YES

Problem:
 a(l(x1)) -> l(a(x1))
 a(c(x1)) -> c(a(x1))
 c(a(r(x1))) -> r(a(x1))
 l(r(a(x1))) -> a(l(c(c(r(x1)))))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5,4,1}
   transitions:
    l0(3) -> 1*
    l0(9) -> 10*
    l2(49) -> 50*
    c2(62) -> 63*
    c2(59) -> 60*
    c0(7) -> 8*
    c0(3) -> 4*
    c0(8) -> 9*
    a0(2) -> 3*
    a0(10) -> 6*
    r1(51) -> 52*
    r1(33) -> 34*
    r1(35) -> 36*
    c1(37) -> 38*
    c1(24) -> 25*
    c1(36) -> 37*
    c1(21) -> 22*
    f40() -> 2*
    r0(2) -> 7*
    r0(3) -> 5*
    a1(23) -> 24*
    a1(11) -> 12*
    a1(32) -> 33*
    a1(20) -> 21*
    l1(38) -> 39*
    l1(12) -> 13*
    r2(71) -> 72*
    a2(48) -> 49*
    a2(70) -> 71*
    a2(58) -> 59*
    a2(61) -> 62*
    a2(73) -> 74*
    74 -> 71*
    35 -> 73*
    7 -> 23*
    63 -> 59*
    4 -> 33,3
    2 -> 35,32
    22 -> 12*
    52 -> 36*
    72 -> 63,59
    36 -> 61*
    38 -> 48*
    60 -> 49*
    13 -> 6*
    8 -> 20*
    1 -> 74,33,3
    34 -> 25,21
    37 -> 58*
    5 -> 4*
    9 -> 11*
    50 -> 71,1
    39 -> 32*
    51 -> 70*
    32 -> 51*
    25 -> 21*
    33 -> 1,3
  problem:
   
  Qed