YES

Problem:
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(2nd(X)) -> 2nd(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(from(X)) -> from(active(X))
 active(s(X)) -> s(active(X))
 active(cons1(X1,X2)) -> cons1(active(X1),X2)
 active(cons1(X1,X2)) -> cons1(X1,active(X2))
 2nd(mark(X)) -> mark(2nd(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 from(mark(X)) -> mark(from(X))
 s(mark(X)) -> mark(s(X))
 cons1(mark(X1),X2) -> mark(cons1(X1,X2))
 cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
 proper(2nd(X)) -> 2nd(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(s(X)) -> s(proper(X))
 proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
 2nd(ok(X)) -> ok(2nd(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 from(ok(X)) -> ok(from(X))
 s(ok(X)) -> ok(s(X))
 cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(2nd(cons(X,X1))) -> cons1#(X,X1)
   active#(2nd(cons(X,X1))) -> 2nd#(cons1(X,X1))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(2nd(X)) -> active#(X)
   active#(2nd(X)) -> 2nd#(active(X))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(from(X)) -> active#(X)
   active#(from(X)) -> from#(active(X))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(cons1(X1,X2)) -> active#(X1)
   active#(cons1(X1,X2)) -> cons1#(active(X1),X2)
   active#(cons1(X1,X2)) -> active#(X2)
   active#(cons1(X1,X2)) -> cons1#(X1,active(X2))
   2nd#(mark(X)) -> 2nd#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   from#(mark(X)) -> from#(X)
   s#(mark(X)) -> s#(X)
   cons1#(mark(X1),X2) -> cons1#(X1,X2)
   cons1#(X1,mark(X2)) -> cons1#(X1,X2)
   proper#(2nd(X)) -> proper#(X)
   proper#(2nd(X)) -> 2nd#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(cons1(X1,X2)) -> proper#(X2)
   proper#(cons1(X1,X2)) -> proper#(X1)
   proper#(cons1(X1,X2)) -> cons1#(proper(X1),proper(X2))
   2nd#(ok(X)) -> 2nd#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   from#(ok(X)) -> from#(X)
   s#(ok(X)) -> s#(X)
   cons1#(ok(X1),ok(X2)) -> cons1#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
   active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(2nd(X)) -> 2nd(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(from(X)) -> from(active(X))
   active(s(X)) -> s(active(X))
   active(cons1(X1,X2)) -> cons1(active(X1),X2)
   active(cons1(X1,X2)) -> cons1(X1,active(X2))
   2nd(mark(X)) -> mark(2nd(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   cons1(mark(X1),X2) -> mark(cons1(X1,X2))
   cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
   2nd(ok(X)) -> ok(2nd(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   from(ok(X)) -> ok(from(X))
   s(ok(X)) -> ok(s(X))
   cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top#](x0) = 2x0 + 2,
    
    [proper#](x0) = 1/2x0 + 5/2,
    
    [cons#](x0, x1) = x0,
    
    [from#](x0) = x0 + 2,
    
    [s#](x0) = x0 + 5/2,
    
    [2nd#](x0) = x0,
    
    [cons1#](x0, x1) = x0 + x1,
    
    [active#](x0) = 3/2x0 + 3,
    
    [top](x0) = 0,
    
    [ok](x0) = 3x0 + 3,
    
    [proper](x0) = x0,
    
    [s](x0) = 2x0 + 1,
    
    [from](x0) = 3x0 + 3,
    
    [mark](x0) = x0 + 1/2,
    
    [active](x0) = 3x0 + 3/2,
    
    [2nd](x0) = 2x0 + 1,
    
    [cons1](x0, x1) = 2x0 + 2x1 + 2,
    
    [cons](x0, x1) = 2x0 + x1 + 1
   orientation:
    active#(2nd(cons(X,X1))) = 6X + 3X1 + 15/2 >= X + X1 = cons1#(X,X1)
    
    active#(2nd(cons(X,X1))) = 6X + 3X1 + 15/2 >= 2X + 2X1 + 2 = 2nd#(cons1(X,X1))
    
    active#(from(X)) = 9/2X + 15/2 >= X + 5/2 = s#(X)
    
    active#(from(X)) = 9/2X + 15/2 >= 2X + 3 = from#(s(X))
    
    active#(from(X)) = 9/2X + 15/2 >= X = cons#(X,from(s(X)))
    
    active#(2nd(X)) = 3X + 9/2 >= 3/2X + 3 = active#(X)
    
    active#(2nd(X)) = 3X + 9/2 >= 3X + 3/2 = 2nd#(active(X))
    
    active#(cons(X1,X2)) = 3X1 + 3/2X2 + 9/2 >= 3/2X1 + 3 = active#(X1)
    
    active#(cons(X1,X2)) = 3X1 + 3/2X2 + 9/2 >= 3X1 + 3/2 = cons#(active(X1),X2)
    
    active#(from(X)) = 9/2X + 15/2 >= 3/2X + 3 = active#(X)
    
    active#(from(X)) = 9/2X + 15/2 >= 3X + 7/2 = from#(active(X))
    
    active#(s(X)) = 3X + 9/2 >= 3/2X + 3 = active#(X)
    
    active#(s(X)) = 3X + 9/2 >= 3X + 4 = s#(active(X))
    
    active#(cons1(X1,X2)) = 3X1 + 3X2 + 6 >= 3/2X1 + 3 = active#(X1)
    
    active#(cons1(X1,X2)) = 3X1 + 3X2 + 6 >= 3X1 + X2 + 3/2 = cons1#(active(X1),X2)
    
    active#(cons1(X1,X2)) = 3X1 + 3X2 + 6 >= 3/2X2 + 3 = active#(X2)
    
    active#(cons1(X1,X2)) = 3X1 + 3X2 + 6 >= X1 + 3X2 + 3/2 = cons1#(X1,active(X2))
    
    2nd#(mark(X)) = X + 1/2 >= X = 2nd#(X)
    
    cons#(mark(X1),X2) = X1 + 1/2 >= X1 = cons#(X1,X2)
    
    from#(mark(X)) = X + 5/2 >= X + 2 = from#(X)
    
    s#(mark(X)) = X + 3 >= X + 5/2 = s#(X)
    
    cons1#(mark(X1),X2) = X1 + X2 + 1/2 >= X1 + X2 = cons1#(X1,X2)
    
    cons1#(X1,mark(X2)) = X1 + X2 + 1/2 >= X1 + X2 = cons1#(X1,X2)
    
    proper#(2nd(X)) = X + 3 >= 1/2X + 5/2 = proper#(X)
    
    proper#(2nd(X)) = X + 3 >= X = 2nd#(proper(X))
    
    proper#(cons(X1,X2)) = X1 + 1/2X2 + 3 >= 1/2X2 + 5/2 = proper#(X2)
    
    proper#(cons(X1,X2)) = X1 + 1/2X2 + 3 >= 1/2X1 + 5/2 = proper#(X1)
    
    proper#(cons(X1,X2)) = X1 + 1/2X2 + 3 >= X1 = cons#(proper(X1),proper(X2))
    
    proper#(from(X)) = 3/2X + 4 >= 1/2X + 5/2 = proper#(X)
    
    proper#(from(X)) = 3/2X + 4 >= X + 2 = from#(proper(X))
    
    proper#(s(X)) = X + 3 >= 1/2X + 5/2 = proper#(X)
    
    proper#(s(X)) = X + 3 >= X + 5/2 = s#(proper(X))
    
    proper#(cons1(X1,X2)) = X1 + X2 + 7/2 >= 1/2X2 + 5/2 = proper#(X2)
    
    proper#(cons1(X1,X2)) = X1 + X2 + 7/2 >= 1/2X1 + 5/2 = proper#(X1)
    
    proper#(cons1(X1,X2)) = X1 + X2 + 7/2 >= X1 + X2 = cons1#(proper(X1),proper(X2))
    
    2nd#(ok(X)) = 3X + 3 >= X = 2nd#(X)
    
    cons#(ok(X1),ok(X2)) = 3X1 + 3 >= X1 = cons#(X1,X2)
    
    from#(ok(X)) = 3X + 5 >= X + 2 = from#(X)
    
    s#(ok(X)) = 3X + 11/2 >= X + 5/2 = s#(X)
    
    cons1#(ok(X1),ok(X2)) = 3X1 + 3X2 + 6 >= X1 + X2 = cons1#(X1,X2)
    
    top#(mark(X)) = 2X + 3 >= 1/2X + 5/2 = proper#(X)
    
    top#(mark(X)) = 2X + 3 >= 2X + 2 = top#(proper(X))
    
    top#(ok(X)) = 6X + 8 >= 3/2X + 3 = active#(X)
    
    top#(ok(X)) = 6X + 8 >= 6X + 5 = top#(active(X))
    
    active(2nd(cons1(X,cons(Y,Z)))) = 12X + 24Y + 12Z + 57/2 >= Y + 1/2 = mark(Y)
    
    active(2nd(cons(X,X1))) = 12X + 6X1 + 21/2 >= 4X + 4X1 + 11/2 = mark(2nd(cons1(X,X1)))
    
    active(from(X)) = 9X + 21/2 >= 8X + 15/2 = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 6X + 9/2 >= 6X + 4 = 2nd(active(X))
    
    active(cons(X1,X2)) = 6X1 + 3X2 + 9/2 >= 6X1 + X2 + 4 = cons(active(X1),X2)
    
    active(from(X)) = 9X + 21/2 >= 9X + 15/2 = from(active(X))
    
    active(s(X)) = 6X + 9/2 >= 6X + 4 = s(active(X))
    
    active(cons1(X1,X2)) = 6X1 + 6X2 + 15/2 >= 6X1 + 2X2 + 5 = cons1(active(X1),X2)
    
    active(cons1(X1,X2)) = 6X1 + 6X2 + 15/2 >= 2X1 + 6X2 + 5 = cons1(X1,active(X2))
    
    2nd(mark(X)) = 2X + 2 >= 2X + 3/2 = mark(2nd(X))
    
    cons(mark(X1),X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 3/2 = mark(cons(X1,X2))
    
    from(mark(X)) = 3X + 9/2 >= 3X + 7/2 = mark(from(X))
    
    s(mark(X)) = 2X + 2 >= 2X + 3/2 = mark(s(X))
    
    cons1(mark(X1),X2) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 5/2 = mark(cons1(X1,X2))
    
    cons1(X1,mark(X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 5/2 = mark(cons1(X1,X2))
    
    proper(2nd(X)) = 2X + 1 >= 2X + 1 = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 3X + 3 >= 3X + 3 = from(proper(X))
    
    proper(s(X)) = 2X + 1 >= 2X + 1 = s(proper(X))
    
    proper(cons1(X1,X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = cons1(proper(X1),proper(X2))
    
    2nd(ok(X)) = 6X + 7 >= 6X + 6 = ok(2nd(X))
    
    cons(ok(X1),ok(X2)) = 6X1 + 3X2 + 10 >= 6X1 + 3X2 + 6 = ok(cons(X1,X2))
    
    from(ok(X)) = 9X + 12 >= 9X + 12 = ok(from(X))
    
    s(ok(X)) = 6X + 7 >= 6X + 6 = ok(s(X))
    
    cons1(ok(X1),ok(X2)) = 6X1 + 6X2 + 14 >= 6X1 + 6X2 + 9 = ok(cons1(X1,X2))
    
    top(mark(X)) = 0 >= 0 = top(proper(X))
    
    top(ok(X)) = 0 >= 0 = top(active(X))
   problem:
    DPs:
     
    TRS:
     active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
     active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(2nd(X)) -> 2nd(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons1(X1,X2)) -> cons1(active(X1),X2)
     active(cons1(X1,X2)) -> cons1(X1,active(X2))
     2nd(mark(X)) -> mark(2nd(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     2nd(ok(X)) -> ok(2nd(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
   Qed