Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1))))))))))
, 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1))))))))))
, 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1))))))))))
, 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1))))))))))
, 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1))))))))))
, 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1))))))))))
, 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1))))))))))
, 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1))))))))))
, 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1))))))))))
, 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1))))))))))
, 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1))))))))))
, 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1))))))))))
, 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1))))))))))
, 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1))))))))))
, 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1))))))))))
, 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1))))))))))
, 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1))))))))))
, 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1))))))))))
, 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1))))))))))
, 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1))))))))))
, 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1))))))))))
, 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1))))))))))
, 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1))))))))))
, 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1))))))))))
, 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1))))))))))
, 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1))))))))))
, 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1))))))))))
, 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1))))))))))
, 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1))))))))))
, 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1))))))))))
, 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1))))))))))
, 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1))))))))))
, 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1))))))))))
, 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(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:
{ 0_0(1) -> 1
, 0_1(1) -> 9
, 0_1(8) -> 7
, 0_1(9) -> 32
, 0_1(10) -> 9
, 0_1(16) -> 15
, 0_1(19) -> 77
, 0_1(24) -> 23
, 0_1(33) -> 32
, 0_1(34) -> 33
, 0_1(35) -> 9
, 0_1(36) -> 35
, 0_1(41) -> 40
, 0_1(47) -> 46
, 0_1(49) -> 21
, 0_1(55) -> 54
, 0_1(56) -> 1
, 0_1(56) -> 9
, 0_1(56) -> 32
, 0_1(56) -> 33
, 0_1(56) -> 55
, 0_1(56) -> 217
, 0_1(60) -> 59
, 0_1(71) -> 20
, 0_1(73) -> 72
, 0_1(76) -> 75
, 0_1(81) -> 80
, 0_1(90) -> 89
, 0_1(96) -> 95
, 0_1(107) -> 106
, 0_1(117) -> 116
, 0_1(131) -> 130
, 0_1(132) -> 131
, 0_1(133) -> 12
, 0_1(154) -> 153
, 0_1(156) -> 155
, 0_1(166) -> 165
, 0_1(190) -> 189
, 0_1(206) -> 205
, 0_1(209) -> 208
, 0_1(210) -> 188
, 0_1(211) -> 210
, 0_1(228) -> 227
, 0_1(241) -> 240
, 0_2(185) -> 184
, 0_2(196) -> 195
, 0_2(199) -> 238
, 0_2(213) -> 194
, 0_2(214) -> 213
, 0_2(222) -> 221
, 0_2(223) -> 222
, 0_2(231) -> 32
, 0_2(235) -> 234
, 0_2(248) -> 247
, 0_2(257) -> 256
, 0_2(266) -> 265
, 0_2(275) -> 274
, 0_2(284) -> 283
, 0_2(293) -> 292
, 0_2(302) -> 301
, 0_2(311) -> 310
, 0_2(320) -> 319
, 0_2(329) -> 328
, 0_2(344) -> 9
, 0_2(344) -> 32
, 0_2(344) -> 54
, 0_2(351) -> 130
, 0_2(360) -> 188
, 0_2(395) -> 394
, 0_3(369) -> 194
, 0_3(378) -> 221
, 0_3(433) -> 432
, 0_3(442) -> 441
, 1_0(1) -> 1
, 1_1(1) -> 55
, 1_1(9) -> 159
, 1_1(14) -> 13
, 1_1(17) -> 16
, 1_1(18) -> 152
, 1_1(25) -> 24
, 1_1(26) -> 93
, 1_1(34) -> 90
, 1_1(35) -> 1
, 1_1(35) -> 19
, 1_1(35) -> 31
, 1_1(35) -> 55
, 1_1(35) -> 120
, 1_1(35) -> 146
, 1_1(35) -> 159
, 1_1(35) -> 217
, 1_1(38) -> 37
, 1_1(44) -> 43
, 1_1(45) -> 44
, 1_1(55) -> 120
, 1_1(56) -> 55
, 1_1(58) -> 57
, 1_1(61) -> 60
, 1_1(64) -> 11
, 1_1(70) -> 69
, 1_1(83) -> 82
, 1_1(84) -> 2
, 1_1(88) -> 87
, 1_1(94) -> 93
, 1_1(99) -> 98
, 1_1(100) -> 99
, 1_1(101) -> 100
, 1_1(102) -> 176
, 1_1(104) -> 103
, 1_1(109) -> 12
, 1_1(112) -> 111
, 1_1(116) -> 115
, 1_1(126) -> 55
, 1_1(127) -> 126
, 1_1(132) -> 338
, 1_1(148) -> 55
, 1_1(151) -> 150
, 1_1(155) -> 154
, 1_1(173) -> 172
, 1_1(230) -> 229
, 1_1(336) -> 335
, 1_1(337) -> 336
, 1_2(1) -> 217
, 1_2(10) -> 217
, 1_2(34) -> 217
, 1_2(35) -> 199
, 1_2(36) -> 226
, 1_2(56) -> 226
, 1_2(99) -> 396
, 1_2(132) -> 359
, 1_2(182) -> 181
, 1_2(211) -> 368
, 1_2(216) -> 343
, 1_2(225) -> 350
, 1_2(233) -> 232
, 1_2(237) -> 236
, 1_2(341) -> 340
, 1_2(342) -> 341
, 1_2(344) -> 199
, 1_2(348) -> 347
, 1_2(349) -> 348
, 1_2(355) -> 354
, 1_2(356) -> 355
, 1_2(358) -> 357
, 1_2(364) -> 363
, 1_2(365) -> 364
, 1_2(367) -> 366
, 1_2(389) -> 388
, 1_2(393) -> 392
, 1_2(405) -> 404
, 1_3(214) -> 377
, 1_3(223) -> 386
, 1_3(373) -> 372
, 1_3(374) -> 373
, 1_3(376) -> 375
, 1_3(382) -> 381
, 1_3(383) -> 382
, 1_3(385) -> 384
, 2_0(1) -> 1
, 2_1(1) -> 19
, 2_1(3) -> 2
, 2_1(5) -> 4
, 2_1(8) -> 102
, 2_1(10) -> 146
, 2_1(11) -> 1
, 2_1(11) -> 8
, 2_1(11) -> 9
, 2_1(11) -> 10
, 2_1(11) -> 19
, 2_1(11) -> 26
, 2_1(11) -> 31
, 2_1(11) -> 32
, 2_1(11) -> 33
, 2_1(11) -> 34
, 2_1(11) -> 42
, 2_1(11) -> 83
, 2_1(11) -> 141
, 2_1(11) -> 173
, 2_1(11) -> 252
, 2_1(11) -> 270
, 2_1(11) -> 279
, 2_1(18) -> 17
, 2_1(20) -> 19
, 2_1(29) -> 28
, 2_1(32) -> 31
, 2_1(34) -> 63
, 2_1(35) -> 19
, 2_1(36) -> 19
, 2_1(37) -> 36
, 2_1(54) -> 88
, 2_1(55) -> 132
, 2_1(56) -> 19
, 2_1(63) -> 62
, 2_1(68) -> 67
, 2_1(89) -> 88
, 2_1(90) -> 132
, 2_1(113) -> 190
, 2_1(120) -> 119
, 2_1(121) -> 57
, 2_1(123) -> 122
, 2_1(124) -> 123
, 2_1(126) -> 19
, 2_1(129) -> 128
, 2_1(132) -> 170
, 2_1(135) -> 134
, 2_1(140) -> 139
, 2_1(141) -> 140
, 2_1(144) -> 143
, 2_1(153) -> 35
, 2_1(157) -> 156
, 2_1(159) -> 158
, 2_1(162) -> 161
, 2_1(166) -> 243
, 2_1(171) -> 170
, 2_1(172) -> 171
, 2_1(176) -> 175
, 2_1(186) -> 11
, 2_1(187) -> 186
, 2_1(200) -> 19
, 2_1(207) -> 206
, 2_1(229) -> 228
, 2_1(239) -> 43
, 2_1(242) -> 241
, 2_2(177) -> 141
, 2_2(177) -> 230
, 2_2(181) -> 180
, 2_2(183) -> 182
, 2_2(191) -> 83
, 2_2(192) -> 191
, 2_2(193) -> 192
, 2_2(197) -> 196
, 2_2(199) -> 216
, 2_2(217) -> 216
, 2_2(218) -> 26
, 2_2(218) -> 53
, 2_2(218) -> 83
, 2_2(218) -> 270
, 2_2(219) -> 218
, 2_2(220) -> 219
, 2_2(226) -> 225
, 2_2(236) -> 235
, 2_2(246) -> 245
, 2_2(249) -> 248
, 2_2(251) -> 250
, 2_2(255) -> 254
, 2_2(258) -> 257
, 2_2(260) -> 259
, 2_2(264) -> 263
, 2_2(267) -> 266
, 2_2(269) -> 268
, 2_2(273) -> 272
, 2_2(276) -> 275
, 2_2(278) -> 277
, 2_2(282) -> 281
, 2_2(285) -> 284
, 2_2(287) -> 286
, 2_2(291) -> 290
, 2_2(294) -> 293
, 2_2(296) -> 295
, 2_2(300) -> 299
, 2_2(303) -> 302
, 2_2(305) -> 304
, 2_2(309) -> 308
, 2_2(312) -> 311
, 2_2(314) -> 313
, 2_2(318) -> 317
, 2_2(321) -> 320
, 2_2(323) -> 322
, 2_2(327) -> 326
, 2_2(330) -> 329
, 2_2(332) -> 331
, 2_2(359) -> 358
, 2_2(368) -> 367
, 2_2(388) -> 113
, 2_2(403) -> 402
, 2_2(404) -> 403
, 2_3(377) -> 376
, 2_3(386) -> 385
, 2_3(431) -> 430
, 2_3(434) -> 433
, 2_3(436) -> 435
, 2_3(440) -> 439
, 2_3(443) -> 442
, 2_3(445) -> 444
, 3_0(1) -> 1
, 3_1(1) -> 34
, 3_1(9) -> 8
, 3_1(10) -> 166
, 3_1(11) -> 34
, 3_1(12) -> 11
, 3_1(15) -> 14
, 3_1(19) -> 18
, 3_1(20) -> 1
, 3_1(20) -> 8
, 3_1(20) -> 9
, 3_1(20) -> 10
, 3_1(20) -> 26
, 3_1(20) -> 32
, 3_1(20) -> 34
, 3_1(20) -> 55
, 3_1(20) -> 83
, 3_1(20) -> 141
, 3_1(20) -> 159
, 3_1(20) -> 173
, 3_1(20) -> 217
, 3_1(20) -> 230
, 3_1(20) -> 252
, 3_1(20) -> 270
, 3_1(21) -> 20
, 3_1(22) -> 21
, 3_1(23) -> 22
, 3_1(33) -> 48
, 3_1(35) -> 8
, 3_1(40) -> 39
, 3_1(48) -> 163
, 3_1(50) -> 49
, 3_1(53) -> 52
, 3_1(62) -> 61
, 3_1(67) -> 66
, 3_1(79) -> 78
, 3_1(91) -> 64
, 3_1(103) -> 36
, 3_1(108) -> 124
, 3_1(111) -> 110
, 3_1(113) -> 112
, 3_1(114) -> 113
, 3_1(125) -> 124
, 3_1(126) -> 34
, 3_1(130) -> 129
, 3_1(134) -> 133
, 3_1(136) -> 135
, 3_1(139) -> 138
, 3_1(140) -> 204
, 3_1(145) -> 144
, 3_1(146) -> 145
, 3_1(152) -> 151
, 3_1(158) -> 157
, 3_1(160) -> 56
, 3_1(161) -> 160
, 3_1(164) -> 163
, 3_1(165) -> 164
, 3_1(167) -> 147
, 3_1(170) -> 169
, 3_1(188) -> 187
, 3_1(189) -> 188
, 3_1(200) -> 35
, 3_1(201) -> 200
, 3_1(202) -> 201
, 3_1(205) -> 13
, 3_1(208) -> 207
, 3_1(227) -> 58
, 3_1(240) -> 239
, 3_1(338) -> 337
, 3_2(184) -> 183
, 3_2(194) -> 193
, 3_2(195) -> 194
, 3_2(198) -> 197
, 3_2(221) -> 220
, 3_2(234) -> 233
, 3_2(247) -> 246
, 3_2(252) -> 251
, 3_2(256) -> 255
, 3_2(261) -> 260
, 3_2(265) -> 264
, 3_2(270) -> 269
, 3_2(274) -> 273
, 3_2(279) -> 278
, 3_2(283) -> 282
, 3_2(288) -> 287
, 3_2(292) -> 291
, 3_2(297) -> 296
, 3_2(301) -> 300
, 3_2(306) -> 305
, 3_2(310) -> 309
, 3_2(315) -> 314
, 3_2(319) -> 318
, 3_2(324) -> 323
, 3_2(328) -> 327
, 3_2(333) -> 332
, 3_2(343) -> 342
, 3_2(350) -> 349
, 3_2(357) -> 356
, 3_2(366) -> 365
, 3_2(390) -> 389
, 3_2(397) -> 230
, 3_2(399) -> 398
, 3_2(402) -> 401
, 3_3(375) -> 374
, 3_3(384) -> 383
, 3_3(432) -> 431
, 3_3(437) -> 436
, 3_3(441) -> 440
, 3_3(446) -> 445
, 5_0(1) -> 1
, 5_1(1) -> 173
, 5_1(9) -> 141
, 5_1(25) -> 136
, 5_1(26) -> 25
, 5_1(28) -> 27
, 5_1(31) -> 114
, 5_1(34) -> 209
, 5_1(51) -> 50
, 5_1(54) -> 230
, 5_1(55) -> 114
, 5_1(69) -> 68
, 5_1(72) -> 71
, 5_1(74) -> 73
, 5_1(75) -> 74
, 5_1(78) -> 2
, 5_1(86) -> 85
, 5_1(93) -> 92
, 5_1(97) -> 11
, 5_1(98) -> 97
, 5_1(106) -> 105
, 5_1(108) -> 107
, 5_1(118) -> 117
, 5_1(119) -> 118
, 5_1(122) -> 121
, 5_1(126) -> 1
, 5_1(126) -> 141
, 5_1(126) -> 173
, 5_1(137) -> 49
, 5_1(138) -> 137
, 5_1(143) -> 142
, 5_1(147) -> 20
, 5_1(148) -> 147
, 5_1(175) -> 174
, 5_1(335) -> 334
, 5_2(126) -> 405
, 5_2(178) -> 177
, 5_2(180) -> 179
, 5_2(199) -> 198
, 5_2(238) -> 237
, 5_2(340) -> 339
, 5_2(347) -> 346
, 5_2(354) -> 353
, 5_2(363) -> 362
, 5_2(392) -> 391
, 5_2(398) -> 397
, 5_3(372) -> 371
, 5_3(381) -> 380
, 4_0(1) -> 1
, 4_1(1) -> 10
, 4_1(2) -> 1
, 4_1(2) -> 10
, 4_1(2) -> 47
, 4_1(2) -> 55
, 4_1(2) -> 70
, 4_1(2) -> 96
, 4_1(2) -> 141
, 4_1(2) -> 172
, 4_1(2) -> 173
, 4_1(2) -> 217
, 4_1(2) -> 252
, 4_1(2) -> 261
, 4_1(2) -> 297
, 4_1(4) -> 3
, 4_1(6) -> 5
, 4_1(7) -> 6
, 4_1(8) -> 47
, 4_1(9) -> 26
, 4_1(10) -> 108
, 4_1(13) -> 12
, 4_1(19) -> 42
, 4_1(27) -> 11
, 4_1(30) -> 29
, 4_1(31) -> 30
, 4_1(32) -> 83
, 4_1(34) -> 70
, 4_1(35) -> 10
, 4_1(36) -> 10
, 4_1(39) -> 38
, 4_1(42) -> 41
, 4_1(43) -> 2
, 4_1(46) -> 45
, 4_1(48) -> 47
, 4_1(52) -> 51
, 4_1(54) -> 53
, 4_1(55) -> 96
, 4_1(56) -> 10
, 4_1(57) -> 56
, 4_1(59) -> 58
, 4_1(65) -> 64
, 4_1(66) -> 65
, 4_1(70) -> 125
, 4_1(77) -> 76
, 4_1(80) -> 79
, 4_1(82) -> 81
, 4_1(85) -> 84
, 4_1(87) -> 86
, 4_1(92) -> 91
, 4_1(95) -> 94
, 4_1(98) -> 1
, 4_1(102) -> 101
, 4_1(105) -> 104
, 4_1(110) -> 109
, 4_1(115) -> 27
, 4_1(126) -> 10
, 4_1(128) -> 127
, 4_1(132) -> 212
, 4_1(142) -> 22
, 4_1(147) -> 10
, 4_1(149) -> 148
, 4_1(150) -> 149
, 4_1(163) -> 162
, 4_1(168) -> 167
, 4_1(169) -> 168
, 4_1(174) -> 97
, 4_1(203) -> 202
, 4_1(204) -> 203
, 4_1(212) -> 211
, 4_1(243) -> 242
, 4_1(334) -> 57
, 4_2(1) -> 252
, 4_2(8) -> 261
, 4_2(9) -> 270
, 4_2(10) -> 252
, 4_2(19) -> 279
, 4_2(33) -> 270
, 4_2(34) -> 252
, 4_2(35) -> 252
, 4_2(36) -> 306
, 4_2(47) -> 288
, 4_2(55) -> 297
, 4_2(56) -> 306
, 4_2(57) -> 185
, 4_2(60) -> 315
, 4_2(81) -> 324
, 4_2(96) -> 333
, 4_2(179) -> 178
, 4_2(215) -> 214
, 4_2(216) -> 215
, 4_2(224) -> 223
, 4_2(225) -> 224
, 4_2(231) -> 270
, 4_2(232) -> 231
, 4_2(244) -> 26
, 4_2(244) -> 53
, 4_2(244) -> 83
, 4_2(244) -> 270
, 4_2(245) -> 244
, 4_2(250) -> 249
, 4_2(253) -> 6
, 4_2(254) -> 253
, 4_2(259) -> 258
, 4_2(262) -> 83
, 4_2(263) -> 262
, 4_2(268) -> 267
, 4_2(271) -> 76
, 4_2(272) -> 271
, 4_2(277) -> 276
, 4_2(280) -> 45
, 4_2(281) -> 280
, 4_2(286) -> 285
, 4_2(289) -> 53
, 4_2(290) -> 289
, 4_2(295) -> 294
, 4_2(298) -> 10
, 4_2(298) -> 26
, 4_2(298) -> 83
, 4_2(298) -> 96
, 4_2(298) -> 252
, 4_2(298) -> 270
, 4_2(298) -> 297
, 4_2(299) -> 298
, 4_2(304) -> 303
, 4_2(307) -> 58
, 4_2(308) -> 307
, 4_2(313) -> 312
, 4_2(316) -> 79
, 4_2(317) -> 316
, 4_2(322) -> 321
, 4_2(325) -> 94
, 4_2(326) -> 325
, 4_2(331) -> 330
, 4_2(339) -> 232
, 4_2(344) -> 252
, 4_2(345) -> 344
, 4_2(346) -> 345
, 4_2(352) -> 351
, 4_2(353) -> 352
, 4_2(361) -> 360
, 4_2(362) -> 361
, 4_2(391) -> 390
, 4_2(394) -> 393
, 4_2(396) -> 395
, 4_2(400) -> 399
, 4_2(401) -> 400
, 4_3(344) -> 437
, 4_3(370) -> 369
, 4_3(371) -> 370
, 4_3(379) -> 378
, 4_3(380) -> 379
, 4_3(395) -> 446
, 4_3(429) -> 270
, 4_3(430) -> 429
, 4_3(435) -> 434
, 4_3(438) -> 393
, 4_3(439) -> 438
, 4_3(444) -> 443}
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(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1))))))))))
, 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1))))))))))
, 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1))))))))))
, 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1))))))))))
, 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1))))))))))
, 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1))))))))))
, 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1))))))))))
, 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1))))))))))
, 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1))))))))))
, 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1))))))))))
, 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1))))))))))
, 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1))))))))))
, 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1))))))))))
, 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1))))))))))
, 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1))))))))))
, 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1))))))))))
, 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1))))))))))
, 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1))))))))))
, 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1))))))))))
, 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1))))))))))
, 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1))))))))))
, 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1))))))))))
, 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1))))))))))
, 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1))))))))))
, 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1))))))))))
, 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1))))))))))
, 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1))))))))))
, 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1))))))))))
, 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1))))))))))
, 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1))))))))))
, 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1))))))))))
, 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1))))))))))
, 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1))))))))))
, 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(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(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1))))))))))
, 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1))))))))))
, 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1))))))))))
, 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1))))))))))
, 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1))))))))))
, 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1))))))))))
, 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1))))))))))
, 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1))))))))))
, 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1))))))))))
, 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1))))))))))
, 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1))))))))))
, 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1))))))))))
, 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1))))))))))
, 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1))))))))))
, 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1))))))))))
, 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1))))))))))
, 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1))))))))))
, 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1))))))))))
, 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1))))))))))
, 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1))))))))))
, 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1))))))))))
, 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1))))))))))
, 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1))))))))))
, 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1))))))))))
, 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1))))))))))
, 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1))))))))))
, 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1))))))))))
, 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1))))))))))
, 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1))))))))))
, 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1))))))))))
, 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1))))))))))
, 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1))))))))))
, 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1))))))))))
, 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(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(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1))))))))))
, 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1))))))))))
, 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1))))))))))
, 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1))))))))))
, 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1))))))))))
, 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1))))))))))
, 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1))))))))))
, 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1))))))))))
, 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1))))))))))
, 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1))))))))))
, 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1))))))))))
, 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1))))))))))
, 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1))))))))))
, 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1))))))))))
, 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1))))))))))
, 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1))))))))))
, 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1))))))))))
, 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1))))))))))
, 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1))))))))))
, 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1))))))))))
, 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1))))))))))
, 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1))))))))))
, 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1))))))))))
, 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1))))))))))
, 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1))))))))))
, 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1))))))))))
, 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1))))))))))
, 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1))))))))))
, 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1))))))))))
, 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1))))))))))
, 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1))))))))))
, 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1))))))))))
, 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1))))))))))
, 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..