YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {9,5,1}
   transitions:
    b0(11) -> 12*
    b0(2) -> 3*
    b0(6) -> 7*
    b0(8) -> 5*
    b2(130) -> 131*
    b2(103) -> 104*
    b2(119) -> 120*
    b2(83) -> 84*
    b2(92) -> 93*
    b2(128) -> 129*
    b2(94) -> 95*
    b2(123) -> 124*
    b2(143) -> 144*
    f30() -> 2*
    c1(72) -> 73*
    c1(34) -> 35*
    c1(57) -> 58*
    c1(32) -> 33*
    c1(70) -> 71*
    c1(53) -> 54*
    c1(26) -> 27*
    c1(55) -> 56*
    c1(28) -> 29*
    c2(104) -> 105*
    c2(127) -> 128*
    c2(142) -> 143*
    c2(139) -> 140*
    c2(93) -> 94*
    c2(91) -> 92*
    c2(144) -> 145*
    c2(129) -> 130*
    c2(102) -> 103*
    a1(69) -> 70*
    a1(14) -> 15*
    a1(15) -> 16*
    a1(113) -> 114*
    a1(46) -> 47*
    a1(67) -> 68*
    a1(31) -> 32*
    b1(71) -> 72*
    b1(13) -> 14*
    b1(27) -> 28*
    b1(87) -> 88*
    b1(29) -> 30*
    b1(56) -> 57*
    b1(43) -> 44*
    b1(45) -> 46*
    b1(58) -> 59*
    b1(33) -> 34*
    a0(3) -> 4*
    a0(4) -> 1*
    a0(2) -> 10*
    a2(141) -> 142*
    a2(153) -> 154*
    a2(101) -> 102*
    a2(85) -> 86*
    a2(84) -> 85*
    a2(120) -> 121*
    a2(121) -> 122*
    c0(12) -> 9*
    c0(2) -> 6*
    c0(10) -> 11*
    c0(7) -> 8*
    131 -> 142,114
    68 -> 32*
    154 -> 142*
    47 -> 31*
    35 -> 1,4,10
    30 -> 53,1,4,10
    7 -> 31,26,13
    140 -> 128*
    114 -> 32*
    16 -> 1,4,10
    28 -> 153,139,123,67,43
    2 -> 69,55,45
    53 -> 141,127,119,113,87
    124 -> 120*
    105 -> 154,142,68,32
    54 -> 29*
    88 -> 14*
    86 -> 154,142,68,32
    26 -> 101,91,83
    73 -> 32*
    44 -> 14*
    1 -> 70,47,31,10,4
    59 -> 32*
    95 -> 154,142,68,32
    5 -> 70,47,31,10,4
    9 -> 70,47,31,10,4
    122 -> 142,114
    145 -> 142,114
    32 -> 102*
  problem:
   
  Qed