YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 5
  enrichment: match
  automaton:
   final states: {2,1}
   transitions:
    a3(212) -> 213*
    a3(177) -> 178*
    a3(167) -> 168*
    a3(152) -> 153*
    a3(214) -> 215*
    a3(154) -> 155*
    a3(144) -> 145*
    a3(114) -> 115*
    a3(176) -> 177*
    a3(166) -> 167*
    a3(141) -> 142*
    a3(121) -> 122*
    a3(116) -> 117*
    a3(213) -> 214*
    a3(168) -> 169*
    a3(153) -> 154*
    a3(143) -> 144*
    a3(175) -> 176*
    a3(150) -> 151*
    a3(145) -> 146*
    a3(115) -> 116*
    b4(252) -> 253*
    b4(237) -> 238*
    b4(274) -> 275*
    b4(259) -> 260*
    b4(254) -> 255*
    b4(194) -> 195*
    b4(281) -> 282*
    b4(261) -> 262*
    b4(236) -> 237*
    b4(196) -> 197*
    b4(273) -> 274*
    b4(253) -> 254*
    b4(238) -> 239*
    b4(280) -> 281*
    b4(275) -> 276*
    b4(260) -> 261*
    b4(195) -> 196*
    b4(282) -> 283*
    a4(277) -> 278*
    a4(272) -> 273*
    a4(257) -> 258*
    a4(192) -> 193*
    a4(279) -> 280*
    a4(249) -> 250*
    a4(234) -> 235*
    a4(271) -> 272*
    a4(256) -> 257*
    a4(251) -> 252*
    a4(191) -> 192*
    a4(278) -> 279*
    a4(258) -> 259*
    a4(233) -> 234*
    a4(193) -> 194*
    a4(270) -> 271*
    a4(250) -> 251*
    a4(240) -> 241*
    a4(235) -> 236*
    a0(2) -> 1*
    a0(1) -> 1*
    b5(299) -> 300*
    b5(291) -> 292*
    b5(298) -> 299*
    b5(293) -> 294*
    b5(300) -> 301*
    b5(292) -> 293*
    b0(2) -> 2*
    b0(1) -> 2*
    a5(289) -> 290*
    a5(296) -> 297*
    a5(288) -> 289*
    a5(295) -> 296*
    a5(290) -> 291*
    a5(297) -> 298*
    b1(30) -> 31*
    b1(32) -> 33*
    b1(7) -> 8*
    b1(9) -> 10*
    b1(31) -> 32*
    b1(8) -> 9*
    a1(25) -> 26*
    a1(5) -> 6*
    a1(27) -> 28*
    a1(29) -> 30*
    a1(4) -> 5*
    a1(61) -> 62*
    a1(36) -> 37*
    a1(6) -> 7*
    a1(63) -> 64*
    a1(28) -> 29*
    b2(70) -> 71*
    b2(137) -> 138*
    b2(77) -> 78*
    b2(72) -> 73*
    b2(42) -> 43*
    b2(94) -> 95*
    b2(79) -> 80*
    b2(136) -> 137*
    b2(71) -> 72*
    b2(41) -> 42*
    b2(93) -> 94*
    b2(78) -> 79*
    b2(43) -> 44*
    b2(135) -> 136*
    b2(95) -> 96*
    a2(75) -> 76*
    a2(40) -> 41*
    a2(132) -> 133*
    a2(97) -> 98*
    a2(92) -> 93*
    a2(67) -> 68*
    a2(134) -> 135*
    a2(74) -> 75*
    a2(69) -> 70*
    a2(39) -> 40*
    a2(101) -> 102*
    a2(91) -> 92*
    a2(76) -> 77*
    a2(133) -> 134*
    a2(103) -> 104*
    a2(68) -> 69*
    a2(38) -> 39*
    a2(105) -> 106*
    a2(90) -> 91*
    b3(217) -> 218*
    b3(157) -> 158*
    b3(147) -> 148*
    b3(117) -> 118*
    b3(179) -> 180*
    b3(169) -> 170*
    b3(119) -> 120*
    b3(216) -> 217*
    b3(171) -> 172*
    b3(156) -> 157*
    b3(146) -> 147*
    b3(178) -> 179*
    b3(148) -> 149*
    b3(118) -> 119*
    b3(215) -> 216*
    b3(180) -> 181*
    b3(170) -> 171*
    b3(155) -> 156*
    1 -> 25*
    2 -> 4*
    7 -> 74*
    8 -> 38,36
    9 -> 27*
    10 -> 26,6,5,1
    26 -> 5*
    30 -> 101*
    31 -> 67,63
    32 -> 61*
    33 -> 26,6,1,5
    37 -> 5*
    41 -> 150*
    42 -> 121,97
    43 -> 105*
    44 -> 40,75,7,6
    62 -> 5*
    64 -> 5*
    70 -> 143*
    71 -> 114,90
    72 -> 103*
    73 -> 75,6,7
    78 -> 132*
    80 -> 29*
    94 -> 141*
    96 -> 75*
    98 -> 91*
    102 -> 39*
    104 -> 39*
    106 -> 39*
    117 -> 191*
    118 -> 240*
    119 -> 175*
    120 -> 151,144,77,76
    122 -> 115*
    136 -> 166*
    138 -> 102*
    142 -> 115*
    147 -> 152*
    149 -> 40*
    151 -> 144*
    156 -> 233*
    158 -> 151,144
    169 -> 256*
    170 -> 249*
    171 -> 212*
    172 -> 41*
    181 -> 134*
    197 -> 177*
    216 -> 277*
    218 -> 92,116
    236 -> 295*
    238 -> 270*
    239 -> 146*
    241 -> 234*
    255 -> 145*
    262 -> 214*
    276 -> 154*
    281 -> 288*
    283 -> 192*
    294 -> 194*
    301 -> 272*
  problem:
   
  Qed