YES
Input TRS:
      1: active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
      2: active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
      3: active(from(X)) -> mark(cons(X,from(s(X))))
      4: active(2nd(X)) -> 2nd(active(X))
      5: active(cons(X1,X2)) -> cons(active(X1),X2)
      6: active(from(X)) -> from(active(X))
      7: active(s(X)) -> s(active(X))
      8: active(cons1(X1,X2)) -> cons1(active(X1),X2)
      9: active(cons1(X1,X2)) -> cons1(X1,active(X2))
      10: 2nd(mark(X)) -> mark(2nd(X))
      11: cons(mark(X1),X2) -> mark(cons(X1,X2))
      12: from(mark(X)) -> mark(from(X))
      13: s(mark(X)) -> mark(s(X))
      14: cons1(mark(X1),X2) -> mark(cons1(X1,X2))
      15: cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
      16: proper(2nd(X)) -> 2nd(proper(X))
      17: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      18: proper(from(X)) -> from(proper(X))
      19: proper(s(X)) -> s(proper(X))
      20: proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
      21: 2nd(ok(X)) -> ok(2nd(X))
      22: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      23: from(ok(X)) -> ok(from(X))
      24: s(ok(X)) -> ok(s(X))
      25: cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
      26: top(mark(X)) -> top(proper(X))
      27: top(ok(X)) -> top(active(X))
Number of strict rules: 27
Direct POLO(bPol) ... removes: 4 15 8 1 3 21 26 27 22 5 10 25 14 9 2
      s 	w: x1
      top	w: x1
      2nd	w: 2 * x1 + 24327
      cons1	w: 2 * x1 + 2 * x2 + 24327
      proper	w: x1
      ok	w: 2 * x1 + 24328
      from	w: x1
      mark	w: x1 + 1
      active	w: 2 * x1 + 24326
      cons	w: x1 + x2 + 24324
Number of strict rules: 12
Direct POLO(bPol) ... removes: 12 23 11 6
      s 	w: x1
      top	w: x1 + 6167
      2nd	w: 2 * x1 + 3
      cons1	w: 2 * x1 + 2 * x2 + 3
      proper	w: x1
      ok	w: 2 * x1 + 5
      from	w: 2 * x1 + 4
      mark	w: x1 + 1
      active	w: 2 * x1 + 3
      cons	w: 2 * x1 + x2 + 3
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #s(mark(X)) -> #s(X)
     #2: #s(ok(X)) -> #s(X)
     #3: #proper(cons1(X1,X2)) -> #proper(X1)
     #4: #proper(cons1(X1,X2)) -> #proper(X2)
     #5: #active(s(X)) -> #s(active(X))
     #6: #active(s(X)) -> #active(X)
     #7: #proper(cons(X1,X2)) -> #proper(X1)
     #8: #proper(cons(X1,X2)) -> #proper(X2)
     #9: #proper(s(X)) -> #s(proper(X))
     #10: #proper(s(X)) -> #proper(X)
     #11: #proper(2nd(X)) -> #proper(X)
     #12: #proper(from(X)) -> #proper(X)
Number of SCCs: 3, DPs: 10
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      2nd	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: 0
      from	w: 0
      #s 	w: 0
      mark	w: 0
      #proper	w: 0
      active	w: 0
      cons	w: 0
      #active	w: x1
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 9
  SCC { #1 #2 }
POLO(Sum)... succeeded.
      s 	w: 1
      top	w: 0
      2nd	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      from	w: 0
      #s 	w: x1
      mark	w: x1 + 1
      #proper	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #2
Number of SCCs: 1, DPs: 7
  SCC { #3 #4 #7 #8 #10..12 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      2nd	w: x1 + 1
      cons1	w: x1 + x2 + 1
      proper	w: 0
      ok	w: 1
      from	w: x1 + 1
      #s 	w: 0
      mark	w: 1
      #proper	w: x1
      active	w: 0
      cons	w: x1 + x2 + 1
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #3 #4 #7 #8 #10..12
Number of SCCs: 0, DPs: 0