Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(5(4(2(4(0(5(x1))))))) -> 3(4(5(5(2(4(3(0(1(0(x1))))))))))
, 5(5(3(0(4(3(0(x1))))))) -> 0(1(0(4(0(2(1(1(5(0(x1))))))))))
, 5(2(3(1(0(4(0(x1))))))) -> 0(2(5(3(4(0(3(5(1(0(x1))))))))))
, 4(1(2(4(2(2(5(x1))))))) -> 4(2(2(2(0(4(1(0(2(5(x1))))))))))
, 2(5(4(3(5(4(5(x1))))))) -> 2(0(0(0(2(3(4(5(5(1(x1))))))))))
, 2(5(4(0(5(5(4(x1))))))) -> 2(0(1(2(0(5(0(4(0(3(x1))))))))))
, 2(2(5(4(1(4(0(x1))))))) -> 3(1(5(2(3(2(3(2(1(4(x1))))))))))
, 2(2(2(5(4(5(5(x1))))))) -> 1(4(1(0(3(5(0(0(5(5(x1))))))))))
, 1(0(4(5(4(3(5(x1))))))) -> 1(2(4(4(3(0(5(3(2(0(x1))))))))))
, 0(4(5(2(5(4(2(x1))))))) -> 1(4(3(1(1(1(4(2(0(1(x1))))))))))
, 0(4(3(0(2(1(5(x1))))))) -> 0(2(0(3(1(5(4(4(2(0(x1))))))))))
, 0(4(2(5(2(2(5(x1))))))) -> 1(4(2(5(3(0(3(1(2(5(x1))))))))))
, 0(4(2(4(2(4(2(x1))))))) -> 1(4(5(1(2(3(1(2(0(1(x1))))))))))
, 0(4(0(3(5(3(0(x1))))))) -> 5(1(2(4(5(3(4(2(5(0(x1))))))))))
, 5(4(2(2(3(0(x1)))))) -> 0(1(1(4(2(1(1(5(1(0(x1))))))))))
, 5(4(2(0(4(0(x1)))))) -> 0(1(1(1(1(4(0(2(5(1(x1))))))))))
, 5(3(0(4(2(1(x1)))))) -> 5(2(1(0(2(5(4(4(1(1(x1))))))))))
, 5(2(5(4(1(0(x1)))))) -> 5(1(1(5(2(1(0(1(3(2(x1))))))))))
, 5(2(5(2(2(4(x1)))))) -> 5(5(0(2(5(1(0(5(2(4(x1))))))))))
, 5(0(5(4(0(5(x1)))))) -> 0(0(4(0(4(0(3(1(3(2(x1))))))))))
, 4(2(4(1(2(5(x1)))))) -> 3(4(0(5(0(5(1(4(1(5(x1))))))))))
, 3(0(4(5(4(2(x1)))))) -> 1(2(3(3(2(0(3(3(4(0(x1))))))))))
, 2(4(5(5(4(0(x1)))))) -> 0(2(3(1(3(4(4(4(0(5(x1))))))))))
, 2(4(0(5(5(4(x1)))))) -> 0(3(1(1(2(0(1(3(4(3(x1))))))))))
, 2(2(5(4(1(2(x1)))))) -> 3(3(0(0(5(2(4(5(1(2(x1))))))))))
, 2(0(4(5(2(1(x1)))))) -> 3(0(3(3(2(5(0(4(3(4(x1))))))))))
, 1(0(4(3(5(2(x1)))))) -> 1(1(5(3(3(4(4(2(2(2(x1))))))))))
, 0(1(3(5(4(0(x1)))))) -> 5(0(3(4(0(3(2(5(0(2(x1))))))))))
, 5(3(5(3(5(x1))))) -> 0(5(5(2(4(1(3(2(5(2(x1))))))))))
, 4(0(5(4(5(x1))))) -> 1(3(4(5(5(0(0(0(1(1(x1))))))))))
, 2(5(4(2(4(x1))))) -> 2(3(2(0(5(0(4(2(0(4(x1))))))))))
, 1(0(4(5(2(x1))))) -> 1(4(1(0(3(3(1(4(0(1(x1))))))))))
, 4(5(3(5(x1)))) -> 3(4(1(4(4(0(2(1(3(2(x1))))))))))
, 4(0(5(4(x1)))) -> 4(0(4(4(1(3(3(3(5(4(x1))))))))))
, 1(4(2(1(x1)))) -> 1(0(1(3(2(0(1(4(1(1(x1))))))))))
, 5(4(5(x1))) -> 0(3(3(0(1(3(0(5(0(1(x1))))))))))
, 5(4(5(x1))) -> 0(0(5(1(0(0(2(1(0(3(x1))))))))))
, 5(4(5(x1))) -> 0(0(4(1(5(0(5(1(1(4(x1))))))))))
, 5(4(2(x1))) -> 5(5(4(4(3(4(0(1(0(1(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:
{ 2_0(1) -> 1
, 2_1(1) -> 118
, 2_1(6) -> 5
, 2_1(8) -> 75
, 2_1(10) -> 70
, 2_1(11) -> 118
, 2_1(16) -> 15
, 2_1(18) -> 96
, 2_1(19) -> 11
, 2_1(24) -> 104
, 2_1(26) -> 25
, 2_1(27) -> 26
, 2_1(28) -> 27
, 2_1(33) -> 32
, 2_1(34) -> 1
, 2_1(34) -> 32
, 2_1(34) -> 118
, 2_1(38) -> 37
, 2_1(42) -> 41
, 2_1(50) -> 49
, 2_1(52) -> 51
, 2_1(54) -> 53
, 2_1(55) -> 125
, 2_1(64) -> 56
, 2_1(81) -> 57
, 2_1(88) -> 87
, 2_1(90) -> 118
, 2_1(92) -> 91
, 2_1(99) -> 98
, 2_1(105) -> 90
, 2_1(108) -> 107
, 2_1(114) -> 113
, 2_1(116) -> 208
, 2_1(118) -> 176
, 2_1(119) -> 118
, 2_1(121) -> 120
, 2_1(124) -> 189
, 2_1(139) -> 138
, 2_1(152) -> 151
, 2_1(160) -> 159
, 2_1(166) -> 165
, 2_1(176) -> 175
, 2_1(182) -> 181
, 2_1(184) -> 118
, 2_1(185) -> 118
, 2_1(186) -> 185
, 2_1(197) -> 196
, 2_1(202) -> 201
, 2_1(209) -> 118
, 2_1(225) -> 118
, 2_1(228) -> 227
, 2_1(257) -> 256
, 2_2(234) -> 233
, 2_2(263) -> 262
, 2_2(443) -> 442
, 2_2(461) -> 460
, 2_2(480) -> 479
, 4_0(1) -> 1
, 4_1(1) -> 55
, 4_1(3) -> 2
, 4_1(7) -> 6
, 4_1(8) -> 204
, 4_1(10) -> 142
, 4_1(11) -> 55
, 4_1(14) -> 13
, 4_1(22) -> 21
, 4_1(24) -> 160
, 4_1(25) -> 1
, 4_1(25) -> 55
, 4_1(25) -> 142
, 4_1(25) -> 147
, 4_1(30) -> 29
, 4_1(32) -> 95
, 4_1(40) -> 39
, 4_1(46) -> 45
, 4_1(47) -> 155
, 4_1(55) -> 79
, 4_1(56) -> 55
, 4_1(57) -> 56
, 4_1(65) -> 64
, 4_1(66) -> 65
, 4_1(70) -> 80
, 4_1(75) -> 74
, 4_1(79) -> 145
, 4_1(80) -> 79
, 4_1(90) -> 55
, 4_1(93) -> 92
, 4_1(96) -> 95
, 4_1(98) -> 97
, 4_1(103) -> 102
, 4_1(106) -> 55
, 4_1(110) -> 109
, 4_1(111) -> 110
, 4_1(118) -> 80
, 4_1(119) -> 55
, 4_1(127) -> 126
, 4_1(129) -> 128
, 4_1(136) -> 135
, 4_1(146) -> 145
, 4_1(147) -> 146
, 4_1(148) -> 147
, 4_1(161) -> 160
, 4_1(169) -> 168
, 4_1(174) -> 173
, 4_1(175) -> 174
, 4_1(176) -> 174
, 4_1(179) -> 178
, 4_1(184) -> 55
, 4_1(185) -> 55
, 4_1(187) -> 186
, 4_1(191) -> 190
, 4_1(201) -> 200
, 4_1(206) -> 205
, 4_1(207) -> 206
, 4_1(209) -> 55
, 4_1(210) -> 209
, 4_1(211) -> 210
, 4_1(277) -> 119
, 4_1(278) -> 277
, 4_1(280) -> 279
, 4_2(4) -> 489
, 4_2(25) -> 224
, 4_2(90) -> 276
, 4_2(106) -> 447
, 4_2(119) -> 276
, 4_2(184) -> 276
, 4_2(185) -> 276
, 4_2(209) -> 276
, 4_2(210) -> 456
, 4_2(216) -> 147
, 4_2(218) -> 217
, 4_2(219) -> 218
, 4_2(237) -> 236
, 4_2(270) -> 258
, 4_2(277) -> 456
, 4_2(284) -> 283
, 4_2(285) -> 284
, 4_2(287) -> 286
, 4_2(293) -> 292
, 4_2(294) -> 293
, 4_2(296) -> 295
, 4_2(446) -> 445
, 4_2(448) -> 55
, 4_2(448) -> 80
, 4_2(448) -> 142
, 4_2(450) -> 449
, 4_2(451) -> 450
, 4_2(464) -> 463
, 4_2(483) -> 475
, 5_0(1) -> 1
, 5_1(1) -> 33
, 5_1(2) -> 18
, 5_1(4) -> 3
, 5_1(5) -> 4
, 5_1(8) -> 243
, 5_1(9) -> 24
, 5_1(10) -> 18
, 5_1(11) -> 33
, 5_1(20) -> 19
, 5_1(24) -> 40
, 5_1(33) -> 63
, 5_1(44) -> 43
, 5_1(49) -> 48
, 5_1(55) -> 215
, 5_1(61) -> 60
, 5_1(69) -> 68
, 5_1(79) -> 78
, 5_1(82) -> 81
, 5_1(86) -> 57
, 5_1(90) -> 1
, 5_1(90) -> 8
, 5_1(90) -> 10
, 5_1(90) -> 33
, 5_1(90) -> 44
, 5_1(90) -> 124
, 5_1(90) -> 202
, 5_1(90) -> 215
, 5_1(94) -> 93
, 5_1(109) -> 108
, 5_1(113) -> 112
, 5_1(117) -> 68
, 5_1(118) -> 124
, 5_1(119) -> 90
, 5_1(122) -> 121
, 5_1(125) -> 124
, 5_1(132) -> 131
, 5_1(134) -> 133
, 5_1(159) -> 158
, 5_1(162) -> 161
, 5_1(167) -> 166
, 5_1(171) -> 170
, 5_1(183) -> 182
, 5_1(184) -> 11
, 5_1(185) -> 184
, 5_1(192) -> 191
, 5_1(193) -> 192
, 5_1(199) -> 198
, 5_1(209) -> 11
, 5_1(253) -> 126
, 5_1(267) -> 266
, 5_1(269) -> 268
, 5_2(224) -> 223
, 5_2(251) -> 250
, 5_2(259) -> 258
, 5_2(272) -> 271
, 5_2(274) -> 273
, 5_2(282) -> 215
, 5_2(283) -> 282
, 5_2(291) -> 33
, 5_2(291) -> 215
, 5_2(291) -> 223
, 5_2(292) -> 291
, 5_2(444) -> 443
, 5_2(456) -> 455
, 5_2(473) -> 472
, 5_2(476) -> 475
, 5_2(485) -> 484
, 5_2(487) -> 486
, 1_0(1) -> 1
, 1_1(1) -> 9
, 1_1(2) -> 9
, 1_1(8) -> 281
, 1_1(9) -> 111
, 1_1(10) -> 9
, 1_1(11) -> 9
, 1_1(12) -> 11
, 1_1(17) -> 16
, 1_1(18) -> 17
, 1_1(24) -> 100
, 1_1(25) -> 9
, 1_1(26) -> 9
, 1_1(31) -> 30
, 1_1(32) -> 85
, 1_1(33) -> 136
, 1_1(34) -> 9
, 1_1(41) -> 35
, 1_1(46) -> 257
, 1_1(48) -> 2
, 1_1(54) -> 269
, 1_1(55) -> 54
, 1_1(56) -> 1
, 1_1(56) -> 9
, 1_1(56) -> 10
, 1_1(56) -> 47
, 1_1(56) -> 54
, 1_1(56) -> 55
, 1_1(56) -> 118
, 1_1(56) -> 142
, 1_1(56) -> 147
, 1_1(56) -> 175
, 1_1(56) -> 176
, 1_1(56) -> 199
, 1_1(56) -> 202
, 1_1(58) -> 57
, 1_1(72) -> 71
, 1_1(73) -> 72
, 1_1(74) -> 73
, 1_1(75) -> 89
, 1_1(78) -> 77
, 1_1(87) -> 86
, 1_1(90) -> 9
, 1_1(91) -> 90
, 1_1(97) -> 12
, 1_1(100) -> 99
, 1_1(101) -> 97
, 1_1(102) -> 101
, 1_1(105) -> 9
, 1_1(106) -> 105
, 1_1(110) -> 229
, 1_1(112) -> 91
, 1_1(115) -> 114
, 1_1(117) -> 116
, 1_1(118) -> 162
, 1_1(119) -> 9
, 1_1(123) -> 122
, 1_1(135) -> 134
, 1_1(136) -> 16
, 1_1(144) -> 143
, 1_1(150) -> 149
, 1_1(151) -> 150
, 1_1(154) -> 153
, 1_1(170) -> 56
, 1_1(184) -> 9
, 1_1(185) -> 9
, 1_1(188) -> 187
, 1_1(204) -> 203
, 1_1(205) -> 3
, 1_1(209) -> 9
, 1_1(212) -> 211
, 1_1(226) -> 225
, 1_1(241) -> 240
, 1_1(254) -> 253
, 1_1(266) -> 127
, 1_2(4) -> 474
, 1_2(19) -> 290
, 1_2(26) -> 299
, 1_2(34) -> 290
, 1_2(64) -> 290
, 1_2(90) -> 252
, 1_2(100) -> 238
, 1_2(105) -> 290
, 1_2(106) -> 465
, 1_2(119) -> 252
, 1_2(184) -> 252
, 1_2(185) -> 252
, 1_2(186) -> 290
, 1_2(209) -> 252
, 1_2(220) -> 219
, 1_2(230) -> 12
, 1_2(232) -> 231
, 1_2(236) -> 235
, 1_2(238) -> 237
, 1_2(248) -> 247
, 1_2(260) -> 259
, 1_2(264) -> 263
, 1_2(271) -> 270
, 1_2(275) -> 274
, 1_2(276) -> 275
, 1_2(289) -> 288
, 1_2(298) -> 297
, 1_2(452) -> 451
, 1_2(457) -> 54
, 1_2(457) -> 275
, 1_2(459) -> 458
, 1_2(463) -> 462
, 1_2(465) -> 464
, 1_2(470) -> 469
, 1_2(477) -> 476
, 1_2(481) -> 480
, 1_2(484) -> 483
, 1_2(488) -> 487
, 1_2(489) -> 488
, 0_0(1) -> 1
, 0_1(1) -> 10
, 0_1(9) -> 8
, 0_1(11) -> 1
, 0_1(11) -> 10
, 0_1(11) -> 18
, 0_1(11) -> 33
, 0_1(11) -> 63
, 0_1(11) -> 118
, 0_1(11) -> 124
, 0_1(11) -> 125
, 0_1(11) -> 202
, 0_1(11) -> 215
, 0_1(13) -> 12
, 0_1(15) -> 14
, 0_1(23) -> 22
, 0_1(26) -> 10
, 0_1(29) -> 28
, 0_1(32) -> 31
, 0_1(33) -> 148
, 0_1(34) -> 10
, 0_1(35) -> 34
, 0_1(36) -> 35
, 0_1(37) -> 36
, 0_1(43) -> 42
, 0_1(45) -> 44
, 0_1(47) -> 46
, 0_1(55) -> 202
, 0_1(59) -> 58
, 0_1(62) -> 61
, 0_1(63) -> 62
, 0_1(68) -> 67
, 0_1(76) -> 19
, 0_1(80) -> 199
, 0_1(84) -> 83
, 0_1(90) -> 1
, 0_1(104) -> 103
, 0_1(107) -> 106
, 0_1(111) -> 195
, 0_1(116) -> 115
, 0_1(118) -> 183
, 0_1(119) -> 1
, 0_1(120) -> 119
, 0_1(124) -> 123
, 0_1(126) -> 11
, 0_1(128) -> 127
, 0_1(130) -> 129
, 0_1(131) -> 3
, 0_1(133) -> 132
, 0_1(140) -> 139
, 0_1(148) -> 61
, 0_1(153) -> 152
, 0_1(157) -> 156
, 0_1(158) -> 157
, 0_1(163) -> 2
, 0_1(168) -> 167
, 0_1(177) -> 90
, 0_1(180) -> 179
, 0_1(184) -> 1
, 0_1(185) -> 1
, 0_1(194) -> 193
, 0_1(195) -> 194
, 0_1(198) -> 197
, 0_1(200) -> 199
, 0_1(208) -> 207
, 0_1(209) -> 25
, 0_1(225) -> 56
, 0_1(229) -> 228
, 0_1(240) -> 239
, 0_1(243) -> 242
, 0_1(255) -> 254
, 0_1(256) -> 255
, 0_1(268) -> 267
, 0_1(281) -> 280
, 0_2(217) -> 216
, 0_2(231) -> 230
, 0_2(235) -> 234
, 0_2(244) -> 215
, 0_2(247) -> 246
, 0_2(250) -> 249
, 0_2(252) -> 251
, 0_2(258) -> 244
, 0_2(261) -> 260
, 0_2(262) -> 261
, 0_2(265) -> 264
, 0_2(273) -> 272
, 0_2(288) -> 287
, 0_2(290) -> 289
, 0_2(297) -> 296
, 0_2(299) -> 298
, 0_2(440) -> 439
, 0_2(445) -> 444
, 0_2(449) -> 448
, 0_2(458) -> 457
, 0_2(462) -> 461
, 0_2(466) -> 18
, 0_2(469) -> 468
, 0_2(472) -> 471
, 0_2(474) -> 473
, 0_2(475) -> 466
, 0_2(478) -> 477
, 0_2(479) -> 478
, 0_2(482) -> 481
, 0_2(486) -> 485
, 3_0(1) -> 1
, 3_1(1) -> 47
, 3_1(2) -> 1
, 3_1(2) -> 33
, 3_1(2) -> 55
, 3_1(2) -> 63
, 3_1(2) -> 70
, 3_1(2) -> 80
, 3_1(2) -> 118
, 3_1(2) -> 176
, 3_1(2) -> 201
, 3_1(8) -> 7
, 3_1(11) -> 214
, 3_1(21) -> 20
, 3_1(24) -> 23
, 3_1(25) -> 47
, 3_1(39) -> 38
, 3_1(47) -> 213
, 3_1(51) -> 50
, 3_1(53) -> 52
, 3_1(55) -> 169
, 3_1(60) -> 59
, 3_1(67) -> 66
, 3_1(70) -> 69
, 3_1(71) -> 57
, 3_1(77) -> 76
, 3_1(83) -> 82
, 3_1(85) -> 84
, 3_1(89) -> 88
, 3_1(90) -> 47
, 3_1(95) -> 94
, 3_1(116) -> 130
, 3_1(118) -> 117
, 3_1(137) -> 64
, 3_1(138) -> 137
, 3_1(141) -> 140
, 3_1(142) -> 141
, 3_1(143) -> 19
, 3_1(145) -> 144
, 3_1(149) -> 11
, 3_1(155) -> 154
, 3_1(156) -> 2
, 3_1(164) -> 163
, 3_1(165) -> 164
, 3_1(172) -> 171
, 3_1(173) -> 172
, 3_1(178) -> 177
, 3_1(181) -> 180
, 3_1(189) -> 188
, 3_1(190) -> 56
, 3_1(196) -> 34
, 3_1(203) -> 60
, 3_1(213) -> 212
, 3_1(214) -> 213
, 3_1(215) -> 214
, 3_1(227) -> 226
, 3_1(239) -> 149
, 3_1(242) -> 241
, 3_1(277) -> 47
, 3_1(279) -> 278
, 3_2(4) -> 482
, 3_2(90) -> 265
, 3_2(119) -> 265
, 3_2(184) -> 265
, 3_2(185) -> 265
, 3_2(209) -> 265
, 3_2(221) -> 220
, 3_2(222) -> 221
, 3_2(223) -> 222
, 3_2(233) -> 232
, 3_2(245) -> 244
, 3_2(246) -> 245
, 3_2(249) -> 248
, 3_2(286) -> 285
, 3_2(295) -> 294
, 3_2(439) -> 201
, 3_2(441) -> 440
, 3_2(442) -> 441
, 3_2(447) -> 446
, 3_2(453) -> 452
, 3_2(454) -> 453
, 3_2(455) -> 454
, 3_2(460) -> 459
, 3_2(467) -> 466
, 3_2(468) -> 467
, 3_2(471) -> 470}
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(5(4(2(4(0(5(x1))))))) -> 3(4(5(5(2(4(3(0(1(0(x1))))))))))
, 5(5(3(0(4(3(0(x1))))))) -> 0(1(0(4(0(2(1(1(5(0(x1))))))))))
, 5(2(3(1(0(4(0(x1))))))) -> 0(2(5(3(4(0(3(5(1(0(x1))))))))))
, 4(1(2(4(2(2(5(x1))))))) -> 4(2(2(2(0(4(1(0(2(5(x1))))))))))
, 2(5(4(3(5(4(5(x1))))))) -> 2(0(0(0(2(3(4(5(5(1(x1))))))))))
, 2(5(4(0(5(5(4(x1))))))) -> 2(0(1(2(0(5(0(4(0(3(x1))))))))))
, 2(2(5(4(1(4(0(x1))))))) -> 3(1(5(2(3(2(3(2(1(4(x1))))))))))
, 2(2(2(5(4(5(5(x1))))))) -> 1(4(1(0(3(5(0(0(5(5(x1))))))))))
, 1(0(4(5(4(3(5(x1))))))) -> 1(2(4(4(3(0(5(3(2(0(x1))))))))))
, 0(4(5(2(5(4(2(x1))))))) -> 1(4(3(1(1(1(4(2(0(1(x1))))))))))
, 0(4(3(0(2(1(5(x1))))))) -> 0(2(0(3(1(5(4(4(2(0(x1))))))))))
, 0(4(2(5(2(2(5(x1))))))) -> 1(4(2(5(3(0(3(1(2(5(x1))))))))))
, 0(4(2(4(2(4(2(x1))))))) -> 1(4(5(1(2(3(1(2(0(1(x1))))))))))
, 0(4(0(3(5(3(0(x1))))))) -> 5(1(2(4(5(3(4(2(5(0(x1))))))))))
, 5(4(2(2(3(0(x1)))))) -> 0(1(1(4(2(1(1(5(1(0(x1))))))))))
, 5(4(2(0(4(0(x1)))))) -> 0(1(1(1(1(4(0(2(5(1(x1))))))))))
, 5(3(0(4(2(1(x1)))))) -> 5(2(1(0(2(5(4(4(1(1(x1))))))))))
, 5(2(5(4(1(0(x1)))))) -> 5(1(1(5(2(1(0(1(3(2(x1))))))))))
, 5(2(5(2(2(4(x1)))))) -> 5(5(0(2(5(1(0(5(2(4(x1))))))))))
, 5(0(5(4(0(5(x1)))))) -> 0(0(4(0(4(0(3(1(3(2(x1))))))))))
, 4(2(4(1(2(5(x1)))))) -> 3(4(0(5(0(5(1(4(1(5(x1))))))))))
, 3(0(4(5(4(2(x1)))))) -> 1(2(3(3(2(0(3(3(4(0(x1))))))))))
, 2(4(5(5(4(0(x1)))))) -> 0(2(3(1(3(4(4(4(0(5(x1))))))))))
, 2(4(0(5(5(4(x1)))))) -> 0(3(1(1(2(0(1(3(4(3(x1))))))))))
, 2(2(5(4(1(2(x1)))))) -> 3(3(0(0(5(2(4(5(1(2(x1))))))))))
, 2(0(4(5(2(1(x1)))))) -> 3(0(3(3(2(5(0(4(3(4(x1))))))))))
, 1(0(4(3(5(2(x1)))))) -> 1(1(5(3(3(4(4(2(2(2(x1))))))))))
, 0(1(3(5(4(0(x1)))))) -> 5(0(3(4(0(3(2(5(0(2(x1))))))))))
, 5(3(5(3(5(x1))))) -> 0(5(5(2(4(1(3(2(5(2(x1))))))))))
, 4(0(5(4(5(x1))))) -> 1(3(4(5(5(0(0(0(1(1(x1))))))))))
, 2(5(4(2(4(x1))))) -> 2(3(2(0(5(0(4(2(0(4(x1))))))))))
, 1(0(4(5(2(x1))))) -> 1(4(1(0(3(3(1(4(0(1(x1))))))))))
, 4(5(3(5(x1)))) -> 3(4(1(4(4(0(2(1(3(2(x1))))))))))
, 4(0(5(4(x1)))) -> 4(0(4(4(1(3(3(3(5(4(x1))))))))))
, 1(4(2(1(x1)))) -> 1(0(1(3(2(0(1(4(1(1(x1))))))))))
, 5(4(5(x1))) -> 0(3(3(0(1(3(0(5(0(1(x1))))))))))
, 5(4(5(x1))) -> 0(0(5(1(0(0(2(1(0(3(x1))))))))))
, 5(4(5(x1))) -> 0(0(4(1(5(0(5(1(1(4(x1))))))))))
, 5(4(2(x1))) -> 5(5(4(4(3(4(0(1(0(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:
{ 5(5(4(2(4(0(5(x1))))))) -> 3(4(5(5(2(4(3(0(1(0(x1))))))))))
, 5(5(3(0(4(3(0(x1))))))) -> 0(1(0(4(0(2(1(1(5(0(x1))))))))))
, 5(2(3(1(0(4(0(x1))))))) -> 0(2(5(3(4(0(3(5(1(0(x1))))))))))
, 4(1(2(4(2(2(5(x1))))))) -> 4(2(2(2(0(4(1(0(2(5(x1))))))))))
, 2(5(4(3(5(4(5(x1))))))) -> 2(0(0(0(2(3(4(5(5(1(x1))))))))))
, 2(5(4(0(5(5(4(x1))))))) -> 2(0(1(2(0(5(0(4(0(3(x1))))))))))
, 2(2(5(4(1(4(0(x1))))))) -> 3(1(5(2(3(2(3(2(1(4(x1))))))))))
, 2(2(2(5(4(5(5(x1))))))) -> 1(4(1(0(3(5(0(0(5(5(x1))))))))))
, 1(0(4(5(4(3(5(x1))))))) -> 1(2(4(4(3(0(5(3(2(0(x1))))))))))
, 0(4(5(2(5(4(2(x1))))))) -> 1(4(3(1(1(1(4(2(0(1(x1))))))))))
, 0(4(3(0(2(1(5(x1))))))) -> 0(2(0(3(1(5(4(4(2(0(x1))))))))))
, 0(4(2(5(2(2(5(x1))))))) -> 1(4(2(5(3(0(3(1(2(5(x1))))))))))
, 0(4(2(4(2(4(2(x1))))))) -> 1(4(5(1(2(3(1(2(0(1(x1))))))))))
, 0(4(0(3(5(3(0(x1))))))) -> 5(1(2(4(5(3(4(2(5(0(x1))))))))))
, 5(4(2(2(3(0(x1)))))) -> 0(1(1(4(2(1(1(5(1(0(x1))))))))))
, 5(4(2(0(4(0(x1)))))) -> 0(1(1(1(1(4(0(2(5(1(x1))))))))))
, 5(3(0(4(2(1(x1)))))) -> 5(2(1(0(2(5(4(4(1(1(x1))))))))))
, 5(2(5(4(1(0(x1)))))) -> 5(1(1(5(2(1(0(1(3(2(x1))))))))))
, 5(2(5(2(2(4(x1)))))) -> 5(5(0(2(5(1(0(5(2(4(x1))))))))))
, 5(0(5(4(0(5(x1)))))) -> 0(0(4(0(4(0(3(1(3(2(x1))))))))))
, 4(2(4(1(2(5(x1)))))) -> 3(4(0(5(0(5(1(4(1(5(x1))))))))))
, 3(0(4(5(4(2(x1)))))) -> 1(2(3(3(2(0(3(3(4(0(x1))))))))))
, 2(4(5(5(4(0(x1)))))) -> 0(2(3(1(3(4(4(4(0(5(x1))))))))))
, 2(4(0(5(5(4(x1)))))) -> 0(3(1(1(2(0(1(3(4(3(x1))))))))))
, 2(2(5(4(1(2(x1)))))) -> 3(3(0(0(5(2(4(5(1(2(x1))))))))))
, 2(0(4(5(2(1(x1)))))) -> 3(0(3(3(2(5(0(4(3(4(x1))))))))))
, 1(0(4(3(5(2(x1)))))) -> 1(1(5(3(3(4(4(2(2(2(x1))))))))))
, 0(1(3(5(4(0(x1)))))) -> 5(0(3(4(0(3(2(5(0(2(x1))))))))))
, 5(3(5(3(5(x1))))) -> 0(5(5(2(4(1(3(2(5(2(x1))))))))))
, 4(0(5(4(5(x1))))) -> 1(3(4(5(5(0(0(0(1(1(x1))))))))))
, 2(5(4(2(4(x1))))) -> 2(3(2(0(5(0(4(2(0(4(x1))))))))))
, 1(0(4(5(2(x1))))) -> 1(4(1(0(3(3(1(4(0(1(x1))))))))))
, 4(5(3(5(x1)))) -> 3(4(1(4(4(0(2(1(3(2(x1))))))))))
, 4(0(5(4(x1)))) -> 4(0(4(4(1(3(3(3(5(4(x1))))))))))
, 1(4(2(1(x1)))) -> 1(0(1(3(2(0(1(4(1(1(x1))))))))))
, 5(4(5(x1))) -> 0(3(3(0(1(3(0(5(0(1(x1))))))))))
, 5(4(5(x1))) -> 0(0(5(1(0(0(2(1(0(3(x1))))))))))
, 5(4(5(x1))) -> 0(0(4(1(5(0(5(1(1(4(x1))))))))))
, 5(4(2(x1))) -> 5(5(4(4(3(4(0(1(0(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:
{ 5(5(4(2(4(0(5(x1))))))) -> 3(4(5(5(2(4(3(0(1(0(x1))))))))))
, 5(5(3(0(4(3(0(x1))))))) -> 0(1(0(4(0(2(1(1(5(0(x1))))))))))
, 5(2(3(1(0(4(0(x1))))))) -> 0(2(5(3(4(0(3(5(1(0(x1))))))))))
, 4(1(2(4(2(2(5(x1))))))) -> 4(2(2(2(0(4(1(0(2(5(x1))))))))))
, 2(5(4(3(5(4(5(x1))))))) -> 2(0(0(0(2(3(4(5(5(1(x1))))))))))
, 2(5(4(0(5(5(4(x1))))))) -> 2(0(1(2(0(5(0(4(0(3(x1))))))))))
, 2(2(5(4(1(4(0(x1))))))) -> 3(1(5(2(3(2(3(2(1(4(x1))))))))))
, 2(2(2(5(4(5(5(x1))))))) -> 1(4(1(0(3(5(0(0(5(5(x1))))))))))
, 1(0(4(5(4(3(5(x1))))))) -> 1(2(4(4(3(0(5(3(2(0(x1))))))))))
, 0(4(5(2(5(4(2(x1))))))) -> 1(4(3(1(1(1(4(2(0(1(x1))))))))))
, 0(4(3(0(2(1(5(x1))))))) -> 0(2(0(3(1(5(4(4(2(0(x1))))))))))
, 0(4(2(5(2(2(5(x1))))))) -> 1(4(2(5(3(0(3(1(2(5(x1))))))))))
, 0(4(2(4(2(4(2(x1))))))) -> 1(4(5(1(2(3(1(2(0(1(x1))))))))))
, 0(4(0(3(5(3(0(x1))))))) -> 5(1(2(4(5(3(4(2(5(0(x1))))))))))
, 5(4(2(2(3(0(x1)))))) -> 0(1(1(4(2(1(1(5(1(0(x1))))))))))
, 5(4(2(0(4(0(x1)))))) -> 0(1(1(1(1(4(0(2(5(1(x1))))))))))
, 5(3(0(4(2(1(x1)))))) -> 5(2(1(0(2(5(4(4(1(1(x1))))))))))
, 5(2(5(4(1(0(x1)))))) -> 5(1(1(5(2(1(0(1(3(2(x1))))))))))
, 5(2(5(2(2(4(x1)))))) -> 5(5(0(2(5(1(0(5(2(4(x1))))))))))
, 5(0(5(4(0(5(x1)))))) -> 0(0(4(0(4(0(3(1(3(2(x1))))))))))
, 4(2(4(1(2(5(x1)))))) -> 3(4(0(5(0(5(1(4(1(5(x1))))))))))
, 3(0(4(5(4(2(x1)))))) -> 1(2(3(3(2(0(3(3(4(0(x1))))))))))
, 2(4(5(5(4(0(x1)))))) -> 0(2(3(1(3(4(4(4(0(5(x1))))))))))
, 2(4(0(5(5(4(x1)))))) -> 0(3(1(1(2(0(1(3(4(3(x1))))))))))
, 2(2(5(4(1(2(x1)))))) -> 3(3(0(0(5(2(4(5(1(2(x1))))))))))
, 2(0(4(5(2(1(x1)))))) -> 3(0(3(3(2(5(0(4(3(4(x1))))))))))
, 1(0(4(3(5(2(x1)))))) -> 1(1(5(3(3(4(4(2(2(2(x1))))))))))
, 0(1(3(5(4(0(x1)))))) -> 5(0(3(4(0(3(2(5(0(2(x1))))))))))
, 5(3(5(3(5(x1))))) -> 0(5(5(2(4(1(3(2(5(2(x1))))))))))
, 4(0(5(4(5(x1))))) -> 1(3(4(5(5(0(0(0(1(1(x1))))))))))
, 2(5(4(2(4(x1))))) -> 2(3(2(0(5(0(4(2(0(4(x1))))))))))
, 1(0(4(5(2(x1))))) -> 1(4(1(0(3(3(1(4(0(1(x1))))))))))
, 4(5(3(5(x1)))) -> 3(4(1(4(4(0(2(1(3(2(x1))))))))))
, 4(0(5(4(x1)))) -> 4(0(4(4(1(3(3(3(5(4(x1))))))))))
, 1(4(2(1(x1)))) -> 1(0(1(3(2(0(1(4(1(1(x1))))))))))
, 5(4(5(x1))) -> 0(3(3(0(1(3(0(5(0(1(x1))))))))))
, 5(4(5(x1))) -> 0(0(5(1(0(0(2(1(0(3(x1))))))))))
, 5(4(5(x1))) -> 0(0(4(1(5(0(5(1(1(4(x1))))))))))
, 5(4(2(x1))) -> 5(5(4(4(3(4(0(1(0(1(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..