YES(?,O(n^1))
1132.41/297.04	YES(?,O(n^1))
1132.41/297.04	
1132.41/297.04	We are left with following problem, upon which TcT provides the
1132.41/297.04	certificate YES(?,O(n^1)).
1132.41/297.04	
1132.41/297.04	Strict Trs:
1132.41/297.04	  { 5(5(x1)) -> 0(5(4(0(2(5(4(5(2(1(x1))))))))))
1132.41/297.04	  , 5(5(x1)) -> 3(4(1(1(1(1(4(4(0(4(x1))))))))))
1132.41/297.04	  , 5(5(5(x1))) -> 5(3(4(1(0(1(4(5(0(0(x1))))))))))
1132.41/297.04	  , 5(5(5(1(4(x1))))) -> 3(3(0(5(0(4(3(4(4(0(x1))))))))))
1132.41/297.04	  , 5(5(2(x1))) -> 0(1(3(2(3(0(3(2(5(3(x1))))))))))
1132.41/297.04	  , 5(5(2(4(5(0(x1)))))) -> 2(1(1(4(2(4(0(4(2(0(x1))))))))))
1132.41/297.04	  , 5(5(3(x1))) -> 0(3(5(4(4(1(0(1(5(0(x1))))))))))
1132.41/297.04	  , 5(2(5(5(0(4(x1)))))) -> 0(4(2(3(3(5(2(1(4(4(x1))))))))))
1132.41/297.04	  , 5(2(4(x1))) -> 0(5(0(2(3(3(4(2(4(2(x1))))))))))
1132.41/297.04	  , 0(4(4(5(5(5(x1)))))) -> 0(4(4(4(3(3(4(1(3(1(x1))))))))))
1132.41/297.04	  , 0(2(5(3(4(x1))))) -> 3(2(4(3(1(5(1(1(3(4(x1))))))))))
1132.41/297.04	  , 0(1(5(5(5(3(5(x1))))))) -> 5(3(2(5(1(0(1(2(0(5(x1))))))))))
1132.41/297.04	  , 4(5(5(5(x1)))) -> 1(5(1(2(0(3(2(1(0(5(x1))))))))))
1132.41/297.04	  , 4(5(2(4(x1)))) -> 4(1(5(5(2(0(3(1(3(3(x1))))))))))
1132.41/297.04	  , 4(4(5(2(4(2(2(x1))))))) -> 4(0(5(5(4(5(1(2(2(1(x1))))))))))
1132.41/297.04	  , 4(2(5(5(1(5(x1)))))) -> 2(3(4(2(1(1(3(4(2(5(x1))))))))))
1132.41/297.04	  , 4(1(5(5(0(4(x1)))))) -> 1(0(3(0(4(2(4(4(3(4(x1))))))))))
1132.41/297.04	  , 2(5(5(x1))) -> 4(2(5(4(4(0(0(1(1(2(x1))))))))))
1132.41/297.04	  , 2(5(5(3(4(x1))))) -> 4(5(4(3(1(4(0(2(4(4(x1))))))))))
1132.41/297.04	  , 2(5(0(4(x1)))) -> 4(4(3(2(4(4(5(1(0(0(x1))))))))))
1132.41/297.04	  , 1(2(4(5(2(4(x1)))))) -> 3(3(5(3(0(4(0(3(1(3(x1)))))))))) }
1132.41/297.04	Obligation:
1132.41/297.04	  derivational complexity
1132.41/297.04	Answer:
1132.41/297.04	  YES(?,O(n^1))
1132.41/297.04	
1132.41/297.04	The problem is match-bounded by 2. The enriched problem is
1132.41/297.04	compatible with the following automaton.
1132.41/297.04	{ 5_0(1) -> 1
1132.41/297.04	, 5_1(1) -> 90
1132.41/297.04	, 5_1(3) -> 2
1132.41/297.04	, 5_1(7) -> 6
1132.41/297.04	, 5_1(9) -> 8
1132.41/297.04	, 5_1(20) -> 1
1132.41/297.04	, 5_1(20) -> 28
1132.41/297.04	, 5_1(20) -> 90
1132.41/297.04	, 5_1(27) -> 26
1132.41/297.04	, 5_1(28) -> 58
1132.41/297.04	, 5_1(31) -> 30
1132.41/297.04	, 5_1(43) -> 42
1132.41/297.04	, 5_1(53) -> 52
1132.41/297.04	, 5_1(63) -> 62
1132.41/297.04	, 5_1(81) -> 80
1132.41/297.04	, 5_1(85) -> 84
1132.41/297.04	, 5_1(92) -> 91
1132.41/297.04	, 5_1(100) -> 99
1132.41/297.04	, 5_1(101) -> 100
1132.41/297.04	, 5_1(107) -> 106
1132.41/297.04	, 5_1(108) -> 107
1132.41/297.04	, 5_1(110) -> 109
1132.41/297.04	, 5_1(126) -> 125
1132.41/297.04	, 5_1(140) -> 98
1132.41/297.04	, 5_1(159) -> 158
1132.41/297.04	, 5_1(168) -> 29
1132.41/297.04	, 5_2(133) -> 132
1132.41/297.04	, 5_2(146) -> 131
1132.41/297.04	, 5_2(165) -> 164
1132.41/297.04	, 5_2(175) -> 174
1132.41/297.04	, 5_2(179) -> 178
1132.41/297.04	, 5_2(181) -> 180
1132.41/297.04	, 5_2(184) -> 183
1132.41/297.04	, 5_2(188) -> 187
1132.41/297.04	, 5_2(190) -> 189
1132.41/297.04	, 5_2(193) -> 192
1132.41/297.04	, 5_2(197) -> 196
1132.41/297.04	, 5_2(199) -> 198
1132.41/297.04	, 5_2(235) -> 234
1132.41/297.04	, 5_2(237) -> 236
1132.41/297.04	, 5_2(243) -> 242
1132.41/297.04	, 0_0(1) -> 1
1132.41/297.04	, 0_1(1) -> 28
1132.41/297.04	, 0_1(2) -> 1
1132.41/297.04	, 0_1(2) -> 18
1132.41/297.04	, 0_1(2) -> 28
1132.41/297.04	, 0_1(2) -> 90
1132.41/297.04	, 0_1(5) -> 4
1132.41/297.04	, 0_1(11) -> 28
1132.41/297.04	, 0_1(19) -> 18
1132.41/297.04	, 0_1(20) -> 28
1132.41/297.04	, 0_1(21) -> 28
1132.41/297.04	, 0_1(24) -> 23
1132.41/297.04	, 0_1(28) -> 27
1132.41/297.04	, 0_1(30) -> 29
1132.41/297.04	, 0_1(32) -> 31
1132.41/297.04	, 0_1(40) -> 39
1132.41/297.04	, 0_1(50) -> 49
1132.41/297.04	, 0_1(57) -> 56
1132.41/297.04	, 0_1(59) -> 28
1132.41/297.04	, 0_1(66) -> 3
1132.41/297.04	, 0_1(87) -> 86
1132.41/297.04	, 0_1(90) -> 89
1132.41/297.04	, 0_1(95) -> 94
1132.41/297.04	, 0_1(98) -> 28
1132.41/297.04	, 0_1(103) -> 102
1132.41/297.04	, 0_1(106) -> 98
1132.41/297.04	, 0_1(119) -> 91
1132.41/297.04	, 0_1(121) -> 120
1132.41/297.04	, 0_1(129) -> 128
1132.41/297.04	, 0_1(130) -> 129
1132.41/297.04	, 0_1(145) -> 144
1132.41/297.04	, 0_1(170) -> 169
1132.41/297.04	, 0_1(172) -> 171
1132.41/297.04	, 0_2(20) -> 167
1132.41/297.04	, 0_2(21) -> 243
1132.41/297.04	, 0_2(59) -> 167
1132.41/297.04	, 0_2(136) -> 135
1132.41/297.04	, 0_2(137) -> 136
1132.41/297.04	, 0_2(151) -> 150
1132.41/297.04	, 0_2(167) -> 166
1132.41/297.04	, 0_2(174) -> 58
1132.41/297.04	, 0_2(174) -> 90
1132.41/297.04	, 0_2(177) -> 176
1132.41/297.04	, 0_2(183) -> 99
1132.41/297.04	, 0_2(186) -> 185
1132.41/297.04	, 0_2(192) -> 106
1132.41/297.04	, 0_2(195) -> 194
1132.41/297.04	, 0_2(209) -> 208
1132.41/297.04	, 0_2(218) -> 217
1132.41/297.04	, 0_2(227) -> 226
1132.41/297.04	, 0_2(232) -> 231
1132.41/297.04	, 0_2(241) -> 240
1132.41/297.04	, 4_0(1) -> 1
1132.41/297.04	, 4_1(1) -> 19
1132.41/297.04	, 4_1(2) -> 65
1132.41/297.04	, 4_1(4) -> 3
1132.41/297.04	, 4_1(8) -> 7
1132.41/297.04	, 4_1(11) -> 65
1132.41/297.04	, 4_1(12) -> 11
1132.41/297.04	, 4_1(17) -> 16
1132.41/297.04	, 4_1(18) -> 17
1132.41/297.04	, 4_1(19) -> 65
1132.41/297.04	, 4_1(20) -> 2
1132.41/297.04	, 4_1(21) -> 65
1132.41/297.04	, 4_1(22) -> 21
1132.41/297.04	, 4_1(26) -> 25
1132.41/297.04	, 4_1(28) -> 35
1132.41/297.04	, 4_1(33) -> 32
1132.41/297.04	, 4_1(35) -> 34
1132.41/297.04	, 4_1(47) -> 46
1132.41/297.04	, 4_1(49) -> 48
1132.41/297.04	, 4_1(51) -> 50
1132.41/297.04	, 4_1(54) -> 53
1132.41/297.04	, 4_1(55) -> 54
1132.41/297.04	, 4_1(59) -> 2
1132.41/297.04	, 4_1(70) -> 69
1132.41/297.04	, 4_1(71) -> 59
1132.41/297.04	, 4_1(72) -> 71
1132.41/297.04	, 4_1(75) -> 74
1132.41/297.04	, 4_1(78) -> 77
1132.41/297.04	, 4_1(83) -> 124
1132.41/297.04	, 4_1(98) -> 1
1132.41/297.04	, 4_1(98) -> 19
1132.41/297.04	, 4_1(98) -> 51
1132.41/297.04	, 4_1(98) -> 65
1132.41/297.04	, 4_1(98) -> 118
1132.41/297.04	, 4_1(109) -> 108
1132.41/297.04	, 4_1(113) -> 112
1132.41/297.04	, 4_1(118) -> 117
1132.41/297.04	, 4_1(122) -> 121
1132.41/297.04	, 4_1(124) -> 123
1132.41/297.04	, 4_1(127) -> 126
1132.41/297.04	, 4_1(128) -> 127
1132.41/297.04	, 4_1(141) -> 140
1132.41/297.04	, 4_1(144) -> 143
1132.41/297.04	, 4_1(154) -> 98
1132.41/297.04	, 4_1(157) -> 156
1132.41/297.04	, 4_1(158) -> 157
1132.41/297.04	, 4_1(171) -> 170
1132.41/297.04	, 4_2(20) -> 209
1132.41/297.04	, 4_2(22) -> 153
1132.41/297.04	, 4_2(101) -> 218
1132.41/297.04	, 4_2(108) -> 227
1132.41/297.04	, 4_2(131) -> 118
1132.41/297.04	, 4_2(134) -> 133
1132.41/297.04	, 4_2(135) -> 134
1132.41/297.04	, 4_2(147) -> 146
1132.41/297.04	, 4_2(150) -> 149
1132.41/297.04	, 4_2(153) -> 152
1132.41/297.04	, 4_2(160) -> 131
1132.41/297.04	, 4_2(163) -> 162
1132.41/297.04	, 4_2(164) -> 163
1132.41/297.04	, 4_2(176) -> 175
1132.41/297.04	, 4_2(180) -> 179
1132.41/297.04	, 4_2(185) -> 184
1132.41/297.04	, 4_2(189) -> 188
1132.41/297.04	, 4_2(194) -> 193
1132.41/297.04	, 4_2(198) -> 197
1132.41/297.04	, 4_2(202) -> 201
1132.41/297.04	, 4_2(207) -> 206
1132.41/297.04	, 4_2(208) -> 207
1132.41/297.04	, 4_2(211) -> 210
1132.41/297.04	, 4_2(216) -> 215
1132.41/297.04	, 4_2(217) -> 216
1132.41/297.04	, 4_2(220) -> 219
1132.41/297.04	, 4_2(225) -> 224
1132.41/297.04	, 4_2(226) -> 225
1132.41/297.04	, 4_2(238) -> 237
1132.41/297.04	, 4_2(239) -> 238
1132.41/297.04	, 2_0(1) -> 1
1132.41/297.04	, 2_1(1) -> 51
1132.41/297.04	, 2_1(6) -> 5
1132.41/297.04	, 2_1(9) -> 111
1132.41/297.04	, 2_1(10) -> 9
1132.41/297.04	, 2_1(20) -> 51
1132.41/297.04	, 2_1(28) -> 51
1132.41/297.04	, 2_1(38) -> 37
1132.41/297.04	, 2_1(42) -> 41
1132.41/297.04	, 2_1(44) -> 1
1132.41/297.04	, 2_1(44) -> 19
1132.41/297.04	, 2_1(44) -> 50
1132.41/297.04	, 2_1(44) -> 90
1132.41/297.04	, 2_1(44) -> 117
1132.41/297.04	, 2_1(48) -> 47
1132.41/297.04	, 2_1(50) -> 70
1132.41/297.04	, 2_1(60) -> 59
1132.41/297.04	, 2_1(64) -> 63
1132.41/297.04	, 2_1(65) -> 145
1132.41/297.04	, 2_1(67) -> 66
1132.41/297.04	, 2_1(77) -> 11
1132.41/297.04	, 2_1(84) -> 21
1132.41/297.04	, 2_1(89) -> 88
1132.41/297.04	, 2_1(90) -> 118
1132.41/297.04	, 2_1(91) -> 51
1132.41/297.04	, 2_1(94) -> 93
1132.41/297.04	, 2_1(97) -> 96
1132.41/297.04	, 2_1(98) -> 51
1132.41/297.04	, 2_1(102) -> 101
1132.41/297.04	, 2_1(114) -> 113
1132.41/297.04	, 2_1(123) -> 122
1132.41/297.04	, 2_1(125) -> 98
1132.41/297.04	, 2_1(156) -> 155
1132.41/297.04	, 2_2(20) -> 139
1132.41/297.04	, 2_2(132) -> 131
1132.41/297.04	, 2_2(152) -> 151
1132.41/297.04	, 2_2(162) -> 161
1132.41/297.04	, 2_2(178) -> 177
1132.41/297.04	, 2_2(182) -> 181
1132.41/297.04	, 2_2(187) -> 186
1132.41/297.04	, 2_2(191) -> 190
1132.41/297.04	, 2_2(196) -> 195
1132.41/297.04	, 2_2(200) -> 199
1132.41/297.04	, 2_2(230) -> 229
1132.41/297.04	, 2_2(234) -> 233
1132.41/297.04	, 1_0(1) -> 1
1132.41/297.04	, 1_1(1) -> 10
1132.41/297.04	, 1_1(10) -> 81
1132.41/297.04	, 1_1(13) -> 12
1132.41/297.04	, 1_1(14) -> 13
1132.41/297.04	, 1_1(15) -> 14
1132.41/297.04	, 1_1(16) -> 15
1132.41/297.04	, 1_1(20) -> 10
1132.41/297.04	, 1_1(23) -> 22
1132.41/297.04	, 1_1(25) -> 24
1132.41/297.04	, 1_1(27) -> 159
1132.41/297.04	, 1_1(28) -> 97
1132.41/297.04	, 1_1(36) -> 2
1132.41/297.04	, 1_1(43) -> 173
1132.41/297.04	, 1_1(44) -> 10
1132.41/297.04	, 1_1(45) -> 44
1132.41/297.04	, 1_1(46) -> 45
1132.41/297.04	, 1_1(51) -> 87
1132.41/297.04	, 1_1(56) -> 55
1132.41/297.04	, 1_1(58) -> 57
1132.41/297.04	, 1_1(65) -> 64
1132.41/297.04	, 1_1(76) -> 75
1132.41/297.04	, 1_1(80) -> 79
1132.41/297.04	, 1_1(82) -> 81
1132.41/297.04	, 1_1(83) -> 82
1132.41/297.04	, 1_1(86) -> 85
1132.41/297.04	, 1_1(87) -> 130
1132.41/297.04	, 1_1(88) -> 87
1132.41/297.04	, 1_1(89) -> 97
1132.41/297.04	, 1_1(91) -> 1
1132.41/297.04	, 1_1(91) -> 19
1132.41/297.04	, 1_1(93) -> 92
1132.41/297.04	, 1_1(99) -> 98
1132.41/297.04	, 1_1(105) -> 104
1132.41/297.04	, 1_1(111) -> 110
1132.41/297.04	, 1_1(115) -> 114
1132.41/297.04	, 1_1(116) -> 115
1132.41/297.04	, 1_1(143) -> 142
1132.41/297.04	, 1_2(20) -> 182
1132.41/297.04	, 1_2(101) -> 191
1132.41/297.04	, 1_2(108) -> 200
1132.41/297.04	, 1_2(138) -> 137
1132.41/297.04	, 1_2(139) -> 138
1132.41/297.04	, 1_2(149) -> 148
1132.41/297.04	, 1_2(166) -> 165
1132.41/297.04	, 1_2(203) -> 202
1132.41/297.04	, 1_2(204) -> 203
1132.41/297.04	, 1_2(205) -> 204
1132.41/297.04	, 1_2(206) -> 205
1132.41/297.04	, 1_2(212) -> 211
1132.41/297.04	, 1_2(213) -> 212
1132.41/297.04	, 1_2(214) -> 213
1132.41/297.04	, 1_2(215) -> 214
1132.41/297.04	, 1_2(221) -> 220
1132.41/297.04	, 1_2(222) -> 221
1132.41/297.04	, 1_2(223) -> 222
1132.41/297.04	, 1_2(224) -> 223
1132.41/297.04	, 1_2(228) -> 183
1132.41/297.04	, 1_2(240) -> 239
1132.41/297.04	, 1_2(242) -> 241
1132.41/297.04	, 3_0(1) -> 1
1132.41/297.04	, 3_1(1) -> 43
1132.41/297.04	, 3_1(2) -> 83
1132.41/297.04	, 3_1(10) -> 76
1132.41/297.04	, 3_1(11) -> 1
1132.41/297.04	, 3_1(11) -> 10
1132.41/297.04	, 3_1(11) -> 28
1132.41/297.04	, 3_1(11) -> 87
1132.41/297.04	, 3_1(11) -> 90
1132.41/297.04	, 3_1(19) -> 83
1132.41/297.04	, 3_1(21) -> 20
1132.41/297.04	, 3_1(29) -> 11
1132.41/297.04	, 3_1(34) -> 33
1132.41/297.04	, 3_1(37) -> 36
1132.41/297.04	, 3_1(39) -> 38
1132.41/297.04	, 3_1(41) -> 40
1132.41/297.04	, 3_1(43) -> 105
1132.41/297.04	, 3_1(44) -> 43
1132.41/297.04	, 3_1(50) -> 116
1132.41/297.04	, 3_1(52) -> 2
1132.41/297.04	, 3_1(61) -> 60
1132.41/297.04	, 3_1(62) -> 61
1132.41/297.04	, 3_1(68) -> 67
1132.41/297.04	, 3_1(69) -> 68
1132.41/297.04	, 3_1(73) -> 72
1132.41/297.04	, 3_1(74) -> 73
1132.41/297.04	, 3_1(79) -> 78
1132.41/297.04	, 3_1(96) -> 95
1132.41/297.04	, 3_1(98) -> 43
1132.41/297.04	, 3_1(104) -> 103
1132.41/297.04	, 3_1(112) -> 44
1132.41/297.04	, 3_1(117) -> 116
1132.41/297.04	, 3_1(120) -> 119
1132.41/297.04	, 3_1(142) -> 141
1132.41/297.04	, 3_1(155) -> 154
1132.41/297.04	, 3_1(169) -> 168
1132.41/297.04	, 3_1(173) -> 172
1132.41/297.04	, 3_2(102) -> 235
1132.41/297.04	, 3_2(148) -> 147
1132.41/297.04	, 3_2(161) -> 160
1132.41/297.04	, 3_2(201) -> 58
1132.41/297.04	, 3_2(201) -> 90
1132.41/297.04	, 3_2(210) -> 99
1132.41/297.04	, 3_2(219) -> 106
1132.41/297.04	, 3_2(229) -> 228
1132.41/297.04	, 3_2(231) -> 230
1132.41/297.04	, 3_2(233) -> 232
1132.41/297.04	, 3_2(236) -> 174 }
1132.41/297.04	
1132.41/297.04	Hurray, we answered YES(?,O(n^1))
1133.39/297.96	EOF