YES

Problem:
 2nd(cons1(X,cons(Y,Z))) -> Y
 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 activate(n__from(X)) -> from(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)) -> from#(X)
  TRS:
   2nd(cons1(X,cons(Y,Z))) -> Y
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   from(X) -> cons(X,n__from(s(X)))
   from(X) -> n__from(X)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    2nd#(cons(X,X1)) -> activate#(X1)
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    activate#(n__from(X)) -> from#(X)
   TRS:
    2nd(cons1(X,cons(Y,Z))) -> Y
    2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
    from(X) -> cons(X,n__from(s(X)))
    from(X) -> n__from(X)
    activate(n__from(X)) -> from(X)
    activate(X) -> X
   graph:
    2nd#(cons(X,X1)) -> activate#(X1) ->
    activate#(n__from(X)) -> from#(X)
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1))) ->
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1))) -> 2nd#(cons(X,X1)) -> activate#(X1)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    TRS:
     2nd(cons1(X,cons(Y,Z))) -> Y
     2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
     from(X) -> cons(X,n__from(s(X)))
     from(X) -> n__from(X)
     activate(n__from(X)) -> from(X)
     activate(X) -> X
    EDG Processor:
     DPs:
      2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
     TRS:
      2nd(cons1(X,cons(Y,Z))) -> Y
      2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
      from(X) -> cons(X,n__from(s(X)))
      from(X) -> n__from(X)
      activate(n__from(X)) -> from(X)
      activate(X) -> X
     graph:
      
     Qed