YES

Problem:
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 from(X) -> cons(X,n__from(s(X)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   activate#(n__first(X1,X2)) -> first#(X1,X2)
   activate#(n__from(X)) -> from#(X)
  TRS:
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
   from(X) -> cons(X,n__from(s(X)))
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   activate(n__first(X1,X2)) -> first(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  KBO Processor:
   argument filtering:
    pi(0) = []
    pi(first) = [0,1]
    pi(nil) = []
    pi(s) = [0]
    pi(cons) = 1
    pi(activate) = [0]
    pi(n__first) = [0,1]
    pi(from) = []
    pi(n__from) = []
    pi(first#) = [1]
    pi(activate#) = 0
    pi(from#) = []
   weight function:
    w0 = 1
    w(from#) = w(n__from) = w(from) = w(activate) = w(s) = w(nil) = w(
    first) = w(0) = 1
    w(activate#) = w(first#) = w(n__first) = w(cons) = 0
   precedence:
    first# ~ s ~ nil ~ 0 > from > n__from > activate > from# ~ activate# ~ n__first ~ cons ~ first
   problem:
    DPs:
     
    TRS:
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
     from(X) -> cons(X,n__from(s(X)))
     first(X1,X2) -> n__first(X1,X2)
     from(X) -> n__from(X)
     activate(n__first(X1,X2)) -> first(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(X) -> X
   Qed