YES

Problem:
 2nd(cons1(X,cons(Y,Z))) -> Y
 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,X1)) -> activate#(X1)
   2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   2nd(cons1(X,cons(Y,Z))) -> Y
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   from(X) -> cons(X,n__from(n__s(X)))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    2nd#(cons(X,X1)) -> activate#(X1)
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
   TRS:
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
    from(X) -> cons(X,n__from(n__s(X)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [s#](x0) = 0,
     
     [from#](x0) = 0,
     
     [activate#](x0) = 2x0,
     
     [2nd#](x0) = 3x0 + 0,
     
     [s](x0) = 4x0 + 8,
     
     [n__from](x0) = 1x0 + 0,
     
     [n__s](x0) = 1x0 + 0,
     
     [from](x0) = 2,
     
     [activate](x0) = x0 + 0,
     
     [cons1](x0, x1) = 1x0 + 0,
     
     [cons](x0, x1) = 3x0 + 1x1 + 3
    orientation:
     2nd#(cons(X,X1)) = 6X + 4X1 + 6 >= 2X1 = activate#(X1)
     
     2nd#(cons(X,X1)) = 6X + 4X1 + 6 >= 4X + 3 = 2nd#(cons1(X,activate(X1)))
     
     activate#(n__from(X)) = 3X + 2 >= 2X = activate#(X)
     
     activate#(n__from(X)) = 3X + 2 >= 0 = from#(activate(X))
     
     activate#(n__s(X)) = 3X + 2 >= 2X = activate#(X)
     
     activate#(n__s(X)) = 3X + 2 >= 0 = s#(activate(X))
     
     activate(n__from(X)) = 1X + 0 >= 2 = from(activate(X))
     
     activate(n__s(X)) = 1X + 0 >= 4X + 8 = s(activate(X))
     
     activate(X) = X + 0 >= X = X
     
     from(X) = 2 >= 3X + 3 = cons(X,n__from(n__s(X)))
     
     from(X) = 2 >= 1X + 0 = n__from(X)
     
     s(X) = 4X + 8 >= 1X + 0 = n__s(X)
    problem:
     DPs:
      
     TRS:
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(X) -> X
      from(X) -> cons(X,n__from(n__s(X)))
      from(X) -> n__from(X)
      s(X) -> n__s(X)
    Qed