0(0(0(5(x1)))))) -> 5(5(0(2(4(4(1(1(3(5(x1))))))))))
, 0(0(5(3(2(0(x1)))))) -> 0(3(0(4(3(3(0(1(3(0(x1))))))))))
, 0(0(3(5(0(5(x1)))))) -> 0(4(1(5(2(0(4(2(4(3(x1))))))))))
, 5(1(3(0(5(x1))))) -> 0(4(0(3(2(5(4(5(3(0(x1))))))))))
, 4(0(0(5(1(x1))))) -> 1(0(2(4(0(4(2(0(3(0(x1))))))))))
, 2(1(2(1(2(x1))))) -> 2(3(2(4(2(2(5(3(4(3(x1))))))))))
, 2(0(5(1(4(x1))))) -> 4(5(5(4(4(5(3(2(2(3(x1))))))))))
, 1(0(5(1(0(x1))))) -> 0(2(1(3(1(1(4(0(1(0(x1))))))))))
, 0(5(5(0(5(x1))))) -> 5(3(5(1(4(0(2(5(4(4(x1))))))))))
, 0(5(2(1(5(x1))))) -> 5(4(0(3(5(4(4(2(2(4(x1))))))))))
, 0(5(2(0(3(x1))))) -> 3(0(0(1(1(0(4(5(1(3(x1))))))))))
, 4(1(0(5(x1)))) -> 4(0(2(1(3(1(4(5(3(1(x1))))))))))
, 2(0(5(5(x1)))) -> 3(5(4(3(3(4(3(3(4(2(x1))))))))))
, 1(5(0(5(x1)))) -> 1(3(5(4(2(2(4(5(0(1(x1))))))))))
, 0(5(1(4(x1)))) -> 5(3(1(4(4(4(3(4(5(4(x1))))))))))
, 0(5(0(5(x1)))) -> 4(4(1(3(0(4(3(4(2(4(x1))))))))))
, 0(0(5(3(x1)))) -> 5(4(4(3(3(3(4(3(3(3(x1))))))))))
, 1(5(2(x1))) -> 1(1(2(3(3(3(4(4(4(4(x1))))))))))
, 1(0(5(x1))) -> 1(1(1(4(4(4(5(5(0(4(x1))))))))))
, 0(5(x1)) -> 5(1(3(2(4(0(4(1(4(5(x1))))))))))
, 0(5(x1)) -> 3(3(4(2(4(4(3(5(0(2(x1))))))))))
, 0(5(x1)) -> 2(4(5(0(4(2(5(2(3(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..