YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    b0(3) -> 4*
    b0(8) -> 9*
    f30() -> 2*
    a1(13) -> 14*
    a1(44) -> 45*
    a1(14) -> 15*
    a1(43) -> 44*
    a1(19) -> 20*
    a1(48) -> 49*
    a1(49) -> 50*
    a1(18) -> 19*
    c1(15) -> 16*
    c1(45) -> 46*
    c1(41) -> 42*
    c1(11) -> 12*
    c1(46) -> 47*
    c1(16) -> 17*
    b1(17) -> 18*
    b1(12) -> 13*
    b1(47) -> 48*
    b1(42) -> 43*
    a0(4) -> 5*
    a0(10) -> 1*
    a0(9) -> 10*
    a0(5) -> 6*
    c0(6) -> 7*
    c0(2) -> 3*
    c0(7) -> 8*
    1 -> 3,7
    20 -> 8*
    9 -> 41*
    50 -> 16*
    10 -> 11*
  problem:
   
  Qed