Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(4(5(3(5(2(4(4(1(4(2(0(5(5(1(0(1(5(0(4(3(x1)))))))))))))))))))))
-> 4(4(2(2(3(2(0(5(5(0(2(4(0(0(0(1(3(5(2(3(x1))))))))))))))))))))
, 0(3(4(1(5(3(4(5(1(5(0(2(3(1(1(0(1(0(5(4(2(x1)))))))))))))))))))))
-> 0(5(5(0(2(4(1(0(1(4(1(5(3(0(1(5(2(5(2(x1)))))))))))))))))))
, 4(4(0(2(4(0(0(2(3(0(1(4(1(0(0(0(3(0(2(3(x1)))))))))))))))))))) ->
5(2(4(4(0(4(1(5(0(5(3(3(1(4(1(0(2(4(2(x1)))))))))))))))))))
, 2(2(2(3(0(3(1(4(4(1(1(0(5(1(0(0(5(4(1(2(x1)))))))))))))))))))) ->
2(3(4(3(5(5(2(1(1(2(5(3(5(0(4(1(2(2(1(4(x1))))))))))))))))))))
, 2(0(4(4(2(4(3(3(2(0(0(3(3(0(1(0(2(2(2(5(x1)))))))))))))))))))) ->
2(3(2(3(5(1(1(0(1(3(0(4(3(2(4(2(5(2(5(x1)))))))))))))))))))
, 5(5(4(3(2(1(3(3(1(4(1(1(3(3(3(4(0(1(2(x1))))))))))))))))))) ->
4(0(1(3(1(2(4(5(3(5(0(0(3(2(4(5(5(3(x1))))))))))))))))))
, 5(2(2(2(1(1(4(0(4(3(5(3(4(4(4(4(0(5(0(x1))))))))))))))))))) ->
3(4(5(0(2(4(3(5(1(1(5(5(4(1(4(5(5(0(0(x1)))))))))))))))))))
, 1(1(5(3(2(0(4(1(3(4(5(3(0(2(5(2(3(3(0(x1))))))))))))))))))) ->
0(1(3(4(3(5(0(2(2(0(2(4(5(0(3(3(2(0(x1))))))))))))))))))
, 1(1(1(0(3(0(1(4(3(1(1(2(5(2(1(2(1(1(0(x1))))))))))))))))))) ->
1(5(5(2(3(1(3(3(2(0(1(5(5(4(1(2(4(x1)))))))))))))))))
, 5(5(5(3(2(1(0(4(1(3(4(4(3(1(1(4(3(2(x1)))))))))))))))))) ->
5(5(4(3(2(2(3(0(3(4(4(5(5(4(4(3(0(3(x1))))))))))))))))))
, 3(1(3(2(4(2(3(3(1(5(4(0(3(1(0(4(1(0(x1)))))))))))))))))) ->
5(1(3(5(0(2(3(2(0(4(0(1(2(2(2(2(0(x1)))))))))))))))))
, 0(3(3(4(2(4(3(1(4(1(0(4(1(4(0(4(1(1(x1)))))))))))))))))) ->
0(2(2(1(1(2(3(1(3(2(2(2(5(5(5(0(3(4(2(x1)))))))))))))))))))
, 4(3(3(4(2(0(0(1(3(3(0(1(3(1(2(1(x1)))))))))))))))) ->
4(3(3(1(1(4(4(4(5(2(0(5(0(5(4(1(x1))))))))))))))))
, 5(3(4(3(2(1(4(2(2(1(3(3(1(4(4(x1))))))))))))))) ->
1(1(5(3(4(5(4(3(3(3(3(2(0(2(4(x1)))))))))))))))
, 3(0(2(5(1(1(4(1(3(4(2(5(3(1(0(x1))))))))))))))) ->
3(5(5(4(0(5(2(1(5(0(4(0(4(4(3(0(x1))))))))))))))))
, 0(0(0(4(0(0(3(2(0(5(4(4(2(1(2(x1))))))))))))))) ->
0(4(4(2(1(0(2(1(5(0(2(3(4(2(x1))))))))))))))
, 2(4(4(5(1(5(1(0(2(5(4(1(2(x1))))))))))))) ->
5(1(5(2(1(2(3(2(0(3(1(2(3(3(x1))))))))))))))
, 0(1(3(3(0(4(1(0(2(2(4(3(2(x1))))))))))))) ->
1(3(4(2(4(1(3(3(4(2(1(x1)))))))))))
, 5(3(2(0(5(4(5(2(2(3(4(5(x1)))))))))))) ->
2(4(3(5(0(2(0(2(0(4(4(x1)))))))))))
, 0(0(2(1(0(1(2(1(0(3(2(2(x1)))))))))))) ->
0(1(2(5(1(4(5(2(1(4(1(x1)))))))))))
, 5(4(2(1(4(4(1(3(2(1(2(x1))))))))))) ->
5(4(1(2(3(1(3(0(0(0(1(x1)))))))))))
, 5(3(2(5(5(5(4(3(3(4(5(x1))))))))))) ->
3(0(2(3(2(5(3(0(2(4(x1))))))))))
, 5(0(5(3(0(5(0(4(0(5(5(x1))))))))))) ->
3(4(4(3(4(0(3(5(3(5(x1))))))))))
, 5(5(1(1(4(5(0(5(1(3(x1)))))))))) ->
5(1(1(2(5(3(3(4(3(3(x1))))))))))
, 2(3(0(3(0(5(3(2(1(3(x1)))))))))) -> 2(5(0(2(2(5(0(1(x1))))))))
, 1(0(1(5(3(3(4(5(5(1(x1)))))))))) ->
1(1(5(4(3(5(1(1(5(1(x1))))))))))
, 3(5(5(4(4(1(5(1(4(x1))))))))) -> 3(2(5(0(4(0(0(5(4(x1)))))))))
, 2(3(1(3(1(3(1(5(3(x1))))))))) -> 5(4(1(0(4(1(3(x1)))))))
, 1(2(4(5(4(0(5(2(1(x1))))))))) -> 1(5(0(5(4(4(0(4(1(x1)))))))))
, 3(3(1(5(0(3(2(4(x1)))))))) -> 4(3(3(1(0(4(4(x1)))))))
, 3(0(2(2(2(1(0(3(x1)))))))) -> 3(5(2(3(0(0(4(x1)))))))
, 0(1(2(5(1(5(3(0(x1)))))))) -> 0(0(5(2(5(4(4(x1)))))))
, 5(2(2(2(4(0(3(x1))))))) -> 4(5(4(0(1(5(x1))))))
, 3(2(5(3(1(0(3(x1))))))) -> 3(5(3(4(0(1(x1))))))
, 3(1(0(0(0(1(1(x1))))))) -> 5(3(2(0(2(0(1(x1)))))))
, 4(3(5(3(2(5(x1)))))) -> 2(3(1(2(5(x1)))))
, 5(2(3(0(x1)))) -> 2(0(0(x1)))
, 5(2(1(5(x1)))) -> 4(2(5(x1)))
, 3(0(2(2(x1)))) -> 3(4(3(2(x1))))
, 0(1(1(2(x1)))) -> 0(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) -> 38
, 2_1(2) -> 153
, 2_1(4) -> 3
, 2_1(5) -> 4
, 2_1(7) -> 6
, 2_1(12) -> 11
, 2_1(20) -> 19
, 2_1(21) -> 261
, 2_1(25) -> 24
, 2_1(37) -> 36
, 2_1(38) -> 181
, 2_1(40) -> 39
, 2_1(53) -> 220
, 2_1(55) -> 54
, 2_1(56) -> 1
, 2_1(56) -> 19
, 2_1(56) -> 38
, 2_1(56) -> 74
, 2_1(56) -> 90
, 2_1(56) -> 105
, 2_1(56) -> 106
, 2_1(56) -> 138
, 2_1(56) -> 180
, 2_1(56) -> 181
, 2_1(56) -> 267
, 2_1(56) -> 338
, 2_1(57) -> 38
, 2_1(62) -> 61
, 2_1(65) -> 64
, 2_1(72) -> 71
, 2_1(73) -> 72
, 2_1(74) -> 153
, 2_1(75) -> 57
, 2_1(86) -> 85
, 2_1(88) -> 87
, 2_1(90) -> 89
, 2_1(95) -> 94
, 2_1(103) -> 102
, 2_1(106) -> 38
, 2_1(110) -> 109
, 2_1(122) -> 1
, 2_1(122) -> 18
, 2_1(122) -> 37
, 2_1(122) -> 90
, 2_1(122) -> 338
, 2_1(123) -> 138
, 2_1(130) -> 129
, 2_1(131) -> 130
, 2_1(133) -> 132
, 2_1(138) -> 181
, 2_1(139) -> 38
, 2_1(142) -> 141
, 2_1(147) -> 146
, 2_1(157) -> 156
, 2_1(158) -> 157
, 2_1(173) -> 172
, 2_1(175) -> 174
, 2_1(180) -> 179
, 2_1(181) -> 180
, 2_1(182) -> 21
, 2_1(183) -> 182
, 2_1(186) -> 185
, 2_1(190) -> 189
, 2_1(191) -> 190
, 2_1(192) -> 191
, 2_1(196) -> 243
, 2_1(205) -> 204
, 2_1(210) -> 261
, 2_1(211) -> 38
, 2_1(221) -> 220
, 2_1(227) -> 226
, 2_1(237) -> 236
, 2_1(240) -> 239
, 2_1(245) -> 244
, 2_1(247) -> 246
, 2_1(249) -> 248
, 2_1(253) -> 252
, 2_1(256) -> 255
, 2_1(260) -> 54
, 2_1(266) -> 265
, 2_1(268) -> 267
, 2_1(270) -> 124
, 2_1(275) -> 274
, 2_1(278) -> 277
, 2_1(283) -> 332
, 2_1(285) -> 284
, 2_1(286) -> 38
, 2_1(287) -> 286
, 2_1(296) -> 295
, 2_1(302) -> 301
, 2_1(303) -> 302
, 2_1(309) -> 106
, 2_1(320) -> 222
, 2_1(325) -> 324
, 2_1(328) -> 38
, 2_1(329) -> 139
, 2_1(331) -> 330
, 2_1(333) -> 1
, 2_1(344) -> 2
, 2_2(56) -> 343
, 2_2(183) -> 346
, 2_2(333) -> 18
, 2_2(333) -> 35
, 2_2(333) -> 37
, 2_2(333) -> 88
, 2_2(333) -> 90
, 2_2(333) -> 104
, 2_2(333) -> 208
, 2_2(333) -> 338
, 2_2(335) -> 106
, 2_2(338) -> 337
, 2_2(340) -> 339
, 2_2(343) -> 337
, 2_2(344) -> 343
, 2_2(749) -> 748
, 2_2(751) -> 750
, 2_2(765) -> 764
, 1_0(1) -> 1
, 1_1(1) -> 210
, 1_1(17) -> 16
, 1_1(20) -> 314
, 1_1(27) -> 26
, 1_1(29) -> 28
, 1_1(31) -> 30
, 1_1(35) -> 34
, 1_1(39) -> 314
, 1_1(45) -> 44
, 1_1(51) -> 50
, 1_1(53) -> 52
, 1_1(56) -> 210
, 1_1(63) -> 62
, 1_1(64) -> 63
, 1_1(71) -> 70
, 1_1(74) -> 73
, 1_1(78) -> 77
, 1_1(79) -> 78
, 1_1(81) -> 80
, 1_1(88) -> 34
, 1_1(89) -> 57
, 1_1(90) -> 328
, 1_1(92) -> 91
, 1_1(94) -> 93
, 1_1(106) -> 210
, 1_1(114) -> 113
, 1_1(115) -> 114
, 1_1(119) -> 118
, 1_1(122) -> 21
, 1_1(124) -> 21
, 1_1(139) -> 1
, 1_1(139) -> 90
, 1_1(139) -> 104
, 1_1(139) -> 105
, 1_1(139) -> 120
, 1_1(139) -> 123
, 1_1(139) -> 152
, 1_1(139) -> 210
, 1_1(139) -> 283
, 1_1(139) -> 287
, 1_1(139) -> 293
, 1_1(139) -> 306
, 1_1(139) -> 338
, 1_1(144) -> 143
, 1_1(149) -> 148
, 1_1(153) -> 152
, 1_1(169) -> 39
, 1_1(179) -> 178
, 1_1(184) -> 183
, 1_1(185) -> 184
, 1_1(188) -> 187
, 1_1(199) -> 198
, 1_1(200) -> 199
, 1_1(209) -> 275
, 1_1(210) -> 306
, 1_1(211) -> 139
, 1_1(228) -> 227
, 1_1(238) -> 237
, 1_1(241) -> 240
, 1_1(246) -> 245
, 1_1(252) -> 251
, 1_1(254) -> 210
, 1_1(258) -> 257
, 1_1(268) -> 198
, 1_1(269) -> 73
, 1_1(272) -> 271
, 1_1(277) -> 276
, 1_1(280) -> 279
, 1_1(295) -> 169
, 1_1(307) -> 306
, 1_1(308) -> 307
, 1_1(309) -> 21
, 1_1(322) -> 198
, 1_1(329) -> 21
, 1_1(333) -> 21
, 1_1(335) -> 21
, 1_2(139) -> 752
, 1_2(211) -> 752
, 1_2(329) -> 767
, 1_2(337) -> 763
, 1_2(343) -> 763
, 1_2(728) -> 727
, 1_2(731) -> 730
, 1_2(747) -> 730
, 1_2(764) -> 763
, 0_0(1) -> 1
, 0_1(1) -> 123
, 0_1(8) -> 7
, 0_1(11) -> 10
, 0_1(14) -> 13
, 0_1(15) -> 14
, 0_1(16) -> 15
, 0_1(19) -> 242
, 0_1(20) -> 168
, 0_1(21) -> 1
, 0_1(21) -> 122
, 0_1(21) -> 123
, 0_1(21) -> 168
, 0_1(21) -> 210
, 0_1(21) -> 283
, 0_1(21) -> 306
, 0_1(21) -> 333
, 0_1(21) -> 334
, 0_1(21) -> 335
, 0_1(24) -> 23
, 0_1(28) -> 27
, 0_1(34) -> 33
, 0_1(38) -> 53
, 0_1(43) -> 42
, 0_1(47) -> 46
, 0_1(54) -> 53
, 0_1(69) -> 68
, 0_1(74) -> 322
, 0_1(80) -> 79
, 0_1(83) -> 82
, 0_1(89) -> 53
, 0_1(90) -> 207
, 0_1(91) -> 2
, 0_1(100) -> 99
, 0_1(101) -> 100
, 0_1(106) -> 56
, 0_1(109) -> 108
, 0_1(123) -> 122
, 0_1(129) -> 128
, 0_1(132) -> 131
, 0_1(136) -> 135
, 0_1(139) -> 283
, 0_1(148) -> 147
, 0_1(153) -> 221
, 0_1(160) -> 159
, 0_1(172) -> 171
, 0_1(176) -> 175
, 0_1(178) -> 177
, 0_1(196) -> 195
, 0_1(206) -> 205
, 0_1(207) -> 312
, 0_1(208) -> 207
, 0_1(209) -> 318
, 0_1(210) -> 283
, 0_1(225) -> 224
, 0_1(230) -> 229
, 0_1(232) -> 231
, 0_1(239) -> 238
, 0_1(243) -> 242
, 0_1(250) -> 249
, 0_1(265) -> 264
, 0_1(267) -> 266
, 0_1(269) -> 268
, 0_1(282) -> 281
, 0_1(283) -> 1
, 0_1(283) -> 123
, 0_1(283) -> 282
, 0_1(283) -> 283
, 0_1(284) -> 106
, 0_1(292) -> 291
, 0_1(301) -> 300
, 0_1(311) -> 310
, 0_1(313) -> 277
, 0_1(315) -> 140
, 0_1(322) -> 321
, 0_1(323) -> 21
, 0_1(328) -> 327
, 0_1(332) -> 331
, 0_2(21) -> 334
, 0_2(106) -> 334
, 0_2(123) -> 334
, 0_2(283) -> 334
, 0_2(284) -> 334
, 0_2(322) -> 336
, 0_2(333) -> 333
, 0_2(334) -> 333
, 0_2(335) -> 333
, 0_2(336) -> 335
, 0_2(729) -> 728
, 0_2(750) -> 749
, 0_2(752) -> 751
, 0_2(766) -> 283
, 0_2(766) -> 327
, 0_2(767) -> 766
, 3_0(1) -> 1
, 3_1(1) -> 20
, 3_1(6) -> 5
, 3_1(18) -> 17
, 3_1(20) -> 253
, 3_1(22) -> 294
, 3_1(33) -> 32
, 3_1(37) -> 17
, 3_1(38) -> 137
, 3_1(39) -> 294
, 3_1(49) -> 48
, 3_1(50) -> 49
, 3_1(55) -> 196
, 3_1(56) -> 20
, 3_1(57) -> 56
, 3_1(59) -> 58
, 3_1(67) -> 66
, 3_1(74) -> 20
, 3_1(76) -> 75
, 3_1(82) -> 81
, 3_1(85) -> 84
, 3_1(90) -> 294
, 3_1(93) -> 92
, 3_1(98) -> 97
, 3_1(102) -> 101
, 3_1(105) -> 292
, 3_1(106) -> 1
, 3_1(106) -> 20
, 3_1(106) -> 37
, 3_1(106) -> 90
, 3_1(106) -> 105
, 3_1(106) -> 121
, 3_1(106) -> 137
, 3_1(106) -> 206
, 3_1(106) -> 234
, 3_1(106) -> 294
, 3_1(106) -> 338
, 3_1(112) -> 111
, 3_1(122) -> 20
, 3_1(123) -> 234
, 3_1(125) -> 124
, 3_1(127) -> 126
, 3_1(137) -> 136
, 3_1(138) -> 137
, 3_1(139) -> 253
, 3_1(143) -> 142
, 3_1(145) -> 144
, 3_1(146) -> 145
, 3_1(156) -> 155
, 3_1(159) -> 158
, 3_1(161) -> 160
, 3_1(168) -> 167
, 3_1(169) -> 253
, 3_1(170) -> 169
, 3_1(174) -> 173
, 3_1(182) -> 107
, 3_1(187) -> 186
, 3_1(189) -> 188
, 3_1(197) -> 2
, 3_1(198) -> 197
, 3_1(210) -> 56
, 3_1(213) -> 212
, 3_1(217) -> 216
, 3_1(218) -> 217
, 3_1(219) -> 218
, 3_1(220) -> 219
, 3_1(221) -> 288
, 3_1(222) -> 253
, 3_1(248) -> 247
, 3_1(251) -> 250
, 3_1(254) -> 139
, 3_1(259) -> 258
, 3_1(260) -> 259
, 3_1(263) -> 262
, 3_1(270) -> 20
, 3_1(278) -> 20
, 3_1(279) -> 278
, 3_1(281) -> 280
, 3_1(286) -> 285
, 3_1(290) -> 289
, 3_1(293) -> 292
, 3_1(298) -> 297
, 3_1(299) -> 298
, 3_1(305) -> 304
, 3_1(309) -> 20
, 3_1(321) -> 320
, 3_1(328) -> 56
, 3_1(329) -> 222
, 3_1(330) -> 39
, 3_1(333) -> 20
, 3_1(335) -> 20
, 3_2(106) -> 731
, 3_2(329) -> 731
, 3_2(330) -> 731
, 3_2(341) -> 288
, 3_2(343) -> 342
, 3_2(344) -> 20
, 3_2(344) -> 56
, 3_2(344) -> 167
, 3_2(344) -> 234
, 3_2(346) -> 345
, 3_2(748) -> 747
, 3_2(763) -> 335
, 4_0(1) -> 1
, 4_1(1) -> 74
, 4_1(2) -> 1
, 4_1(2) -> 20
, 4_1(2) -> 37
, 4_1(2) -> 74
, 4_1(2) -> 90
, 4_1(2) -> 106
, 4_1(2) -> 123
, 4_1(2) -> 253
, 4_1(2) -> 299
, 4_1(2) -> 322
, 4_1(2) -> 338
, 4_1(3) -> 2
, 4_1(13) -> 12
, 4_1(20) -> 106
, 4_1(21) -> 74
, 4_1(26) -> 25
, 4_1(30) -> 29
, 4_1(36) -> 86
, 4_1(38) -> 1
, 4_1(38) -> 55
, 4_1(38) -> 90
, 4_1(38) -> 338
, 4_1(39) -> 74
, 4_1(41) -> 40
, 4_1(42) -> 41
, 4_1(44) -> 43
, 4_1(52) -> 51
, 4_1(56) -> 269
, 4_1(58) -> 57
, 4_1(70) -> 69
, 4_1(74) -> 269
, 4_1(84) -> 83
, 4_1(87) -> 86
, 4_1(89) -> 1
, 4_1(89) -> 37
, 4_1(89) -> 90
, 4_1(89) -> 338
, 4_1(90) -> 103
, 4_1(96) -> 95
, 4_1(104) -> 103
, 4_1(106) -> 74
, 4_1(107) -> 106
, 4_1(108) -> 74
, 4_1(111) -> 110
, 4_1(118) -> 117
, 4_1(120) -> 119
, 4_1(122) -> 74
, 4_1(126) -> 125
, 4_1(134) -> 133
, 4_1(137) -> 106
, 4_1(139) -> 1
, 4_1(140) -> 56
, 4_1(152) -> 151
, 4_1(155) -> 154
, 4_1(162) -> 161
, 4_1(163) -> 162
, 4_1(166) -> 165
, 4_1(167) -> 166
, 4_1(177) -> 176
, 4_1(201) -> 200
, 4_1(202) -> 201
, 4_1(203) -> 202
, 4_1(210) -> 209
, 4_1(214) -> 213
, 4_1(216) -> 215
, 4_1(224) -> 223
, 4_1(231) -> 230
, 4_1(233) -> 232
, 4_1(234) -> 233
, 4_1(235) -> 21
, 4_1(236) -> 235
, 4_1(253) -> 299
, 4_1(255) -> 254
, 4_1(257) -> 256
, 4_1(261) -> 260
, 4_1(262) -> 56
, 4_1(267) -> 37
, 4_1(273) -> 272
, 4_1(276) -> 39
, 4_1(278) -> 74
, 4_1(283) -> 329
, 4_1(284) -> 56
, 4_1(289) -> 107
, 4_1(291) -> 290
, 4_1(294) -> 106
, 4_1(304) -> 212
, 4_1(312) -> 311
, 4_1(314) -> 313
, 4_1(317) -> 316
, 4_1(318) -> 317
, 4_1(326) -> 56
, 4_1(327) -> 326
, 4_1(329) -> 269
, 4_1(333) -> 74
, 4_1(726) -> 56
, 4_2(337) -> 37
, 4_2(337) -> 88
, 4_2(337) -> 273
, 4_2(339) -> 225
, 4_2(342) -> 341
, 4_2(345) -> 344
, 4_2(727) -> 726
, 4_2(730) -> 729
, 5_0(1) -> 1
, 5_1(1) -> 90
, 5_1(2) -> 37
, 5_1(9) -> 8
, 5_1(10) -> 9
, 5_1(19) -> 18
, 5_1(20) -> 105
, 5_1(22) -> 21
, 5_1(23) -> 22
, 5_1(32) -> 31
, 5_1(36) -> 35
, 5_1(38) -> 37
, 5_1(39) -> 1
, 5_1(39) -> 19
, 5_1(39) -> 20
, 5_1(39) -> 38
, 5_1(39) -> 56
, 5_1(39) -> 74
, 5_1(39) -> 90
, 5_1(39) -> 105
, 5_1(39) -> 106
, 5_1(39) -> 138
, 5_1(39) -> 153
, 5_1(39) -> 180
, 5_1(39) -> 181
, 5_1(39) -> 208
, 5_1(39) -> 267
, 5_1(39) -> 269
, 5_1(39) -> 338
, 5_1(39) -> 343
, 5_1(46) -> 45
, 5_1(48) -> 47
, 5_1(60) -> 59
, 5_1(61) -> 60
, 5_1(66) -> 65
, 5_1(68) -> 67
, 5_1(72) -> 273
, 5_1(74) -> 208
, 5_1(77) -> 76
, 5_1(87) -> 35
, 5_1(89) -> 88
, 5_1(97) -> 96
, 5_1(99) -> 98
, 5_1(105) -> 104
, 5_1(106) -> 90
, 5_1(108) -> 107
, 5_1(113) -> 112
, 5_1(116) -> 115
, 5_1(117) -> 116
, 5_1(121) -> 120
, 5_1(122) -> 121
, 5_1(123) -> 121
, 5_1(128) -> 127
, 5_1(135) -> 134
, 5_1(139) -> 37
, 5_1(140) -> 139
, 5_1(141) -> 140
, 5_1(150) -> 149
, 5_1(151) -> 150
, 5_1(153) -> 18
, 5_1(154) -> 39
, 5_1(164) -> 163
, 5_1(165) -> 164
, 5_1(171) -> 170
, 5_1(193) -> 192
, 5_1(194) -> 193
, 5_1(195) -> 194
, 5_1(204) -> 203
, 5_1(207) -> 206
, 5_1(209) -> 208
, 5_1(210) -> 308
, 5_1(212) -> 211
, 5_1(215) -> 214
, 5_1(222) -> 106
, 5_1(223) -> 222
, 5_1(226) -> 225
, 5_1(229) -> 228
, 5_1(234) -> 287
, 5_1(242) -> 241
, 5_1(244) -> 169
, 5_1(264) -> 263
, 5_1(269) -> 325
, 5_1(271) -> 270
, 5_1(274) -> 273
, 5_1(283) -> 303
, 5_1(288) -> 287
, 5_1(294) -> 293
, 5_1(297) -> 296
, 5_1(300) -> 56
, 5_1(306) -> 305
, 5_1(310) -> 309
, 5_1(316) -> 315
, 5_1(324) -> 323
, 5_1(326) -> 2
, 5_1(726) -> 56
, 5_1(747) -> 56
, 5_2(1) -> 338
, 5_2(39) -> 338
, 5_2(106) -> 338
, 5_2(140) -> 338
, 5_2(212) -> 338
, 5_2(229) -> 340
, 5_2(300) -> 338
, 5_2(310) -> 765
, 5_2(726) -> 1
, 5_2(726) -> 19
, 5_2(726) -> 38
, 5_2(726) -> 74
, 5_2(726) -> 90
, 5_2(726) -> 105
, 5_2(726) -> 106
, 5_2(726) -> 138
, 5_2(726) -> 180
, 5_2(726) -> 181
, 5_2(726) -> 267
, 5_2(726) -> 338
, 5_2(726) -> 343
, 5_2(747) -> 56}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(4(5(3(5(2(4(4(1(4(2(0(5(5(1(0(1(5(0(4(3(x1)))))))))))))))))))))
-> 4(4(2(2(3(2(0(5(5(0(2(4(0(0(0(1(3(5(2(3(x1))))))))))))))))))))
, 0(3(4(1(5(3(4(5(1(5(0(2(3(1(1(0(1(0(5(4(2(x1)))))))))))))))))))))
-> 0(5(5(0(2(4(1(0(1(4(1(5(3(0(1(5(2(5(2(x1)))))))))))))))))))
, 4(4(0(2(4(0(0(2(3(0(1(4(1(0(0(0(3(0(2(3(x1)))))))))))))))))))) ->
5(2(4(4(0(4(1(5(0(5(3(3(1(4(1(0(2(4(2(x1)))))))))))))))))))
, 2(2(2(3(0(3(1(4(4(1(1(0(5(1(0(0(5(4(1(2(x1)))))))))))))))))))) ->
2(3(4(3(5(5(2(1(1(2(5(3(5(0(4(1(2(2(1(4(x1))))))))))))))))))))
, 2(0(4(4(2(4(3(3(2(0(0(3(3(0(1(0(2(2(2(5(x1)))))))))))))))))))) ->
2(3(2(3(5(1(1(0(1(3(0(4(3(2(4(2(5(2(5(x1)))))))))))))))))))
, 5(5(4(3(2(1(3(3(1(4(1(1(3(3(3(4(0(1(2(x1))))))))))))))))))) ->
4(0(1(3(1(2(4(5(3(5(0(0(3(2(4(5(5(3(x1))))))))))))))))))
, 5(2(2(2(1(1(4(0(4(3(5(3(4(4(4(4(0(5(0(x1))))))))))))))))))) ->
3(4(5(0(2(4(3(5(1(1(5(5(4(1(4(5(5(0(0(x1)))))))))))))))))))
, 1(1(5(3(2(0(4(1(3(4(5(3(0(2(5(2(3(3(0(x1))))))))))))))))))) ->
0(1(3(4(3(5(0(2(2(0(2(4(5(0(3(3(2(0(x1))))))))))))))))))
, 1(1(1(0(3(0(1(4(3(1(1(2(5(2(1(2(1(1(0(x1))))))))))))))))))) ->
1(5(5(2(3(1(3(3(2(0(1(5(5(4(1(2(4(x1)))))))))))))))))
, 5(5(5(3(2(1(0(4(1(3(4(4(3(1(1(4(3(2(x1)))))))))))))))))) ->
5(5(4(3(2(2(3(0(3(4(4(5(5(4(4(3(0(3(x1))))))))))))))))))
, 3(1(3(2(4(2(3(3(1(5(4(0(3(1(0(4(1(0(x1)))))))))))))))))) ->
5(1(3(5(0(2(3(2(0(4(0(1(2(2(2(2(0(x1)))))))))))))))))
, 0(3(3(4(2(4(3(1(4(1(0(4(1(4(0(4(1(1(x1)))))))))))))))))) ->
0(2(2(1(1(2(3(1(3(2(2(2(5(5(5(0(3(4(2(x1)))))))))))))))))))
, 4(3(3(4(2(0(0(1(3(3(0(1(3(1(2(1(x1)))))))))))))))) ->
4(3(3(1(1(4(4(4(5(2(0(5(0(5(4(1(x1))))))))))))))))
, 5(3(4(3(2(1(4(2(2(1(3(3(1(4(4(x1))))))))))))))) ->
1(1(5(3(4(5(4(3(3(3(3(2(0(2(4(x1)))))))))))))))
, 3(0(2(5(1(1(4(1(3(4(2(5(3(1(0(x1))))))))))))))) ->
3(5(5(4(0(5(2(1(5(0(4(0(4(4(3(0(x1))))))))))))))))
, 0(0(0(4(0(0(3(2(0(5(4(4(2(1(2(x1))))))))))))))) ->
0(4(4(2(1(0(2(1(5(0(2(3(4(2(x1))))))))))))))
, 2(4(4(5(1(5(1(0(2(5(4(1(2(x1))))))))))))) ->
5(1(5(2(1(2(3(2(0(3(1(2(3(3(x1))))))))))))))
, 0(1(3(3(0(4(1(0(2(2(4(3(2(x1))))))))))))) ->
1(3(4(2(4(1(3(3(4(2(1(x1)))))))))))
, 5(3(2(0(5(4(5(2(2(3(4(5(x1)))))))))))) ->
2(4(3(5(0(2(0(2(0(4(4(x1)))))))))))
, 0(0(2(1(0(1(2(1(0(3(2(2(x1)))))))))))) ->
0(1(2(5(1(4(5(2(1(4(1(x1)))))))))))
, 5(4(2(1(4(4(1(3(2(1(2(x1))))))))))) ->
5(4(1(2(3(1(3(0(0(0(1(x1)))))))))))
, 5(3(2(5(5(5(4(3(3(4(5(x1))))))))))) ->
3(0(2(3(2(5(3(0(2(4(x1))))))))))
, 5(0(5(3(0(5(0(4(0(5(5(x1))))))))))) ->
3(4(4(3(4(0(3(5(3(5(x1))))))))))
, 5(5(1(1(4(5(0(5(1(3(x1)))))))))) ->
5(1(1(2(5(3(3(4(3(3(x1))))))))))
, 2(3(0(3(0(5(3(2(1(3(x1)))))))))) -> 2(5(0(2(2(5(0(1(x1))))))))
, 1(0(1(5(3(3(4(5(5(1(x1)))))))))) ->
1(1(5(4(3(5(1(1(5(1(x1))))))))))
, 3(5(5(4(4(1(5(1(4(x1))))))))) -> 3(2(5(0(4(0(0(5(4(x1)))))))))
, 2(3(1(3(1(3(1(5(3(x1))))))))) -> 5(4(1(0(4(1(3(x1)))))))
, 1(2(4(5(4(0(5(2(1(x1))))))))) -> 1(5(0(5(4(4(0(4(1(x1)))))))))
, 3(3(1(5(0(3(2(4(x1)))))))) -> 4(3(3(1(0(4(4(x1)))))))
, 3(0(2(2(2(1(0(3(x1)))))))) -> 3(5(2(3(0(0(4(x1)))))))
, 0(1(2(5(1(5(3(0(x1)))))))) -> 0(0(5(2(5(4(4(x1)))))))
, 5(2(2(2(4(0(3(x1))))))) -> 4(5(4(0(1(5(x1))))))
, 3(2(5(3(1(0(3(x1))))))) -> 3(5(3(4(0(1(x1))))))
, 3(1(0(0(0(1(1(x1))))))) -> 5(3(2(0(2(0(1(x1)))))))
, 4(3(5(3(2(5(x1)))))) -> 2(3(1(2(5(x1)))))
, 5(2(3(0(x1)))) -> 2(0(0(x1)))
, 5(2(1(5(x1)))) -> 4(2(5(x1)))
, 3(0(2(2(x1)))) -> 3(4(3(2(x1))))
, 0(1(1(2(x1)))) -> 0(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:
{ 0(4(5(3(5(2(4(4(1(4(2(0(5(5(1(0(1(5(0(4(3(x1)))))))))))))))))))))
-> 4(4(2(2(3(2(0(5(5(0(2(4(0(0(0(1(3(5(2(3(x1))))))))))))))))))))
, 0(3(4(1(5(3(4(5(1(5(0(2(3(1(1(0(1(0(5(4(2(x1)))))))))))))))))))))
-> 0(5(5(0(2(4(1(0(1(4(1(5(3(0(1(5(2(5(2(x1)))))))))))))))))))
, 4(4(0(2(4(0(0(2(3(0(1(4(1(0(0(0(3(0(2(3(x1)))))))))))))))))))) ->
5(2(4(4(0(4(1(5(0(5(3(3(1(4(1(0(2(4(2(x1)))))))))))))))))))
, 2(2(2(3(0(3(1(4(4(1(1(0(5(1(0(0(5(4(1(2(x1)))))))))))))))))))) ->
2(3(4(3(5(5(2(1(1(2(5(3(5(0(4(1(2(2(1(4(x1))))))))))))))))))))
, 2(0(4(4(2(4(3(3(2(0(0(3(3(0(1(0(2(2(2(5(x1)))))))))))))))))))) ->
2(3(2(3(5(1(1(0(1(3(0(4(3(2(4(2(5(2(5(x1)))))))))))))))))))
, 5(5(4(3(2(1(3(3(1(4(1(1(3(3(3(4(0(1(2(x1))))))))))))))))))) ->
4(0(1(3(1(2(4(5(3(5(0(0(3(2(4(5(5(3(x1))))))))))))))))))
, 5(2(2(2(1(1(4(0(4(3(5(3(4(4(4(4(0(5(0(x1))))))))))))))))))) ->
3(4(5(0(2(4(3(5(1(1(5(5(4(1(4(5(5(0(0(x1)))))))))))))))))))
, 1(1(5(3(2(0(4(1(3(4(5(3(0(2(5(2(3(3(0(x1))))))))))))))))))) ->
0(1(3(4(3(5(0(2(2(0(2(4(5(0(3(3(2(0(x1))))))))))))))))))
, 1(1(1(0(3(0(1(4(3(1(1(2(5(2(1(2(1(1(0(x1))))))))))))))))))) ->
1(5(5(2(3(1(3(3(2(0(1(5(5(4(1(2(4(x1)))))))))))))))))
, 5(5(5(3(2(1(0(4(1(3(4(4(3(1(1(4(3(2(x1)))))))))))))))))) ->
5(5(4(3(2(2(3(0(3(4(4(5(5(4(4(3(0(3(x1))))))))))))))))))
, 3(1(3(2(4(2(3(3(1(5(4(0(3(1(0(4(1(0(x1)))))))))))))))))) ->
5(1(3(5(0(2(3(2(0(4(0(1(2(2(2(2(0(x1)))))))))))))))))
, 0(3(3(4(2(4(3(1(4(1(0(4(1(4(0(4(1(1(x1)))))))))))))))))) ->
0(2(2(1(1(2(3(1(3(2(2(2(5(5(5(0(3(4(2(x1)))))))))))))))))))
, 4(3(3(4(2(0(0(1(3(3(0(1(3(1(2(1(x1)))))))))))))))) ->
4(3(3(1(1(4(4(4(5(2(0(5(0(5(4(1(x1))))))))))))))))
, 5(3(4(3(2(1(4(2(2(1(3(3(1(4(4(x1))))))))))))))) ->
1(1(5(3(4(5(4(3(3(3(3(2(0(2(4(x1)))))))))))))))
, 3(0(2(5(1(1(4(1(3(4(2(5(3(1(0(x1))))))))))))))) ->
3(5(5(4(0(5(2(1(5(0(4(0(4(4(3(0(x1))))))))))))))))
, 0(0(0(4(0(0(3(2(0(5(4(4(2(1(2(x1))))))))))))))) ->
0(4(4(2(1(0(2(1(5(0(2(3(4(2(x1))))))))))))))
, 2(4(4(5(1(5(1(0(2(5(4(1(2(x1))))))))))))) ->
5(1(5(2(1(2(3(2(0(3(1(2(3(3(x1))))))))))))))
, 0(1(3(3(0(4(1(0(2(2(4(3(2(x1))))))))))))) ->
1(3(4(2(4(1(3(3(4(2(1(x1)))))))))))
, 5(3(2(0(5(4(5(2(2(3(4(5(x1)))))))))))) ->
2(4(3(5(0(2(0(2(0(4(4(x1)))))))))))
, 0(0(2(1(0(1(2(1(0(3(2(2(x1)))))))))))) ->
0(1(2(5(1(4(5(2(1(4(1(x1)))))))))))
, 5(4(2(1(4(4(1(3(2(1(2(x1))))))))))) ->
5(4(1(2(3(1(3(0(0(0(1(x1)))))))))))
, 5(3(2(5(5(5(4(3(3(4(5(x1))))))))))) ->
3(0(2(3(2(5(3(0(2(4(x1))))))))))
, 5(0(5(3(0(5(0(4(0(5(5(x1))))))))))) ->
3(4(4(3(4(0(3(5(3(5(x1))))))))))
, 5(5(1(1(4(5(0(5(1(3(x1)))))))))) ->
5(1(1(2(5(3(3(4(3(3(x1))))))))))
, 2(3(0(3(0(5(3(2(1(3(x1)))))))))) -> 2(5(0(2(2(5(0(1(x1))))))))
, 1(0(1(5(3(3(4(5(5(1(x1)))))))))) ->
1(1(5(4(3(5(1(1(5(1(x1))))))))))
, 3(5(5(4(4(1(5(1(4(x1))))))))) -> 3(2(5(0(4(0(0(5(4(x1)))))))))
, 2(3(1(3(1(3(1(5(3(x1))))))))) -> 5(4(1(0(4(1(3(x1)))))))
, 1(2(4(5(4(0(5(2(1(x1))))))))) -> 1(5(0(5(4(4(0(4(1(x1)))))))))
, 3(3(1(5(0(3(2(4(x1)))))))) -> 4(3(3(1(0(4(4(x1)))))))
, 3(0(2(2(2(1(0(3(x1)))))))) -> 3(5(2(3(0(0(4(x1)))))))
, 0(1(2(5(1(5(3(0(x1)))))))) -> 0(0(5(2(5(4(4(x1)))))))
, 5(2(2(2(4(0(3(x1))))))) -> 4(5(4(0(1(5(x1))))))
, 3(2(5(3(1(0(3(x1))))))) -> 3(5(3(4(0(1(x1))))))
, 3(1(0(0(0(1(1(x1))))))) -> 5(3(2(0(2(0(1(x1)))))))
, 4(3(5(3(2(5(x1)))))) -> 2(3(1(2(5(x1)))))
, 5(2(3(0(x1)))) -> 2(0(0(x1)))
, 5(2(1(5(x1)))) -> 4(2(5(x1)))
, 3(0(2(2(x1)))) -> 3(4(3(2(x1))))
, 0(1(1(2(x1)))) -> 0(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:
{ 0(4(5(3(5(2(4(4(1(4(2(0(5(5(1(0(1(5(0(4(3(x1)))))))))))))))))))))
-> 4(4(2(2(3(2(0(5(5(0(2(4(0(0(0(1(3(5(2(3(x1))))))))))))))))))))
, 0(3(4(1(5(3(4(5(1(5(0(2(3(1(1(0(1(0(5(4(2(x1)))))))))))))))))))))
-> 0(5(5(0(2(4(1(0(1(4(1(5(3(0(1(5(2(5(2(x1)))))))))))))))))))
, 4(4(0(2(4(0(0(2(3(0(1(4(1(0(0(0(3(0(2(3(x1)))))))))))))))))))) ->
5(2(4(4(0(4(1(5(0(5(3(3(1(4(1(0(2(4(2(x1)))))))))))))))))))
, 2(2(2(3(0(3(1(4(4(1(1(0(5(1(0(0(5(4(1(2(x1)))))))))))))))))))) ->
2(3(4(3(5(5(2(1(1(2(5(3(5(0(4(1(2(2(1(4(x1))))))))))))))))))))
, 2(0(4(4(2(4(3(3(2(0(0(3(3(0(1(0(2(2(2(5(x1)))))))))))))))))))) ->
2(3(2(3(5(1(1(0(1(3(0(4(3(2(4(2(5(2(5(x1)))))))))))))))))))
, 5(5(4(3(2(1(3(3(1(4(1(1(3(3(3(4(0(1(2(x1))))))))))))))))))) ->
4(0(1(3(1(2(4(5(3(5(0(0(3(2(4(5(5(3(x1))))))))))))))))))
, 5(2(2(2(1(1(4(0(4(3(5(3(4(4(4(4(0(5(0(x1))))))))))))))))))) ->
3(4(5(0(2(4(3(5(1(1(5(5(4(1(4(5(5(0(0(x1)))))))))))))))))))
, 1(1(5(3(2(0(4(1(3(4(5(3(0(2(5(2(3(3(0(x1))))))))))))))))))) ->
0(1(3(4(3(5(0(2(2(0(2(4(5(0(3(3(2(0(x1))))))))))))))))))
, 1(1(1(0(3(0(1(4(3(1(1(2(5(2(1(2(1(1(0(x1))))))))))))))))))) ->
1(5(5(2(3(1(3(3(2(0(1(5(5(4(1(2(4(x1)))))))))))))))))
, 5(5(5(3(2(1(0(4(1(3(4(4(3(1(1(4(3(2(x1)))))))))))))))))) ->
5(5(4(3(2(2(3(0(3(4(4(5(5(4(4(3(0(3(x1))))))))))))))))))
, 3(1(3(2(4(2(3(3(1(5(4(0(3(1(0(4(1(0(x1)))))))))))))))))) ->
5(1(3(5(0(2(3(2(0(4(0(1(2(2(2(2(0(x1)))))))))))))))))
, 0(3(3(4(2(4(3(1(4(1(0(4(1(4(0(4(1(1(x1)))))))))))))))))) ->
0(2(2(1(1(2(3(1(3(2(2(2(5(5(5(0(3(4(2(x1)))))))))))))))))))
, 4(3(3(4(2(0(0(1(3(3(0(1(3(1(2(1(x1)))))))))))))))) ->
4(3(3(1(1(4(4(4(5(2(0(5(0(5(4(1(x1))))))))))))))))
, 5(3(4(3(2(1(4(2(2(1(3(3(1(4(4(x1))))))))))))))) ->
1(1(5(3(4(5(4(3(3(3(3(2(0(2(4(x1)))))))))))))))
, 3(0(2(5(1(1(4(1(3(4(2(5(3(1(0(x1))))))))))))))) ->
3(5(5(4(0(5(2(1(5(0(4(0(4(4(3(0(x1))))))))))))))))
, 0(0(0(4(0(0(3(2(0(5(4(4(2(1(2(x1))))))))))))))) ->
0(4(4(2(1(0(2(1(5(0(2(3(4(2(x1))))))))))))))
, 2(4(4(5(1(5(1(0(2(5(4(1(2(x1))))))))))))) ->
5(1(5(2(1(2(3(2(0(3(1(2(3(3(x1))))))))))))))
, 0(1(3(3(0(4(1(0(2(2(4(3(2(x1))))))))))))) ->
1(3(4(2(4(1(3(3(4(2(1(x1)))))))))))
, 5(3(2(0(5(4(5(2(2(3(4(5(x1)))))))))))) ->
2(4(3(5(0(2(0(2(0(4(4(x1)))))))))))
, 0(0(2(1(0(1(2(1(0(3(2(2(x1)))))))))))) ->
0(1(2(5(1(4(5(2(1(4(1(x1)))))))))))
, 5(4(2(1(4(4(1(3(2(1(2(x1))))))))))) ->
5(4(1(2(3(1(3(0(0(0(1(x1)))))))))))
, 5(3(2(5(5(5(4(3(3(4(5(x1))))))))))) ->
3(0(2(3(2(5(3(0(2(4(x1))))))))))
, 5(0(5(3(0(5(0(4(0(5(5(x1))))))))))) ->
3(4(4(3(4(0(3(5(3(5(x1))))))))))
, 5(5(1(1(4(5(0(5(1(3(x1)))))))))) ->
5(1(1(2(5(3(3(4(3(3(x1))))))))))
, 2(3(0(3(0(5(3(2(1(3(x1)))))))))) -> 2(5(0(2(2(5(0(1(x1))))))))
, 1(0(1(5(3(3(4(5(5(1(x1)))))))))) ->
1(1(5(4(3(5(1(1(5(1(x1))))))))))
, 3(5(5(4(4(1(5(1(4(x1))))))))) -> 3(2(5(0(4(0(0(5(4(x1)))))))))
, 2(3(1(3(1(3(1(5(3(x1))))))))) -> 5(4(1(0(4(1(3(x1)))))))
, 1(2(4(5(4(0(5(2(1(x1))))))))) -> 1(5(0(5(4(4(0(4(1(x1)))))))))
, 3(3(1(5(0(3(2(4(x1)))))))) -> 4(3(3(1(0(4(4(x1)))))))
, 3(0(2(2(2(1(0(3(x1)))))))) -> 3(5(2(3(0(0(4(x1)))))))
, 0(1(2(5(1(5(3(0(x1)))))))) -> 0(0(5(2(5(4(4(x1)))))))
, 5(2(2(2(4(0(3(x1))))))) -> 4(5(4(0(1(5(x1))))))
, 3(2(5(3(1(0(3(x1))))))) -> 3(5(3(4(0(1(x1))))))
, 3(1(0(0(0(1(1(x1))))))) -> 5(3(2(0(2(0(1(x1)))))))
, 4(3(5(3(2(5(x1)))))) -> 2(3(1(2(5(x1)))))
, 5(2(3(0(x1)))) -> 2(0(0(x1)))
, 5(2(1(5(x1)))) -> 4(2(5(x1)))
, 3(0(2(2(x1)))) -> 3(4(3(2(x1))))
, 0(1(1(2(x1)))) -> 0(0(1(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..