YES

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

Proof:
 Bounds Processor:
  bound: 5
  enrichment: match
  automaton:
   final states: {5,1}
   transitions:
    a0(7) -> 8*
    a0(2) -> 3*
    a0(6) -> 7*
    a0(8) -> 9*
    b3(68) -> 69*
    b3(130) -> 131*
    b3(126) -> 127*
    b3(114) -> 115*
    b3(110) -> 111*
    b3(72) -> 73*
    b3(54) -> 55*
    b3(136) -> 137*
    b3(50) -> 51*
    b3(86) -> 87*
    b3(82) -> 83*
    b3(132) -> 133*
    f30() -> 2*
    a4(174) -> 175*
    a4(170) -> 171*
    a4(171) -> 172*
    a4(155) -> 156*
    a4(226) -> 227*
    a4(148) -> 149*
    a4(234) -> 235*
    a4(153) -> 154*
    a4(169) -> 170*
    a4(154) -> 155*
    b4(152) -> 153*
    b4(172) -> 173*
    b4(168) -> 169*
    b4(156) -> 157*
    b1(16) -> 17*
    b1(20) -> 21*
    b1(22) -> 23*
    b1(26) -> 27*
    a2(34) -> 35*
    a2(46) -> 47*
    a2(78) -> 79*
    c3(117) -> 118*
    c3(118) -> 119*
    c2(47) -> 48*
    c2(36) -> 37*
    c2(79) -> 80*
    c2(80) -> 81*
    c2(48) -> 49*
    c2(35) -> 36*
    b5(282) -> 283*
    b5(266) -> 267*
    b5(196) -> 197*
    b5(218) -> 219*
    b5(270) -> 271*
    b5(194) -> 195*
    b5(224) -> 225*
    b5(190) -> 191*
    b5(200) -> 201*
    b5(214) -> 215*
    b5(252) -> 253*
    b5(242) -> 243*
    b5(248) -> 249*
    b5(246) -> 247*
    b5(220) -> 221*
    b5(278) -> 279*
    a1(24) -> 25*
    a1(17) -> 18*
    a1(25) -> 26*
    a1(18) -> 19*
    a1(19) -> 20*
    a1(23) -> 24*
    a5(267) -> 268*
    a5(250) -> 251*
    a5(281) -> 282*
    a5(217) -> 218*
    a5(243) -> 244*
    a5(198) -> 199*
    a5(199) -> 200*
    a5(245) -> 246*
    a5(279) -> 280*
    a5(192) -> 193*
    a5(269) -> 270*
    a5(244) -> 245*
    a5(221) -> 222*
    a5(222) -> 223*
    a5(249) -> 250*
    a5(215) -> 216*
    a5(193) -> 194*
    a5(191) -> 192*
    a5(280) -> 281*
    a5(251) -> 252*
    a5(216) -> 217*
    a5(268) -> 269*
    a5(197) -> 198*
    a5(223) -> 224*
    c0(3) -> 4*
    c0(4) -> 1*
    c4(149) -> 150*
    c4(150) -> 151*
    c4(176) -> 177*
    c4(228) -> 229*
    c4(175) -> 176*
    c4(227) -> 228*
    c4(236) -> 237*
    c4(235) -> 236*
    a3(112) -> 113*
    a3(51) -> 52*
    a3(134) -> 135*
    a3(52) -> 53*
    a3(116) -> 117*
    a3(129) -> 130*
    a3(113) -> 114*
    a3(83) -> 84*
    a3(111) -> 112*
    a3(85) -> 86*
    a3(127) -> 128*
    a3(71) -> 72*
    a3(84) -> 85*
    a3(69) -> 70*
    a3(133) -> 134*
    a3(128) -> 129*
    a3(53) -> 54*
    a3(135) -> 136*
    a3(70) -> 71*
    b0(2) -> 6*
    b0(9) -> 5*
    247 -> 229*
    228 -> 242*
    151 -> 235,117
    27 -> 4*
    195 -> 151*
    131 -> 81*
    68 -> 234,116
    47 -> 110*
    48 -> 82*
    115 -> 48*
    35 -> 68*
    137 -> 80*
    236 -> 266*
    16 -> 34*
    118 -> 152*
    4 -> 16*
    117 -> 168*
    82 -> 148*
    283 -> 236*
    237 -> 227*
    22 -> 46*
    173 -> 118*
    150 -> 190*
    21 -> 1*
    177 -> 149*
    201 -> 150*
    36 -> 50*
    79 -> 132*
    253 -> 228*
    235 -> 278*
    73 -> 36*
    1 -> 112,222,3,22,7,24
    49 -> 35*
    175 -> 220*
    55 -> 37,25
    110 -> 174*
    37 -> 113,223,47,8,25
    219 -> 177*
    225 -> 176*
    50 -> 226,78
    3 -> 22*
    227 -> 248*
    119 -> 79*
    149 -> 196*
    229 -> 114,224,175,220
    80 -> 126*
    87 -> 49,35,68
    271 -> 237*
    81 -> 9,26
    176 -> 214*
    157 -> 119*
  problem:
   
  Qed