YES
Input TRS:
AC symbols: app
C symbols: max'
      1: 1() -> s(0())
      2: 2() -> s(1())
      3: 3() -> s(2())
      4: 4() -> s(3())
      5: 5() -> s(4())
      6: 6() -> s(5())
      7: 7() -> s(6())
      8: 8() -> s(7())
      9: 9() -> s(8())
      10: max'(0(),x) -> x
      11: max'(s(x),s(y)) -> s(max'(x,y))
      12: app(empty(),X) -> X
      13: max(singl(x)) -> x
      14: max(app(singl(x),Y)) -> max2(x,Y)
      15: max2(x,empty()) -> x
      16: max2(x,singl(y)) -> max'(x,y)
      17: max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
Number of strict rules: 17
Direct POLO(bPol) ... removes: 4 15 8 1 3 16 17 5 10 7 14 12 11 9 13 6 2
      7 	w: 2644676
      1 	w: 21104
      4 	w: 312612
      s 	w: 2 * x1 + 20539
      max2	w: x1 + 2 * x2
      max'	w: x1 + x2 + 1
      5 	w: 645764
      3 	w: 146036
      9 	w: 10640324
      8 	w: 5309892
      0 	w: 282
      max	w: 2 * x1
      singl	w: x1 + 1143
      2 	w: 62748
      empty	w: 1
      6 	w: 1312068
      app	w: x1 + x2
Number of strict rules: 0