Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(x1) ->
1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2(x1) ->
3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(4(5(x1)))))))) -> 0(1(2(3(4(4(5(5(x1))))))))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(x1) ->
1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2(x1) ->
3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(4(5(x1)))))))) -> 0(1(2(3(4(4(5(5(x1))))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 1_0(2) -> 2
, 1_1(2) -> 459
, 1_1(3) -> 1
, 1_1(4) -> 3
, 1_1(5) -> 4
, 1_1(6) -> 5
, 1_1(7) -> 6
, 1_1(8) -> 7
, 1_1(9) -> 8
, 1_1(10) -> 9
, 1_1(11) -> 10
, 1_1(12) -> 11
, 1_1(13) -> 12
, 1_1(14) -> 13
, 1_1(15) -> 14
, 1_1(16) -> 15
, 1_1(17) -> 16
, 1_1(18) -> 17
, 1_1(19) -> 18
, 1_1(20) -> 19
, 1_1(21) -> 20
, 1_1(22) -> 21
, 1_1(23) -> 22
, 1_1(24) -> 23
, 1_1(25) -> 24
, 1_1(26) -> 25
, 1_1(27) -> 26
, 1_1(28) -> 27
, 1_1(29) -> 28
, 1_1(30) -> 29
, 1_1(31) -> 30
, 1_1(32) -> 31
, 1_1(33) -> 32
, 1_1(34) -> 33
, 1_1(35) -> 34
, 1_1(36) -> 35
, 1_1(37) -> 36
, 1_1(38) -> 37
, 1_1(39) -> 38
, 1_1(40) -> 39
, 1_1(41) -> 40
, 1_1(42) -> 41
, 1_1(43) -> 42
, 1_1(44) -> 43
, 1_1(45) -> 44
, 1_1(46) -> 45
, 1_1(47) -> 46
, 1_1(48) -> 47
, 1_1(49) -> 48
, 1_1(50) -> 49
, 1_1(51) -> 50
, 1_1(52) -> 51
, 1_1(53) -> 52
, 1_1(54) -> 53
, 1_1(55) -> 54
, 1_1(56) -> 55
, 1_1(57) -> 56
, 1_1(58) -> 57
, 1_1(59) -> 58
, 1_1(60) -> 59
, 1_1(61) -> 60
, 1_1(62) -> 61
, 1_1(63) -> 62
, 1_1(64) -> 63
, 1_1(65) -> 64
, 1_1(66) -> 65
, 1_1(67) -> 66
, 1_1(68) -> 67
, 1_1(69) -> 68
, 1_1(70) -> 69
, 1_1(71) -> 70
, 1_1(72) -> 71
, 1_1(73) -> 72
, 1_1(74) -> 73
, 1_1(75) -> 74
, 1_1(76) -> 75
, 1_1(77) -> 76
, 1_1(78) -> 77
, 1_1(79) -> 78
, 1_1(80) -> 79
, 1_1(81) -> 80
, 1_1(82) -> 81
, 1_1(83) -> 82
, 1_1(84) -> 83
, 1_1(85) -> 84
, 1_1(86) -> 85
, 1_1(87) -> 86
, 1_1(88) -> 87
, 1_1(89) -> 88
, 1_1(90) -> 89
, 1_1(91) -> 90
, 1_1(92) -> 91
, 1_1(93) -> 92
, 1_1(94) -> 93
, 1_1(95) -> 94
, 1_1(96) -> 95
, 1_1(97) -> 96
, 1_1(98) -> 97
, 1_1(99) -> 98
, 1_1(100) -> 99
, 1_1(101) -> 100
, 1_1(102) -> 101
, 1_1(103) -> 102
, 1_1(104) -> 103
, 1_1(105) -> 104
, 1_1(106) -> 105
, 1_1(107) -> 106
, 1_1(108) -> 107
, 1_1(109) -> 108
, 1_1(110) -> 109
, 1_1(111) -> 110
, 1_1(112) -> 111
, 1_1(113) -> 112
, 1_1(114) -> 113
, 1_1(115) -> 114
, 1_1(116) -> 115
, 1_1(117) -> 116
, 1_1(118) -> 117
, 1_1(119) -> 118
, 1_1(120) -> 119
, 1_1(121) -> 120
, 1_1(122) -> 121
, 1_1(123) -> 122
, 1_1(124) -> 123
, 1_1(125) -> 124
, 1_1(126) -> 125
, 1_1(127) -> 126
, 1_1(128) -> 127
, 1_1(129) -> 128
, 1_1(130) -> 129
, 1_1(131) -> 130
, 1_1(132) -> 131
, 1_1(133) -> 132
, 1_1(134) -> 133
, 1_1(135) -> 134
, 1_1(136) -> 135
, 1_1(137) -> 136
, 1_1(138) -> 137
, 1_1(139) -> 138
, 1_1(140) -> 139
, 1_1(141) -> 140
, 1_1(142) -> 141
, 1_1(143) -> 142
, 1_1(144) -> 143
, 1_1(145) -> 144
, 1_1(146) -> 145
, 1_1(147) -> 146
, 1_1(148) -> 147
, 1_1(149) -> 148
, 1_1(150) -> 149
, 1_1(151) -> 150
, 1_1(152) -> 151
, 1_1(153) -> 152
, 1_1(154) -> 153
, 1_1(155) -> 154
, 1_1(156) -> 155
, 1_1(157) -> 156
, 1_1(158) -> 157
, 1_1(159) -> 158
, 1_1(160) -> 159
, 1_1(161) -> 160
, 1_1(162) -> 161
, 1_1(163) -> 162
, 1_1(164) -> 163
, 1_1(165) -> 164
, 1_1(166) -> 165
, 1_1(167) -> 166
, 1_1(168) -> 167
, 1_1(169) -> 168
, 1_1(170) -> 169
, 1_1(171) -> 170
, 1_1(172) -> 171
, 1_1(173) -> 172
, 1_1(174) -> 173
, 1_1(175) -> 174
, 1_1(176) -> 175
, 1_1(177) -> 176
, 1_1(178) -> 177
, 1_1(179) -> 178
, 1_1(180) -> 179
, 1_1(181) -> 180
, 1_1(182) -> 181
, 1_1(183) -> 182
, 1_1(184) -> 183
, 1_1(185) -> 184
, 1_1(186) -> 185
, 1_1(187) -> 186
, 1_1(188) -> 187
, 1_1(189) -> 188
, 1_1(190) -> 189
, 1_1(191) -> 190
, 1_1(192) -> 191
, 1_1(193) -> 192
, 1_1(194) -> 193
, 1_1(195) -> 194
, 1_1(196) -> 195
, 1_1(197) -> 196
, 1_1(198) -> 197
, 1_1(199) -> 198
, 1_1(200) -> 199
, 1_1(201) -> 200
, 1_1(202) -> 201
, 1_1(203) -> 202
, 1_1(204) -> 203
, 1_1(205) -> 204
, 1_1(206) -> 205
, 1_1(207) -> 206
, 1_1(208) -> 207
, 1_1(209) -> 208
, 1_1(210) -> 209
, 1_1(211) -> 210
, 1_1(212) -> 211
, 1_1(213) -> 212
, 1_1(214) -> 213
, 1_1(215) -> 214
, 1_1(216) -> 215
, 1_1(217) -> 216
, 1_1(218) -> 217
, 1_1(219) -> 218
, 1_1(220) -> 219
, 1_1(221) -> 220
, 1_1(222) -> 221
, 1_1(223) -> 222
, 1_1(224) -> 223
, 1_1(225) -> 224
, 1_1(226) -> 225
, 1_1(227) -> 226
, 1_1(228) -> 227
, 1_1(229) -> 228
, 1_1(230) -> 229
, 1_1(231) -> 230
, 1_1(232) -> 231
, 1_1(233) -> 232
, 1_1(234) -> 233
, 1_1(235) -> 234
, 1_1(236) -> 235
, 1_1(237) -> 236
, 1_1(238) -> 237
, 1_1(239) -> 238
, 1_1(240) -> 239
, 1_1(241) -> 240
, 1_1(242) -> 241
, 1_1(243) -> 242
, 1_1(244) -> 243
, 1_1(245) -> 244
, 1_1(246) -> 245
, 1_1(247) -> 246
, 1_1(248) -> 247
, 1_1(249) -> 248
, 1_1(250) -> 249
, 1_1(251) -> 250
, 1_1(252) -> 251
, 1_1(253) -> 252
, 1_1(254) -> 253
, 1_1(255) -> 254
, 1_1(256) -> 255
, 1_1(257) -> 256
, 1_1(258) -> 257
, 1_1(259) -> 258
, 1_1(260) -> 259
, 1_1(261) -> 260
, 1_1(262) -> 261
, 1_1(263) -> 262
, 1_1(264) -> 263
, 1_1(265) -> 264
, 1_1(266) -> 265
, 1_1(267) -> 266
, 1_1(268) -> 267
, 1_1(269) -> 268
, 1_1(270) -> 269
, 1_1(271) -> 270
, 1_1(272) -> 271
, 1_1(273) -> 272
, 1_1(274) -> 273
, 1_1(275) -> 274
, 1_1(276) -> 275
, 1_1(277) -> 276
, 1_1(278) -> 277
, 1_1(279) -> 278
, 1_1(280) -> 279
, 1_1(281) -> 280
, 1_1(282) -> 281
, 1_1(283) -> 282
, 1_1(284) -> 283
, 1_1(285) -> 284
, 1_1(286) -> 285
, 1_1(287) -> 286
, 1_1(288) -> 287
, 1_1(289) -> 288
, 1_1(290) -> 289
, 1_1(291) -> 290
, 1_1(292) -> 291
, 1_1(293) -> 292
, 1_1(294) -> 293
, 1_1(295) -> 294
, 1_1(296) -> 295
, 1_1(297) -> 296
, 1_1(298) -> 297
, 1_1(299) -> 298
, 1_1(300) -> 299
, 1_1(301) -> 300
, 1_1(302) -> 301
, 1_1(303) -> 302
, 1_1(304) -> 303
, 1_1(305) -> 304
, 1_1(306) -> 305
, 1_1(307) -> 306
, 1_1(308) -> 307
, 1_1(309) -> 308
, 1_1(310) -> 309
, 1_1(311) -> 310
, 1_1(312) -> 311
, 1_1(313) -> 312
, 1_1(314) -> 313
, 1_1(315) -> 314
, 1_1(316) -> 315
, 1_1(317) -> 316
, 1_1(318) -> 317
, 1_1(319) -> 318
, 1_1(320) -> 319
, 1_1(321) -> 320
, 1_1(322) -> 321
, 1_1(323) -> 322
, 1_1(324) -> 323
, 1_1(325) -> 324
, 1_1(326) -> 325
, 1_1(327) -> 326
, 1_1(328) -> 327
, 1_1(329) -> 328
, 1_1(330) -> 329
, 1_1(331) -> 330
, 1_1(332) -> 331
, 1_1(333) -> 332
, 1_1(334) -> 333
, 1_1(335) -> 334
, 1_1(336) -> 335
, 1_1(337) -> 336
, 1_1(338) -> 337
, 1_1(339) -> 338
, 1_1(340) -> 339
, 1_1(341) -> 340
, 1_1(342) -> 341
, 1_1(343) -> 342
, 1_1(344) -> 343
, 1_1(345) -> 344
, 1_1(346) -> 345
, 1_1(347) -> 346
, 1_1(348) -> 347
, 1_1(349) -> 348
, 1_1(350) -> 349
, 1_1(351) -> 350
, 1_1(352) -> 351
, 1_1(353) -> 352
, 1_1(354) -> 353
, 1_1(355) -> 354
, 1_1(356) -> 355
, 1_1(357) -> 356
, 1_1(358) -> 357
, 1_1(359) -> 358
, 1_1(360) -> 359
, 1_1(361) -> 360
, 1_1(362) -> 361
, 1_1(363) -> 362
, 1_1(364) -> 363
, 1_1(365) -> 364
, 1_1(366) -> 365
, 1_1(367) -> 366
, 1_1(368) -> 367
, 1_1(369) -> 368
, 1_1(370) -> 369
, 1_1(371) -> 370
, 1_1(372) -> 371
, 1_1(373) -> 372
, 1_1(374) -> 373
, 1_1(375) -> 374
, 1_1(376) -> 375
, 1_1(377) -> 376
, 1_1(378) -> 377
, 1_1(379) -> 378
, 1_1(380) -> 379
, 1_1(381) -> 380
, 1_1(382) -> 381
, 1_1(383) -> 382
, 1_1(384) -> 383
, 1_1(385) -> 384
, 1_1(386) -> 385
, 1_1(387) -> 386
, 1_1(388) -> 387
, 1_1(389) -> 388
, 1_1(390) -> 389
, 1_1(391) -> 390
, 1_1(392) -> 391
, 1_1(393) -> 392
, 1_1(394) -> 393
, 1_1(395) -> 394
, 1_1(396) -> 395
, 1_1(397) -> 396
, 1_1(398) -> 397
, 1_1(399) -> 398
, 1_1(400) -> 399
, 1_1(401) -> 400
, 1_1(402) -> 401
, 1_1(403) -> 402
, 1_1(404) -> 403
, 1_1(405) -> 404
, 1_1(406) -> 405
, 1_1(407) -> 406
, 1_1(408) -> 407
, 1_1(409) -> 408
, 1_1(410) -> 409
, 1_1(411) -> 410
, 1_1(412) -> 411
, 1_1(413) -> 412
, 1_1(414) -> 413
, 1_1(415) -> 414
, 1_1(416) -> 415
, 1_1(417) -> 416
, 1_1(418) -> 417
, 1_1(419) -> 418
, 1_1(420) -> 419
, 1_1(421) -> 420
, 1_1(422) -> 421
, 1_1(423) -> 422
, 1_1(424) -> 423
, 1_1(425) -> 424
, 1_1(426) -> 425
, 1_1(427) -> 426
, 1_1(428) -> 427
, 1_1(429) -> 428
, 1_1(430) -> 429
, 1_1(431) -> 430
, 1_1(432) -> 431
, 1_1(433) -> 432
, 1_1(434) -> 433
, 1_1(435) -> 434
, 1_1(436) -> 435
, 1_1(437) -> 436
, 1_1(438) -> 437
, 1_1(439) -> 438
, 1_1(440) -> 439
, 1_1(441) -> 440
, 1_1(442) -> 441
, 1_1(443) -> 442
, 1_1(444) -> 443
, 1_1(445) -> 444
, 1_1(446) -> 445
, 1_1(447) -> 446
, 1_1(448) -> 447
, 1_1(449) -> 448
, 1_1(450) -> 449
, 1_1(451) -> 450
, 1_1(452) -> 451
, 1_1(453) -> 452
, 1_1(454) -> 453
, 1_1(455) -> 454
, 1_1(456) -> 455
, 1_1(457) -> 456
, 1_1(458) -> 457
, 1_1(459) -> 458
, 2_0(2) -> 1
, 3_0(2) -> 2
, 3_1(2) -> 918
, 3_1(460) -> 1
, 3_1(461) -> 460
, 3_1(462) -> 461
, 3_1(463) -> 462
, 3_1(464) -> 463
, 3_1(465) -> 464
, 3_1(466) -> 465
, 3_1(467) -> 466
, 3_1(468) -> 467
, 3_1(469) -> 468
, 3_1(470) -> 469
, 3_1(471) -> 470
, 3_1(472) -> 471
, 3_1(473) -> 472
, 3_1(474) -> 473
, 3_1(475) -> 474
, 3_1(476) -> 475
, 3_1(477) -> 476
, 3_1(478) -> 477
, 3_1(479) -> 478
, 3_1(480) -> 479
, 3_1(481) -> 480
, 3_1(482) -> 481
, 3_1(483) -> 482
, 3_1(484) -> 483
, 3_1(485) -> 484
, 3_1(486) -> 485
, 3_1(487) -> 486
, 3_1(488) -> 487
, 3_1(489) -> 488
, 3_1(490) -> 489
, 3_1(491) -> 490
, 3_1(492) -> 491
, 3_1(493) -> 492
, 3_1(494) -> 493
, 3_1(495) -> 494
, 3_1(496) -> 495
, 3_1(497) -> 496
, 3_1(498) -> 497
, 3_1(499) -> 498
, 3_1(500) -> 499
, 3_1(501) -> 500
, 3_1(502) -> 501
, 3_1(503) -> 502
, 3_1(504) -> 503
, 3_1(505) -> 504
, 3_1(506) -> 505
, 3_1(507) -> 506
, 3_1(508) -> 507
, 3_1(509) -> 508
, 3_1(510) -> 509
, 3_1(511) -> 510
, 3_1(512) -> 511
, 3_1(513) -> 512
, 3_1(514) -> 513
, 3_1(515) -> 514
, 3_1(516) -> 515
, 3_1(517) -> 516
, 3_1(518) -> 517
, 3_1(519) -> 518
, 3_1(520) -> 519
, 3_1(521) -> 520
, 3_1(522) -> 521
, 3_1(523) -> 522
, 3_1(524) -> 523
, 3_1(525) -> 524
, 3_1(526) -> 525
, 3_1(527) -> 526
, 3_1(528) -> 527
, 3_1(529) -> 528
, 3_1(530) -> 529
, 3_1(531) -> 530
, 3_1(532) -> 531
, 3_1(533) -> 532
, 3_1(534) -> 533
, 3_1(535) -> 534
, 3_1(536) -> 535
, 3_1(537) -> 536
, 3_1(538) -> 537
, 3_1(539) -> 538
, 3_1(540) -> 539
, 3_1(541) -> 540
, 3_1(542) -> 541
, 3_1(543) -> 542
, 3_1(544) -> 543
, 3_1(545) -> 544
, 3_1(546) -> 545
, 3_1(547) -> 546
, 3_1(548) -> 547
, 3_1(549) -> 548
, 3_1(550) -> 549
, 3_1(551) -> 550
, 3_1(552) -> 551
, 3_1(553) -> 552
, 3_1(554) -> 553
, 3_1(555) -> 554
, 3_1(556) -> 555
, 3_1(557) -> 556
, 3_1(558) -> 557
, 3_1(559) -> 558
, 3_1(560) -> 559
, 3_1(561) -> 560
, 3_1(562) -> 561
, 3_1(563) -> 562
, 3_1(564) -> 563
, 3_1(565) -> 564
, 3_1(566) -> 565
, 3_1(567) -> 566
, 3_1(568) -> 567
, 3_1(569) -> 568
, 3_1(570) -> 569
, 3_1(571) -> 570
, 3_1(572) -> 571
, 3_1(573) -> 572
, 3_1(574) -> 573
, 3_1(575) -> 574
, 3_1(576) -> 575
, 3_1(577) -> 576
, 3_1(578) -> 577
, 3_1(579) -> 578
, 3_1(580) -> 579
, 3_1(581) -> 580
, 3_1(582) -> 581
, 3_1(583) -> 582
, 3_1(584) -> 583
, 3_1(585) -> 584
, 3_1(586) -> 585
, 3_1(587) -> 586
, 3_1(588) -> 587
, 3_1(589) -> 588
, 3_1(590) -> 589
, 3_1(591) -> 590
, 3_1(592) -> 591
, 3_1(593) -> 592
, 3_1(594) -> 593
, 3_1(595) -> 594
, 3_1(596) -> 595
, 3_1(597) -> 596
, 3_1(598) -> 597
, 3_1(599) -> 598
, 3_1(600) -> 599
, 3_1(601) -> 600
, 3_1(602) -> 601
, 3_1(603) -> 602
, 3_1(604) -> 603
, 3_1(605) -> 604
, 3_1(606) -> 605
, 3_1(607) -> 606
, 3_1(608) -> 607
, 3_1(609) -> 608
, 3_1(610) -> 609
, 3_1(611) -> 610
, 3_1(612) -> 611
, 3_1(613) -> 612
, 3_1(614) -> 613
, 3_1(615) -> 614
, 3_1(616) -> 615
, 3_1(617) -> 616
, 3_1(618) -> 617
, 3_1(619) -> 618
, 3_1(620) -> 619
, 3_1(621) -> 620
, 3_1(622) -> 621
, 3_1(623) -> 622
, 3_1(624) -> 623
, 3_1(625) -> 624
, 3_1(626) -> 625
, 3_1(627) -> 626
, 3_1(628) -> 627
, 3_1(629) -> 628
, 3_1(630) -> 629
, 3_1(631) -> 630
, 3_1(632) -> 631
, 3_1(633) -> 632
, 3_1(634) -> 633
, 3_1(635) -> 634
, 3_1(636) -> 635
, 3_1(637) -> 636
, 3_1(638) -> 637
, 3_1(639) -> 638
, 3_1(640) -> 639
, 3_1(641) -> 640
, 3_1(642) -> 641
, 3_1(643) -> 642
, 3_1(644) -> 643
, 3_1(645) -> 644
, 3_1(646) -> 645
, 3_1(647) -> 646
, 3_1(648) -> 647
, 3_1(649) -> 648
, 3_1(650) -> 649
, 3_1(651) -> 650
, 3_1(652) -> 651
, 3_1(653) -> 652
, 3_1(654) -> 653
, 3_1(655) -> 654
, 3_1(656) -> 655
, 3_1(657) -> 656
, 3_1(658) -> 657
, 3_1(659) -> 658
, 3_1(660) -> 659
, 3_1(661) -> 660
, 3_1(662) -> 661
, 3_1(663) -> 662
, 3_1(664) -> 663
, 3_1(665) -> 664
, 3_1(666) -> 665
, 3_1(667) -> 666
, 3_1(668) -> 667
, 3_1(669) -> 668
, 3_1(670) -> 669
, 3_1(671) -> 670
, 3_1(672) -> 671
, 3_1(673) -> 672
, 3_1(674) -> 673
, 3_1(675) -> 674
, 3_1(676) -> 675
, 3_1(677) -> 676
, 3_1(678) -> 677
, 3_1(679) -> 678
, 3_1(680) -> 679
, 3_1(681) -> 680
, 3_1(682) -> 681
, 3_1(683) -> 682
, 3_1(684) -> 683
, 3_1(685) -> 684
, 3_1(686) -> 685
, 3_1(687) -> 686
, 3_1(688) -> 687
, 3_1(689) -> 688
, 3_1(690) -> 689
, 3_1(691) -> 690
, 3_1(692) -> 691
, 3_1(693) -> 692
, 3_1(694) -> 693
, 3_1(695) -> 694
, 3_1(696) -> 695
, 3_1(697) -> 696
, 3_1(698) -> 697
, 3_1(699) -> 698
, 3_1(700) -> 699
, 3_1(701) -> 700
, 3_1(702) -> 701
, 3_1(703) -> 702
, 3_1(704) -> 703
, 3_1(705) -> 704
, 3_1(706) -> 705
, 3_1(707) -> 706
, 3_1(708) -> 707
, 3_1(709) -> 708
, 3_1(710) -> 709
, 3_1(711) -> 710
, 3_1(712) -> 711
, 3_1(713) -> 712
, 3_1(714) -> 713
, 3_1(715) -> 714
, 3_1(716) -> 715
, 3_1(717) -> 716
, 3_1(718) -> 717
, 3_1(719) -> 718
, 3_1(720) -> 719
, 3_1(721) -> 720
, 3_1(722) -> 721
, 3_1(723) -> 722
, 3_1(724) -> 723
, 3_1(725) -> 724
, 3_1(726) -> 725
, 3_1(727) -> 726
, 3_1(728) -> 727
, 3_1(729) -> 728
, 3_1(730) -> 729
, 3_1(731) -> 730
, 3_1(732) -> 731
, 3_1(733) -> 732
, 3_1(734) -> 733
, 3_1(735) -> 734
, 3_1(736) -> 735
, 3_1(737) -> 736
, 3_1(738) -> 737
, 3_1(739) -> 738
, 3_1(740) -> 739
, 3_1(741) -> 740
, 3_1(742) -> 741
, 3_1(743) -> 742
, 3_1(744) -> 743
, 3_1(745) -> 744
, 3_1(746) -> 745
, 3_1(747) -> 746
, 3_1(748) -> 747
, 3_1(749) -> 748
, 3_1(750) -> 749
, 3_1(751) -> 750
, 3_1(752) -> 751
, 3_1(753) -> 752
, 3_1(754) -> 753
, 3_1(755) -> 754
, 3_1(756) -> 755
, 3_1(757) -> 756
, 3_1(758) -> 757
, 3_1(759) -> 758
, 3_1(760) -> 759
, 3_1(761) -> 760
, 3_1(762) -> 761
, 3_1(763) -> 762
, 3_1(764) -> 763
, 3_1(765) -> 764
, 3_1(766) -> 765
, 3_1(767) -> 766
, 3_1(768) -> 767
, 3_1(769) -> 768
, 3_1(770) -> 769
, 3_1(771) -> 770
, 3_1(772) -> 771
, 3_1(773) -> 772
, 3_1(774) -> 773
, 3_1(775) -> 774
, 3_1(776) -> 775
, 3_1(777) -> 776
, 3_1(778) -> 777
, 3_1(779) -> 778
, 3_1(780) -> 779
, 3_1(781) -> 780
, 3_1(782) -> 781
, 3_1(783) -> 782
, 3_1(784) -> 783
, 3_1(785) -> 784
, 3_1(786) -> 785
, 3_1(787) -> 786
, 3_1(788) -> 787
, 3_1(789) -> 788
, 3_1(790) -> 789
, 3_1(791) -> 790
, 3_1(792) -> 791
, 3_1(793) -> 792
, 3_1(794) -> 793
, 3_1(795) -> 794
, 3_1(796) -> 795
, 3_1(797) -> 796
, 3_1(798) -> 797
, 3_1(799) -> 798
, 3_1(800) -> 799
, 3_1(801) -> 800
, 3_1(802) -> 801
, 3_1(803) -> 802
, 3_1(804) -> 803
, 3_1(805) -> 804
, 3_1(806) -> 805
, 3_1(807) -> 806
, 3_1(808) -> 807
, 3_1(809) -> 808
, 3_1(810) -> 809
, 3_1(811) -> 810
, 3_1(812) -> 811
, 3_1(813) -> 812
, 3_1(814) -> 813
, 3_1(815) -> 814
, 3_1(816) -> 815
, 3_1(817) -> 816
, 3_1(818) -> 817
, 3_1(819) -> 818
, 3_1(820) -> 819
, 3_1(821) -> 820
, 3_1(822) -> 821
, 3_1(823) -> 822
, 3_1(824) -> 823
, 3_1(825) -> 824
, 3_1(826) -> 825
, 3_1(827) -> 826
, 3_1(828) -> 827
, 3_1(829) -> 828
, 3_1(830) -> 829
, 3_1(831) -> 830
, 3_1(832) -> 831
, 3_1(833) -> 832
, 3_1(834) -> 833
, 3_1(835) -> 834
, 3_1(836) -> 835
, 3_1(837) -> 836
, 3_1(838) -> 837
, 3_1(839) -> 838
, 3_1(840) -> 839
, 3_1(841) -> 840
, 3_1(842) -> 841
, 3_1(843) -> 842
, 3_1(844) -> 843
, 3_1(845) -> 844
, 3_1(846) -> 845
, 3_1(847) -> 846
, 3_1(848) -> 847
, 3_1(849) -> 848
, 3_1(850) -> 849
, 3_1(851) -> 850
, 3_1(852) -> 851
, 3_1(853) -> 852
, 3_1(854) -> 853
, 3_1(855) -> 854
, 3_1(856) -> 855
, 3_1(857) -> 856
, 3_1(858) -> 857
, 3_1(859) -> 858
, 3_1(860) -> 859
, 3_1(861) -> 860
, 3_1(862) -> 861
, 3_1(863) -> 862
, 3_1(864) -> 863
, 3_1(865) -> 864
, 3_1(866) -> 865
, 3_1(867) -> 866
, 3_1(868) -> 867
, 3_1(869) -> 868
, 3_1(870) -> 869
, 3_1(871) -> 870
, 3_1(872) -> 871
, 3_1(873) -> 872
, 3_1(874) -> 873
, 3_1(875) -> 874
, 3_1(876) -> 875
, 3_1(877) -> 876
, 3_1(878) -> 877
, 3_1(879) -> 878
, 3_1(880) -> 879
, 3_1(881) -> 880
, 3_1(882) -> 881
, 3_1(883) -> 882
, 3_1(884) -> 883
, 3_1(885) -> 884
, 3_1(886) -> 885
, 3_1(887) -> 886
, 3_1(888) -> 887
, 3_1(889) -> 888
, 3_1(890) -> 889
, 3_1(891) -> 890
, 3_1(892) -> 891
, 3_1(893) -> 892
, 3_1(894) -> 893
, 3_1(895) -> 894
, 3_1(896) -> 895
, 3_1(897) -> 896
, 3_1(898) -> 897
, 3_1(899) -> 898
, 3_1(900) -> 899
, 3_1(901) -> 900
, 3_1(902) -> 901
, 3_1(903) -> 902
, 3_1(904) -> 903
, 3_1(905) -> 904
, 3_1(906) -> 905
, 3_1(907) -> 906
, 3_1(908) -> 907
, 3_1(909) -> 908
, 3_1(910) -> 909
, 3_1(911) -> 910
, 3_1(912) -> 911
, 3_1(913) -> 912
, 3_1(914) -> 913
, 3_1(915) -> 914
, 3_1(916) -> 915
, 3_1(917) -> 916
, 3_1(918) -> 917
, 4_0(2) -> 2
, 5_0(2) -> 2}Tool RC1
stdout:
MAYBE
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(x1) ->
1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2(x1) ->
3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(4(5(x1)))))))) -> 0(1(2(3(4(4(5(5(x1))))))))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(x1) ->
1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2(x1) ->
3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(3(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(1(2(3(4(5(4(5(x1)))))))) -> 0(1(2(3(4(4(5(5(x1))))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 1_0(2) -> 2
, 1_1(2) -> 459
, 1_1(3) -> 1
, 1_1(4) -> 3
, 1_1(5) -> 4
, 1_1(6) -> 5
, 1_1(7) -> 6
, 1_1(8) -> 7
, 1_1(9) -> 8
, 1_1(10) -> 9
, 1_1(11) -> 10
, 1_1(12) -> 11
, 1_1(13) -> 12
, 1_1(14) -> 13
, 1_1(15) -> 14
, 1_1(16) -> 15
, 1_1(17) -> 16
, 1_1(18) -> 17
, 1_1(19) -> 18
, 1_1(20) -> 19
, 1_1(21) -> 20
, 1_1(22) -> 21
, 1_1(23) -> 22
, 1_1(24) -> 23
, 1_1(25) -> 24
, 1_1(26) -> 25
, 1_1(27) -> 26
, 1_1(28) -> 27
, 1_1(29) -> 28
, 1_1(30) -> 29
, 1_1(31) -> 30
, 1_1(32) -> 31
, 1_1(33) -> 32
, 1_1(34) -> 33
, 1_1(35) -> 34
, 1_1(36) -> 35
, 1_1(37) -> 36
, 1_1(38) -> 37
, 1_1(39) -> 38
, 1_1(40) -> 39
, 1_1(41) -> 40
, 1_1(42) -> 41
, 1_1(43) -> 42
, 1_1(44) -> 43
, 1_1(45) -> 44
, 1_1(46) -> 45
, 1_1(47) -> 46
, 1_1(48) -> 47
, 1_1(49) -> 48
, 1_1(50) -> 49
, 1_1(51) -> 50
, 1_1(52) -> 51
, 1_1(53) -> 52
, 1_1(54) -> 53
, 1_1(55) -> 54
, 1_1(56) -> 55
, 1_1(57) -> 56
, 1_1(58) -> 57
, 1_1(59) -> 58
, 1_1(60) -> 59
, 1_1(61) -> 60
, 1_1(62) -> 61
, 1_1(63) -> 62
, 1_1(64) -> 63
, 1_1(65) -> 64
, 1_1(66) -> 65
, 1_1(67) -> 66
, 1_1(68) -> 67
, 1_1(69) -> 68
, 1_1(70) -> 69
, 1_1(71) -> 70
, 1_1(72) -> 71
, 1_1(73) -> 72
, 1_1(74) -> 73
, 1_1(75) -> 74
, 1_1(76) -> 75
, 1_1(77) -> 76
, 1_1(78) -> 77
, 1_1(79) -> 78
, 1_1(80) -> 79
, 1_1(81) -> 80
, 1_1(82) -> 81
, 1_1(83) -> 82
, 1_1(84) -> 83
, 1_1(85) -> 84
, 1_1(86) -> 85
, 1_1(87) -> 86
, 1_1(88) -> 87
, 1_1(89) -> 88
, 1_1(90) -> 89
, 1_1(91) -> 90
, 1_1(92) -> 91
, 1_1(93) -> 92
, 1_1(94) -> 93
, 1_1(95) -> 94
, 1_1(96) -> 95
, 1_1(97) -> 96
, 1_1(98) -> 97
, 1_1(99) -> 98
, 1_1(100) -> 99
, 1_1(101) -> 100
, 1_1(102) -> 101
, 1_1(103) -> 102
, 1_1(104) -> 103
, 1_1(105) -> 104
, 1_1(106) -> 105
, 1_1(107) -> 106
, 1_1(108) -> 107
, 1_1(109) -> 108
, 1_1(110) -> 109
, 1_1(111) -> 110
, 1_1(112) -> 111
, 1_1(113) -> 112
, 1_1(114) -> 113
, 1_1(115) -> 114
, 1_1(116) -> 115
, 1_1(117) -> 116
, 1_1(118) -> 117
, 1_1(119) -> 118
, 1_1(120) -> 119
, 1_1(121) -> 120
, 1_1(122) -> 121
, 1_1(123) -> 122
, 1_1(124) -> 123
, 1_1(125) -> 124
, 1_1(126) -> 125
, 1_1(127) -> 126
, 1_1(128) -> 127
, 1_1(129) -> 128
, 1_1(130) -> 129
, 1_1(131) -> 130
, 1_1(132) -> 131
, 1_1(133) -> 132
, 1_1(134) -> 133
, 1_1(135) -> 134
, 1_1(136) -> 135
, 1_1(137) -> 136
, 1_1(138) -> 137
, 1_1(139) -> 138
, 1_1(140) -> 139
, 1_1(141) -> 140
, 1_1(142) -> 141
, 1_1(143) -> 142
, 1_1(144) -> 143
, 1_1(145) -> 144
, 1_1(146) -> 145
, 1_1(147) -> 146
, 1_1(148) -> 147
, 1_1(149) -> 148
, 1_1(150) -> 149
, 1_1(151) -> 150
, 1_1(152) -> 151
, 1_1(153) -> 152
, 1_1(154) -> 153
, 1_1(155) -> 154
, 1_1(156) -> 155
, 1_1(157) -> 156
, 1_1(158) -> 157
, 1_1(159) -> 158
, 1_1(160) -> 159
, 1_1(161) -> 160
, 1_1(162) -> 161
, 1_1(163) -> 162
, 1_1(164) -> 163
, 1_1(165) -> 164
, 1_1(166) -> 165
, 1_1(167) -> 166
, 1_1(168) -> 167
, 1_1(169) -> 168
, 1_1(170) -> 169
, 1_1(171) -> 170
, 1_1(172) -> 171
, 1_1(173) -> 172
, 1_1(174) -> 173
, 1_1(175) -> 174
, 1_1(176) -> 175
, 1_1(177) -> 176
, 1_1(178) -> 177
, 1_1(179) -> 178
, 1_1(180) -> 179
, 1_1(181) -> 180
, 1_1(182) -> 181
, 1_1(183) -> 182
, 1_1(184) -> 183
, 1_1(185) -> 184
, 1_1(186) -> 185
, 1_1(187) -> 186
, 1_1(188) -> 187
, 1_1(189) -> 188
, 1_1(190) -> 189
, 1_1(191) -> 190
, 1_1(192) -> 191
, 1_1(193) -> 192
, 1_1(194) -> 193
, 1_1(195) -> 194
, 1_1(196) -> 195
, 1_1(197) -> 196
, 1_1(198) -> 197
, 1_1(199) -> 198
, 1_1(200) -> 199
, 1_1(201) -> 200
, 1_1(202) -> 201
, 1_1(203) -> 202
, 1_1(204) -> 203
, 1_1(205) -> 204
, 1_1(206) -> 205
, 1_1(207) -> 206
, 1_1(208) -> 207
, 1_1(209) -> 208
, 1_1(210) -> 209
, 1_1(211) -> 210
, 1_1(212) -> 211
, 1_1(213) -> 212
, 1_1(214) -> 213
, 1_1(215) -> 214
, 1_1(216) -> 215
, 1_1(217) -> 216
, 1_1(218) -> 217
, 1_1(219) -> 218
, 1_1(220) -> 219
, 1_1(221) -> 220
, 1_1(222) -> 221
, 1_1(223) -> 222
, 1_1(224) -> 223
, 1_1(225) -> 224
, 1_1(226) -> 225
, 1_1(227) -> 226
, 1_1(228) -> 227
, 1_1(229) -> 228
, 1_1(230) -> 229
, 1_1(231) -> 230
, 1_1(232) -> 231
, 1_1(233) -> 232
, 1_1(234) -> 233
, 1_1(235) -> 234
, 1_1(236) -> 235
, 1_1(237) -> 236
, 1_1(238) -> 237
, 1_1(239) -> 238
, 1_1(240) -> 239
, 1_1(241) -> 240
, 1_1(242) -> 241
, 1_1(243) -> 242
, 1_1(244) -> 243
, 1_1(245) -> 244
, 1_1(246) -> 245
, 1_1(247) -> 246
, 1_1(248) -> 247
, 1_1(249) -> 248
, 1_1(250) -> 249
, 1_1(251) -> 250
, 1_1(252) -> 251
, 1_1(253) -> 252
, 1_1(254) -> 253
, 1_1(255) -> 254
, 1_1(256) -> 255
, 1_1(257) -> 256
, 1_1(258) -> 257
, 1_1(259) -> 258
, 1_1(260) -> 259
, 1_1(261) -> 260
, 1_1(262) -> 261
, 1_1(263) -> 262
, 1_1(264) -> 263
, 1_1(265) -> 264
, 1_1(266) -> 265
, 1_1(267) -> 266
, 1_1(268) -> 267
, 1_1(269) -> 268
, 1_1(270) -> 269
, 1_1(271) -> 270
, 1_1(272) -> 271
, 1_1(273) -> 272
, 1_1(274) -> 273
, 1_1(275) -> 274
, 1_1(276) -> 275
, 1_1(277) -> 276
, 1_1(278) -> 277
, 1_1(279) -> 278
, 1_1(280) -> 279
, 1_1(281) -> 280
, 1_1(282) -> 281
, 1_1(283) -> 282
, 1_1(284) -> 283
, 1_1(285) -> 284
, 1_1(286) -> 285
, 1_1(287) -> 286
, 1_1(288) -> 287
, 1_1(289) -> 288
, 1_1(290) -> 289
, 1_1(291) -> 290
, 1_1(292) -> 291
, 1_1(293) -> 292
, 1_1(294) -> 293
, 1_1(295) -> 294
, 1_1(296) -> 295
, 1_1(297) -> 296
, 1_1(298) -> 297
, 1_1(299) -> 298
, 1_1(300) -> 299
, 1_1(301) -> 300
, 1_1(302) -> 301
, 1_1(303) -> 302
, 1_1(304) -> 303
, 1_1(305) -> 304
, 1_1(306) -> 305
, 1_1(307) -> 306
, 1_1(308) -> 307
, 1_1(309) -> 308
, 1_1(310) -> 309
, 1_1(311) -> 310
, 1_1(312) -> 311
, 1_1(313) -> 312
, 1_1(314) -> 313
, 1_1(315) -> 314
, 1_1(316) -> 315
, 1_1(317) -> 316
, 1_1(318) -> 317
, 1_1(319) -> 318
, 1_1(320) -> 319
, 1_1(321) -> 320
, 1_1(322) -> 321
, 1_1(323) -> 322
, 1_1(324) -> 323
, 1_1(325) -> 324
, 1_1(326) -> 325
, 1_1(327) -> 326
, 1_1(328) -> 327
, 1_1(329) -> 328
, 1_1(330) -> 329
, 1_1(331) -> 330
, 1_1(332) -> 331
, 1_1(333) -> 332
, 1_1(334) -> 333
, 1_1(335) -> 334
, 1_1(336) -> 335
, 1_1(337) -> 336
, 1_1(338) -> 337
, 1_1(339) -> 338
, 1_1(340) -> 339
, 1_1(341) -> 340
, 1_1(342) -> 341
, 1_1(343) -> 342
, 1_1(344) -> 343
, 1_1(345) -> 344
, 1_1(346) -> 345
, 1_1(347) -> 346
, 1_1(348) -> 347
, 1_1(349) -> 348
, 1_1(350) -> 349
, 1_1(351) -> 350
, 1_1(352) -> 351
, 1_1(353) -> 352
, 1_1(354) -> 353
, 1_1(355) -> 354
, 1_1(356) -> 355
, 1_1(357) -> 356
, 1_1(358) -> 357
, 1_1(359) -> 358
, 1_1(360) -> 359
, 1_1(361) -> 360
, 1_1(362) -> 361
, 1_1(363) -> 362
, 1_1(364) -> 363
, 1_1(365) -> 364
, 1_1(366) -> 365
, 1_1(367) -> 366
, 1_1(368) -> 367
, 1_1(369) -> 368
, 1_1(370) -> 369
, 1_1(371) -> 370
, 1_1(372) -> 371
, 1_1(373) -> 372
, 1_1(374) -> 373
, 1_1(375) -> 374
, 1_1(376) -> 375
, 1_1(377) -> 376
, 1_1(378) -> 377
, 1_1(379) -> 378
, 1_1(380) -> 379
, 1_1(381) -> 380
, 1_1(382) -> 381
, 1_1(383) -> 382
, 1_1(384) -> 383
, 1_1(385) -> 384
, 1_1(386) -> 385
, 1_1(387) -> 386
, 1_1(388) -> 387
, 1_1(389) -> 388
, 1_1(390) -> 389
, 1_1(391) -> 390
, 1_1(392) -> 391
, 1_1(393) -> 392
, 1_1(394) -> 393
, 1_1(395) -> 394
, 1_1(396) -> 395
, 1_1(397) -> 396
, 1_1(398) -> 397
, 1_1(399) -> 398
, 1_1(400) -> 399
, 1_1(401) -> 400
, 1_1(402) -> 401
, 1_1(403) -> 402
, 1_1(404) -> 403
, 1_1(405) -> 404
, 1_1(406) -> 405
, 1_1(407) -> 406
, 1_1(408) -> 407
, 1_1(409) -> 408
, 1_1(410) -> 409
, 1_1(411) -> 410
, 1_1(412) -> 411
, 1_1(413) -> 412
, 1_1(414) -> 413
, 1_1(415) -> 414
, 1_1(416) -> 415
, 1_1(417) -> 416
, 1_1(418) -> 417
, 1_1(419) -> 418
, 1_1(420) -> 419
, 1_1(421) -> 420
, 1_1(422) -> 421
, 1_1(423) -> 422
, 1_1(424) -> 423
, 1_1(425) -> 424
, 1_1(426) -> 425
, 1_1(427) -> 426
, 1_1(428) -> 427
, 1_1(429) -> 428
, 1_1(430) -> 429
, 1_1(431) -> 430
, 1_1(432) -> 431
, 1_1(433) -> 432
, 1_1(434) -> 433
, 1_1(435) -> 434
, 1_1(436) -> 435
, 1_1(437) -> 436
, 1_1(438) -> 437
, 1_1(439) -> 438
, 1_1(440) -> 439
, 1_1(441) -> 440
, 1_1(442) -> 441
, 1_1(443) -> 442
, 1_1(444) -> 443
, 1_1(445) -> 444
, 1_1(446) -> 445
, 1_1(447) -> 446
, 1_1(448) -> 447
, 1_1(449) -> 448
, 1_1(450) -> 449
, 1_1(451) -> 450
, 1_1(452) -> 451
, 1_1(453) -> 452
, 1_1(454) -> 453
, 1_1(455) -> 454
, 1_1(456) -> 455
, 1_1(457) -> 456
, 1_1(458) -> 457
, 1_1(459) -> 458
, 2_0(2) -> 1
, 3_0(2) -> 2
, 3_1(2) -> 918
, 3_1(460) -> 1
, 3_1(461) -> 460
, 3_1(462) -> 461
, 3_1(463) -> 462
, 3_1(464) -> 463
, 3_1(465) -> 464
, 3_1(466) -> 465
, 3_1(467) -> 466
, 3_1(468) -> 467
, 3_1(469) -> 468
, 3_1(470) -> 469
, 3_1(471) -> 470
, 3_1(472) -> 471
, 3_1(473) -> 472
, 3_1(474) -> 473
, 3_1(475) -> 474
, 3_1(476) -> 475
, 3_1(477) -> 476
, 3_1(478) -> 477
, 3_1(479) -> 478
, 3_1(480) -> 479
, 3_1(481) -> 480
, 3_1(482) -> 481
, 3_1(483) -> 482
, 3_1(484) -> 483
, 3_1(485) -> 484
, 3_1(486) -> 485
, 3_1(487) -> 486
, 3_1(488) -> 487
, 3_1(489) -> 488
, 3_1(490) -> 489
, 3_1(491) -> 490
, 3_1(492) -> 491
, 3_1(493) -> 492
, 3_1(494) -> 493
, 3_1(495) -> 494
, 3_1(496) -> 495
, 3_1(497) -> 496
, 3_1(498) -> 497
, 3_1(499) -> 498
, 3_1(500) -> 499
, 3_1(501) -> 500
, 3_1(502) -> 501
, 3_1(503) -> 502
, 3_1(504) -> 503
, 3_1(505) -> 504
, 3_1(506) -> 505
, 3_1(507) -> 506
, 3_1(508) -> 507
, 3_1(509) -> 508
, 3_1(510) -> 509
, 3_1(511) -> 510
, 3_1(512) -> 511
, 3_1(513) -> 512
, 3_1(514) -> 513
, 3_1(515) -> 514
, 3_1(516) -> 515
, 3_1(517) -> 516
, 3_1(518) -> 517
, 3_1(519) -> 518
, 3_1(520) -> 519
, 3_1(521) -> 520
, 3_1(522) -> 521
, 3_1(523) -> 522
, 3_1(524) -> 523
, 3_1(525) -> 524
, 3_1(526) -> 525
, 3_1(527) -> 526
, 3_1(528) -> 527
, 3_1(529) -> 528
, 3_1(530) -> 529
, 3_1(531) -> 530
, 3_1(532) -> 531
, 3_1(533) -> 532
, 3_1(534) -> 533
, 3_1(535) -> 534
, 3_1(536) -> 535
, 3_1(537) -> 536
, 3_1(538) -> 537
, 3_1(539) -> 538
, 3_1(540) -> 539
, 3_1(541) -> 540
, 3_1(542) -> 541
, 3_1(543) -> 542
, 3_1(544) -> 543
, 3_1(545) -> 544
, 3_1(546) -> 545
, 3_1(547) -> 546
, 3_1(548) -> 547
, 3_1(549) -> 548
, 3_1(550) -> 549
, 3_1(551) -> 550
, 3_1(552) -> 551
, 3_1(553) -> 552
, 3_1(554) -> 553
, 3_1(555) -> 554
, 3_1(556) -> 555
, 3_1(557) -> 556
, 3_1(558) -> 557
, 3_1(559) -> 558
, 3_1(560) -> 559
, 3_1(561) -> 560
, 3_1(562) -> 561
, 3_1(563) -> 562
, 3_1(564) -> 563
, 3_1(565) -> 564
, 3_1(566) -> 565
, 3_1(567) -> 566
, 3_1(568) -> 567
, 3_1(569) -> 568
, 3_1(570) -> 569
, 3_1(571) -> 570
, 3_1(572) -> 571
, 3_1(573) -> 572
, 3_1(574) -> 573
, 3_1(575) -> 574
, 3_1(576) -> 575
, 3_1(577) -> 576
, 3_1(578) -> 577
, 3_1(579) -> 578
, 3_1(580) -> 579
, 3_1(581) -> 580
, 3_1(582) -> 581
, 3_1(583) -> 582
, 3_1(584) -> 583
, 3_1(585) -> 584
, 3_1(586) -> 585
, 3_1(587) -> 586
, 3_1(588) -> 587
, 3_1(589) -> 588
, 3_1(590) -> 589
, 3_1(591) -> 590
, 3_1(592) -> 591
, 3_1(593) -> 592
, 3_1(594) -> 593
, 3_1(595) -> 594
, 3_1(596) -> 595
, 3_1(597) -> 596
, 3_1(598) -> 597
, 3_1(599) -> 598
, 3_1(600) -> 599
, 3_1(601) -> 600
, 3_1(602) -> 601
, 3_1(603) -> 602
, 3_1(604) -> 603
, 3_1(605) -> 604
, 3_1(606) -> 605
, 3_1(607) -> 606
, 3_1(608) -> 607
, 3_1(609) -> 608
, 3_1(610) -> 609
, 3_1(611) -> 610
, 3_1(612) -> 611
, 3_1(613) -> 612
, 3_1(614) -> 613
, 3_1(615) -> 614
, 3_1(616) -> 615
, 3_1(617) -> 616
, 3_1(618) -> 617
, 3_1(619) -> 618
, 3_1(620) -> 619
, 3_1(621) -> 620
, 3_1(622) -> 621
, 3_1(623) -> 622
, 3_1(624) -> 623
, 3_1(625) -> 624
, 3_1(626) -> 625
, 3_1(627) -> 626
, 3_1(628) -> 627
, 3_1(629) -> 628
, 3_1(630) -> 629
, 3_1(631) -> 630
, 3_1(632) -> 631
, 3_1(633) -> 632
, 3_1(634) -> 633
, 3_1(635) -> 634
, 3_1(636) -> 635
, 3_1(637) -> 636
, 3_1(638) -> 637
, 3_1(639) -> 638
, 3_1(640) -> 639
, 3_1(641) -> 640
, 3_1(642) -> 641
, 3_1(643) -> 642
, 3_1(644) -> 643
, 3_1(645) -> 644
, 3_1(646) -> 645
, 3_1(647) -> 646
, 3_1(648) -> 647
, 3_1(649) -> 648
, 3_1(650) -> 649
, 3_1(651) -> 650
, 3_1(652) -> 651
, 3_1(653) -> 652
, 3_1(654) -> 653
, 3_1(655) -> 654
, 3_1(656) -> 655
, 3_1(657) -> 656
, 3_1(658) -> 657
, 3_1(659) -> 658
, 3_1(660) -> 659
, 3_1(661) -> 660
, 3_1(662) -> 661
, 3_1(663) -> 662
, 3_1(664) -> 663
, 3_1(665) -> 664
, 3_1(666) -> 665
, 3_1(667) -> 666
, 3_1(668) -> 667
, 3_1(669) -> 668
, 3_1(670) -> 669
, 3_1(671) -> 670
, 3_1(672) -> 671
, 3_1(673) -> 672
, 3_1(674) -> 673
, 3_1(675) -> 674
, 3_1(676) -> 675
, 3_1(677) -> 676
, 3_1(678) -> 677
, 3_1(679) -> 678
, 3_1(680) -> 679
, 3_1(681) -> 680
, 3_1(682) -> 681
, 3_1(683) -> 682
, 3_1(684) -> 683
, 3_1(685) -> 684
, 3_1(686) -> 685
, 3_1(687) -> 686
, 3_1(688) -> 687
, 3_1(689) -> 688
, 3_1(690) -> 689
, 3_1(691) -> 690
, 3_1(692) -> 691
, 3_1(693) -> 692
, 3_1(694) -> 693
, 3_1(695) -> 694
, 3_1(696) -> 695
, 3_1(697) -> 696
, 3_1(698) -> 697
, 3_1(699) -> 698
, 3_1(700) -> 699
, 3_1(701) -> 700
, 3_1(702) -> 701
, 3_1(703) -> 702
, 3_1(704) -> 703
, 3_1(705) -> 704
, 3_1(706) -> 705
, 3_1(707) -> 706
, 3_1(708) -> 707
, 3_1(709) -> 708
, 3_1(710) -> 709
, 3_1(711) -> 710
, 3_1(712) -> 711
, 3_1(713) -> 712
, 3_1(714) -> 713
, 3_1(715) -> 714
, 3_1(716) -> 715
, 3_1(717) -> 716
, 3_1(718) -> 717
, 3_1(719) -> 718
, 3_1(720) -> 719
, 3_1(721) -> 720
, 3_1(722) -> 721
, 3_1(723) -> 722
, 3_1(724) -> 723
, 3_1(725) -> 724
, 3_1(726) -> 725
, 3_1(727) -> 726
, 3_1(728) -> 727
, 3_1(729) -> 728
, 3_1(730) -> 729
, 3_1(731) -> 730
, 3_1(732) -> 731
, 3_1(733) -> 732
, 3_1(734) -> 733
, 3_1(735) -> 734
, 3_1(736) -> 735
, 3_1(737) -> 736
, 3_1(738) -> 737
, 3_1(739) -> 738
, 3_1(740) -> 739
, 3_1(741) -> 740
, 3_1(742) -> 741
, 3_1(743) -> 742
, 3_1(744) -> 743
, 3_1(745) -> 744
, 3_1(746) -> 745
, 3_1(747) -> 746
, 3_1(748) -> 747
, 3_1(749) -> 748
, 3_1(750) -> 749
, 3_1(751) -> 750
, 3_1(752) -> 751
, 3_1(753) -> 752
, 3_1(754) -> 753
, 3_1(755) -> 754
, 3_1(756) -> 755
, 3_1(757) -> 756
, 3_1(758) -> 757
, 3_1(759) -> 758
, 3_1(760) -> 759
, 3_1(761) -> 760
, 3_1(762) -> 761
, 3_1(763) -> 762
, 3_1(764) -> 763
, 3_1(765) -> 764
, 3_1(766) -> 765
, 3_1(767) -> 766
, 3_1(768) -> 767
, 3_1(769) -> 768
, 3_1(770) -> 769
, 3_1(771) -> 770
, 3_1(772) -> 771
, 3_1(773) -> 772
, 3_1(774) -> 773
, 3_1(775) -> 774
, 3_1(776) -> 775
, 3_1(777) -> 776
, 3_1(778) -> 777
, 3_1(779) -> 778
, 3_1(780) -> 779
, 3_1(781) -> 780
, 3_1(782) -> 781
, 3_1(783) -> 782
, 3_1(784) -> 783
, 3_1(785) -> 784
, 3_1(786) -> 785
, 3_1(787) -> 786
, 3_1(788) -> 787
, 3_1(789) -> 788
, 3_1(790) -> 789
, 3_1(791) -> 790
, 3_1(792) -> 791
, 3_1(793) -> 792
, 3_1(794) -> 793
, 3_1(795) -> 794
, 3_1(796) -> 795
, 3_1(797) -> 796
, 3_1(798) -> 797
, 3_1(799) -> 798
, 3_1(800) -> 799
, 3_1(801) -> 800
, 3_1(802) -> 801
, 3_1(803) -> 802
, 3_1(804) -> 803
, 3_1(805) -> 804
, 3_1(806) -> 805
, 3_1(807) -> 806
, 3_1(808) -> 807
, 3_1(809) -> 808
, 3_1(810) -> 809
, 3_1(811) -> 810
, 3_1(812) -> 811
, 3_1(813) -> 812
, 3_1(814) -> 813
, 3_1(815) -> 814
, 3_1(816) -> 815
, 3_1(817) -> 816
, 3_1(818) -> 817
, 3_1(819) -> 818
, 3_1(820) -> 819
, 3_1(821) -> 820
, 3_1(822) -> 821
, 3_1(823) -> 822
, 3_1(824) -> 823
, 3_1(825) -> 824
, 3_1(826) -> 825
, 3_1(827) -> 826
, 3_1(828) -> 827
, 3_1(829) -> 828
, 3_1(830) -> 829
, 3_1(831) -> 830
, 3_1(832) -> 831
, 3_1(833) -> 832
, 3_1(834) -> 833
, 3_1(835) -> 834
, 3_1(836) -> 835
, 3_1(837) -> 836
, 3_1(838) -> 837
, 3_1(839) -> 838
, 3_1(840) -> 839
, 3_1(841) -> 840
, 3_1(842) -> 841
, 3_1(843) -> 842
, 3_1(844) -> 843
, 3_1(845) -> 844
, 3_1(846) -> 845
, 3_1(847) -> 846
, 3_1(848) -> 847
, 3_1(849) -> 848
, 3_1(850) -> 849
, 3_1(851) -> 850
, 3_1(852) -> 851
, 3_1(853) -> 852
, 3_1(854) -> 853
, 3_1(855) -> 854
, 3_1(856) -> 855
, 3_1(857) -> 856
, 3_1(858) -> 857
, 3_1(859) -> 858
, 3_1(860) -> 859
, 3_1(861) -> 860
, 3_1(862) -> 861
, 3_1(863) -> 862
, 3_1(864) -> 863
, 3_1(865) -> 864
, 3_1(866) -> 865
, 3_1(867) -> 866
, 3_1(868) -> 867
, 3_1(869) -> 868
, 3_1(870) -> 869
, 3_1(871) -> 870
, 3_1(872) -> 871
, 3_1(873) -> 872
, 3_1(874) -> 873
, 3_1(875) -> 874
, 3_1(876) -> 875
, 3_1(877) -> 876
, 3_1(878) -> 877
, 3_1(879) -> 878
, 3_1(880) -> 879
, 3_1(881) -> 880
, 3_1(882) -> 881
, 3_1(883) -> 882
, 3_1(884) -> 883
, 3_1(885) -> 884
, 3_1(886) -> 885
, 3_1(887) -> 886
, 3_1(888) -> 887
, 3_1(889) -> 888
, 3_1(890) -> 889
, 3_1(891) -> 890
, 3_1(892) -> 891
, 3_1(893) -> 892
, 3_1(894) -> 893
, 3_1(895) -> 894
, 3_1(896) -> 895
, 3_1(897) -> 896
, 3_1(898) -> 897
, 3_1(899) -> 898
, 3_1(900) -> 899
, 3_1(901) -> 900
, 3_1(902) -> 901
, 3_1(903) -> 902
, 3_1(904) -> 903
, 3_1(905) -> 904
, 3_1(906) -> 905
, 3_1(907) -> 906
, 3_1(908) -> 907
, 3_1(909) -> 908
, 3_1(910) -> 909
, 3_1(911) -> 910
, 3_1(912) -> 911
, 3_1(913) -> 912
, 3_1(914) -> 913
, 3_1(915) -> 914
, 3_1(916) -> 915
, 3_1(917) -> 916
, 3_1(918) -> 917
, 4_0(2) -> 2
, 5_0(2) -> 2}