YES
Input TRS:
      1: top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
      2: top(left(car(x,car(old(),y)),z)) -> top(right(car(old(),y),z))
      3: top(right(x,car(y,car(old(),z)))) -> top(left(x,car(old(),z)))
      4: top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
      5: top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
      6: top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
      7: top(left(car(x,y),z)) ->= top(left(y,z))
      8: top(right(x,car(y,z))) ->= top(right(x,z))
      9: bot() ->= car(new(),bot())
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 5 6
      new	w: 0
      left	w: x1 + 2 * x2 + 2805
      top	w: x1 + 30319
      bot	w: 0
      old	w: 1
      right	w: 2 * x1 + x2 + 2805
      car	w: x1 + 2 * x2
Number of strict rules: 2
Direct POLO(bPol) ... removes: 2
      new	w: 0
      left	w: x1 + 2 * x2 + 2232
      top	w: x1 + 43041
      bot	w: 0
      old	w: 1
      right	w: x1 + x2 + 2232
      car	w: x1 + 2 * x2
Number of strict rules: 1
Direct POLO(bPol) ... removes: 3
      new	w: 0
      left	w: x1 + 2 * x2 + 17829
      top	w: x1 + 9965
      bot	w: 0
      old	w: 19711
      right	w: x1 + x2 + 17830
      car	w: x1 + 2 * x2
Number of strict rules: 0