Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(4(1(2(0(4(1(x1))))))) -> 4(5(4(2(2(3(4(5(5(3(x1))))))))))
, 5(0(4(2(5(5(0(x1))))))) -> 0(3(3(1(2(3(0(0(2(3(x1))))))))))
, 5(0(4(2(0(4(2(x1))))))) -> 5(2(2(0(1(5(5(2(4(2(x1))))))))))
, 4(3(4(1(4(4(3(x1))))))) -> 1(4(3(3(3(1(3(1(2(2(x1))))))))))
, 4(3(0(1(2(4(2(x1))))))) -> 4(3(3(1(1(0(3(2(2(5(x1))))))))))
, 4(1(5(2(0(1(5(x1))))))) -> 2(5(4(2(3(3(0(0(0(5(x1))))))))))
, 3(5(0(5(5(5(3(x1))))))) -> 3(3(5(4(0(1(4(5(3(0(x1))))))))))
, 3(5(0(4(1(5(0(x1))))))) -> 2(3(1(0(5(4(3(0(3(3(x1))))))))))
, 3(4(4(1(4(1(1(x1))))))) -> 4(2(0(3(2(1(3(0(0(1(x1))))))))))
, 3(4(0(4(4(2(3(x1))))))) -> 3(2(4(4(5(1(1(4(5(0(x1))))))))))
, 3(0(4(3(0(3(4(x1))))))) -> 3(5(3(1(0(3(2(3(0(4(x1))))))))))
, 3(0(4(1(0(0(0(x1))))))) -> 5(2(3(5(4(5(5(1(3(0(x1))))))))))
, 2(0(4(0(4(3(0(x1))))))) -> 3(1(3(3(4(5(2(3(0(3(x1))))))))))
, 2(0(1(5(1(4(2(x1))))))) -> 2(2(5(5(2(1(2(4(0(5(x1))))))))))
, 1(4(0(0(2(5(0(x1))))))) -> 1(0(3(2(2(2(1(0(5(0(x1))))))))))
, 1(3(5(4(4(1(2(x1))))))) -> 2(0(5(0(2(3(2(2(2(2(x1))))))))))
, 1(3(2(0(1(2(1(x1))))))) -> 5(2(4(2(4(4(2(5(1(3(x1))))))))))
, 1(3(1(0(4(1(0(x1))))))) -> 1(3(3(3(3(0(0(3(1(0(x1))))))))))
, 0(5(1(1(3(4(1(x1))))))) -> 0(2(2(0(2(3(1(5(5(3(x1))))))))))
, 0(1(4(1(4(4(3(x1))))))) -> 0(1(0(1(1(2(0(5(2(3(x1))))))))))
, 0(1(3(4(2(1(2(x1))))))) -> 0(1(2(0(3(1(2(5(2(2(x1))))))))))
, 0(0(2(0(5(2(1(x1))))))) -> 0(4(3(5(2(3(5(5(2(1(x1))))))))))
, 5(5(4(3(2(4(x1)))))) -> 5(4(2(2(5(2(1(2(3(4(x1))))))))))
, 5(0(4(3(0(1(x1)))))) -> 0(3(1(2(5(1(1(1(2(1(x1))))))))))
, 3(5(5(5(0(2(x1)))))) -> 3(3(5(1(0(0(3(3(1(0(x1))))))))))
, 3(4(3(2(0(5(x1)))))) -> 2(3(3(5(3(3(1(3(3(5(x1))))))))))
, 3(2(4(3(5(5(x1)))))) -> 3(5(5(5(1(4(4(5(4(5(x1))))))))))
, 1(4(1(0(1(2(x1)))))) -> 1(0(3(1(5(3(3(4(5(2(x1))))))))))
, 1(3(5(4(3(5(x1)))))) -> 1(3(3(1(1(5(1(0(1(5(x1))))))))))
, 1(2(0(1(3(2(x1)))))) -> 2(0(3(2(1(2(3(1(0(3(x1))))))))))
, 0(0(0(2(0(1(x1)))))) -> 3(3(5(3(1(3(1(4(0(1(x1))))))))))
, 5(2(4(3(0(x1))))) -> 2(5(5(2(3(2(5(4(0(0(x1))))))))))
, 4(4(2(3(4(x1))))) -> 2(2(4(5(3(3(1(1(1(4(x1))))))))))
, 2(4(3(4(0(x1))))) -> 2(5(2(2(5(5(0(3(2(3(x1))))))))))
, 0(5(0(4(2(x1))))) -> 0(0(3(5(3(3(2(3(4(5(x1))))))))))
, 0(0(4(1(4(x1))))) -> 3(3(1(1(0(3(1(4(2(4(x1))))))))))
, 4(4(1(3(x1)))) -> 5(1(1(4(5(5(3(3(2(3(x1))))))))))
, 4(1(1(3(x1)))) -> 4(4(5(1(4(0(2(0(3(3(x1))))))))))
, 5(4(1(x1))) -> 2(5(5(1(1(1(0(2(3(4(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) -> 74
, 1_1(8) -> 158
, 1_1(10) -> 94
, 1_1(11) -> 34
, 1_1(14) -> 13
, 1_1(18) -> 183
, 1_1(23) -> 22
, 1_1(26) -> 313
, 1_1(27) -> 34
, 1_1(28) -> 1
, 1_1(28) -> 32
, 1_1(28) -> 74
, 1_1(28) -> 89
, 1_1(28) -> 94
, 1_1(28) -> 271
, 1_1(33) -> 32
, 1_1(35) -> 34
, 1_1(38) -> 37
, 1_1(39) -> 38
, 1_1(43) -> 251
, 1_1(51) -> 112
, 1_1(52) -> 11
, 1_1(57) -> 56
, 1_1(59) -> 94
, 1_1(61) -> 60
, 1_1(66) -> 233
, 1_1(71) -> 70
, 1_1(73) -> 249
, 1_1(79) -> 78
, 1_1(80) -> 79
, 1_1(84) -> 83
, 1_1(89) -> 271
, 1_1(94) -> 270
, 1_1(95) -> 52
, 1_1(101) -> 256
, 1_1(102) -> 11
, 1_1(106) -> 105
, 1_1(113) -> 112
, 1_1(153) -> 32
, 1_1(155) -> 74
, 1_1(159) -> 11
, 1_1(161) -> 160
, 1_1(162) -> 161
, 1_1(168) -> 167
, 1_1(176) -> 226
, 1_1(184) -> 183
, 1_1(222) -> 12
, 1_1(225) -> 224
, 1_1(226) -> 225
, 1_1(227) -> 54
, 1_1(234) -> 233
, 1_1(238) -> 237
, 1_1(241) -> 79
, 1_1(242) -> 109
, 1_1(247) -> 149
, 1_1(248) -> 247
, 1_1(250) -> 249
, 1_1(254) -> 253
, 1_1(258) -> 257
, 1_1(260) -> 259
, 1_1(270) -> 269
, 1_1(271) -> 270
, 1_1(310) -> 53
, 1_1(311) -> 310
, 1_1(314) -> 313
, 1_1(316) -> 19
, 1_1(319) -> 316
, 1_1(345) -> 344
, 1_1(348) -> 261
, 1_1(349) -> 348
, 1_1(350) -> 349
, 1_2(354) -> 353
, 1_2(355) -> 354
, 1_2(356) -> 355
, 1_2(396) -> 395
, 4_0(1) -> 1
, 4_1(1) -> 89
, 4_1(2) -> 1
, 4_1(2) -> 10
, 4_1(2) -> 43
, 4_1(2) -> 89
, 4_1(2) -> 185
, 4_1(2) -> 240
, 4_1(4) -> 3
, 4_1(8) -> 7
, 4_1(9) -> 57
, 4_1(27) -> 26
, 4_1(28) -> 89
, 4_1(29) -> 28
, 4_1(43) -> 241
, 4_1(44) -> 89
, 4_1(46) -> 45
, 4_1(50) -> 265
, 4_1(51) -> 107
, 4_1(55) -> 54
, 4_1(58) -> 57
, 4_1(64) -> 63
, 4_1(73) -> 260
, 4_1(76) -> 75
, 4_1(77) -> 76
, 4_1(81) -> 80
, 4_1(82) -> 89
, 4_1(92) -> 91
, 4_1(98) -> 97
, 4_1(100) -> 63
, 4_1(103) -> 89
, 4_1(120) -> 20
, 4_1(122) -> 121
, 4_1(123) -> 122
, 4_1(170) -> 11
, 4_1(177) -> 19
, 4_1(239) -> 238
, 4_1(240) -> 239
, 4_1(246) -> 245
, 4_1(266) -> 102
, 4_1(315) -> 314
, 4_1(322) -> 319
, 4_1(343) -> 2
, 4_1(346) -> 345
, 4_2(28) -> 359
, 4_2(309) -> 308
, 4_2(397) -> 396
, 4_2(398) -> 397
, 4_2(400) -> 399
, 4_2(603) -> 602
, 5_0(1) -> 1
, 5_1(1) -> 43
, 5_1(3) -> 2
, 5_1(9) -> 8
, 5_1(10) -> 9
, 5_1(18) -> 164
, 5_1(19) -> 1
, 5_1(19) -> 10
, 5_1(19) -> 43
, 5_1(19) -> 59
, 5_1(19) -> 74
, 5_1(19) -> 81
, 5_1(19) -> 87
, 5_1(19) -> 89
, 5_1(19) -> 94
, 5_1(24) -> 23
, 5_1(25) -> 24
, 5_1(27) -> 246
, 5_1(35) -> 169
, 5_1(44) -> 1
, 5_1(45) -> 44
, 5_1(51) -> 81
, 5_1(52) -> 246
, 5_1(54) -> 53
, 5_1(59) -> 58
, 5_1(63) -> 62
, 5_1(67) -> 1
, 5_1(74) -> 93
, 5_1(78) -> 77
, 5_1(82) -> 52
, 5_1(86) -> 98
, 5_1(89) -> 240
, 5_1(91) -> 90
, 5_1(93) -> 92
, 5_1(94) -> 93
, 5_1(99) -> 98
, 5_1(103) -> 102
, 5_1(104) -> 103
, 5_1(107) -> 264
, 5_1(115) -> 114
, 5_1(155) -> 43
, 5_1(156) -> 1
, 5_1(159) -> 246
, 5_1(172) -> 171
, 5_1(175) -> 174
, 5_1(176) -> 175
, 5_1(182) -> 181
, 5_1(224) -> 223
, 5_1(231) -> 230
, 5_1(236) -> 82
, 5_1(237) -> 236
, 5_1(241) -> 240
, 5_1(243) -> 242
, 5_1(246) -> 23
, 5_1(249) -> 248
, 5_1(261) -> 45
, 5_1(265) -> 264
, 5_1(267) -> 266
, 5_1(274) -> 273
, 5_1(275) -> 274
, 5_1(283) -> 252
, 5_1(315) -> 24
, 5_1(325) -> 322
, 5_1(328) -> 325
, 5_1(344) -> 343
, 5_2(67) -> 309
, 5_2(104) -> 400
, 5_2(304) -> 303
, 5_2(352) -> 351
, 5_2(353) -> 352
, 5_2(393) -> 392
, 5_2(394) -> 393
, 5_2(395) -> 394
, 5_2(399) -> 398
, 5_2(597) -> 596
, 5_2(598) -> 597
, 5_2(602) -> 601
, 3_0(1) -> 1
, 3_1(1) -> 10
, 3_1(2) -> 66
, 3_1(7) -> 6
, 3_1(10) -> 66
, 3_1(11) -> 10
, 3_1(12) -> 11
, 3_1(13) -> 12
, 3_1(16) -> 15
, 3_1(18) -> 276
, 3_1(27) -> 276
, 3_1(28) -> 10
, 3_1(30) -> 29
, 3_1(31) -> 30
, 3_1(32) -> 31
, 3_1(34) -> 33
, 3_1(35) -> 40
, 3_1(36) -> 2
, 3_1(37) -> 36
, 3_1(41) -> 40
, 3_1(43) -> 235
, 3_1(44) -> 10
, 3_1(48) -> 47
, 3_1(49) -> 48
, 3_1(50) -> 71
, 3_1(51) -> 59
, 3_1(52) -> 1
, 3_1(52) -> 10
, 3_1(52) -> 27
, 3_1(52) -> 49
, 3_1(52) -> 50
, 3_1(52) -> 51
, 3_1(52) -> 59
, 3_1(52) -> 87
, 3_1(52) -> 185
, 3_1(52) -> 235
, 3_1(52) -> 276
, 3_1(53) -> 52
, 3_1(60) -> 44
, 3_1(65) -> 64
, 3_1(68) -> 2
, 3_1(69) -> 68
, 3_1(71) -> 47
, 3_1(72) -> 71
, 3_1(74) -> 153
, 3_1(75) -> 2
, 3_1(83) -> 82
, 3_1(86) -> 85
, 3_1(88) -> 87
, 3_1(89) -> 185
, 3_1(90) -> 20
, 3_1(96) -> 95
, 3_1(97) -> 96
, 3_1(101) -> 100
, 3_1(102) -> 2
, 3_1(109) -> 108
, 3_1(112) -> 153
, 3_1(114) -> 10
, 3_1(118) -> 117
, 3_1(119) -> 117
, 3_1(148) -> 28
, 3_1(149) -> 148
, 3_1(150) -> 149
, 3_1(151) -> 150
, 3_1(153) -> 229
, 3_1(154) -> 2
, 3_1(155) -> 1
, 3_1(156) -> 1
, 3_1(157) -> 2
, 3_1(158) -> 157
, 3_1(167) -> 166
, 3_1(171) -> 170
, 3_1(174) -> 173
, 3_1(184) -> 284
, 3_1(226) -> 33
, 3_1(230) -> 60
, 3_1(232) -> 231
, 3_1(233) -> 232
, 3_1(235) -> 234
, 3_1(241) -> 286
, 3_1(244) -> 243
, 3_1(245) -> 244
, 3_1(252) -> 114
, 3_1(256) -> 255
, 3_1(257) -> 54
, 3_1(259) -> 258
, 3_1(263) -> 262
, 3_1(268) -> 267
, 3_1(269) -> 268
, 3_1(276) -> 328
, 3_1(284) -> 283
, 3_1(285) -> 284
, 3_1(286) -> 243
, 3_1(313) -> 312
, 3_2(303) -> 302
, 3_2(305) -> 304
, 3_2(306) -> 305
, 3_2(308) -> 307
, 3_2(359) -> 358
, 3_2(392) -> 262
, 3_2(392) -> 276
, 3_2(392) -> 284
, 3_2(600) -> 599
, 2_0(1) -> 1
, 2_1(1) -> 27
, 2_1(2) -> 18
, 2_1(5) -> 4
, 2_1(6) -> 5
, 2_1(10) -> 18
, 2_1(11) -> 176
, 2_1(15) -> 14
, 2_1(20) -> 19
, 2_1(21) -> 20
, 2_1(26) -> 25
, 2_1(27) -> 35
, 2_1(28) -> 27
, 2_1(35) -> 119
, 2_1(36) -> 27
, 2_1(42) -> 41
, 2_1(43) -> 42
, 2_1(44) -> 1
, 2_1(44) -> 10
, 2_1(44) -> 24
, 2_1(44) -> 27
, 2_1(44) -> 34
, 2_1(44) -> 43
, 2_1(44) -> 74
, 2_1(44) -> 89
, 2_1(44) -> 94
, 2_1(44) -> 185
, 2_1(44) -> 235
, 2_1(44) -> 240
, 2_1(44) -> 246
, 2_1(44) -> 315
, 2_1(47) -> 46
, 2_1(52) -> 27
, 2_1(59) -> 86
, 2_1(65) -> 347
, 2_1(67) -> 2
, 2_1(68) -> 27
, 2_1(70) -> 69
, 2_1(74) -> 176
, 2_1(75) -> 52
, 2_1(87) -> 86
, 2_1(89) -> 315
, 2_1(93) -> 123
, 2_1(100) -> 99
, 2_1(101) -> 347
, 2_1(102) -> 44
, 2_1(105) -> 104
, 2_1(107) -> 106
, 2_1(110) -> 109
, 2_1(111) -> 110
, 2_1(112) -> 111
, 2_1(117) -> 116
, 2_1(119) -> 118
, 2_1(121) -> 120
, 2_1(153) -> 254
, 2_1(154) -> 11
, 2_1(155) -> 154
, 2_1(156) -> 1
, 2_1(157) -> 156
, 2_1(163) -> 162
, 2_1(165) -> 159
, 2_1(169) -> 168
, 2_1(173) -> 172
, 2_1(180) -> 177
, 2_1(181) -> 180
, 2_1(183) -> 182
, 2_1(185) -> 184
, 2_1(223) -> 222
, 2_1(240) -> 263
, 2_1(246) -> 168
, 2_1(253) -> 252
, 2_1(255) -> 254
, 2_1(262) -> 261
, 2_1(264) -> 263
, 2_1(272) -> 45
, 2_1(273) -> 272
, 2_1(286) -> 285
, 2_2(307) -> 306
, 2_2(351) -> 240
, 2_2(358) -> 357
, 2_2(596) -> 24
, 2_2(599) -> 598
, 2_2(601) -> 600
, 0_0(1) -> 1
, 0_1(1) -> 51
, 0_1(2) -> 101
, 0_1(10) -> 101
, 0_1(11) -> 1
, 0_1(11) -> 16
, 0_1(11) -> 43
, 0_1(11) -> 50
, 0_1(11) -> 51
, 0_1(11) -> 73
, 0_1(11) -> 81
, 0_1(17) -> 16
, 0_1(18) -> 17
, 0_1(22) -> 21
, 0_1(27) -> 17
, 0_1(40) -> 39
, 0_1(43) -> 51
, 0_1(44) -> 1
, 0_1(44) -> 51
, 0_1(44) -> 113
, 0_1(50) -> 49
, 0_1(51) -> 50
, 0_1(52) -> 51
, 0_1(56) -> 55
, 0_1(60) -> 51
, 0_1(62) -> 61
, 0_1(66) -> 65
, 0_1(68) -> 67
, 0_1(73) -> 72
, 0_1(74) -> 73
, 0_1(79) -> 55
, 0_1(81) -> 113
, 0_1(85) -> 84
, 0_1(89) -> 88
, 0_1(102) -> 1
, 0_1(108) -> 28
, 0_1(114) -> 44
, 0_1(116) -> 115
, 0_1(152) -> 151
, 0_1(153) -> 152
, 0_1(154) -> 1
, 0_1(155) -> 1
, 0_1(156) -> 155
, 0_1(160) -> 159
, 0_1(164) -> 163
, 0_1(166) -> 165
, 0_1(184) -> 350
, 0_1(228) -> 227
, 0_1(229) -> 228
, 0_1(246) -> 163
, 0_1(251) -> 250
, 0_1(276) -> 275
, 0_1(312) -> 311
, 0_1(347) -> 346
, 0_2(156) -> 604
, 0_2(301) -> 113
, 0_2(302) -> 301
, 0_2(357) -> 356
, 0_2(604) -> 603}
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(1(2(0(4(1(x1))))))) -> 4(5(4(2(2(3(4(5(5(3(x1))))))))))
, 5(0(4(2(5(5(0(x1))))))) -> 0(3(3(1(2(3(0(0(2(3(x1))))))))))
, 5(0(4(2(0(4(2(x1))))))) -> 5(2(2(0(1(5(5(2(4(2(x1))))))))))
, 4(3(4(1(4(4(3(x1))))))) -> 1(4(3(3(3(1(3(1(2(2(x1))))))))))
, 4(3(0(1(2(4(2(x1))))))) -> 4(3(3(1(1(0(3(2(2(5(x1))))))))))
, 4(1(5(2(0(1(5(x1))))))) -> 2(5(4(2(3(3(0(0(0(5(x1))))))))))
, 3(5(0(5(5(5(3(x1))))))) -> 3(3(5(4(0(1(4(5(3(0(x1))))))))))
, 3(5(0(4(1(5(0(x1))))))) -> 2(3(1(0(5(4(3(0(3(3(x1))))))))))
, 3(4(4(1(4(1(1(x1))))))) -> 4(2(0(3(2(1(3(0(0(1(x1))))))))))
, 3(4(0(4(4(2(3(x1))))))) -> 3(2(4(4(5(1(1(4(5(0(x1))))))))))
, 3(0(4(3(0(3(4(x1))))))) -> 3(5(3(1(0(3(2(3(0(4(x1))))))))))
, 3(0(4(1(0(0(0(x1))))))) -> 5(2(3(5(4(5(5(1(3(0(x1))))))))))
, 2(0(4(0(4(3(0(x1))))))) -> 3(1(3(3(4(5(2(3(0(3(x1))))))))))
, 2(0(1(5(1(4(2(x1))))))) -> 2(2(5(5(2(1(2(4(0(5(x1))))))))))
, 1(4(0(0(2(5(0(x1))))))) -> 1(0(3(2(2(2(1(0(5(0(x1))))))))))
, 1(3(5(4(4(1(2(x1))))))) -> 2(0(5(0(2(3(2(2(2(2(x1))))))))))
, 1(3(2(0(1(2(1(x1))))))) -> 5(2(4(2(4(4(2(5(1(3(x1))))))))))
, 1(3(1(0(4(1(0(x1))))))) -> 1(3(3(3(3(0(0(3(1(0(x1))))))))))
, 0(5(1(1(3(4(1(x1))))))) -> 0(2(2(0(2(3(1(5(5(3(x1))))))))))
, 0(1(4(1(4(4(3(x1))))))) -> 0(1(0(1(1(2(0(5(2(3(x1))))))))))
, 0(1(3(4(2(1(2(x1))))))) -> 0(1(2(0(3(1(2(5(2(2(x1))))))))))
, 0(0(2(0(5(2(1(x1))))))) -> 0(4(3(5(2(3(5(5(2(1(x1))))))))))
, 5(5(4(3(2(4(x1)))))) -> 5(4(2(2(5(2(1(2(3(4(x1))))))))))
, 5(0(4(3(0(1(x1)))))) -> 0(3(1(2(5(1(1(1(2(1(x1))))))))))
, 3(5(5(5(0(2(x1)))))) -> 3(3(5(1(0(0(3(3(1(0(x1))))))))))
, 3(4(3(2(0(5(x1)))))) -> 2(3(3(5(3(3(1(3(3(5(x1))))))))))
, 3(2(4(3(5(5(x1)))))) -> 3(5(5(5(1(4(4(5(4(5(x1))))))))))
, 1(4(1(0(1(2(x1)))))) -> 1(0(3(1(5(3(3(4(5(2(x1))))))))))
, 1(3(5(4(3(5(x1)))))) -> 1(3(3(1(1(5(1(0(1(5(x1))))))))))
, 1(2(0(1(3(2(x1)))))) -> 2(0(3(2(1(2(3(1(0(3(x1))))))))))
, 0(0(0(2(0(1(x1)))))) -> 3(3(5(3(1(3(1(4(0(1(x1))))))))))
, 5(2(4(3(0(x1))))) -> 2(5(5(2(3(2(5(4(0(0(x1))))))))))
, 4(4(2(3(4(x1))))) -> 2(2(4(5(3(3(1(1(1(4(x1))))))))))
, 2(4(3(4(0(x1))))) -> 2(5(2(2(5(5(0(3(2(3(x1))))))))))
, 0(5(0(4(2(x1))))) -> 0(0(3(5(3(3(2(3(4(5(x1))))))))))
, 0(0(4(1(4(x1))))) -> 3(3(1(1(0(3(1(4(2(4(x1))))))))))
, 4(4(1(3(x1)))) -> 5(1(1(4(5(5(3(3(2(3(x1))))))))))
, 4(1(1(3(x1)))) -> 4(4(5(1(4(0(2(0(3(3(x1))))))))))
, 5(4(1(x1))) -> 2(5(5(1(1(1(0(2(3(4(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(1(2(0(4(1(x1))))))) -> 4(5(4(2(2(3(4(5(5(3(x1))))))))))
, 5(0(4(2(5(5(0(x1))))))) -> 0(3(3(1(2(3(0(0(2(3(x1))))))))))
, 5(0(4(2(0(4(2(x1))))))) -> 5(2(2(0(1(5(5(2(4(2(x1))))))))))
, 4(3(4(1(4(4(3(x1))))))) -> 1(4(3(3(3(1(3(1(2(2(x1))))))))))
, 4(3(0(1(2(4(2(x1))))))) -> 4(3(3(1(1(0(3(2(2(5(x1))))))))))
, 4(1(5(2(0(1(5(x1))))))) -> 2(5(4(2(3(3(0(0(0(5(x1))))))))))
, 3(5(0(5(5(5(3(x1))))))) -> 3(3(5(4(0(1(4(5(3(0(x1))))))))))
, 3(5(0(4(1(5(0(x1))))))) -> 2(3(1(0(5(4(3(0(3(3(x1))))))))))
, 3(4(4(1(4(1(1(x1))))))) -> 4(2(0(3(2(1(3(0(0(1(x1))))))))))
, 3(4(0(4(4(2(3(x1))))))) -> 3(2(4(4(5(1(1(4(5(0(x1))))))))))
, 3(0(4(3(0(3(4(x1))))))) -> 3(5(3(1(0(3(2(3(0(4(x1))))))))))
, 3(0(4(1(0(0(0(x1))))))) -> 5(2(3(5(4(5(5(1(3(0(x1))))))))))
, 2(0(4(0(4(3(0(x1))))))) -> 3(1(3(3(4(5(2(3(0(3(x1))))))))))
, 2(0(1(5(1(4(2(x1))))))) -> 2(2(5(5(2(1(2(4(0(5(x1))))))))))
, 1(4(0(0(2(5(0(x1))))))) -> 1(0(3(2(2(2(1(0(5(0(x1))))))))))
, 1(3(5(4(4(1(2(x1))))))) -> 2(0(5(0(2(3(2(2(2(2(x1))))))))))
, 1(3(2(0(1(2(1(x1))))))) -> 5(2(4(2(4(4(2(5(1(3(x1))))))))))
, 1(3(1(0(4(1(0(x1))))))) -> 1(3(3(3(3(0(0(3(1(0(x1))))))))))
, 0(5(1(1(3(4(1(x1))))))) -> 0(2(2(0(2(3(1(5(5(3(x1))))))))))
, 0(1(4(1(4(4(3(x1))))))) -> 0(1(0(1(1(2(0(5(2(3(x1))))))))))
, 0(1(3(4(2(1(2(x1))))))) -> 0(1(2(0(3(1(2(5(2(2(x1))))))))))
, 0(0(2(0(5(2(1(x1))))))) -> 0(4(3(5(2(3(5(5(2(1(x1))))))))))
, 5(5(4(3(2(4(x1)))))) -> 5(4(2(2(5(2(1(2(3(4(x1))))))))))
, 5(0(4(3(0(1(x1)))))) -> 0(3(1(2(5(1(1(1(2(1(x1))))))))))
, 3(5(5(5(0(2(x1)))))) -> 3(3(5(1(0(0(3(3(1(0(x1))))))))))
, 3(4(3(2(0(5(x1)))))) -> 2(3(3(5(3(3(1(3(3(5(x1))))))))))
, 3(2(4(3(5(5(x1)))))) -> 3(5(5(5(1(4(4(5(4(5(x1))))))))))
, 1(4(1(0(1(2(x1)))))) -> 1(0(3(1(5(3(3(4(5(2(x1))))))))))
, 1(3(5(4(3(5(x1)))))) -> 1(3(3(1(1(5(1(0(1(5(x1))))))))))
, 1(2(0(1(3(2(x1)))))) -> 2(0(3(2(1(2(3(1(0(3(x1))))))))))
, 0(0(0(2(0(1(x1)))))) -> 3(3(5(3(1(3(1(4(0(1(x1))))))))))
, 5(2(4(3(0(x1))))) -> 2(5(5(2(3(2(5(4(0(0(x1))))))))))
, 4(4(2(3(4(x1))))) -> 2(2(4(5(3(3(1(1(1(4(x1))))))))))
, 2(4(3(4(0(x1))))) -> 2(5(2(2(5(5(0(3(2(3(x1))))))))))
, 0(5(0(4(2(x1))))) -> 0(0(3(5(3(3(2(3(4(5(x1))))))))))
, 0(0(4(1(4(x1))))) -> 3(3(1(1(0(3(1(4(2(4(x1))))))))))
, 4(4(1(3(x1)))) -> 5(1(1(4(5(5(3(3(2(3(x1))))))))))
, 4(1(1(3(x1)))) -> 4(4(5(1(4(0(2(0(3(3(x1))))))))))
, 5(4(1(x1))) -> 2(5(5(1(1(1(0(2(3(4(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(1(2(0(4(1(x1))))))) -> 4(5(4(2(2(3(4(5(5(3(x1))))))))))
, 5(0(4(2(5(5(0(x1))))))) -> 0(3(3(1(2(3(0(0(2(3(x1))))))))))
, 5(0(4(2(0(4(2(x1))))))) -> 5(2(2(0(1(5(5(2(4(2(x1))))))))))
, 4(3(4(1(4(4(3(x1))))))) -> 1(4(3(3(3(1(3(1(2(2(x1))))))))))
, 4(3(0(1(2(4(2(x1))))))) -> 4(3(3(1(1(0(3(2(2(5(x1))))))))))
, 4(1(5(2(0(1(5(x1))))))) -> 2(5(4(2(3(3(0(0(0(5(x1))))))))))
, 3(5(0(5(5(5(3(x1))))))) -> 3(3(5(4(0(1(4(5(3(0(x1))))))))))
, 3(5(0(4(1(5(0(x1))))))) -> 2(3(1(0(5(4(3(0(3(3(x1))))))))))
, 3(4(4(1(4(1(1(x1))))))) -> 4(2(0(3(2(1(3(0(0(1(x1))))))))))
, 3(4(0(4(4(2(3(x1))))))) -> 3(2(4(4(5(1(1(4(5(0(x1))))))))))
, 3(0(4(3(0(3(4(x1))))))) -> 3(5(3(1(0(3(2(3(0(4(x1))))))))))
, 3(0(4(1(0(0(0(x1))))))) -> 5(2(3(5(4(5(5(1(3(0(x1))))))))))
, 2(0(4(0(4(3(0(x1))))))) -> 3(1(3(3(4(5(2(3(0(3(x1))))))))))
, 2(0(1(5(1(4(2(x1))))))) -> 2(2(5(5(2(1(2(4(0(5(x1))))))))))
, 1(4(0(0(2(5(0(x1))))))) -> 1(0(3(2(2(2(1(0(5(0(x1))))))))))
, 1(3(5(4(4(1(2(x1))))))) -> 2(0(5(0(2(3(2(2(2(2(x1))))))))))
, 1(3(2(0(1(2(1(x1))))))) -> 5(2(4(2(4(4(2(5(1(3(x1))))))))))
, 1(3(1(0(4(1(0(x1))))))) -> 1(3(3(3(3(0(0(3(1(0(x1))))))))))
, 0(5(1(1(3(4(1(x1))))))) -> 0(2(2(0(2(3(1(5(5(3(x1))))))))))
, 0(1(4(1(4(4(3(x1))))))) -> 0(1(0(1(1(2(0(5(2(3(x1))))))))))
, 0(1(3(4(2(1(2(x1))))))) -> 0(1(2(0(3(1(2(5(2(2(x1))))))))))
, 0(0(2(0(5(2(1(x1))))))) -> 0(4(3(5(2(3(5(5(2(1(x1))))))))))
, 5(5(4(3(2(4(x1)))))) -> 5(4(2(2(5(2(1(2(3(4(x1))))))))))
, 5(0(4(3(0(1(x1)))))) -> 0(3(1(2(5(1(1(1(2(1(x1))))))))))
, 3(5(5(5(0(2(x1)))))) -> 3(3(5(1(0(0(3(3(1(0(x1))))))))))
, 3(4(3(2(0(5(x1)))))) -> 2(3(3(5(3(3(1(3(3(5(x1))))))))))
, 3(2(4(3(5(5(x1)))))) -> 3(5(5(5(1(4(4(5(4(5(x1))))))))))
, 1(4(1(0(1(2(x1)))))) -> 1(0(3(1(5(3(3(4(5(2(x1))))))))))
, 1(3(5(4(3(5(x1)))))) -> 1(3(3(1(1(5(1(0(1(5(x1))))))))))
, 1(2(0(1(3(2(x1)))))) -> 2(0(3(2(1(2(3(1(0(3(x1))))))))))
, 0(0(0(2(0(1(x1)))))) -> 3(3(5(3(1(3(1(4(0(1(x1))))))))))
, 5(2(4(3(0(x1))))) -> 2(5(5(2(3(2(5(4(0(0(x1))))))))))
, 4(4(2(3(4(x1))))) -> 2(2(4(5(3(3(1(1(1(4(x1))))))))))
, 2(4(3(4(0(x1))))) -> 2(5(2(2(5(5(0(3(2(3(x1))))))))))
, 0(5(0(4(2(x1))))) -> 0(0(3(5(3(3(2(3(4(5(x1))))))))))
, 0(0(4(1(4(x1))))) -> 3(3(1(1(0(3(1(4(2(4(x1))))))))))
, 4(4(1(3(x1)))) -> 5(1(1(4(5(5(3(3(2(3(x1))))))))))
, 4(1(1(3(x1)))) -> 4(4(5(1(4(0(2(0(3(3(x1))))))))))
, 5(4(1(x1))) -> 2(5(5(1(1(1(0(2(3(4(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..