Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(4(5(5(2(5(3(x1))))))) -> 5(4(0(1(1(3(1(3(5(3(x1))))))))))
, 5(4(2(2(2(4(2(x1))))))) -> 0(3(5(3(1(3(1(3(4(2(x1))))))))))
, 5(0(4(0(2(2(4(x1))))))) -> 5(1(1(1(3(0(5(1(1(1(x1))))))))))
, 4(5(2(5(4(4(1(x1))))))) -> 0(0(2(0(2(5(4(4(0(3(x1))))))))))
, 4(5(0(5(2(2(5(x1))))))) -> 4(2(0(0(5(4(3(0(3(4(x1))))))))))
, 4(1(4(0(1(5(3(x1))))))) -> 4(0(0(2(4(5(1(2(1(2(x1))))))))))
, 4(1(1(4(2(1(0(x1))))))) -> 4(1(2(4(3(1(3(2(3(0(x1))))))))))
, 3(3(5(2(2(5(0(x1))))))) -> 3(1(3(2(4(2(2(0(0(1(x1))))))))))
, 2(5(2(3(5(2(1(x1))))))) -> 2(4(5(0(1(1(4(5(1(3(x1))))))))))
, 2(5(1(5(3(5(2(x1))))))) -> 2(2(4(4(3(1(3(0(3(3(x1))))))))))
, 2(5(1(4(1(5(2(x1))))))) -> 2(1(1(5(4(5(4(0(3(3(x1))))))))))
, 2(4(5(1(1(5(2(x1))))))) -> 2(3(0(3(3(3(0(0(4(2(x1))))))))))
, 2(3(5(5(4(0(0(x1))))))) -> 3(3(4(1(5(1(3(2(2(0(x1))))))))))
, 2(2(5(3(2(2(5(x1))))))) -> 3(2(2(5(4(3(1(3(1(5(x1))))))))))
, 2(2(0(4(2(4(2(x1))))))) -> 2(1(1(2(4(1(4(4(1(1(x1))))))))))
, 2(0(4(4(2(0(4(x1))))))) -> 3(1(5(5(2(3(2(1(3(2(x1))))))))))
, 1(5(0(2(2(0(4(x1))))))) -> 0(0(1(1(2(0(2(4(3(4(x1))))))))))
, 1(4(4(1(4(0(4(x1))))))) -> 1(0(3(1(1(4(5(3(1(5(x1))))))))))
, 0(5(5(3(0(4(1(x1))))))) -> 4(3(1(2(0(2(2(5(4(1(x1))))))))))
, 0(5(2(4(1(5(0(x1))))))) -> 3(5(3(0(3(0(5(5(5(1(x1))))))))))
, 0(4(5(0(4(0(5(x1))))))) -> 1(1(3(3(4(2(3(1(1(4(x1))))))))))
, 0(4(2(4(2(3(0(x1))))))) -> 1(5(1(0(2(0(3(0(1(0(x1))))))))))
, 0(4(1(4(1(5(0(x1))))))) -> 1(1(3(4(2(1(2(0(5(1(x1))))))))))
, 0(4(1(0(0(5(0(x1))))))) -> 0(5(5(0(1(5(0(3(1(3(x1))))))))))
, 0(4(0(1(4(5(2(x1))))))) -> 1(3(4(1(2(3(1(5(2(2(x1))))))))))
, 0(0(4(5(2(4(4(x1))))))) -> 3(0(0(1(1(2(3(0(0(2(x1))))))))))
, 5(1(1(5(0(4(x1)))))) -> 5(1(2(0(2(0(2(4(1(2(x1))))))))))
, 4(2(5(4(0(5(x1)))))) -> 0(1(0(2(0(4(0(3(3(4(x1))))))))))
, 3(5(2(0(5(2(x1)))))) -> 3(4(2(3(2(0(3(3(3(4(x1))))))))))
, 3(4(5(2(2(0(x1)))))) -> 3(5(0(1(3(2(3(2(3(0(x1))))))))))
, 2(5(0(5(2(5(x1)))))) -> 3(3(3(4(0(2(3(3(3(4(x1))))))))))
, 1(5(0(5(2(0(x1)))))) -> 0(0(2(1(0(2(2(4(4(1(x1))))))))))
, 0(5(4(4(1(1(x1)))))) -> 0(5(5(4(1(1(2(1(3(2(x1))))))))))
, 0(5(2(0(4(1(x1)))))) -> 3(1(2(1(1(2(0(0(4(1(x1))))))))))
, 0(4(5(1(0(0(x1)))))) -> 1(4(0(1(3(1(1(3(1(0(x1))))))))))
, 0(4(2(5(5(0(x1)))))) -> 1(4(0(1(3(3(2(4(1(2(x1))))))))))
, 5(4(2(5(0(x1))))) -> 5(1(2(3(2(3(4(0(0(3(x1))))))))))
, 4(4(4(5(2(x1))))) -> 4(4(1(2(1(0(3(3(1(4(x1))))))))))
, 3(5(2(5(3(x1))))) -> 5(3(4(1(1(2(1(1(2(2(x1))))))))))
, 2(2(5(2(0(x1))))) -> 2(4(4(4(4(0(3(1(1(3(x1))))))))))
, 2(1(4(1(4(x1))))) -> 2(0(3(1(1(4(4(1(2(4(x1))))))))))
, 1(4(2(4(0(x1))))) -> 0(2(3(3(2(1(3(5(3(1(x1))))))))))
, 1(4(2(0(4(x1))))) -> 0(3(1(1(5(5(0(3(0(3(x1))))))))))
, 0(5(5(1(5(x1))))) -> 3(5(1(2(1(0(1(1(0(2(x1))))))))))
, 0(4(2(5(0(x1))))) -> 0(3(5(4(1(1(0(2(0(3(x1))))))))))
, 4(0(5(2(x1)))) -> 4(1(3(2(3(1(2(4(3(1(x1))))))))))
, 1(5(1(0(x1)))) -> 3(4(0(3(1(3(3(2(2(0(x1))))))))))
, 0(4(2(1(x1)))) -> 0(2(0(1(0(3(1(1(0(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:
{ 1_0(1) -> 1
, 1_1(1) -> 27
, 1_1(5) -> 4
, 1_1(6) -> 5
, 1_1(8) -> 7
, 1_1(10) -> 74
, 1_1(11) -> 27
, 1_1(15) -> 14
, 1_1(17) -> 16
, 1_1(19) -> 50
, 1_1(20) -> 2
, 1_1(21) -> 20
, 1_1(22) -> 21
, 1_1(26) -> 25
, 1_1(27) -> 26
, 1_1(34) -> 362
, 1_1(35) -> 27
, 1_1(36) -> 27
, 1_1(37) -> 27
, 1_1(43) -> 149
, 1_1(44) -> 27
, 1_1(49) -> 48
, 1_1(51) -> 35
, 1_1(55) -> 54
, 1_1(58) -> 156
, 1_1(59) -> 27
, 1_1(60) -> 59
, 1_1(67) -> 27
, 1_1(68) -> 27
, 1_1(71) -> 70
, 1_1(72) -> 71
, 1_1(74) -> 278
, 1_1(76) -> 27
, 1_1(79) -> 78
, 1_1(82) -> 67
, 1_1(83) -> 82
, 1_1(87) -> 27
, 1_1(95) -> 94
, 1_1(97) -> 96
, 1_1(98) -> 257
, 1_1(101) -> 27
, 1_1(104) -> 220
, 1_1(105) -> 104
, 1_1(107) -> 106
, 1_1(110) -> 109
, 1_1(115) -> 211
, 1_1(117) -> 116
, 1_1(118) -> 28
, 1_1(119) -> 118
, 1_1(123) -> 1
, 1_1(123) -> 27
, 1_1(123) -> 58
, 1_1(123) -> 92
, 1_1(123) -> 149
, 1_1(123) -> 216
, 1_1(126) -> 125
, 1_1(127) -> 126
, 1_1(130) -> 129
, 1_1(143) -> 123
, 1_1(149) -> 148
, 1_1(151) -> 150
, 1_1(159) -> 158
, 1_1(164) -> 163
, 1_1(166) -> 5
, 1_1(169) -> 168
, 1_1(172) -> 171
, 1_1(175) -> 174
, 1_1(176) -> 175
, 1_1(179) -> 309
, 1_1(189) -> 11
, 1_1(201) -> 200
, 1_1(206) -> 29
, 1_1(211) -> 210
, 1_1(213) -> 212
, 1_1(214) -> 213
, 1_1(219) -> 218
, 1_1(221) -> 220
, 1_1(222) -> 221
, 1_1(242) -> 241
, 1_1(244) -> 243
, 1_1(254) -> 253
, 1_1(255) -> 254
, 1_1(257) -> 256
, 1_1(288) -> 27
, 1_1(290) -> 289
, 1_1(291) -> 290
, 1_1(294) -> 293
, 1_1(299) -> 298
, 1_1(300) -> 12
, 1_1(301) -> 300
, 1_1(305) -> 136
, 1_1(307) -> 306
, 1_1(309) -> 308
, 1_1(311) -> 310
, 1_1(312) -> 311
, 1_1(326) -> 325
, 1_1(339) -> 338
, 1_1(359) -> 358
, 1_1(362) -> 361
, 1_2(36) -> 336
, 1_2(223) -> 92
, 1_2(226) -> 225
, 1_2(231) -> 230
, 1_2(286) -> 285
, 1_2(287) -> 286
, 1_2(318) -> 317
, 1_2(319) -> 318
, 1_2(329) -> 328
, 1_2(333) -> 332
, 1_2(344) -> 343
, 1_2(353) -> 352
, 1_2(365) -> 364
, 1_2(368) -> 367
, 1_2(369) -> 368
, 1_2(412) -> 411
, 1_2(414) -> 413
, 2_0(1) -> 1
, 2_1(1) -> 19
, 2_1(2) -> 19
, 2_1(10) -> 56
, 2_1(11) -> 19
, 2_1(19) -> 98
, 2_1(29) -> 28
, 2_1(31) -> 30
, 2_1(34) -> 313
, 2_1(35) -> 19
, 2_1(36) -> 35
, 2_1(43) -> 294
, 2_1(44) -> 19
, 2_1(46) -> 45
, 2_1(50) -> 49
, 2_1(52) -> 51
, 2_1(55) -> 202
, 2_1(57) -> 56
, 2_1(58) -> 99
, 2_1(59) -> 19
, 2_1(62) -> 61
, 2_1(64) -> 63
, 2_1(65) -> 64
, 2_1(67) -> 1
, 2_1(67) -> 19
, 2_1(67) -> 98
, 2_1(67) -> 132
, 2_1(67) -> 133
, 2_1(67) -> 294
, 2_1(75) -> 67
, 2_1(99) -> 98
, 2_1(100) -> 59
, 2_1(101) -> 100
, 2_1(107) -> 133
, 2_1(108) -> 83
, 2_1(114) -> 113
, 2_1(116) -> 115
, 2_1(120) -> 119
, 2_1(122) -> 121
, 2_1(123) -> 19
, 2_1(129) -> 19
, 2_1(131) -> 130
, 2_1(133) -> 132
, 2_1(134) -> 133
, 2_1(143) -> 19
, 2_1(147) -> 146
, 2_1(150) -> 19
, 2_1(153) -> 152
, 2_1(158) -> 157
, 2_1(160) -> 159
, 2_1(170) -> 169
, 2_1(177) -> 176
, 2_1(182) -> 181
, 2_1(184) -> 183
, 2_1(191) -> 190
, 2_1(196) -> 195
, 2_1(198) -> 197
, 2_1(199) -> 205
, 2_1(208) -> 207
, 2_1(209) -> 208
, 2_1(212) -> 60
, 2_1(215) -> 214
, 2_1(234) -> 233
, 2_1(241) -> 19
, 2_1(243) -> 242
, 2_1(256) -> 255
, 2_1(274) -> 19
, 2_1(295) -> 11
, 2_1(298) -> 297
, 2_1(306) -> 305
, 2_1(324) -> 323
, 2_1(327) -> 326
, 2_1(349) -> 19
, 2_2(163) -> 231
, 2_2(229) -> 228
, 2_2(279) -> 98
, 2_2(279) -> 132
, 2_2(321) -> 320
, 2_2(331) -> 330
, 2_2(334) -> 333
, 2_2(347) -> 346
, 2_2(348) -> 347
, 2_2(356) -> 355
, 2_2(357) -> 356
, 2_2(363) -> 314
, 2_2(407) -> 406
, 2_2(408) -> 407
, 4_0(1) -> 1
, 4_1(1) -> 43
, 4_1(2) -> 43
, 4_1(3) -> 2
, 4_1(19) -> 18
, 4_1(26) -> 111
, 4_1(27) -> 135
, 4_1(33) -> 32
, 4_1(34) -> 33
, 4_1(35) -> 1
, 4_1(35) -> 43
, 4_1(35) -> 58
, 4_1(35) -> 111
, 4_1(35) -> 135
, 4_1(36) -> 43
, 4_1(40) -> 39
, 4_1(42) -> 122
, 4_1(47) -> 46
, 4_1(50) -> 184
, 4_1(53) -> 52
, 4_1(63) -> 62
, 4_1(67) -> 43
, 4_1(68) -> 67
, 4_1(73) -> 72
, 4_1(76) -> 75
, 4_1(77) -> 76
, 4_1(80) -> 86
, 4_1(85) -> 84
, 4_1(94) -> 93
, 4_1(103) -> 102
, 4_1(105) -> 327
, 4_1(109) -> 108
, 4_1(111) -> 110
, 4_1(128) -> 127
, 4_1(135) -> 209
, 4_1(146) -> 145
, 4_1(157) -> 144
, 4_1(161) -> 43
, 4_1(168) -> 167
, 4_1(184) -> 291
, 4_1(193) -> 192
, 4_1(195) -> 59
, 4_1(204) -> 203
, 4_1(210) -> 162
, 4_1(217) -> 123
, 4_1(238) -> 237
, 4_1(241) -> 35
, 4_1(253) -> 129
, 4_1(274) -> 68
, 4_1(275) -> 274
, 4_1(276) -> 275
, 4_1(292) -> 291
, 4_1(293) -> 292
, 4_1(310) -> 13
, 4_2(224) -> 223
, 4_2(230) -> 229
, 4_2(280) -> 279
, 4_2(281) -> 280
, 4_2(282) -> 281
, 4_2(283) -> 282
, 4_2(317) -> 316
, 4_2(328) -> 33
, 4_2(335) -> 334
, 4_2(341) -> 340
, 4_2(350) -> 349
, 4_2(410) -> 409
, 0_0(1) -> 1
, 0_1(1) -> 58
, 0_1(4) -> 3
, 0_1(10) -> 34
, 0_1(11) -> 1
, 0_1(11) -> 18
, 0_1(11) -> 27
, 0_1(11) -> 43
, 0_1(11) -> 58
, 0_1(11) -> 92
, 0_1(11) -> 106
, 0_1(11) -> 107
, 0_1(11) -> 149
, 0_1(11) -> 216
, 0_1(18) -> 92
, 0_1(19) -> 179
, 0_1(24) -> 23
, 0_1(27) -> 66
, 0_1(28) -> 11
, 0_1(30) -> 29
, 0_1(34) -> 238
, 0_1(37) -> 36
, 0_1(38) -> 37
, 0_1(42) -> 41
, 0_1(44) -> 35
, 0_1(45) -> 44
, 0_1(58) -> 215
, 0_1(66) -> 65
, 0_1(70) -> 69
, 0_1(81) -> 80
, 0_1(88) -> 87
, 0_1(92) -> 91
, 0_1(121) -> 120
, 0_1(124) -> 123
, 0_1(132) -> 131
, 0_1(135) -> 216
, 0_1(138) -> 137
, 0_1(140) -> 139
, 0_1(142) -> 160
, 0_1(152) -> 151
, 0_1(154) -> 153
, 0_1(156) -> 155
, 0_1(163) -> 162
, 0_1(166) -> 165
, 0_1(173) -> 59
, 0_1(174) -> 173
, 0_1(179) -> 178
, 0_1(181) -> 52
, 0_1(183) -> 182
, 0_1(190) -> 189
, 0_1(192) -> 191
, 0_1(194) -> 193
, 0_1(199) -> 198
, 0_1(200) -> 136
, 0_1(205) -> 204
, 0_1(207) -> 206
, 0_1(216) -> 215
, 0_1(218) -> 217
, 0_1(245) -> 244
, 0_1(277) -> 276
, 0_1(288) -> 67
, 0_1(304) -> 303
, 0_1(308) -> 307
, 0_1(313) -> 312
, 0_1(337) -> 195
, 0_1(358) -> 295
, 0_1(360) -> 359
, 0_2(124) -> 348
, 0_2(152) -> 357
, 0_2(225) -> 224
, 0_2(284) -> 283
, 0_2(314) -> 92
, 0_2(320) -> 319
, 0_2(322) -> 321
, 0_2(342) -> 341
, 0_2(351) -> 350
, 0_2(364) -> 363
, 0_2(366) -> 365
, 0_2(370) -> 369
, 3_0(1) -> 1
, 3_1(1) -> 10
, 3_1(5) -> 13
, 3_1(7) -> 6
, 3_1(9) -> 8
, 3_1(10) -> 81
, 3_1(11) -> 10
, 3_1(12) -> 11
, 3_1(14) -> 13
, 3_1(16) -> 15
, 3_1(18) -> 17
, 3_1(19) -> 117
, 3_1(23) -> 22
, 3_1(27) -> 105
, 3_1(34) -> 304
, 3_1(35) -> 10
, 3_1(36) -> 10
, 3_1(37) -> 10
, 3_1(41) -> 40
, 3_1(42) -> 194
, 3_1(43) -> 42
, 3_1(44) -> 10
, 3_1(51) -> 10
, 3_1(54) -> 53
, 3_1(56) -> 55
, 3_1(58) -> 57
, 3_1(59) -> 1
, 3_1(59) -> 10
, 3_1(59) -> 19
, 3_1(59) -> 27
, 3_1(59) -> 42
, 3_1(59) -> 56
, 3_1(59) -> 58
, 3_1(59) -> 81
, 3_1(59) -> 98
, 3_1(59) -> 99
, 3_1(59) -> 106
, 3_1(59) -> 132
, 3_1(59) -> 133
, 3_1(59) -> 215
, 3_1(61) -> 60
, 3_1(66) -> 154
, 3_1(67) -> 10
, 3_1(74) -> 166
, 3_1(78) -> 77
, 3_1(80) -> 79
, 3_1(82) -> 10
, 3_1(87) -> 67
, 3_1(89) -> 88
, 3_1(90) -> 89
, 3_1(91) -> 90
, 3_1(93) -> 59
, 3_1(97) -> 339
, 3_1(98) -> 97
, 3_1(104) -> 103
, 3_1(106) -> 105
, 3_1(115) -> 114
, 3_1(123) -> 10
, 3_1(125) -> 124
, 3_1(128) -> 299
, 3_1(129) -> 35
, 3_1(137) -> 136
, 3_1(139) -> 138
, 3_1(144) -> 143
, 3_1(145) -> 144
, 3_1(148) -> 147
, 3_1(149) -> 246
, 3_1(155) -> 154
, 3_1(156) -> 222
, 3_1(167) -> 123
, 3_1(171) -> 170
, 3_1(178) -> 177
, 3_1(183) -> 220
, 3_1(194) -> 199
, 3_1(197) -> 196
, 3_1(202) -> 201
, 3_1(203) -> 93
, 3_1(215) -> 90
, 3_1(220) -> 219
, 3_1(233) -> 52
, 3_1(237) -> 234
, 3_1(242) -> 10
, 3_1(246) -> 245
, 3_1(278) -> 277
, 3_1(288) -> 10
, 3_1(289) -> 288
, 3_1(296) -> 295
, 3_1(297) -> 296
, 3_1(323) -> 51
, 3_1(325) -> 324
, 3_1(338) -> 337
, 3_1(349) -> 2
, 3_1(361) -> 360
, 3_2(20) -> 370
, 3_2(37) -> 287
, 3_2(44) -> 322
, 3_2(51) -> 370
, 3_2(60) -> 370
, 3_2(82) -> 370
, 3_2(123) -> 370
, 3_2(130) -> 370
, 3_2(143) -> 370
, 3_2(151) -> 370
, 3_2(189) -> 370
, 3_2(200) -> 322
, 3_2(227) -> 226
, 3_2(228) -> 227
, 3_2(242) -> 370
, 3_2(285) -> 284
, 3_2(288) -> 287
, 3_2(315) -> 314
, 3_2(330) -> 329
, 3_2(332) -> 331
, 3_2(336) -> 335
, 3_2(340) -> 106
, 3_2(343) -> 342
, 3_2(345) -> 344
, 3_2(346) -> 345
, 3_2(349) -> 1
, 3_2(349) -> 27
, 3_2(349) -> 58
, 3_2(349) -> 92
, 3_2(349) -> 149
, 3_2(349) -> 216
, 3_2(352) -> 351
, 3_2(354) -> 353
, 3_2(355) -> 354
, 3_2(367) -> 366
, 3_2(406) -> 132
, 3_2(411) -> 410
, 3_2(413) -> 412
, 5_0(1) -> 1
, 5_1(1) -> 107
, 5_1(2) -> 1
, 5_1(2) -> 107
, 5_1(10) -> 9
, 5_1(13) -> 12
, 5_1(19) -> 172
, 5_1(25) -> 24
, 5_1(27) -> 142
, 5_1(32) -> 31
, 5_1(35) -> 1
, 5_1(35) -> 10
, 5_1(35) -> 107
, 5_1(35) -> 142
, 5_1(39) -> 38
, 5_1(48) -> 47
, 5_1(69) -> 68
, 5_1(74) -> 73
, 5_1(84) -> 83
, 5_1(86) -> 85
, 5_1(96) -> 95
, 5_1(98) -> 172
, 5_1(102) -> 101
, 5_1(105) -> 128
, 5_1(112) -> 60
, 5_1(113) -> 112
, 5_1(135) -> 134
, 5_1(136) -> 59
, 5_1(141) -> 140
, 5_1(142) -> 141
, 5_1(150) -> 123
, 5_1(161) -> 11
, 5_1(162) -> 161
, 5_1(165) -> 164
, 5_1(302) -> 301
, 5_1(303) -> 302
, 5_2(102) -> 414
, 5_2(316) -> 315
, 5_2(409) -> 408}
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(4(5(5(2(5(3(x1))))))) -> 5(4(0(1(1(3(1(3(5(3(x1))))))))))
, 5(4(2(2(2(4(2(x1))))))) -> 0(3(5(3(1(3(1(3(4(2(x1))))))))))
, 5(0(4(0(2(2(4(x1))))))) -> 5(1(1(1(3(0(5(1(1(1(x1))))))))))
, 4(5(2(5(4(4(1(x1))))))) -> 0(0(2(0(2(5(4(4(0(3(x1))))))))))
, 4(5(0(5(2(2(5(x1))))))) -> 4(2(0(0(5(4(3(0(3(4(x1))))))))))
, 4(1(4(0(1(5(3(x1))))))) -> 4(0(0(2(4(5(1(2(1(2(x1))))))))))
, 4(1(1(4(2(1(0(x1))))))) -> 4(1(2(4(3(1(3(2(3(0(x1))))))))))
, 3(3(5(2(2(5(0(x1))))))) -> 3(1(3(2(4(2(2(0(0(1(x1))))))))))
, 2(5(2(3(5(2(1(x1))))))) -> 2(4(5(0(1(1(4(5(1(3(x1))))))))))
, 2(5(1(5(3(5(2(x1))))))) -> 2(2(4(4(3(1(3(0(3(3(x1))))))))))
, 2(5(1(4(1(5(2(x1))))))) -> 2(1(1(5(4(5(4(0(3(3(x1))))))))))
, 2(4(5(1(1(5(2(x1))))))) -> 2(3(0(3(3(3(0(0(4(2(x1))))))))))
, 2(3(5(5(4(0(0(x1))))))) -> 3(3(4(1(5(1(3(2(2(0(x1))))))))))
, 2(2(5(3(2(2(5(x1))))))) -> 3(2(2(5(4(3(1(3(1(5(x1))))))))))
, 2(2(0(4(2(4(2(x1))))))) -> 2(1(1(2(4(1(4(4(1(1(x1))))))))))
, 2(0(4(4(2(0(4(x1))))))) -> 3(1(5(5(2(3(2(1(3(2(x1))))))))))
, 1(5(0(2(2(0(4(x1))))))) -> 0(0(1(1(2(0(2(4(3(4(x1))))))))))
, 1(4(4(1(4(0(4(x1))))))) -> 1(0(3(1(1(4(5(3(1(5(x1))))))))))
, 0(5(5(3(0(4(1(x1))))))) -> 4(3(1(2(0(2(2(5(4(1(x1))))))))))
, 0(5(2(4(1(5(0(x1))))))) -> 3(5(3(0(3(0(5(5(5(1(x1))))))))))
, 0(4(5(0(4(0(5(x1))))))) -> 1(1(3(3(4(2(3(1(1(4(x1))))))))))
, 0(4(2(4(2(3(0(x1))))))) -> 1(5(1(0(2(0(3(0(1(0(x1))))))))))
, 0(4(1(4(1(5(0(x1))))))) -> 1(1(3(4(2(1(2(0(5(1(x1))))))))))
, 0(4(1(0(0(5(0(x1))))))) -> 0(5(5(0(1(5(0(3(1(3(x1))))))))))
, 0(4(0(1(4(5(2(x1))))))) -> 1(3(4(1(2(3(1(5(2(2(x1))))))))))
, 0(0(4(5(2(4(4(x1))))))) -> 3(0(0(1(1(2(3(0(0(2(x1))))))))))
, 5(1(1(5(0(4(x1)))))) -> 5(1(2(0(2(0(2(4(1(2(x1))))))))))
, 4(2(5(4(0(5(x1)))))) -> 0(1(0(2(0(4(0(3(3(4(x1))))))))))
, 3(5(2(0(5(2(x1)))))) -> 3(4(2(3(2(0(3(3(3(4(x1))))))))))
, 3(4(5(2(2(0(x1)))))) -> 3(5(0(1(3(2(3(2(3(0(x1))))))))))
, 2(5(0(5(2(5(x1)))))) -> 3(3(3(4(0(2(3(3(3(4(x1))))))))))
, 1(5(0(5(2(0(x1)))))) -> 0(0(2(1(0(2(2(4(4(1(x1))))))))))
, 0(5(4(4(1(1(x1)))))) -> 0(5(5(4(1(1(2(1(3(2(x1))))))))))
, 0(5(2(0(4(1(x1)))))) -> 3(1(2(1(1(2(0(0(4(1(x1))))))))))
, 0(4(5(1(0(0(x1)))))) -> 1(4(0(1(3(1(1(3(1(0(x1))))))))))
, 0(4(2(5(5(0(x1)))))) -> 1(4(0(1(3(3(2(4(1(2(x1))))))))))
, 5(4(2(5(0(x1))))) -> 5(1(2(3(2(3(4(0(0(3(x1))))))))))
, 4(4(4(5(2(x1))))) -> 4(4(1(2(1(0(3(3(1(4(x1))))))))))
, 3(5(2(5(3(x1))))) -> 5(3(4(1(1(2(1(1(2(2(x1))))))))))
, 2(2(5(2(0(x1))))) -> 2(4(4(4(4(0(3(1(1(3(x1))))))))))
, 2(1(4(1(4(x1))))) -> 2(0(3(1(1(4(4(1(2(4(x1))))))))))
, 1(4(2(4(0(x1))))) -> 0(2(3(3(2(1(3(5(3(1(x1))))))))))
, 1(4(2(0(4(x1))))) -> 0(3(1(1(5(5(0(3(0(3(x1))))))))))
, 0(5(5(1(5(x1))))) -> 3(5(1(2(1(0(1(1(0(2(x1))))))))))
, 0(4(2(5(0(x1))))) -> 0(3(5(4(1(1(0(2(0(3(x1))))))))))
, 4(0(5(2(x1)))) -> 4(1(3(2(3(1(2(4(3(1(x1))))))))))
, 1(5(1(0(x1)))) -> 3(4(0(3(1(3(3(2(2(0(x1))))))))))
, 0(4(2(1(x1)))) -> 0(2(0(1(0(3(1(1(0(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:
{ 5(4(5(5(2(5(3(x1))))))) -> 5(4(0(1(1(3(1(3(5(3(x1))))))))))
, 5(4(2(2(2(4(2(x1))))))) -> 0(3(5(3(1(3(1(3(4(2(x1))))))))))
, 5(0(4(0(2(2(4(x1))))))) -> 5(1(1(1(3(0(5(1(1(1(x1))))))))))
, 4(5(2(5(4(4(1(x1))))))) -> 0(0(2(0(2(5(4(4(0(3(x1))))))))))
, 4(5(0(5(2(2(5(x1))))))) -> 4(2(0(0(5(4(3(0(3(4(x1))))))))))
, 4(1(4(0(1(5(3(x1))))))) -> 4(0(0(2(4(5(1(2(1(2(x1))))))))))
, 4(1(1(4(2(1(0(x1))))))) -> 4(1(2(4(3(1(3(2(3(0(x1))))))))))
, 3(3(5(2(2(5(0(x1))))))) -> 3(1(3(2(4(2(2(0(0(1(x1))))))))))
, 2(5(2(3(5(2(1(x1))))))) -> 2(4(5(0(1(1(4(5(1(3(x1))))))))))
, 2(5(1(5(3(5(2(x1))))))) -> 2(2(4(4(3(1(3(0(3(3(x1))))))))))
, 2(5(1(4(1(5(2(x1))))))) -> 2(1(1(5(4(5(4(0(3(3(x1))))))))))
, 2(4(5(1(1(5(2(x1))))))) -> 2(3(0(3(3(3(0(0(4(2(x1))))))))))
, 2(3(5(5(4(0(0(x1))))))) -> 3(3(4(1(5(1(3(2(2(0(x1))))))))))
, 2(2(5(3(2(2(5(x1))))))) -> 3(2(2(5(4(3(1(3(1(5(x1))))))))))
, 2(2(0(4(2(4(2(x1))))))) -> 2(1(1(2(4(1(4(4(1(1(x1))))))))))
, 2(0(4(4(2(0(4(x1))))))) -> 3(1(5(5(2(3(2(1(3(2(x1))))))))))
, 1(5(0(2(2(0(4(x1))))))) -> 0(0(1(1(2(0(2(4(3(4(x1))))))))))
, 1(4(4(1(4(0(4(x1))))))) -> 1(0(3(1(1(4(5(3(1(5(x1))))))))))
, 0(5(5(3(0(4(1(x1))))))) -> 4(3(1(2(0(2(2(5(4(1(x1))))))))))
, 0(5(2(4(1(5(0(x1))))))) -> 3(5(3(0(3(0(5(5(5(1(x1))))))))))
, 0(4(5(0(4(0(5(x1))))))) -> 1(1(3(3(4(2(3(1(1(4(x1))))))))))
, 0(4(2(4(2(3(0(x1))))))) -> 1(5(1(0(2(0(3(0(1(0(x1))))))))))
, 0(4(1(4(1(5(0(x1))))))) -> 1(1(3(4(2(1(2(0(5(1(x1))))))))))
, 0(4(1(0(0(5(0(x1))))))) -> 0(5(5(0(1(5(0(3(1(3(x1))))))))))
, 0(4(0(1(4(5(2(x1))))))) -> 1(3(4(1(2(3(1(5(2(2(x1))))))))))
, 0(0(4(5(2(4(4(x1))))))) -> 3(0(0(1(1(2(3(0(0(2(x1))))))))))
, 5(1(1(5(0(4(x1)))))) -> 5(1(2(0(2(0(2(4(1(2(x1))))))))))
, 4(2(5(4(0(5(x1)))))) -> 0(1(0(2(0(4(0(3(3(4(x1))))))))))
, 3(5(2(0(5(2(x1)))))) -> 3(4(2(3(2(0(3(3(3(4(x1))))))))))
, 3(4(5(2(2(0(x1)))))) -> 3(5(0(1(3(2(3(2(3(0(x1))))))))))
, 2(5(0(5(2(5(x1)))))) -> 3(3(3(4(0(2(3(3(3(4(x1))))))))))
, 1(5(0(5(2(0(x1)))))) -> 0(0(2(1(0(2(2(4(4(1(x1))))))))))
, 0(5(4(4(1(1(x1)))))) -> 0(5(5(4(1(1(2(1(3(2(x1))))))))))
, 0(5(2(0(4(1(x1)))))) -> 3(1(2(1(1(2(0(0(4(1(x1))))))))))
, 0(4(5(1(0(0(x1)))))) -> 1(4(0(1(3(1(1(3(1(0(x1))))))))))
, 0(4(2(5(5(0(x1)))))) -> 1(4(0(1(3(3(2(4(1(2(x1))))))))))
, 5(4(2(5(0(x1))))) -> 5(1(2(3(2(3(4(0(0(3(x1))))))))))
, 4(4(4(5(2(x1))))) -> 4(4(1(2(1(0(3(3(1(4(x1))))))))))
, 3(5(2(5(3(x1))))) -> 5(3(4(1(1(2(1(1(2(2(x1))))))))))
, 2(2(5(2(0(x1))))) -> 2(4(4(4(4(0(3(1(1(3(x1))))))))))
, 2(1(4(1(4(x1))))) -> 2(0(3(1(1(4(4(1(2(4(x1))))))))))
, 1(4(2(4(0(x1))))) -> 0(2(3(3(2(1(3(5(3(1(x1))))))))))
, 1(4(2(0(4(x1))))) -> 0(3(1(1(5(5(0(3(0(3(x1))))))))))
, 0(5(5(1(5(x1))))) -> 3(5(1(2(1(0(1(1(0(2(x1))))))))))
, 0(4(2(5(0(x1))))) -> 0(3(5(4(1(1(0(2(0(3(x1))))))))))
, 4(0(5(2(x1)))) -> 4(1(3(2(3(1(2(4(3(1(x1))))))))))
, 1(5(1(0(x1)))) -> 3(4(0(3(1(3(3(2(2(0(x1))))))))))
, 0(4(2(1(x1)))) -> 0(2(0(1(0(3(1(1(0(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:
{ 5(4(5(5(2(5(3(x1))))))) -> 5(4(0(1(1(3(1(3(5(3(x1))))))))))
, 5(4(2(2(2(4(2(x1))))))) -> 0(3(5(3(1(3(1(3(4(2(x1))))))))))
, 5(0(4(0(2(2(4(x1))))))) -> 5(1(1(1(3(0(5(1(1(1(x1))))))))))
, 4(5(2(5(4(4(1(x1))))))) -> 0(0(2(0(2(5(4(4(0(3(x1))))))))))
, 4(5(0(5(2(2(5(x1))))))) -> 4(2(0(0(5(4(3(0(3(4(x1))))))))))
, 4(1(4(0(1(5(3(x1))))))) -> 4(0(0(2(4(5(1(2(1(2(x1))))))))))
, 4(1(1(4(2(1(0(x1))))))) -> 4(1(2(4(3(1(3(2(3(0(x1))))))))))
, 3(3(5(2(2(5(0(x1))))))) -> 3(1(3(2(4(2(2(0(0(1(x1))))))))))
, 2(5(2(3(5(2(1(x1))))))) -> 2(4(5(0(1(1(4(5(1(3(x1))))))))))
, 2(5(1(5(3(5(2(x1))))))) -> 2(2(4(4(3(1(3(0(3(3(x1))))))))))
, 2(5(1(4(1(5(2(x1))))))) -> 2(1(1(5(4(5(4(0(3(3(x1))))))))))
, 2(4(5(1(1(5(2(x1))))))) -> 2(3(0(3(3(3(0(0(4(2(x1))))))))))
, 2(3(5(5(4(0(0(x1))))))) -> 3(3(4(1(5(1(3(2(2(0(x1))))))))))
, 2(2(5(3(2(2(5(x1))))))) -> 3(2(2(5(4(3(1(3(1(5(x1))))))))))
, 2(2(0(4(2(4(2(x1))))))) -> 2(1(1(2(4(1(4(4(1(1(x1))))))))))
, 2(0(4(4(2(0(4(x1))))))) -> 3(1(5(5(2(3(2(1(3(2(x1))))))))))
, 1(5(0(2(2(0(4(x1))))))) -> 0(0(1(1(2(0(2(4(3(4(x1))))))))))
, 1(4(4(1(4(0(4(x1))))))) -> 1(0(3(1(1(4(5(3(1(5(x1))))))))))
, 0(5(5(3(0(4(1(x1))))))) -> 4(3(1(2(0(2(2(5(4(1(x1))))))))))
, 0(5(2(4(1(5(0(x1))))))) -> 3(5(3(0(3(0(5(5(5(1(x1))))))))))
, 0(4(5(0(4(0(5(x1))))))) -> 1(1(3(3(4(2(3(1(1(4(x1))))))))))
, 0(4(2(4(2(3(0(x1))))))) -> 1(5(1(0(2(0(3(0(1(0(x1))))))))))
, 0(4(1(4(1(5(0(x1))))))) -> 1(1(3(4(2(1(2(0(5(1(x1))))))))))
, 0(4(1(0(0(5(0(x1))))))) -> 0(5(5(0(1(5(0(3(1(3(x1))))))))))
, 0(4(0(1(4(5(2(x1))))))) -> 1(3(4(1(2(3(1(5(2(2(x1))))))))))
, 0(0(4(5(2(4(4(x1))))))) -> 3(0(0(1(1(2(3(0(0(2(x1))))))))))
, 5(1(1(5(0(4(x1)))))) -> 5(1(2(0(2(0(2(4(1(2(x1))))))))))
, 4(2(5(4(0(5(x1)))))) -> 0(1(0(2(0(4(0(3(3(4(x1))))))))))
, 3(5(2(0(5(2(x1)))))) -> 3(4(2(3(2(0(3(3(3(4(x1))))))))))
, 3(4(5(2(2(0(x1)))))) -> 3(5(0(1(3(2(3(2(3(0(x1))))))))))
, 2(5(0(5(2(5(x1)))))) -> 3(3(3(4(0(2(3(3(3(4(x1))))))))))
, 1(5(0(5(2(0(x1)))))) -> 0(0(2(1(0(2(2(4(4(1(x1))))))))))
, 0(5(4(4(1(1(x1)))))) -> 0(5(5(4(1(1(2(1(3(2(x1))))))))))
, 0(5(2(0(4(1(x1)))))) -> 3(1(2(1(1(2(0(0(4(1(x1))))))))))
, 0(4(5(1(0(0(x1)))))) -> 1(4(0(1(3(1(1(3(1(0(x1))))))))))
, 0(4(2(5(5(0(x1)))))) -> 1(4(0(1(3(3(2(4(1(2(x1))))))))))
, 5(4(2(5(0(x1))))) -> 5(1(2(3(2(3(4(0(0(3(x1))))))))))
, 4(4(4(5(2(x1))))) -> 4(4(1(2(1(0(3(3(1(4(x1))))))))))
, 3(5(2(5(3(x1))))) -> 5(3(4(1(1(2(1(1(2(2(x1))))))))))
, 2(2(5(2(0(x1))))) -> 2(4(4(4(4(0(3(1(1(3(x1))))))))))
, 2(1(4(1(4(x1))))) -> 2(0(3(1(1(4(4(1(2(4(x1))))))))))
, 1(4(2(4(0(x1))))) -> 0(2(3(3(2(1(3(5(3(1(x1))))))))))
, 1(4(2(0(4(x1))))) -> 0(3(1(1(5(5(0(3(0(3(x1))))))))))
, 0(5(5(1(5(x1))))) -> 3(5(1(2(1(0(1(1(0(2(x1))))))))))
, 0(4(2(5(0(x1))))) -> 0(3(5(4(1(1(0(2(0(3(x1))))))))))
, 4(0(5(2(x1)))) -> 4(1(3(2(3(1(2(4(3(1(x1))))))))))
, 1(5(1(0(x1)))) -> 3(4(0(3(1(3(3(2(2(0(x1))))))))))
, 0(4(2(1(x1)))) -> 0(2(0(1(0(3(1(1(0(3(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI2
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 5(4(5(5(2(5(3(x1))))))) -> 5(4(0(1(1(3(1(3(5(3(x1))))))))))
, 5(4(2(2(2(4(2(x1))))))) -> 0(3(5(3(1(3(1(3(4(2(x1))))))))))
, 5(0(4(0(2(2(4(x1))))))) -> 5(1(1(1(3(0(5(1(1(1(x1))))))))))
, 4(5(2(5(4(4(1(x1))))))) -> 0(0(2(0(2(5(4(4(0(3(x1))))))))))
, 4(5(0(5(2(2(5(x1))))))) -> 4(2(0(0(5(4(3(0(3(4(x1))))))))))
, 4(1(4(0(1(5(3(x1))))))) -> 4(0(0(2(4(5(1(2(1(2(x1))))))))))
, 4(1(1(4(2(1(0(x1))))))) -> 4(1(2(4(3(1(3(2(3(0(x1))))))))))
, 3(3(5(2(2(5(0(x1))))))) -> 3(1(3(2(4(2(2(0(0(1(x1))))))))))
, 2(5(2(3(5(2(1(x1))))))) -> 2(4(5(0(1(1(4(5(1(3(x1))))))))))
, 2(5(1(5(3(5(2(x1))))))) -> 2(2(4(4(3(1(3(0(3(3(x1))))))))))
, 2(5(1(4(1(5(2(x1))))))) -> 2(1(1(5(4(5(4(0(3(3(x1))))))))))
, 2(4(5(1(1(5(2(x1))))))) -> 2(3(0(3(3(3(0(0(4(2(x1))))))))))
, 2(3(5(5(4(0(0(x1))))))) -> 3(3(4(1(5(1(3(2(2(0(x1))))))))))
, 2(2(5(3(2(2(5(x1))))))) -> 3(2(2(5(4(3(1(3(1(5(x1))))))))))
, 2(2(0(4(2(4(2(x1))))))) -> 2(1(1(2(4(1(4(4(1(1(x1))))))))))
, 2(0(4(4(2(0(4(x1))))))) -> 3(1(5(5(2(3(2(1(3(2(x1))))))))))
, 1(5(0(2(2(0(4(x1))))))) -> 0(0(1(1(2(0(2(4(3(4(x1))))))))))
, 1(4(4(1(4(0(4(x1))))))) -> 1(0(3(1(1(4(5(3(1(5(x1))))))))))
, 0(5(5(3(0(4(1(x1))))))) -> 4(3(1(2(0(2(2(5(4(1(x1))))))))))
, 0(5(2(4(1(5(0(x1))))))) -> 3(5(3(0(3(0(5(5(5(1(x1))))))))))
, 0(4(5(0(4(0(5(x1))))))) -> 1(1(3(3(4(2(3(1(1(4(x1))))))))))
, 0(4(2(4(2(3(0(x1))))))) -> 1(5(1(0(2(0(3(0(1(0(x1))))))))))
, 0(4(1(4(1(5(0(x1))))))) -> 1(1(3(4(2(1(2(0(5(1(x1))))))))))
, 0(4(1(0(0(5(0(x1))))))) -> 0(5(5(0(1(5(0(3(1(3(x1))))))))))
, 0(4(0(1(4(5(2(x1))))))) -> 1(3(4(1(2(3(1(5(2(2(x1))))))))))
, 0(0(4(5(2(4(4(x1))))))) -> 3(0(0(1(1(2(3(0(0(2(x1))))))))))
, 5(1(1(5(0(4(x1)))))) -> 5(1(2(0(2(0(2(4(1(2(x1))))))))))
, 4(2(5(4(0(5(x1)))))) -> 0(1(0(2(0(4(0(3(3(4(x1))))))))))
, 3(5(2(0(5(2(x1)))))) -> 3(4(2(3(2(0(3(3(3(4(x1))))))))))
, 3(4(5(2(2(0(x1)))))) -> 3(5(0(1(3(2(3(2(3(0(x1))))))))))
, 2(5(0(5(2(5(x1)))))) -> 3(3(3(4(0(2(3(3(3(4(x1))))))))))
, 1(5(0(5(2(0(x1)))))) -> 0(0(2(1(0(2(2(4(4(1(x1))))))))))
, 0(5(4(4(1(1(x1)))))) -> 0(5(5(4(1(1(2(1(3(2(x1))))))))))
, 0(5(2(0(4(1(x1)))))) -> 3(1(2(1(1(2(0(0(4(1(x1))))))))))
, 0(4(5(1(0(0(x1)))))) -> 1(4(0(1(3(1(1(3(1(0(x1))))))))))
, 0(4(2(5(5(0(x1)))))) -> 1(4(0(1(3(3(2(4(1(2(x1))))))))))
, 5(4(2(5(0(x1))))) -> 5(1(2(3(2(3(4(0(0(3(x1))))))))))
, 4(4(4(5(2(x1))))) -> 4(4(1(2(1(0(3(3(1(4(x1))))))))))
, 3(5(2(5(3(x1))))) -> 5(3(4(1(1(2(1(1(2(2(x1))))))))))
, 2(2(5(2(0(x1))))) -> 2(4(4(4(4(0(3(1(1(3(x1))))))))))
, 2(1(4(1(4(x1))))) -> 2(0(3(1(1(4(4(1(2(4(x1))))))))))
, 1(4(2(4(0(x1))))) -> 0(2(3(3(2(1(3(5(3(1(x1))))))))))
, 1(4(2(0(4(x1))))) -> 0(3(1(1(5(5(0(3(0(3(x1))))))))))
, 0(5(5(1(5(x1))))) -> 3(5(1(2(1(0(1(1(0(2(x1))))))))))
, 0(4(2(5(0(x1))))) -> 0(3(5(4(1(1(0(2(0(3(x1))))))))))
, 4(0(5(2(x1)))) -> 4(1(3(2(3(1(2(4(3(1(x1))))))))))
, 1(5(1(0(x1)))) -> 3(4(0(3(1(3(3(2(2(0(x1))))))))))
, 0(4(2(1(x1)))) -> 0(2(0(1(0(3(1(1(0(3(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..