YES
Input TRS:
      1: q0(a(x1)) -> x(q1(x1))
      2: q1(a(x1)) -> a(q1(x1))
      3: q1(y(x1)) -> y(q1(x1))
      4: a(q1(b(x1))) -> q2(a(y(x1)))
      5: a(q2(a(x1))) -> q2(a(a(x1)))
      6: a(q2(y(x1))) -> q2(a(y(x1)))
      7: y(q1(b(x1))) -> q2(y(y(x1)))
      8: y(q2(a(x1))) -> q2(y(a(x1)))
      9: y(q2(y(x1))) -> q2(y(y(x1)))
      10: q2(x(x1)) -> x(q0(x1))
      11: q0(y(x1)) -> y(q3(x1))
      12: q3(y(x1)) -> y(q3(x1))
      13: q3(bl(x1)) -> bl(q4(x1))
Number of strict rules: 13
Direct POLO(bPol) ... removes: 4 8 1 3 5 10 7 12 11 9 13 6 2
      a 	w: 2 * x1 + 2
      b 	w: 2 * x1 + 44046
      q3	w: 2 * x1 + 29363
      q4	w: 2 * x1 + 14681
      y 	w: 2 * x1 + 29364
      x 	w: 2 * x1 + 29362
      q1	w: 2 * x1 + 1
      q2	w: 2 * x1 + 29365
      bl	w: 2 * x1 + 1
      q0	w: 2 * x1 + 29363
Number of strict rules: 0