YES

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {9,6,1}
   transitions:
    b0(7) -> 8*
    b0(4) -> 5*
    b0(3) -> 4*
    b0(2) -> 3*
    b0(8) -> 6*
    b3(128) -> 129*
    b3(119) -> 120*
    b3(127) -> 128*
    b3(120) -> 121*
    a1(41) -> 42*
    a1(42) -> 43*
    a1(15) -> 16*
    a1(43) -> 44*
    a1(30) -> 31*
    c0(2) -> 7*
    a2(67) -> 68*
    a2(53) -> 54*
    c2(102) -> 103*
    c2(90) -> 91*
    c2(78) -> 79*
    c2(100) -> 101*
    c2(106) -> 107*
    a0(3) -> 10*
    a0(11) -> 9*
    a0(10) -> 11*
    a0(5) -> 1*
    f30() -> 2*
    b1(62) -> 63*
    b1(13) -> 14*
    b1(27) -> 28*
    b1(12) -> 13*
    b1(40) -> 41*
    b1(28) -> 29*
    b1(29) -> 30*
    b1(88) -> 89*
    b1(32) -> 33*
    b1(14) -> 15*
    b2(65) -> 66*
    b2(52) -> 53*
    b2(66) -> 67*
    b2(79) -> 80*
    b2(64) -> 65*
    b2(92) -> 93*
    b2(91) -> 92*
    b2(80) -> 81*
    b2(112) -> 113*
    b2(50) -> 51*
    b2(110) -> 111*
    b2(51) -> 52*
    b2(82) -> 83*
    c1(38) -> 39*
    c3(118) -> 119*
    c3(126) -> 127*
    43 -> 112,78,62
    68 -> 43*
    83 -> 51*
    42 -> 100,50
    113 -> 65*
    63 -> 13*
    93 -> 113,65,63
    16 -> 11*
    2 -> 40*
    53 -> 118,110,102,88
    67 -> 126,90,82
    54 -> 44*
    6 -> 41,106,3,38
    121 -> 51*
    44 -> 42,50,100,10,27
    101 -> 91*
    31 -> 9*
    107 -> 66*
    3 -> 38,12
    39 -> 14*
    41 -> 106,64
    129 -> 113,65
    15 -> 32*
    10 -> 27*
    103 -> 79*
    81 -> 51,28
    89 -> 13*
    111 -> 65*
    33 -> 28*
  problem:
   
  Qed