YES(?,O(n^1))

Problem:
 q0(a(x1)) -> x(q1(x1))
 q1(a(x1)) -> a(q1(x1))
 q1(y(x1)) -> y(q1(x1))
 a(q1(b(x1))) -> q2(a(y(x1)))
 a(q2(a(x1))) -> q2(a(a(x1)))
 a(q2(y(x1))) -> q2(a(y(x1)))
 y(q1(b(x1))) -> q2(y(y(x1)))
 y(q2(a(x1))) -> q2(y(a(x1)))
 y(q2(y(x1))) -> q2(y(y(x1)))
 q2(x(x1)) -> x(q0(x1))
 q0(y(x1)) -> y(q3(x1))
 q3(y(x1)) -> y(q3(x1))
 q3(bl(x1)) -> bl(q4(x1))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {10,9,8,7,6,5}
   transitions:
    bl1(33) -> 34*
    q41(35) -> 36*
    q41(32) -> 33*
    q41(41) -> 42*
    q41(43) -> 44*
    x1(15) -> 16*
    q01(25) -> 26*
    q01(17) -> 18*
    q01(14) -> 15*
    q01(23) -> 24*
    q00(2) -> 5*
    q00(4) -> 5*
    q00(1) -> 5*
    q00(3) -> 5*
    a0(2) -> 7*
    a0(4) -> 7*
    a0(1) -> 7*
    a0(3) -> 7*
    x0(2) -> 1*
    x0(4) -> 1*
    x0(1) -> 1*
    x0(3) -> 1*
    q10(2) -> 6*
    q10(4) -> 6*
    q10(1) -> 6*
    q10(3) -> 6*
    y0(2) -> 8*
    y0(4) -> 8*
    y0(1) -> 8*
    y0(3) -> 8*
    b0(2) -> 2*
    b0(4) -> 2*
    b0(1) -> 2*
    b0(3) -> 2*
    q20(2) -> 9*
    q20(4) -> 9*
    q20(1) -> 9*
    q20(3) -> 9*
    q30(2) -> 10*
    q30(4) -> 10*
    q30(1) -> 10*
    q30(3) -> 10*
    bl0(2) -> 3*
    bl0(4) -> 3*
    bl0(1) -> 3*
    bl0(3) -> 3*
    q40(2) -> 4*
    q40(4) -> 4*
    q40(1) -> 4*
    q40(3) -> 4*
    1 -> 41,23
    2 -> 32,14
    3 -> 43,25
    4 -> 35,17
    16 -> 9*
    18 -> 15*
    24 -> 15*
    26 -> 15*
    34 -> 10*
    36 -> 33*
    42 -> 33*
    44 -> 33*
  problem:
   
  Qed