Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ 1_0(1) -> 1
, 1_1(2) -> 1
, 1_1(2) -> 26
, 1_1(7) -> 6
, 1_1(8) -> 7
, 1_1(10) -> 9
, 1_1(14) -> 7
, 1_1(16) -> 15
, 1_1(20) -> 66
, 1_1(22) -> 21
, 1_1(28) -> 27
, 1_1(66) -> 65
, 1_2(37) -> 8
, 1_2(37) -> 14
, 1_2(37) -> 20
, 1_2(37) -> 26
, 1_2(42) -> 41
, 1_2(43) -> 42
, 1_2(45) -> 44
, 1_2(49) -> 72
, 1_2(51) -> 50
, 1_2(57) -> 56
, 1_2(72) -> 71
, 1_2(73) -> 8
, 1_2(73) -> 14
, 1_2(73) -> 20
, 1_2(73) -> 26
, 1_2(78) -> 77
, 1_2(79) -> 78
, 1_2(81) -> 80
, 1_2(85) -> 8
, 1_2(85) -> 14
, 1_2(85) -> 20
, 1_2(90) -> 89
, 1_2(91) -> 90
, 1_2(93) -> 92
, 1_2(97) -> 72
, 1_2(99) -> 98
, 1_2(105) -> 104
, 1_2(114) -> 113
, 1_2(115) -> 114
, 1_2(117) -> 116
, 1_2(123) -> 122
, 1_2(145) -> 8
, 1_2(145) -> 14
, 1_2(150) -> 149
, 1_2(151) -> 150
, 1_2(153) -> 152
, 1_2(157) -> 90
, 1_2(159) -> 158
, 1_3(132) -> 131
, 1_3(133) -> 132
, 1_3(135) -> 134
, 1_3(141) -> 140
, 1_3(163) -> 55
, 1_3(168) -> 167
, 1_3(169) -> 168
, 1_3(171) -> 170
, 1_3(175) -> 168
, 1_3(177) -> 176
, 1_3(186) -> 49
, 1_3(191) -> 190
, 1_3(192) -> 191
, 1_3(194) -> 193
, 1_3(198) -> 225
, 1_3(200) -> 199
, 1_3(206) -> 205
, 1_3(225) -> 224
, 1_3(231) -> 230
, 1_3(232) -> 231
, 1_3(234) -> 233
, 1_3(240) -> 239
, 1_3(244) -> 43
, 1_3(249) -> 248
, 1_3(250) -> 249
, 1_3(252) -> 251
, 1_3(256) -> 249
, 1_3(258) -> 257
, 1_3(262) -> 79
, 1_3(267) -> 266
, 1_3(268) -> 267
, 1_3(270) -> 269
, 1_3(274) -> 291
, 1_3(276) -> 275
, 1_3(282) -> 281
, 1_3(291) -> 290
, 5_0(1) -> 1
, 5_1(1) -> 31
, 5_1(2) -> 25
, 5_1(6) -> 5
, 5_1(7) -> 25
, 5_1(8) -> 13
, 5_1(14) -> 13
, 5_1(20) -> 19
, 5_1(26) -> 25
, 5_1(65) -> 64
, 5_2(2) -> 60
, 5_2(8) -> 60
, 5_2(14) -> 60
, 5_2(37) -> 60
, 5_2(41) -> 40
, 5_2(43) -> 84
, 5_2(49) -> 48
, 5_2(55) -> 54
, 5_2(71) -> 70
, 5_2(73) -> 108
, 5_2(77) -> 76
, 5_2(85) -> 126
, 5_2(89) -> 88
, 5_2(91) -> 84
, 5_2(97) -> 96
, 5_2(103) -> 102
, 5_2(113) -> 112
, 5_2(115) -> 162
, 5_2(121) -> 120
, 5_2(145) -> 108
, 5_2(149) -> 148
, 5_2(157) -> 156
, 5_3(37) -> 144
, 5_3(73) -> 138
, 5_3(85) -> 144
, 5_3(131) -> 130
, 5_3(133) -> 180
, 5_3(139) -> 138
, 5_3(145) -> 138
, 5_3(163) -> 209
, 5_3(167) -> 166
, 5_3(169) -> 174
, 5_3(175) -> 174
, 5_3(186) -> 243
, 5_3(190) -> 189
, 5_3(192) -> 197
, 5_3(198) -> 197
, 5_3(204) -> 203
, 5_3(224) -> 223
, 5_3(230) -> 229
, 5_3(232) -> 261
, 5_3(238) -> 237
, 5_3(244) -> 285
, 5_3(248) -> 247
, 5_3(256) -> 255
, 5_3(266) -> 265
, 5_3(268) -> 273
, 5_3(274) -> 273
, 5_3(280) -> 279
, 5_3(290) -> 289
, 4_0(1) -> 1
, 4_1(5) -> 4
, 4_1(13) -> 12
, 4_1(19) -> 18
, 4_1(25) -> 24
, 4_1(31) -> 30
, 4_1(64) -> 63
, 4_2(40) -> 39
, 4_2(48) -> 47
, 4_2(54) -> 53
, 4_2(60) -> 59
, 4_2(70) -> 69
, 4_2(76) -> 75
, 4_2(84) -> 83
, 4_2(88) -> 87
, 4_2(96) -> 95
, 4_2(102) -> 101
, 4_2(108) -> 107
, 4_2(112) -> 111
, 4_2(120) -> 119
, 4_2(126) -> 125
, 4_2(148) -> 147
, 4_2(156) -> 155
, 4_2(162) -> 161
, 4_3(130) -> 129
, 4_3(138) -> 137
, 4_3(144) -> 143
, 4_3(166) -> 165
, 4_3(174) -> 173
, 4_3(180) -> 179
, 4_3(189) -> 188
, 4_3(197) -> 196
, 4_3(203) -> 202
, 4_3(209) -> 208
, 4_3(223) -> 222
, 4_3(229) -> 228
, 4_3(237) -> 236
, 4_3(243) -> 242
, 4_3(247) -> 246
, 4_3(255) -> 254
, 4_3(261) -> 260
, 4_3(265) -> 264
, 4_3(273) -> 272
, 4_3(279) -> 278
, 4_3(285) -> 284
, 4_3(289) -> 288
, 3_0(1) -> 1
, 3_1(4) -> 3
, 3_1(12) -> 11
, 3_1(18) -> 17
, 3_1(24) -> 23
, 3_1(30) -> 29
, 3_1(63) -> 62
, 3_2(39) -> 38
, 3_2(47) -> 46
, 3_2(53) -> 52
, 3_2(59) -> 58
, 3_2(69) -> 68
, 3_2(75) -> 74
, 3_2(83) -> 82
, 3_2(87) -> 86
, 3_2(95) -> 94
, 3_2(101) -> 100
, 3_2(107) -> 106
, 3_2(111) -> 110
, 3_2(119) -> 118
, 3_2(125) -> 124
, 3_2(147) -> 146
, 3_2(155) -> 154
, 3_2(161) -> 160
, 3_3(129) -> 128
, 3_3(137) -> 136
, 3_3(143) -> 142
, 3_3(165) -> 164
, 3_3(173) -> 172
, 3_3(179) -> 178
, 3_3(188) -> 187
, 3_3(196) -> 195
, 3_3(202) -> 201
, 3_3(208) -> 207
, 3_3(222) -> 221
, 3_3(228) -> 227
, 3_3(236) -> 235
, 3_3(242) -> 241
, 3_3(246) -> 245
, 3_3(254) -> 253
, 3_3(260) -> 259
, 3_3(264) -> 263
, 3_3(272) -> 271
, 3_3(278) -> 277
, 3_3(284) -> 283
, 3_3(288) -> 287
, 2_0(1) -> 1
, 2_1(3) -> 2
, 2_1(11) -> 10
, 2_1(17) -> 16
, 2_1(23) -> 22
, 2_1(29) -> 28
, 2_1(62) -> 61
, 2_2(38) -> 37
, 2_2(46) -> 45
, 2_2(52) -> 51
, 2_2(58) -> 57
, 2_2(68) -> 67
, 2_2(74) -> 73
, 2_2(82) -> 81
, 2_2(86) -> 85
, 2_2(94) -> 93
, 2_2(100) -> 99
, 2_2(106) -> 105
, 2_2(110) -> 109
, 2_2(118) -> 117
, 2_2(124) -> 123
, 2_2(146) -> 145
, 2_2(154) -> 153
, 2_2(160) -> 159
, 2_3(128) -> 127
, 2_3(136) -> 135
, 2_3(142) -> 141
, 2_3(164) -> 163
, 2_3(172) -> 171
, 2_3(178) -> 177
, 2_3(187) -> 186
, 2_3(195) -> 194
, 2_3(201) -> 200
, 2_3(207) -> 206
, 2_3(221) -> 220
, 2_3(227) -> 226
, 2_3(235) -> 234
, 2_3(241) -> 240
, 2_3(245) -> 244
, 2_3(253) -> 252
, 2_3(259) -> 258
, 2_3(263) -> 262
, 2_3(271) -> 270
, 2_3(277) -> 276
, 2_3(283) -> 282
, 2_3(287) -> 286
, 0_0(1) -> 1
, 0_1(2) -> 1
, 0_1(9) -> 8
, 0_1(15) -> 14
, 0_1(21) -> 20
, 0_1(27) -> 26
, 0_1(61) -> 1
, 0_1(61) -> 26
, 0_2(44) -> 43
, 0_2(50) -> 49
, 0_2(56) -> 55
, 0_2(67) -> 8
, 0_2(67) -> 14
, 0_2(67) -> 20
, 0_2(67) -> 26
, 0_2(80) -> 79
, 0_2(92) -> 91
, 0_2(98) -> 97
, 0_2(104) -> 103
, 0_2(109) -> 8
, 0_2(109) -> 14
, 0_2(116) -> 115
, 0_2(122) -> 121
, 0_2(152) -> 151
, 0_2(158) -> 157
, 0_3(127) -> 55
, 0_3(134) -> 133
, 0_3(140) -> 139
, 0_3(163) -> 55
, 0_3(170) -> 169
, 0_3(176) -> 175
, 0_3(193) -> 192
, 0_3(199) -> 198
, 0_3(205) -> 204
, 0_3(220) -> 49
, 0_3(226) -> 43
, 0_3(233) -> 232
, 0_3(239) -> 238
, 0_3(251) -> 250
, 0_3(257) -> 256
, 0_3(269) -> 268
, 0_3(275) -> 274
, 0_3(281) -> 280
, 0_3(286) -> 79}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(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(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(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(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(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:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..