YES

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {7,1}
   transitions:
    a0(9) -> 10*
    a0(2) -> 3*
    a0(8) -> 9*
    b1(31) -> 32*
    b1(34) -> 35*
    b1(29) -> 30*
    b1(14) -> 15*
    b1(11) -> 12*
    b1(26) -> 27*
    b1(49) -> 50*
    b1(46) -> 47*
    b0(2) -> 8*
    b0(10) -> 7*
    a3(195) -> 196*
    a3(81) -> 82*
    a3(154) -> 155*
    a3(86) -> 87*
    a3(153) -> 154*
    a3(102) -> 103*
    a3(196) -> 197*
    a3(226) -> 227*
    a3(101) -> 102*
    a3(149) -> 150*
    a3(210) -> 211*
    a3(143) -> 144*
    a3(231) -> 232*
    a3(174) -> 175*
    a3(82) -> 83*
    a3(240) -> 241*
    a3(148) -> 149*
    a3(216) -> 217*
    a3(144) -> 145*
    a3(241) -> 242*
    a3(117) -> 118*
    a3(215) -> 216*
    a3(191) -> 192*
    a3(190) -> 191*
    a3(225) -> 226*
    a3(211) -> 212*
    a3(139) -> 140*
    a3(118) -> 119*
    a3(175) -> 176*
    a3(230) -> 231*
    a3(87) -> 88*
    a3(138) -> 139*
    b3(212) -> 213*
    b3(214) -> 215*
    b3(85) -> 86*
    b3(173) -> 174*
    b3(176) -> 177*
    b3(150) -> 151*
    b3(229) -> 230*
    b3(197) -> 198*
    b3(224) -> 225*
    b3(137) -> 138*
    b3(217) -> 218*
    b3(80) -> 81*
    b3(189) -> 190*
    b3(145) -> 146*
    b3(103) -> 104*
    b3(119) -> 120*
    b3(194) -> 195*
    b3(232) -> 233*
    b3(116) -> 117*
    b3(83) -> 84*
    b3(209) -> 210*
    b3(155) -> 156*
    b3(147) -> 148*
    b3(239) -> 240*
    b3(242) -> 243*
    b3(152) -> 153*
    b3(88) -> 89*
    b3(227) -> 228*
    b3(192) -> 193*
    b3(142) -> 143*
    b3(100) -> 101*
    b3(140) -> 141*
    c0(3) -> 4*
    c0(4) -> 5*
    c0(6) -> 1*
    c0(5) -> 6*
    f30() -> 2*
    a1(48) -> 49*
    a1(13) -> 14*
    a1(27) -> 28*
    a1(12) -> 13*
    a1(47) -> 48*
    a1(28) -> 29*
    a1(32) -> 33*
    a1(33) -> 34*
    a2(121) -> 122*
    a2(63) -> 64*
    a2(57) -> 58*
    a2(167) -> 168*
    c2(168) -> 169*
    c2(122) -> 123*
    c2(124) -> 125*
    c2(171) -> 172*
    c2(60) -> 61*
    c2(59) -> 60*
    c2(64) -> 65*
    c2(170) -> 171*
    c2(61) -> 62*
    c2(123) -> 124*
    c2(58) -> 59*
    c2(66) -> 67*
    c2(125) -> 126*
    c2(169) -> 170*
    c2(65) -> 66*
    c2(67) -> 68*
    156 -> 65*
    228 -> 171*
    151 -> 66*
    68 -> 58*
    168 -> 239*
    198 -> 124*
    35 -> 1*
    46 -> 167*
    64 -> 152*
    30 -> 6*
    126 -> 64*
    104 -> 59*
    169 -> 229*
    66 -> 137*
    4 -> 11*
    11 -> 121*
    67 -> 142*
    124 -> 173*
    6 -> 31*
    171 -> 214*
    172 -> 122*
    141 -> 67*
    177 -> 125*
    170 -> 224*
    58 -> 100*
    233 -> 170*
    125 -> 189*
    26 -> 63*
    60 -> 116*
    123 -> 194*
    1 -> 241,3,46,9,48
    31 -> 57*
    62 -> 242,168,239,10,49
    193 -> 126*
    243 -> 169*
    65 -> 147*
    59 -> 80*
    5 -> 26*
    146 -> 68*
    213 -> 123*
    218 -> 172*
    50 -> 4*
    3 -> 46*
    120 -> 61*
    122 -> 209*
    84 -> 60*
    15 -> 5*
    89 -> 62,49
    61 -> 85*
  problem:
   
  Qed