Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 4(5(5(4(2(3(2(x1))))))) -> 4(1(1(5(3(5(1(2(4(2(x1))))))))))
, 4(2(5(5(4(2(4(x1))))))) -> 5(5(3(2(0(2(1(0(3(0(x1))))))))))
, 4(2(5(3(4(5(5(x1))))))) -> 5(1(5(2(5(0(4(1(1(0(x1))))))))))
, 3(4(2(3(3(5(5(x1))))))) -> 5(3(2(4(0(2(4(4(0(5(x1))))))))))
, 2(2(3(5(1(2(5(x1))))))) -> 2(2(1(2(4(0(3(3(2(5(x1))))))))))
, 1(4(0(5(5(0(5(x1))))))) -> 1(4(3(3(0(4(1(5(3(3(x1))))))))))
, 5(5(5(5(2(5(x1)))))) -> 2(2(3(1(1(4(3(2(4(5(x1))))))))))
, 5(5(4(5(5(4(x1)))))) -> 2(2(2(5(5(4(3(4(0(4(x1))))))))))
, 5(5(2(5(5(0(x1)))))) -> 3(4(5(2(5(3(4(4(1(0(x1))))))))))
, 5(5(1(1(1(5(x1)))))) -> 5(0(1(0(1(1(0(1(4(1(x1))))))))))
, 5(4(2(3(0(5(x1)))))) -> 5(5(4(5(4(3(4(1(3(1(x1))))))))))
, 5(2(5(5(1(0(x1)))))) -> 5(5(4(4(0(4(2(0(1(4(x1))))))))))
, 4(0(2(3(4(2(x1)))))) -> 4(0(0(3(1(4(3(0(2(2(x1))))))))))
, 3(5(0(4(5(5(x1)))))) -> 3(4(0(3(4(5(2(0(3(3(x1))))))))))
, 2(5(3(0(2(1(x1)))))) -> 2(1(4(5(2(1(2(5(2(1(x1))))))))))
, 2(5(0(5(5(5(x1)))))) -> 2(0(1(2(4(0(5(3(5(5(x1))))))))))
, 2(1(0(0(3(2(x1)))))) -> 2(1(4(3(0(0(3(0(3(2(x1))))))))))
, 1(1(5(0(2(3(x1)))))) -> 0(0(4(5(1(1(1(2(2(3(x1))))))))))
, 1(0(5(2(3(4(x1)))))) -> 1(0(0(1(3(0(4(1(0(3(x1))))))))))
, 0(2(5(4(3(2(x1)))))) -> 0(2(1(5(2(0(1(2(1(2(x1))))))))))
, 3(1(5(2(5(x1))))) -> 3(0(2(4(1(2(0(0(5(2(x1))))))))))
, 5(5(1(0(x1)))) -> 3(2(2(0(5(1(3(4(0(4(x1))))))))))
, 2(3(0(4(x1)))) -> 2(0(0(1(1(3(0(2(4(4(x1))))))))))
, 4(5(4(x1))) -> 4(1(1(1(2(1(4(5(2(4(x1))))))))))
, 2(5(5(x1))) -> 2(0(3(0(4(0(3(3(3(4(x1))))))))))
, 2(3(5(x1))) -> 2(4(0(0(1(5(1(2(2(1(x1))))))))))
, 1(5(0(x1))) -> 1(4(4(4(4(0(4(0(1(1(x1))))))))))
, 2(5(x1)) -> 2(4(3(0(2(2(2(1(4(3(x1))))))))))
, 2(5(x1)) -> 2(4(0(0(4(1(0(0(1(3(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 5_0(1) -> 1
, 5_1(1) -> 34
, 5_1(5) -> 4
, 5_1(7) -> 6
, 5_1(10) -> 108
, 5_1(11) -> 1
, 5_1(11) -> 9
, 5_1(11) -> 34
, 5_1(11) -> 51
, 5_1(11) -> 64
, 5_1(11) -> 108
, 5_1(11) -> 116
, 5_1(11) -> 226
, 5_1(11) -> 304
, 5_1(12) -> 11
, 5_1(21) -> 20
, 5_1(23) -> 22
, 5_1(34) -> 116
, 5_1(50) -> 49
, 5_1(51) -> 114
, 5_1(59) -> 58
, 5_1(60) -> 59
, 5_1(67) -> 66
, 5_1(69) -> 68
, 5_1(81) -> 80
, 5_1(101) -> 100
, 5_1(105) -> 104
, 5_1(109) -> 108
, 5_1(115) -> 114
, 5_1(121) -> 108
, 5_1(124) -> 123
, 5_1(138) -> 137
, 5_1(161) -> 160
, 5_1(175) -> 190
, 5_1(258) -> 257
, 5_2(157) -> 156
, 5_2(166) -> 165
, 5_2(210) -> 209
, 5_2(219) -> 218
, 5_2(265) -> 264
, 5_2(443) -> 442
, 2_0(1) -> 1
, 2_1(1) -> 10
, 2_1(9) -> 8
, 2_1(10) -> 97
, 2_1(11) -> 10
, 2_1(14) -> 13
, 2_1(16) -> 15
, 2_1(22) -> 21
, 2_1(28) -> 27
, 2_1(31) -> 30
, 2_1(34) -> 42
, 2_1(35) -> 1
, 2_1(35) -> 10
, 2_1(35) -> 34
, 2_1(35) -> 42
, 2_1(35) -> 97
, 2_1(35) -> 109
, 2_1(35) -> 116
, 2_1(35) -> 127
, 2_1(35) -> 128
, 2_1(36) -> 35
, 2_1(38) -> 37
, 2_1(51) -> 128
, 2_1(57) -> 56
, 2_1(58) -> 36
, 2_1(64) -> 175
, 2_1(68) -> 67
, 2_1(79) -> 109
, 2_1(89) -> 88
, 2_1(102) -> 101
, 2_1(106) -> 105
, 2_1(108) -> 107
, 2_1(109) -> 259
, 2_1(112) -> 111
, 2_1(121) -> 97
, 2_1(128) -> 127
, 2_1(136) -> 121
, 2_1(139) -> 138
, 2_1(142) -> 141
, 2_1(144) -> 143
, 2_1(147) -> 146
, 2_1(158) -> 65
, 2_1(159) -> 158
, 2_1(176) -> 175
, 2_1(178) -> 177
, 2_1(286) -> 285
, 2_1(287) -> 286
, 2_1(288) -> 287
, 2_2(12) -> 210
, 2_2(23) -> 157
, 2_2(151) -> 150
, 2_2(154) -> 153
, 2_2(163) -> 162
, 2_2(164) -> 163
, 2_2(170) -> 210
, 2_2(207) -> 206
, 2_2(211) -> 210
, 2_2(216) -> 215
, 2_2(220) -> 219
, 2_2(227) -> 42
, 2_2(236) -> 8
, 2_2(236) -> 10
, 2_2(236) -> 42
, 2_2(236) -> 107
, 2_2(236) -> 128
, 2_2(236) -> 175
, 2_2(245) -> 36
, 2_2(260) -> 128
, 2_2(267) -> 266
, 2_2(268) -> 267
, 2_2(293) -> 292
, 2_2(294) -> 293
, 2_2(295) -> 294
, 2_2(306) -> 107
, 2_2(310) -> 309
, 2_2(311) -> 310
, 2_2(312) -> 311
, 2_2(318) -> 317
, 2_2(319) -> 318
, 2_2(320) -> 319
, 2_2(323) -> 21
, 2_2(327) -> 326
, 2_2(328) -> 327
, 2_2(329) -> 328
, 2_2(335) -> 334
, 2_2(336) -> 335
, 2_2(337) -> 336
, 2_2(340) -> 67
, 2_2(344) -> 343
, 2_2(345) -> 344
, 2_2(346) -> 345
, 2_2(434) -> 433
, 2_2(440) -> 439
, 2_2(444) -> 443
, 3_0(1) -> 1
, 3_1(1) -> 51
, 3_1(2) -> 51
, 3_1(6) -> 5
, 3_1(10) -> 41
, 3_1(11) -> 51
, 3_1(12) -> 51
, 3_1(13) -> 12
, 3_1(19) -> 18
, 3_1(27) -> 11
, 3_1(32) -> 61
, 3_1(41) -> 40
, 3_1(42) -> 41
, 3_1(43) -> 18
, 3_1(45) -> 44
, 3_1(46) -> 45
, 3_1(51) -> 50
, 3_1(52) -> 36
, 3_1(56) -> 55
, 3_1(62) -> 61
, 3_1(64) -> 226
, 3_1(65) -> 1
, 3_1(65) -> 34
, 3_1(65) -> 51
, 3_1(65) -> 85
, 3_1(65) -> 116
, 3_1(65) -> 304
, 3_1(66) -> 51
, 3_1(70) -> 69
, 3_1(79) -> 85
, 3_1(83) -> 82
, 3_1(93) -> 92
, 3_1(96) -> 95
, 3_1(99) -> 98
, 3_1(116) -> 115
, 3_1(117) -> 104
, 3_1(120) -> 119
, 3_1(121) -> 51
, 3_1(129) -> 51
, 3_1(132) -> 131
, 3_1(174) -> 173
, 3_1(212) -> 51
, 3_1(221) -> 110
, 3_1(225) -> 224
, 3_1(226) -> 225
, 3_1(284) -> 254
, 3_2(1) -> 304
, 3_2(10) -> 314
, 3_2(11) -> 322
, 3_2(12) -> 322
, 3_2(23) -> 331
, 3_2(59) -> 339
, 3_2(69) -> 348
, 3_2(109) -> 314
, 3_2(121) -> 314
, 3_2(149) -> 51
, 3_2(149) -> 322
, 3_2(162) -> 116
, 3_2(168) -> 167
, 3_2(229) -> 228
, 3_2(233) -> 232
, 3_2(234) -> 233
, 3_2(235) -> 234
, 3_2(238) -> 237
, 3_2(242) -> 241
, 3_2(243) -> 242
, 3_2(244) -> 243
, 3_2(247) -> 246
, 3_2(251) -> 250
, 3_2(252) -> 251
, 3_2(253) -> 252
, 3_2(291) -> 290
, 3_2(308) -> 307
, 3_2(316) -> 315
, 3_2(325) -> 324
, 3_2(333) -> 332
, 3_2(342) -> 341
, 3_2(432) -> 431
, 1_0(1) -> 1
, 1_1(1) -> 79
, 1_1(3) -> 2
, 1_1(4) -> 3
, 1_1(8) -> 7
, 1_1(10) -> 142
, 1_1(11) -> 79
, 1_1(17) -> 16
, 1_1(19) -> 26
, 1_1(20) -> 11
, 1_1(26) -> 25
, 1_1(37) -> 36
, 1_1(43) -> 1
, 1_1(43) -> 26
, 1_1(43) -> 79
, 1_1(43) -> 90
, 1_1(49) -> 48
, 1_1(51) -> 352
, 1_1(53) -> 52
, 1_1(54) -> 53
, 1_1(61) -> 161
, 1_1(64) -> 90
, 1_1(65) -> 142
, 1_1(72) -> 79
, 1_1(73) -> 72
, 1_1(75) -> 74
, 1_1(76) -> 75
, 1_1(78) -> 77
, 1_1(79) -> 274
, 1_1(85) -> 84
, 1_1(94) -> 93
, 1_1(103) -> 35
, 1_1(107) -> 106
, 1_1(111) -> 110
, 1_1(121) -> 79
, 1_1(125) -> 124
, 1_1(126) -> 125
, 1_1(127) -> 126
, 1_1(131) -> 130
, 1_1(135) -> 134
, 1_1(137) -> 136
, 1_1(141) -> 140
, 1_1(146) -> 145
, 1_1(172) -> 171
, 1_1(173) -> 172
, 1_1(177) -> 4
, 1_1(187) -> 178
, 1_1(257) -> 256
, 1_1(259) -> 258
, 1_1(289) -> 288
, 1_1(350) -> 349
, 1_2(11) -> 268
, 1_2(12) -> 268
, 1_2(67) -> 268
, 1_2(72) -> 283
, 1_2(153) -> 152
, 1_2(167) -> 166
, 1_2(204) -> 203
, 1_2(205) -> 204
, 1_2(206) -> 205
, 1_2(208) -> 207
, 1_2(213) -> 212
, 1_2(214) -> 213
, 1_2(215) -> 214
, 1_2(217) -> 216
, 1_2(264) -> 263
, 1_2(266) -> 265
, 1_2(275) -> 79
, 1_2(275) -> 90
, 1_2(275) -> 352
, 1_2(275) -> 358
, 1_2(283) -> 282
, 1_2(296) -> 295
, 1_2(304) -> 358
, 1_2(313) -> 312
, 1_2(314) -> 370
, 1_2(321) -> 320
, 1_2(322) -> 376
, 1_2(330) -> 329
, 1_2(331) -> 382
, 1_2(338) -> 337
, 1_2(339) -> 388
, 1_2(347) -> 346
, 1_2(348) -> 394
, 1_2(356) -> 355
, 1_2(368) -> 367
, 1_2(374) -> 373
, 1_2(380) -> 379
, 1_2(386) -> 385
, 1_2(392) -> 391
, 1_2(430) -> 429
, 1_2(431) -> 430
, 1_2(437) -> 436
, 1_2(438) -> 437
, 1_2(439) -> 438
, 1_2(441) -> 440
, 0_0(1) -> 1
, 0_1(1) -> 19
, 0_1(2) -> 19
, 0_1(11) -> 19
, 0_1(12) -> 19
, 0_1(15) -> 14
, 0_1(17) -> 117
, 0_1(18) -> 17
, 0_1(24) -> 23
, 0_1(30) -> 29
, 0_1(34) -> 33
, 0_1(40) -> 39
, 0_1(41) -> 120
, 0_1(47) -> 46
, 0_1(50) -> 102
, 0_1(51) -> 135
, 0_1(64) -> 63
, 0_1(72) -> 11
, 0_1(74) -> 73
, 0_1(77) -> 76
, 0_1(79) -> 89
, 0_1(87) -> 86
, 0_1(90) -> 89
, 0_1(91) -> 2
, 0_1(92) -> 91
, 0_1(97) -> 96
, 0_1(98) -> 66
, 0_1(108) -> 148
, 0_1(110) -> 35
, 0_1(114) -> 113
, 0_1(118) -> 117
, 0_1(119) -> 118
, 0_1(121) -> 1
, 0_1(121) -> 19
, 0_1(121) -> 79
, 0_1(121) -> 274
, 0_1(122) -> 121
, 0_1(129) -> 43
, 0_1(130) -> 129
, 0_1(133) -> 132
, 0_1(140) -> 139
, 0_1(143) -> 65
, 0_1(148) -> 147
, 0_1(160) -> 159
, 0_1(171) -> 110
, 0_1(175) -> 174
, 0_1(212) -> 19
, 0_1(222) -> 221
, 0_1(224) -> 223
, 0_1(254) -> 19
, 0_1(255) -> 254
, 0_1(256) -> 255
, 0_1(272) -> 271
, 0_1(274) -> 273
, 0_1(285) -> 284
, 0_1(351) -> 350
, 0_1(352) -> 351
, 0_2(150) -> 149
, 0_2(155) -> 154
, 0_2(156) -> 155
, 0_2(165) -> 164
, 0_2(170) -> 169
, 0_2(228) -> 227
, 0_2(230) -> 229
, 0_2(232) -> 231
, 0_2(237) -> 236
, 0_2(239) -> 238
, 0_2(241) -> 240
, 0_2(246) -> 245
, 0_2(248) -> 247
, 0_2(250) -> 249
, 0_2(262) -> 261
, 0_2(263) -> 262
, 0_2(280) -> 279
, 0_2(282) -> 281
, 0_2(292) -> 291
, 0_2(309) -> 308
, 0_2(317) -> 316
, 0_2(326) -> 325
, 0_2(334) -> 333
, 0_2(343) -> 342
, 0_2(353) -> 290
, 0_2(354) -> 353
, 0_2(357) -> 356
, 0_2(358) -> 357
, 0_2(365) -> 307
, 0_2(366) -> 365
, 0_2(369) -> 368
, 0_2(370) -> 369
, 0_2(371) -> 315
, 0_2(372) -> 371
, 0_2(375) -> 374
, 0_2(376) -> 375
, 0_2(377) -> 324
, 0_2(378) -> 377
, 0_2(381) -> 380
, 0_2(382) -> 381
, 0_2(383) -> 332
, 0_2(384) -> 383
, 0_2(387) -> 386
, 0_2(388) -> 387
, 0_2(389) -> 341
, 0_2(390) -> 389
, 0_2(393) -> 392
, 0_2(394) -> 393
, 0_2(428) -> 260
, 0_2(429) -> 428
, 0_2(433) -> 432
, 4_0(1) -> 1
, 4_1(1) -> 64
, 4_1(2) -> 1
, 4_1(2) -> 32
, 4_1(2) -> 57
, 4_1(2) -> 64
, 4_1(9) -> 57
, 4_1(10) -> 9
, 4_1(11) -> 64
, 4_1(12) -> 64
, 4_1(19) -> 32
, 4_1(25) -> 24
, 4_1(26) -> 71
, 4_1(29) -> 28
, 4_1(32) -> 31
, 4_1(33) -> 32
, 4_1(34) -> 57
, 4_1(39) -> 38
, 4_1(44) -> 43
, 4_1(48) -> 47
, 4_1(51) -> 289
, 4_1(55) -> 54
, 4_1(61) -> 60
, 4_1(63) -> 62
, 4_1(64) -> 176
, 4_1(65) -> 9
, 4_1(66) -> 65
, 4_1(71) -> 70
, 4_1(78) -> 70
, 4_1(79) -> 78
, 4_1(80) -> 12
, 4_1(82) -> 81
, 4_1(84) -> 83
, 4_1(86) -> 80
, 4_1(88) -> 87
, 4_1(95) -> 94
, 4_1(100) -> 99
, 4_1(104) -> 103
, 4_1(108) -> 187
, 4_1(113) -> 112
, 4_1(121) -> 1
, 4_1(123) -> 122
, 4_1(129) -> 1
, 4_1(134) -> 133
, 4_1(145) -> 144
, 4_1(190) -> 187
, 4_1(212) -> 1
, 4_1(223) -> 222
, 4_1(254) -> 35
, 4_1(269) -> 44
, 4_1(270) -> 269
, 4_1(271) -> 270
, 4_1(273) -> 272
, 4_1(349) -> 256
, 4_2(2) -> 211
, 4_2(11) -> 235
, 4_2(12) -> 244
, 4_2(60) -> 253
, 4_2(80) -> 444
, 4_2(82) -> 220
, 4_2(121) -> 211
, 4_2(123) -> 435
, 4_2(129) -> 170
, 4_2(152) -> 151
, 4_2(169) -> 168
, 4_2(203) -> 57
, 4_2(203) -> 64
, 4_2(203) -> 235
, 4_2(209) -> 208
, 4_2(212) -> 12
, 4_2(212) -> 444
, 4_2(218) -> 217
, 4_2(231) -> 230
, 4_2(240) -> 239
, 4_2(249) -> 248
, 4_2(261) -> 260
, 4_2(276) -> 275
, 4_2(277) -> 276
, 4_2(278) -> 277
, 4_2(279) -> 278
, 4_2(281) -> 280
, 4_2(290) -> 227
, 4_2(304) -> 296
, 4_2(307) -> 306
, 4_2(314) -> 313
, 4_2(315) -> 236
, 4_2(322) -> 321
, 4_2(324) -> 323
, 4_2(331) -> 330
, 4_2(332) -> 245
, 4_2(339) -> 338
, 4_2(341) -> 340
, 4_2(348) -> 347
, 4_2(355) -> 354
, 4_2(367) -> 366
, 4_2(373) -> 372
, 4_2(379) -> 378
, 4_2(385) -> 384
, 4_2(391) -> 390
, 4_2(435) -> 434
, 4_2(436) -> 64
, 4_2(436) -> 235
, 4_2(442) -> 441}
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:
{ 4(5(5(4(2(3(2(x1))))))) -> 4(1(1(5(3(5(1(2(4(2(x1))))))))))
, 4(2(5(5(4(2(4(x1))))))) -> 5(5(3(2(0(2(1(0(3(0(x1))))))))))
, 4(2(5(3(4(5(5(x1))))))) -> 5(1(5(2(5(0(4(1(1(0(x1))))))))))
, 3(4(2(3(3(5(5(x1))))))) -> 5(3(2(4(0(2(4(4(0(5(x1))))))))))
, 2(2(3(5(1(2(5(x1))))))) -> 2(2(1(2(4(0(3(3(2(5(x1))))))))))
, 1(4(0(5(5(0(5(x1))))))) -> 1(4(3(3(0(4(1(5(3(3(x1))))))))))
, 5(5(5(5(2(5(x1)))))) -> 2(2(3(1(1(4(3(2(4(5(x1))))))))))
, 5(5(4(5(5(4(x1)))))) -> 2(2(2(5(5(4(3(4(0(4(x1))))))))))
, 5(5(2(5(5(0(x1)))))) -> 3(4(5(2(5(3(4(4(1(0(x1))))))))))
, 5(5(1(1(1(5(x1)))))) -> 5(0(1(0(1(1(0(1(4(1(x1))))))))))
, 5(4(2(3(0(5(x1)))))) -> 5(5(4(5(4(3(4(1(3(1(x1))))))))))
, 5(2(5(5(1(0(x1)))))) -> 5(5(4(4(0(4(2(0(1(4(x1))))))))))
, 4(0(2(3(4(2(x1)))))) -> 4(0(0(3(1(4(3(0(2(2(x1))))))))))
, 3(5(0(4(5(5(x1)))))) -> 3(4(0(3(4(5(2(0(3(3(x1))))))))))
, 2(5(3(0(2(1(x1)))))) -> 2(1(4(5(2(1(2(5(2(1(x1))))))))))
, 2(5(0(5(5(5(x1)))))) -> 2(0(1(2(4(0(5(3(5(5(x1))))))))))
, 2(1(0(0(3(2(x1)))))) -> 2(1(4(3(0(0(3(0(3(2(x1))))))))))
, 1(1(5(0(2(3(x1)))))) -> 0(0(4(5(1(1(1(2(2(3(x1))))))))))
, 1(0(5(2(3(4(x1)))))) -> 1(0(0(1(3(0(4(1(0(3(x1))))))))))
, 0(2(5(4(3(2(x1)))))) -> 0(2(1(5(2(0(1(2(1(2(x1))))))))))
, 3(1(5(2(5(x1))))) -> 3(0(2(4(1(2(0(0(5(2(x1))))))))))
, 5(5(1(0(x1)))) -> 3(2(2(0(5(1(3(4(0(4(x1))))))))))
, 2(3(0(4(x1)))) -> 2(0(0(1(1(3(0(2(4(4(x1))))))))))
, 4(5(4(x1))) -> 4(1(1(1(2(1(4(5(2(4(x1))))))))))
, 2(5(5(x1))) -> 2(0(3(0(4(0(3(3(3(4(x1))))))))))
, 2(3(5(x1))) -> 2(4(0(0(1(5(1(2(2(1(x1))))))))))
, 1(5(0(x1))) -> 1(4(4(4(4(0(4(0(1(1(x1))))))))))
, 2(5(x1)) -> 2(4(3(0(2(2(2(1(4(3(x1))))))))))
, 2(5(x1)) -> 2(4(0(0(4(1(0(0(1(3(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:
{ 4(5(5(4(2(3(2(x1))))))) -> 4(1(1(5(3(5(1(2(4(2(x1))))))))))
, 4(2(5(5(4(2(4(x1))))))) -> 5(5(3(2(0(2(1(0(3(0(x1))))))))))
, 4(2(5(3(4(5(5(x1))))))) -> 5(1(5(2(5(0(4(1(1(0(x1))))))))))
, 3(4(2(3(3(5(5(x1))))))) -> 5(3(2(4(0(2(4(4(0(5(x1))))))))))
, 2(2(3(5(1(2(5(x1))))))) -> 2(2(1(2(4(0(3(3(2(5(x1))))))))))
, 1(4(0(5(5(0(5(x1))))))) -> 1(4(3(3(0(4(1(5(3(3(x1))))))))))
, 5(5(5(5(2(5(x1)))))) -> 2(2(3(1(1(4(3(2(4(5(x1))))))))))
, 5(5(4(5(5(4(x1)))))) -> 2(2(2(5(5(4(3(4(0(4(x1))))))))))
, 5(5(2(5(5(0(x1)))))) -> 3(4(5(2(5(3(4(4(1(0(x1))))))))))
, 5(5(1(1(1(5(x1)))))) -> 5(0(1(0(1(1(0(1(4(1(x1))))))))))
, 5(4(2(3(0(5(x1)))))) -> 5(5(4(5(4(3(4(1(3(1(x1))))))))))
, 5(2(5(5(1(0(x1)))))) -> 5(5(4(4(0(4(2(0(1(4(x1))))))))))
, 4(0(2(3(4(2(x1)))))) -> 4(0(0(3(1(4(3(0(2(2(x1))))))))))
, 3(5(0(4(5(5(x1)))))) -> 3(4(0(3(4(5(2(0(3(3(x1))))))))))
, 2(5(3(0(2(1(x1)))))) -> 2(1(4(5(2(1(2(5(2(1(x1))))))))))
, 2(5(0(5(5(5(x1)))))) -> 2(0(1(2(4(0(5(3(5(5(x1))))))))))
, 2(1(0(0(3(2(x1)))))) -> 2(1(4(3(0(0(3(0(3(2(x1))))))))))
, 1(1(5(0(2(3(x1)))))) -> 0(0(4(5(1(1(1(2(2(3(x1))))))))))
, 1(0(5(2(3(4(x1)))))) -> 1(0(0(1(3(0(4(1(0(3(x1))))))))))
, 0(2(5(4(3(2(x1)))))) -> 0(2(1(5(2(0(1(2(1(2(x1))))))))))
, 3(1(5(2(5(x1))))) -> 3(0(2(4(1(2(0(0(5(2(x1))))))))))
, 5(5(1(0(x1)))) -> 3(2(2(0(5(1(3(4(0(4(x1))))))))))
, 2(3(0(4(x1)))) -> 2(0(0(1(1(3(0(2(4(4(x1))))))))))
, 4(5(4(x1))) -> 4(1(1(1(2(1(4(5(2(4(x1))))))))))
, 2(5(5(x1))) -> 2(0(3(0(4(0(3(3(3(4(x1))))))))))
, 2(3(5(x1))) -> 2(4(0(0(1(5(1(2(2(1(x1))))))))))
, 1(5(0(x1))) -> 1(4(4(4(4(0(4(0(1(1(x1))))))))))
, 2(5(x1)) -> 2(4(3(0(2(2(2(1(4(3(x1))))))))))
, 2(5(x1)) -> 2(4(0(0(4(1(0(0(1(3(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:
{ 4(5(5(4(2(3(2(x1))))))) -> 4(1(1(5(3(5(1(2(4(2(x1))))))))))
, 4(2(5(5(4(2(4(x1))))))) -> 5(5(3(2(0(2(1(0(3(0(x1))))))))))
, 4(2(5(3(4(5(5(x1))))))) -> 5(1(5(2(5(0(4(1(1(0(x1))))))))))
, 3(4(2(3(3(5(5(x1))))))) -> 5(3(2(4(0(2(4(4(0(5(x1))))))))))
, 2(2(3(5(1(2(5(x1))))))) -> 2(2(1(2(4(0(3(3(2(5(x1))))))))))
, 1(4(0(5(5(0(5(x1))))))) -> 1(4(3(3(0(4(1(5(3(3(x1))))))))))
, 5(5(5(5(2(5(x1)))))) -> 2(2(3(1(1(4(3(2(4(5(x1))))))))))
, 5(5(4(5(5(4(x1)))))) -> 2(2(2(5(5(4(3(4(0(4(x1))))))))))
, 5(5(2(5(5(0(x1)))))) -> 3(4(5(2(5(3(4(4(1(0(x1))))))))))
, 5(5(1(1(1(5(x1)))))) -> 5(0(1(0(1(1(0(1(4(1(x1))))))))))
, 5(4(2(3(0(5(x1)))))) -> 5(5(4(5(4(3(4(1(3(1(x1))))))))))
, 5(2(5(5(1(0(x1)))))) -> 5(5(4(4(0(4(2(0(1(4(x1))))))))))
, 4(0(2(3(4(2(x1)))))) -> 4(0(0(3(1(4(3(0(2(2(x1))))))))))
, 3(5(0(4(5(5(x1)))))) -> 3(4(0(3(4(5(2(0(3(3(x1))))))))))
, 2(5(3(0(2(1(x1)))))) -> 2(1(4(5(2(1(2(5(2(1(x1))))))))))
, 2(5(0(5(5(5(x1)))))) -> 2(0(1(2(4(0(5(3(5(5(x1))))))))))
, 2(1(0(0(3(2(x1)))))) -> 2(1(4(3(0(0(3(0(3(2(x1))))))))))
, 1(1(5(0(2(3(x1)))))) -> 0(0(4(5(1(1(1(2(2(3(x1))))))))))
, 1(0(5(2(3(4(x1)))))) -> 1(0(0(1(3(0(4(1(0(3(x1))))))))))
, 0(2(5(4(3(2(x1)))))) -> 0(2(1(5(2(0(1(2(1(2(x1))))))))))
, 3(1(5(2(5(x1))))) -> 3(0(2(4(1(2(0(0(5(2(x1))))))))))
, 5(5(1(0(x1)))) -> 3(2(2(0(5(1(3(4(0(4(x1))))))))))
, 2(3(0(4(x1)))) -> 2(0(0(1(1(3(0(2(4(4(x1))))))))))
, 4(5(4(x1))) -> 4(1(1(1(2(1(4(5(2(4(x1))))))))))
, 2(5(5(x1))) -> 2(0(3(0(4(0(3(3(3(4(x1))))))))))
, 2(3(5(x1))) -> 2(4(0(0(1(5(1(2(2(1(x1))))))))))
, 1(5(0(x1))) -> 1(4(4(4(4(0(4(0(1(1(x1))))))))))
, 2(5(x1)) -> 2(4(3(0(2(2(2(1(4(3(x1))))))))))
, 2(5(x1)) -> 2(4(0(0(4(1(0(0(1(3(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..