YES
Input TRS:
      1: q0(0(x1)) -> 0'(q1(x1))
      2: q1(0(x1)) -> 0(q1(x1))
      3: q1(1'(x1)) -> 1'(q1(x1))
      4: 0(q1(1(x1))) -> q2(0(1'(x1)))
      5: 0'(q1(1(x1))) -> q2(0'(1'(x1)))
      6: 1'(q1(1(x1))) -> q2(1'(1'(x1)))
      7: 0(q2(0(x1))) -> q2(0(0(x1)))
      8: 0'(q2(0(x1))) -> q2(0'(0(x1)))
      9: 1'(q2(0(x1))) -> q2(1'(0(x1)))
      10: 0(q2(1'(x1))) -> q2(0(1'(x1)))
      11: 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
      12: 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
      13: q2(0'(x1)) -> 0'(q0(x1))
      14: q0(1'(x1)) -> 1'(q3(x1))
      15: q3(1'(x1)) -> 1'(q3(x1))
      16: q3(b(x1)) -> b(q4(x1))
Number of strict rules: 16
Direct POLO(bPol) ... removes: 4 1 16 5 14 13 6
      1 	w: x1 + 63911
      1'	w: x1 + 1
      b 	w: x1 + 1
      q3	w: x1 + 2
      q4	w: x1 + 1
      0 	w: x1 + 1
      0'	w: x1 + 1
      q1	w: x1 + 7
      q2	w: x1 + 43332
      q0	w: x1 + 31119
Number of strict rules: 9
Direct POLO(bPol) ... removes: 3 10 7 12 9
      1 	w: x1 + 1
      1'	w: 2 * x1 + 15262
      b 	w: x1
      q3	w: x1
      q4	w: x1
      0 	w: 2 * x1 + 15261
      0'	w: x1 + 1
      q1	w: 2 * x1 + 15261
      q2	w: x1 + 1
      q0	w: x1 + 1
Number of strict rules: 4
Direct POLO(bPol) ... removes: 2
      1 	w: x1 + 2748
      1'	w: 2 * x1 + 1
      b 	w: x1
      q3	w: x1
      q4	w: x1
      0 	w: 2 * x1 + 2
      0'	w: x1 + 1
      q1	w: 2 * x1 + 1
      q2	w: x1 + 1
      q0	w: x1 + 1
Number of strict rules: 3
Direct POLO(bPol) ... removes: 8 11
      1 	w: 2 * x1 + 20535
      1'	w: 2 * x1 + 20534
      b 	w: 2 * x1
      q3	w: x1
      q4	w: x1
      0 	w: 2 * x1 + 3024
      0'	w: 2 * x1 + 1261
      q1	w: x1
      q2	w: x1 + 2
      q0	w: x1 + 1
Number of strict rules: 1
Direct POLO(bPol) ... removes: 15
      1 	w: 2 * x1 + 21097
      1'	w: 2 * x1 + 2
      b 	w: 2 * x1 + 1
      q3	w: 2 * x1 + 1
      q4	w: x1
      0 	w: 2 * x1 + 1
      0'	w: x1
      q1	w: 2 * x1 + 1
      q2	w: 2 * x1 + 2
      q0	w: 2 * x1 + 2
Number of strict rules: 0