YES(?,O(n^1))

Problem:
 a(c(b(x1))) -> b(a(b(a(x1))))
 b(x1) -> c(a(c(x1)))
 a(a(x1)) -> a(b(c(a(x1))))

Proof:
 Bounds Processor:
  bound: 5
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    a3(262) -> 263*
    a3(192) -> 193*
    a3(122) -> 123*
    a3(189) -> 190*
    a3(179) -> 180*
    a3(159) -> 160*
    a3(236) -> 237*
    a3(166) -> 167*
    a3(243) -> 244*
    a3(148) -> 149*
    a3(210) -> 211*
    a3(170) -> 171*
    a3(150) -> 151*
    a3(130) -> 131*
    a3(105) -> 106*
    b3(149) -> 150*
    b3(261) -> 262*
    b3(191) -> 192*
    b3(151) -> 152*
    c4(227) -> 228*
    c4(212) -> 213*
    c4(264) -> 265*
    c4(239) -> 240*
    c4(214) -> 215*
    c4(266) -> 267*
    c4(241) -> 242*
    c4(250) -> 251*
    c4(225) -> 226*
    a4(252) -> 253*
    a4(249) -> 250*
    a4(226) -> 227*
    a4(213) -> 214*
    a4(265) -> 266*
    a4(240) -> 241*
    a0(4) -> 4*
    b4(251) -> 252*
    c0(4) -> 4*
    c5(276) -> 277*
    c5(278) -> 279*
    b0(4) -> 4*
    a5(277) -> 278*
    a1(247) -> 248*
    a1(25) -> 26*
    a1(10) -> 11*
    a1(27) -> 28*
    a1(12) -> 13*
    a1(29) -> 30*
    a1(16) -> 17*
    a1(98) -> 99*
    a1(100) -> 101*
    b1(30) -> 31*
    b1(24) -> 25*
    b1(11) -> 12*
    b1(28) -> 29*
    b1(13) -> 14*
    c1(15) -> 16*
    c1(17) -> 18*
    c1(23) -> 24*
    a2(75) -> 76*
    a2(55) -> 56*
    a2(182) -> 183*
    a2(102) -> 103*
    a2(109) -> 110*
    a2(59) -> 60*
    a2(44) -> 45*
    a2(196) -> 197*
    a2(46) -> 47*
    a2(138) -> 139*
    a2(118) -> 119*
    a2(88) -> 89*
    a2(280) -> 281*
    a2(78) -> 79*
    a2(68) -> 69*
    a2(200) -> 201*
    a2(135) -> 136*
    a2(90) -> 91*
    b2(45) -> 46*
    b2(137) -> 138*
    b2(77) -> 78*
    b2(47) -> 48*
    b2(89) -> 90*
    b2(91) -> 92*
    b2(195) -> 196*
    c2(60) -> 61*
    c2(117) -> 118*
    c2(67) -> 68*
    c2(194) -> 195*
    c2(119) -> 120*
    c2(69) -> 70*
    c2(54) -> 55*
    c2(136) -> 137*
    c2(76) -> 77*
    c2(56) -> 57*
    c2(108) -> 109*
    c2(58) -> 59*
    c2(110) -> 111*
    c3(237) -> 238*
    c3(167) -> 168*
    c3(169) -> 170*
    c3(129) -> 130*
    c3(104) -> 105*
    c3(171) -> 172*
    c3(131) -> 132*
    c3(121) -> 122*
    c3(106) -> 107*
    c3(178) -> 179*
    c3(123) -> 124*
    c3(260) -> 261*
    c3(235) -> 236*
    c3(190) -> 191*
    c3(180) -> 181*
    c3(165) -> 166*
    4 -> 15,10
    11 -> 54,23
    12 -> 135*
    13 -> 58,44,27
    14 -> 11,17,23,4
    18 -> 4*
    24 -> 67*
    25 -> 75*
    26 -> 11,23,4
    28 -> 117*
    29 -> 182*
    30 -> 108,102,98
    31 -> 11,4,23
    45 -> 129*
    46 -> 189*
    47 -> 194,148,121,100,88
    48 -> 56,11,17
    57 -> 12*
    61 -> 14,4
    70 -> 25*
    77 -> 104*
    79 -> 248,11,23
    89 -> 169*
    90 -> 243*
    91 -> 165,159
    92 -> 13,11
    99 -> 11*
    101 -> 11*
    103 -> 45*
    107 -> 78*
    111 -> 31*
    120 -> 29*
    124 -> 48,17
    132 -> 46*
    137 -> 178*
    139 -> 103,99,11,23,45,28
    149 -> 239*
    150 -> 280,249
    151 -> 260,247,225,210,200
    152 -> 60,56,136
    160 -> 149*
    168 -> 92*
    172 -> 90*
    181 -> 138*
    183 -> 136*
    191 -> 212*
    193 -> 160,149,89
    195 -> 235*
    197 -> 101*
    201 -> 89*
    211 -> 149*
    215 -> 192*
    228 -> 152,56,136
    238 -> 196*
    242 -> 150*
    244 -> 190*
    248 -> 11*
    251 -> 276*
    253 -> 211*
    261 -> 264*
    263 -> 201*
    267 -> 262*
    279 -> 252*
    281 -> 76*
  problem:
   
  Qed