Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1)))))))))))))))))))))
->
5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(x1)))))))))))))))))))))
, 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1)))))))))))))))))))))
-> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1))))))))))))))))))
, 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1)))))))))))))))))))))
-> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1))))))))))))))))))))
, 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1)))))))))))))))))))))
->
3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1)))))))))))))))))))))
, 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1)))))))))))))))))))))
->
0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1)))))))))))))))))))))
, 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) ->
5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1))))))))))))))))))))
, 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) ->
0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1)))))))))))))))))))
, 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) ->
2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1)))))))))))))))))
, 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) ->
3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1))))))))))))))))
, 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) ->
0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1)))))))))))))))))
, 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) ->
0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1)))))))))))))))))
, 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) ->
1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1))))))))))))))))))
, 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) ->
4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1)))))))))))))))))
, 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) ->
2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1))))))))))))))))
, 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) ->
1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1)))))))))))))))))
, 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) ->
4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1)))))))))))))))
, 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) ->
2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1)))))))))))))))
, 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) ->
2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1))))))))))))))))
, 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) ->
0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1)))))))))))))))
, 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) ->
0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1))))))))))))))))
, 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) ->
2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1)))))))))))))))
, 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) ->
0(2(2(2(4(5(2(0(2(0(0(3(2(x1)))))))))))))
, 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) ->
1(2(3(4(4(3(3(5(0(1(1(5(2(x1)))))))))))))
, 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) ->
4(5(2(3(2(5(3(2(1(0(2(1(x1))))))))))))
, 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) ->
0(0(5(1(0(5(3(1(0(1(5(3(x1))))))))))))
, 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) ->
3(2(3(1(5(0(4(4(2(3(5(5(x1))))))))))))
, 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) ->
2(4(4(4(2(1(0(4(3(3(2(5(x1))))))))))))
, 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) ->
2(4(0(5(2(3(0(0(5(4(x1))))))))))
, 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) ->
4(2(3(3(3(5(3(1(0(1(5(x1)))))))))))
, 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1)))))))))
, 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1))))))
, 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1))))))
, 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1))))))
, 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1)))))))
, 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1))))))
, 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1))))))
, 4(5(1(2(0(x1))))) -> 4(5(5(3(x1))))
, 2(3(3(5(1(x1))))) -> 3(5(5(3(x1))))
, 0(5(1(5(x1)))) -> 2(3(1(x1)))
, 0(1(2(0(x1)))) -> 3(4(0(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:
{ 0_0(1) -> 1
, 0_1(1) -> 305
, 0_1(2) -> 305
, 0_1(4) -> 305
, 0_1(10) -> 9
, 0_1(20) -> 19
, 0_1(21) -> 155
, 0_1(33) -> 32
, 0_1(36) -> 35
, 0_1(37) -> 195
, 0_1(39) -> 3
, 0_1(47) -> 46
, 0_1(55) -> 74
, 0_1(56) -> 74
, 0_1(57) -> 56
, 0_1(59) -> 58
, 0_1(60) -> 59
, 0_1(64) -> 63
, 0_1(74) -> 181
, 0_1(75) -> 1
, 0_1(75) -> 38
, 0_1(75) -> 74
, 0_1(75) -> 93
, 0_1(75) -> 169
, 0_1(75) -> 181
, 0_1(75) -> 270
, 0_1(75) -> 281
, 0_1(75) -> 294
, 0_1(75) -> 303
, 0_1(75) -> 305
, 0_1(75) -> 367
, 0_1(75) -> 372
, 0_1(75) -> 375
, 0_1(75) -> 380
, 0_1(78) -> 77
, 0_1(83) -> 82
, 0_1(85) -> 84
, 0_1(87) -> 86
, 0_1(90) -> 89
, 0_1(93) -> 372
, 0_1(94) -> 270
, 0_1(95) -> 2
, 0_1(97) -> 96
, 0_1(116) -> 115
, 0_1(118) -> 117
, 0_1(123) -> 122
, 0_1(127) -> 360
, 0_1(129) -> 128
, 0_1(130) -> 129
, 0_1(131) -> 130
, 0_1(133) -> 132
, 0_1(155) -> 181
, 0_1(156) -> 75
, 0_1(162) -> 161
, 0_1(167) -> 166
, 0_1(175) -> 174
, 0_1(178) -> 177
, 0_1(189) -> 188
, 0_1(193) -> 192
, 0_1(196) -> 74
, 0_1(197) -> 305
, 0_1(198) -> 197
, 0_1(202) -> 201
, 0_1(203) -> 202
, 0_1(204) -> 203
, 0_1(212) -> 211
, 0_1(223) -> 183
, 0_1(226) -> 225
, 0_1(230) -> 229
, 0_1(234) -> 233
, 0_1(241) -> 240
, 0_1(247) -> 367
, 0_1(263) -> 262
, 0_1(269) -> 301
, 0_1(284) -> 283
, 0_1(287) -> 286
, 0_1(295) -> 212
, 0_1(302) -> 301
, 0_1(304) -> 303
, 0_1(305) -> 181
, 0_1(312) -> 311
, 0_1(314) -> 313
, 0_1(315) -> 314
, 0_1(322) -> 321
, 0_1(331) -> 330
, 0_1(334) -> 333
, 0_1(338) -> 337
, 0_1(339) -> 305
, 0_1(344) -> 343
, 0_1(354) -> 353
, 0_1(356) -> 349
, 0_1(360) -> 359
, 0_1(372) -> 181
, 0_1(378) -> 306
, 0_1(379) -> 378
, 0_1(381) -> 380
, 0_2(37) -> 392
, 0_2(90) -> 394
, 0_2(129) -> 396
, 2_0(1) -> 1
, 2_1(1) -> 93
, 2_1(11) -> 10
, 2_1(14) -> 13
, 2_1(17) -> 16
, 2_1(21) -> 282
, 2_1(22) -> 93
, 2_1(27) -> 26
, 2_1(30) -> 29
, 2_1(37) -> 1
, 2_1(37) -> 36
, 2_1(37) -> 270
, 2_1(37) -> 305
, 2_1(38) -> 331
, 2_1(54) -> 53
, 2_1(55) -> 209
, 2_1(56) -> 93
, 2_1(63) -> 62
, 2_1(73) -> 72
, 2_1(75) -> 93
, 2_1(77) -> 76
, 2_1(89) -> 88
, 2_1(93) -> 281
, 2_1(94) -> 93
, 2_1(102) -> 101
, 2_1(110) -> 109
, 2_1(111) -> 292
, 2_1(112) -> 331
, 2_1(114) -> 113
, 2_1(115) -> 114
, 2_1(125) -> 124
, 2_1(126) -> 125
, 2_1(128) -> 1
, 2_1(128) -> 19
, 2_1(128) -> 20
, 2_1(128) -> 21
, 2_1(128) -> 93
, 2_1(128) -> 94
, 2_1(128) -> 142
, 2_1(128) -> 155
, 2_1(128) -> 258
, 2_1(128) -> 269
, 2_1(128) -> 304
, 2_1(128) -> 305
, 2_1(128) -> 331
, 2_1(129) -> 93
, 2_1(135) -> 134
, 2_1(139) -> 138
, 2_1(149) -> 148
, 2_1(155) -> 154
, 2_1(157) -> 93
, 2_1(159) -> 158
, 2_1(166) -> 165
, 2_1(171) -> 170
, 2_1(177) -> 176
, 2_1(179) -> 178
, 2_1(180) -> 179
, 2_1(181) -> 312
, 2_1(191) -> 190
, 2_1(195) -> 194
, 2_1(206) -> 205
, 2_1(210) -> 209
, 2_1(213) -> 212
, 2_1(217) -> 216
, 2_1(220) -> 219
, 2_1(224) -> 22
, 2_1(239) -> 238
, 2_1(240) -> 239
, 2_1(245) -> 244
, 2_1(253) -> 252
, 2_1(258) -> 257
, 2_1(261) -> 260
, 2_1(266) -> 265
, 2_1(272) -> 271
, 2_1(277) -> 276
, 2_1(279) -> 278
, 2_1(282) -> 281
, 2_1(286) -> 285
, 2_1(292) -> 291
, 2_1(293) -> 292
, 2_1(298) -> 297
, 2_1(304) -> 72
, 2_1(306) -> 75
, 2_1(307) -> 306
, 2_1(308) -> 307
, 2_1(311) -> 310
, 2_1(313) -> 312
, 2_1(324) -> 197
, 2_1(326) -> 325
, 2_1(329) -> 328
, 2_1(340) -> 56
, 2_1(347) -> 346
, 2_1(348) -> 93
, 2_1(352) -> 351
, 2_1(358) -> 357
, 2_1(361) -> 196
, 2_1(371) -> 72
, 2_1(376) -> 361
, 2_1(389) -> 1
, 2_2(387) -> 166
, 2_2(387) -> 270
, 2_2(387) -> 303
, 2_2(389) -> 128
, 2_2(389) -> 396
, 1_0(1) -> 1
, 1_1(1) -> 38
, 1_1(2) -> 38
, 1_1(6) -> 5
, 1_1(8) -> 7
, 1_1(21) -> 375
, 1_1(22) -> 1
, 1_1(22) -> 38
, 1_1(22) -> 74
, 1_1(22) -> 94
, 1_1(22) -> 168
, 1_1(22) -> 269
, 1_1(22) -> 304
, 1_1(22) -> 305
, 1_1(22) -> 348
, 1_1(22) -> 375
, 1_1(23) -> 38
, 1_1(31) -> 30
, 1_1(37) -> 379
, 1_1(38) -> 111
, 1_1(44) -> 43
, 1_1(46) -> 45
, 1_1(50) -> 49
, 1_1(55) -> 294
, 1_1(57) -> 38
, 1_1(58) -> 57
, 1_1(62) -> 61
, 1_1(75) -> 38
, 1_1(84) -> 83
, 1_1(88) -> 87
, 1_1(91) -> 90
, 1_1(92) -> 91
, 1_1(93) -> 169
, 1_1(94) -> 247
, 1_1(104) -> 103
, 1_1(107) -> 106
, 1_1(113) -> 112
, 1_1(127) -> 126
, 1_1(128) -> 247
, 1_1(140) -> 139
, 1_1(144) -> 143
, 1_1(147) -> 146
, 1_1(152) -> 151
, 1_1(163) -> 162
, 1_1(168) -> 381
, 1_1(172) -> 171
, 1_1(188) -> 187
, 1_1(194) -> 193
, 1_1(196) -> 247
, 1_1(197) -> 38
, 1_1(199) -> 198
, 1_1(211) -> 128
, 1_1(214) -> 213
, 1_1(215) -> 214
, 1_1(218) -> 217
, 1_1(219) -> 218
, 1_1(222) -> 221
, 1_1(225) -> 224
, 1_1(231) -> 230
, 1_1(233) -> 232
, 1_1(242) -> 241
, 1_1(243) -> 242
, 1_1(244) -> 243
, 1_1(247) -> 322
, 1_1(249) -> 248
, 1_1(252) -> 251
, 1_1(256) -> 323
, 1_1(262) -> 261
, 1_1(271) -> 38
, 1_1(275) -> 274
, 1_1(283) -> 156
, 1_1(288) -> 287
, 1_1(290) -> 289
, 1_1(294) -> 293
, 1_1(299) -> 298
, 1_1(300) -> 299
, 1_1(305) -> 377
, 1_1(323) -> 322
, 1_1(330) -> 329
, 1_1(332) -> 38
, 1_1(333) -> 332
, 1_1(337) -> 336
, 1_1(338) -> 111
, 1_1(339) -> 338
, 1_1(342) -> 341
, 1_1(353) -> 352
, 1_1(361) -> 38
, 1_1(367) -> 366
, 1_1(368) -> 56
, 1_1(373) -> 38
, 1_1(374) -> 373
, 1_1(375) -> 374
, 1_1(379) -> 111
, 1_1(380) -> 75
, 1_2(23) -> 388
, 1_2(250) -> 390
, 4_0(1) -> 1
, 4_1(1) -> 21
, 4_1(2) -> 21
, 4_1(3) -> 2
, 4_1(7) -> 6
, 4_1(13) -> 12
, 4_1(15) -> 14
, 4_1(18) -> 17
, 4_1(20) -> 140
, 4_1(21) -> 20
, 4_1(22) -> 54
, 4_1(23) -> 21
, 4_1(25) -> 24
, 4_1(29) -> 28
, 4_1(32) -> 31
, 4_1(38) -> 142
, 4_1(51) -> 50
, 4_1(52) -> 51
, 4_1(55) -> 54
, 4_1(57) -> 21
, 4_1(61) -> 60
, 4_1(68) -> 67
, 4_1(69) -> 68
, 4_1(75) -> 21
, 4_1(86) -> 85
, 4_1(93) -> 92
, 4_1(94) -> 258
, 4_1(96) -> 95
, 4_1(99) -> 98
, 4_1(103) -> 102
, 4_1(112) -> 75
, 4_1(121) -> 120
, 4_1(124) -> 123
, 4_1(128) -> 56
, 4_1(129) -> 21
, 4_1(136) -> 135
, 4_1(137) -> 136
, 4_1(138) -> 137
, 4_1(141) -> 140
, 4_1(142) -> 141
, 4_1(145) -> 144
, 4_1(153) -> 152
, 4_1(156) -> 21
, 4_1(158) -> 157
, 4_1(164) -> 163
, 4_1(183) -> 182
, 4_1(184) -> 183
, 4_1(185) -> 184
, 4_1(186) -> 185
, 4_1(196) -> 1
, 4_1(196) -> 21
, 4_1(196) -> 38
, 4_1(196) -> 94
, 4_1(196) -> 126
, 4_1(196) -> 169
, 4_1(196) -> 247
, 4_1(196) -> 256
, 4_1(196) -> 258
, 4_1(209) -> 208
, 4_1(235) -> 234
, 4_1(251) -> 250
, 4_1(255) -> 254
, 4_1(259) -> 129
, 4_1(264) -> 263
, 4_1(265) -> 264
, 4_1(267) -> 266
, 4_1(271) -> 21
, 4_1(273) -> 272
, 4_1(289) -> 288
, 4_1(291) -> 290
, 4_1(305) -> 56
, 4_1(309) -> 308
, 4_1(317) -> 316
, 4_1(318) -> 317
, 4_1(345) -> 344
, 4_1(346) -> 345
, 4_1(349) -> 128
, 4_1(350) -> 349
, 4_1(351) -> 350
, 4_1(355) -> 354
, 4_2(392) -> 391
, 4_2(394) -> 393
, 4_2(396) -> 395
, 3_0(1) -> 1
, 3_1(1) -> 55
, 3_1(5) -> 4
, 3_1(9) -> 8
, 3_1(12) -> 11
, 3_1(19) -> 18
, 3_1(21) -> 223
, 3_1(22) -> 55
, 3_1(24) -> 23
, 3_1(34) -> 33
, 3_1(38) -> 37
, 3_1(43) -> 42
, 3_1(53) -> 52
, 3_1(55) -> 210
, 3_1(56) -> 1
, 3_1(56) -> 21
, 3_1(56) -> 55
, 3_1(56) -> 93
, 3_1(56) -> 94
, 3_1(56) -> 142
, 3_1(56) -> 196
, 3_1(56) -> 209
, 3_1(56) -> 305
, 3_1(56) -> 315
, 3_1(56) -> 348
, 3_1(67) -> 66
, 3_1(71) -> 70
, 3_1(75) -> 55
, 3_1(76) -> 75
, 3_1(80) -> 79
, 3_1(81) -> 80
, 3_1(93) -> 315
, 3_1(101) -> 100
, 3_1(108) -> 107
, 3_1(109) -> 108
, 3_1(111) -> 110
, 3_1(117) -> 116
, 3_1(119) -> 118
, 3_1(120) -> 119
, 3_1(129) -> 55
, 3_1(134) -> 133
, 3_1(143) -> 56
, 3_1(146) -> 145
, 3_1(157) -> 156
, 3_1(161) -> 160
, 3_1(167) -> 156
, 3_1(170) -> 76
, 3_1(181) -> 180
, 3_1(182) -> 22
, 3_1(190) -> 189
, 3_1(196) -> 1
, 3_1(196) -> 93
, 3_1(196) -> 209
, 3_1(200) -> 199
, 3_1(205) -> 204
, 3_1(207) -> 206
, 3_1(216) -> 215
, 3_1(221) -> 220
, 3_1(228) -> 227
, 3_1(229) -> 228
, 3_1(236) -> 196
, 3_1(247) -> 246
, 3_1(254) -> 253
, 3_1(256) -> 255
, 3_1(260) -> 259
, 3_1(268) -> 267
, 3_1(269) -> 268
, 3_1(274) -> 273
, 3_1(276) -> 275
, 3_1(282) -> 52
, 3_1(296) -> 295
, 3_1(297) -> 296
, 3_1(301) -> 300
, 3_1(315) -> 355
, 3_1(316) -> 224
, 3_1(319) -> 318
, 3_1(320) -> 319
, 3_1(325) -> 324
, 3_1(328) -> 327
, 3_1(336) -> 335
, 3_1(341) -> 340
, 3_1(348) -> 347
, 3_1(359) -> 358
, 3_1(362) -> 361
, 3_1(363) -> 362
, 3_1(364) -> 363
, 3_1(366) -> 365
, 3_1(369) -> 368
, 3_1(380) -> 55
, 3_1(390) -> 1
, 3_2(249) -> 386
, 3_2(384) -> 209
, 3_2(388) -> 387
, 3_2(390) -> 389
, 3_2(391) -> 192
, 3_2(393) -> 86
, 3_2(395) -> 367
, 5_0(1) -> 1
, 5_1(1) -> 94
, 5_1(2) -> 1
, 5_1(2) -> 73
, 5_1(2) -> 94
, 5_1(2) -> 168
, 5_1(2) -> 304
, 5_1(4) -> 3
, 5_1(16) -> 15
, 5_1(21) -> 127
, 5_1(22) -> 348
, 5_1(23) -> 22
, 5_1(26) -> 25
, 5_1(28) -> 27
, 5_1(35) -> 34
, 5_1(38) -> 168
, 5_1(40) -> 39
, 5_1(41) -> 40
, 5_1(42) -> 41
, 5_1(45) -> 44
, 5_1(48) -> 47
, 5_1(49) -> 48
, 5_1(55) -> 339
, 5_1(57) -> 94
, 5_1(65) -> 64
, 5_1(66) -> 65
, 5_1(70) -> 69
, 5_1(72) -> 71
, 5_1(74) -> 73
, 5_1(75) -> 94
, 5_1(79) -> 78
, 5_1(82) -> 81
, 5_1(93) -> 256
, 5_1(94) -> 348
, 5_1(98) -> 97
, 5_1(100) -> 99
, 5_1(105) -> 104
, 5_1(106) -> 105
, 5_1(122) -> 121
, 5_1(132) -> 131
, 5_1(148) -> 147
, 5_1(150) -> 149
, 5_1(151) -> 150
, 5_1(154) -> 153
, 5_1(160) -> 159
, 5_1(165) -> 164
, 5_1(168) -> 167
, 5_1(169) -> 168
, 5_1(173) -> 172
, 5_1(174) -> 173
, 5_1(176) -> 175
, 5_1(187) -> 186
, 5_1(192) -> 191
, 5_1(195) -> 235
, 5_1(197) -> 196
, 5_1(201) -> 200
, 5_1(208) -> 207
, 5_1(212) -> 94
, 5_1(223) -> 222
, 5_1(227) -> 226
, 5_1(232) -> 231
, 5_1(237) -> 236
, 5_1(238) -> 237
, 5_1(246) -> 245
, 5_1(248) -> 129
, 5_1(250) -> 249
, 5_1(257) -> 256
, 5_1(270) -> 269
, 5_1(271) -> 75
, 5_1(278) -> 277
, 5_1(280) -> 279
, 5_1(281) -> 280
, 5_1(285) -> 284
, 5_1(303) -> 302
, 5_1(305) -> 304
, 5_1(310) -> 309
, 5_1(321) -> 320
, 5_1(327) -> 326
, 5_1(332) -> 156
, 5_1(335) -> 334
, 5_1(339) -> 196
, 5_1(343) -> 342
, 5_1(357) -> 356
, 5_1(361) -> 94
, 5_1(365) -> 364
, 5_1(370) -> 369
, 5_1(371) -> 370
, 5_1(372) -> 371
, 5_1(373) -> 128
, 5_1(377) -> 376
, 5_2(385) -> 384
, 5_2(386) -> 385}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1)))))))))))))))))))))
->
5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(x1)))))))))))))))))))))
, 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1)))))))))))))))))))))
-> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1))))))))))))))))))
, 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1)))))))))))))))))))))
-> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1))))))))))))))))))))
, 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1)))))))))))))))))))))
->
3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1)))))))))))))))))))))
, 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1)))))))))))))))))))))
->
0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1)))))))))))))))))))))
, 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) ->
5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1))))))))))))))))))))
, 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) ->
0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1)))))))))))))))))))
, 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) ->
2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1)))))))))))))))))
, 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) ->
3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1))))))))))))))))
, 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) ->
0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1)))))))))))))))))
, 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) ->
0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1)))))))))))))))))
, 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) ->
1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1))))))))))))))))))
, 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) ->
4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1)))))))))))))))))
, 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) ->
2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1))))))))))))))))
, 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) ->
1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1)))))))))))))))))
, 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) ->
4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1)))))))))))))))
, 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) ->
2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1)))))))))))))))
, 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) ->
2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1))))))))))))))))
, 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) ->
0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1)))))))))))))))
, 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) ->
0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1))))))))))))))))
, 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) ->
2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1)))))))))))))))
, 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) ->
0(2(2(2(4(5(2(0(2(0(0(3(2(x1)))))))))))))
, 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) ->
1(2(3(4(4(3(3(5(0(1(1(5(2(x1)))))))))))))
, 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) ->
4(5(2(3(2(5(3(2(1(0(2(1(x1))))))))))))
, 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) ->
0(0(5(1(0(5(3(1(0(1(5(3(x1))))))))))))
, 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) ->
3(2(3(1(5(0(4(4(2(3(5(5(x1))))))))))))
, 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) ->
2(4(4(4(2(1(0(4(3(3(2(5(x1))))))))))))
, 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) ->
2(4(0(5(2(3(0(0(5(4(x1))))))))))
, 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) ->
4(2(3(3(3(5(3(1(0(1(5(x1)))))))))))
, 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1)))))))))
, 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1))))))
, 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1))))))
, 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1))))))
, 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1)))))))
, 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1))))))
, 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1))))))
, 4(5(1(2(0(x1))))) -> 4(5(5(3(x1))))
, 2(3(3(5(1(x1))))) -> 3(5(5(3(x1))))
, 0(5(1(5(x1)))) -> 2(3(1(x1)))
, 0(1(2(0(x1)))) -> 3(4(0(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(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1)))))))))))))))))))))
->
5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(x1)))))))))))))))))))))
, 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1)))))))))))))))))))))
-> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1))))))))))))))))))
, 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1)))))))))))))))))))))
-> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1))))))))))))))))))))
, 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1)))))))))))))))))))))
->
3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1)))))))))))))))))))))
, 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1)))))))))))))))))))))
->
0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1)))))))))))))))))))))
, 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) ->
5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1))))))))))))))))))))
, 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) ->
0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1)))))))))))))))))))
, 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) ->
2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1)))))))))))))))))
, 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) ->
3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1))))))))))))))))
, 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) ->
0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1)))))))))))))))))
, 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) ->
0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1)))))))))))))))))
, 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) ->
1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1))))))))))))))))))
, 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) ->
4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1)))))))))))))))))
, 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) ->
2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1))))))))))))))))
, 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) ->
1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1)))))))))))))))))
, 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) ->
4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1)))))))))))))))
, 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) ->
2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1)))))))))))))))
, 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) ->
2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1))))))))))))))))
, 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) ->
0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1)))))))))))))))
, 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) ->
0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1))))))))))))))))
, 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) ->
2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1)))))))))))))))
, 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) ->
0(2(2(2(4(5(2(0(2(0(0(3(2(x1)))))))))))))
, 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) ->
1(2(3(4(4(3(3(5(0(1(1(5(2(x1)))))))))))))
, 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) ->
4(5(2(3(2(5(3(2(1(0(2(1(x1))))))))))))
, 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) ->
0(0(5(1(0(5(3(1(0(1(5(3(x1))))))))))))
, 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) ->
3(2(3(1(5(0(4(4(2(3(5(5(x1))))))))))))
, 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) ->
2(4(4(4(2(1(0(4(3(3(2(5(x1))))))))))))
, 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) ->
2(4(0(5(2(3(0(0(5(4(x1))))))))))
, 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) ->
4(2(3(3(3(5(3(1(0(1(5(x1)))))))))))
, 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1)))))))))
, 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1))))))
, 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1))))))
, 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1))))))
, 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1)))))))
, 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1))))))
, 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1))))))
, 4(5(1(2(0(x1))))) -> 4(5(5(3(x1))))
, 2(3(3(5(1(x1))))) -> 3(5(5(3(x1))))
, 0(5(1(5(x1)))) -> 2(3(1(x1)))
, 0(1(2(0(x1)))) -> 3(4(0(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(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1)))))))))))))))))))))
->
5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(x1)))))))))))))))))))))
, 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1)))))))))))))))))))))
-> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1))))))))))))))))))
, 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1)))))))))))))))))))))
-> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1))))))))))))))))))))
, 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1)))))))))))))))))))))
->
3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1)))))))))))))))))))))
, 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1)))))))))))))))))))))
->
0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1)))))))))))))))))))))
, 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) ->
5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1))))))))))))))))))))
, 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) ->
0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1)))))))))))))))))))
, 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) ->
2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1)))))))))))))))))
, 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) ->
3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1))))))))))))))))
, 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) ->
0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1)))))))))))))))))
, 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) ->
0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1)))))))))))))))))
, 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) ->
1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1))))))))))))))))))
, 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) ->
4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1)))))))))))))))))
, 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) ->
2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1))))))))))))))))
, 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) ->
1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1)))))))))))))))))
, 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) ->
4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1)))))))))))))))
, 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) ->
2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1)))))))))))))))
, 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) ->
2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1))))))))))))))))
, 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) ->
0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1)))))))))))))))
, 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) ->
0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1))))))))))))))))
, 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) ->
2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1)))))))))))))))
, 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) ->
0(2(2(2(4(5(2(0(2(0(0(3(2(x1)))))))))))))
, 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) ->
1(2(3(4(4(3(3(5(0(1(1(5(2(x1)))))))))))))
, 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) ->
4(5(2(3(2(5(3(2(1(0(2(1(x1))))))))))))
, 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) ->
0(0(5(1(0(5(3(1(0(1(5(3(x1))))))))))))
, 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) ->
3(2(3(1(5(0(4(4(2(3(5(5(x1))))))))))))
, 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) ->
2(4(4(4(2(1(0(4(3(3(2(5(x1))))))))))))
, 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) ->
2(4(0(5(2(3(0(0(5(4(x1))))))))))
, 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) ->
4(2(3(3(3(5(3(1(0(1(5(x1)))))))))))
, 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1)))))))))
, 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1))))))
, 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1))))))
, 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1))))))
, 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1)))))))
, 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1))))))
, 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1))))))
, 4(5(1(2(0(x1))))) -> 4(5(5(3(x1))))
, 2(3(3(5(1(x1))))) -> 3(5(5(3(x1))))
, 0(5(1(5(x1)))) -> 2(3(1(x1)))
, 0(1(2(0(x1)))) -> 3(4(0(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..