Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(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:
{ 1_0(1) -> 1
, 1_1(2) -> 1
, 1_1(2) -> 20
, 1_1(4) -> 3
, 1_1(5) -> 4
, 1_1(7) -> 6
, 1_1(8) -> 4
, 1_1(10) -> 9
, 1_1(11) -> 4
, 1_1(13) -> 12
, 1_1(14) -> 4
, 1_1(16) -> 15
, 1_1(17) -> 4
, 1_1(19) -> 18
, 1_1(22) -> 21
, 1_2(17) -> 44
, 1_2(25) -> 5
, 1_2(25) -> 8
, 1_2(25) -> 11
, 1_2(25) -> 14
, 1_2(25) -> 17
, 1_2(25) -> 20
, 1_2(27) -> 26
, 1_2(28) -> 27
, 1_2(30) -> 29
, 1_2(31) -> 45
, 1_2(33) -> 32
, 1_2(34) -> 45
, 1_2(36) -> 35
, 1_2(37) -> 45
, 1_2(39) -> 38
, 1_2(42) -> 41
, 1_2(43) -> 5
, 1_2(43) -> 8
, 1_2(43) -> 11
, 1_2(43) -> 14
, 1_2(43) -> 17
, 1_2(43) -> 20
, 1_2(45) -> 44
, 1_2(46) -> 5
, 1_2(46) -> 8
, 1_2(46) -> 11
, 1_2(46) -> 14
, 1_2(46) -> 17
, 1_2(48) -> 47
, 1_2(49) -> 48
, 1_2(51) -> 50
, 1_2(52) -> 48
, 1_2(54) -> 53
, 1_2(55) -> 27
, 1_2(57) -> 56
, 1_2(60) -> 5
, 1_2(60) -> 8
, 1_2(60) -> 11
, 1_2(60) -> 14
, 1_2(62) -> 61
, 1_2(63) -> 62
, 1_2(65) -> 64
, 1_2(66) -> 62
, 1_2(68) -> 67
, 1_2(277) -> 276
, 1_2(278) -> 17
, 1_2(280) -> 279
, 1_2(281) -> 5
, 1_2(281) -> 8
, 1_2(281) -> 11
, 1_2(283) -> 282
, 1_2(284) -> 283
, 1_2(286) -> 285
, 1_2(287) -> 283
, 1_2(289) -> 288
, 1_2(290) -> 283
, 1_2(292) -> 291
, 1_2(293) -> 48
, 1_2(295) -> 294
, 1_2(296) -> 48
, 1_2(298) -> 297
, 1_2(301) -> 300
, 1_2(323) -> 5
, 1_2(323) -> 8
, 1_2(325) -> 324
, 1_2(326) -> 325
, 1_2(328) -> 327
, 1_2(329) -> 325
, 1_2(331) -> 330
, 1_2(332) -> 325
, 1_2(334) -> 333
, 1_2(335) -> 62
, 1_2(337) -> 336
, 1_2(340) -> 339
, 1_3(302) -> 28
, 1_3(302) -> 31
, 1_3(302) -> 34
, 1_3(302) -> 37
, 1_3(302) -> 40
, 1_3(304) -> 303
, 1_3(305) -> 304
, 1_3(307) -> 306
, 1_3(308) -> 343
, 1_3(310) -> 309
, 1_3(311) -> 343
, 1_3(313) -> 312
, 1_3(314) -> 343
, 1_3(316) -> 315
, 1_3(317) -> 343
, 1_3(319) -> 318
, 1_3(322) -> 321
, 1_3(341) -> 28
, 1_3(341) -> 31
, 1_3(341) -> 34
, 1_3(341) -> 37
, 1_3(341) -> 40
, 1_3(343) -> 342
, 1_3(344) -> 343
, 1_3(346) -> 345
, 1_3(347) -> 343
, 1_3(349) -> 348
, 1_3(350) -> 343
, 1_3(352) -> 351
, 1_3(353) -> 343
, 1_3(355) -> 354
, 1_3(358) -> 357
, 1_3(359) -> 28
, 1_3(359) -> 31
, 1_3(359) -> 34
, 1_3(359) -> 37
, 1_3(361) -> 360
, 1_3(362) -> 361
, 1_3(364) -> 363
, 1_3(365) -> 361
, 1_3(367) -> 366
, 1_3(368) -> 343
, 1_3(370) -> 369
, 1_3(371) -> 343
, 1_3(373) -> 372
, 1_3(376) -> 375
, 2_0(1) -> 1
, 2_1(1) -> 22
, 2_1(2) -> 19
, 2_1(3) -> 2
, 2_1(4) -> 19
, 2_1(5) -> 7
, 2_1(8) -> 7
, 2_1(11) -> 10
, 2_1(14) -> 13
, 2_1(17) -> 16
, 2_1(20) -> 19
, 2_2(2) -> 42
, 2_2(5) -> 42
, 2_2(8) -> 42
, 2_2(11) -> 39
, 2_2(14) -> 36
, 2_2(17) -> 30
, 2_2(25) -> 42
, 2_2(26) -> 25
, 2_2(28) -> 33
, 2_2(31) -> 30
, 2_2(34) -> 33
, 2_2(37) -> 36
, 2_2(40) -> 39
, 2_2(43) -> 57
, 2_2(44) -> 43
, 2_2(46) -> 68
, 2_2(47) -> 46
, 2_2(49) -> 57
, 2_2(52) -> 51
, 2_2(55) -> 54
, 2_2(60) -> 301
, 2_2(61) -> 60
, 2_2(63) -> 280
, 2_2(66) -> 65
, 2_2(278) -> 277
, 2_2(281) -> 340
, 2_2(282) -> 281
, 2_2(287) -> 286
, 2_2(290) -> 289
, 2_2(293) -> 292
, 2_2(296) -> 295
, 2_2(299) -> 298
, 2_2(323) -> 337
, 2_2(324) -> 323
, 2_2(326) -> 65
, 2_2(329) -> 328
, 2_2(332) -> 331
, 2_2(335) -> 334
, 2_2(338) -> 337
, 2_3(25) -> 358
, 2_3(43) -> 358
, 2_3(46) -> 322
, 2_3(60) -> 322
, 2_3(278) -> 313
, 2_3(281) -> 319
, 2_3(302) -> 376
, 2_3(303) -> 302
, 2_3(305) -> 313
, 2_3(308) -> 307
, 2_3(311) -> 310
, 2_3(314) -> 313
, 2_3(317) -> 316
, 2_3(320) -> 319
, 2_3(323) -> 316
, 2_3(341) -> 373
, 2_3(342) -> 341
, 2_3(344) -> 310
, 2_3(347) -> 346
, 2_3(350) -> 349
, 2_3(353) -> 352
, 2_3(356) -> 355
, 2_3(359) -> 319
, 2_3(360) -> 359
, 2_3(362) -> 310
, 2_3(365) -> 364
, 2_3(368) -> 367
, 2_3(371) -> 370
, 2_3(374) -> 373
, 0_0(1) -> 1
, 0_1(6) -> 5
, 0_1(9) -> 8
, 0_1(12) -> 11
, 0_1(15) -> 14
, 0_1(18) -> 17
, 0_1(21) -> 20
, 0_2(29) -> 28
, 0_2(32) -> 31
, 0_2(35) -> 34
, 0_2(38) -> 37
, 0_2(41) -> 40
, 0_2(50) -> 49
, 0_2(53) -> 52
, 0_2(56) -> 55
, 0_2(64) -> 63
, 0_2(67) -> 66
, 0_2(276) -> 46
, 0_2(279) -> 278
, 0_2(285) -> 284
, 0_2(288) -> 287
, 0_2(291) -> 290
, 0_2(294) -> 293
, 0_2(297) -> 296
, 0_2(300) -> 299
, 0_2(327) -> 326
, 0_2(330) -> 329
, 0_2(333) -> 332
, 0_2(336) -> 335
, 0_2(339) -> 338
, 0_3(306) -> 305
, 0_3(309) -> 308
, 0_3(312) -> 311
, 0_3(315) -> 314
, 0_3(318) -> 317
, 0_3(321) -> 320
, 0_3(345) -> 344
, 0_3(348) -> 347
, 0_3(351) -> 350
, 0_3(354) -> 353
, 0_3(357) -> 356
, 0_3(363) -> 362
, 0_3(366) -> 365
, 0_3(369) -> 368
, 0_3(372) -> 371
, 0_3(375) -> 374}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(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:
{ 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(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:
{ 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..