YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match-rt
  automaton:
   final states: {4}
   transitions:
    c1(23) -> 24*
    c1(21) -> 22*
    c1(165) -> 166*
    c1(18) -> 19*
    c1(132) -> 133*
    c1(93) -> 94*
    c1(148) -> 149*
    c1(22) -> 23*
    b1(145) -> 146*
    b1(147) -> 148*
    b1(131) -> 132*
    b1(133) -> 134*
    b1(149) -> 150*
    a1(17) -> 18*
    a1(43) -> 44*
    a1(57) -> 58*
    a1(19) -> 20*
    a0(4) -> 4*
    c0(4) -> 4*
    b0(4) -> 4*
    a2(89) -> 90*
    a2(39) -> 40*
    a2(181) -> 182*
    a2(61) -> 62*
    a2(75) -> 76*
    a2(129) -> 130*
    a2(77) -> 78*
    a2(167) -> 168*
    a2(59) -> 60*
    a2(91) -> 92*
    a2(41) -> 42*
    b2(335) -> 336*
    b2(271) -> 272*
    b2(313) -> 314*
    b2(273) -> 274*
    b2(359) -> 360*
    b2(315) -> 316*
    b2(277) -> 278*
    b2(251) -> 252*
    b2(253) -> 254*
    b2(199) -> 200*
    b2(333) -> 334*
    b2(203) -> 204*
    b2(229) -> 230*
    b2(233) -> 234*
    b2(289) -> 290*
    b2(309) -> 310*
    b2(291) -> 292*
    b2(293) -> 294*
    b2(249) -> 250*
    b2(361) -> 362*
    b2(337) -> 338*
    b2(201) -> 202*
    b2(205) -> 206*
    b2(275) -> 276*
    b2(295) -> 296*
    b2(311) -> 312*
    b2(235) -> 236*
    b2(255) -> 256*
    b2(231) -> 232*
    b2(339) -> 340*
    c2(294) -> 295*
    c2(360) -> 361*
    c2(40) -> 41*
    c2(250) -> 251*
    c2(338) -> 339*
    c2(90) -> 91*
    c2(76) -> 77*
    c2(230) -> 231*
    c2(204) -> 205*
    c2(60) -> 61*
    c2(314) -> 315*
    c2(272) -> 273*
    c2(290) -> 291*
    c2(334) -> 335*
    c2(276) -> 277*
    c2(234) -> 235*
    c2(200) -> 201*
    c2(310) -> 311*
    c2(254) -> 255*
    312 -> 130*
    94 -> 22*
    166 -> 22*
    43 -> 275*
    19 -> 271,131,21
    24 -> 130,18,4
    92 -> 61,94,19
    340 -> 168*
    206 -> 76*
    168 -> 40*
    17 -> 249,147
    256 -> 58*
    278 -> 44*
    362 -> 182*
    42 -> 23*
    182 -> 60*
    236 -> 92*
    77 -> 229*
    93 -> 129*
    252 -> 18*
    232 -> 78*
    4 -> 145,93,17
    336 -> 90*
    292 -> 42*
    75 -> 203*
    22 -> 89,43
    150 -> 18*
    21 -> 59*
    58 -> 18*
    91 -> 233*
    296 -> 60*
    44 -> 18*
    60 -> 167*
    316 -> 62*
    165 -> 181*
    62 -> 24*
    20 -> 23,94,4
    130 -> 60*
    59 -> 293*
    134 -> 20*
    146 -> 132*
    57 -> 253*
    39 -> 199*
    41 -> 289*
    18 -> 39*
    167 -> 337*
    129 -> 309*
    181 -> 359*
    274 -> 20*
    202 -> 40*
    89 -> 333*
    61 -> 313,165
    23 -> 75,57
    78 -> 166,23,22
  problem:
   strict:
    a(b(a(x1))) -> c(c(c(x1)))
   weak:
    a(x1) -> b(c(b(x1)))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0,
    
    [a](x0) = 15x0,
    
    [c](x0) = 10x0
   orientation:
    a(b(a(x1))) = 30x1 >= 30x1 = c(c(c(x1)))
    
    a(x1) = 15x1 >= 10x1 = b(c(b(x1)))
   problem:
    strict:
     a(b(a(x1))) -> c(c(c(x1)))
    weak:
     
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = 15x0,
     
     [a](x0) = 8x0,
     
     [c](x0) = x0
    orientation:
     a(b(a(x1))) = 31x1 >= x1 = c(c(c(x1)))
    problem:
     strict:
      
     weak:
      
    Qed