YES

Problem:
 2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
 from(X) -> cons(X,n__from(s(X)))
 cons(X1,X2) -> n__cons(X1,X2)
 from(X) -> n__from(X)
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,n__cons(Y,Z))) -> activate#(Y)
   from#(X) -> cons#(X,n__from(s(X)))
   activate#(n__cons(X1,X2)) -> cons#(X1,X2)
   activate#(n__from(X)) -> from#(X)
  TRS:
   2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
   from(X) -> cons(X,n__from(s(X)))
   cons(X1,X2) -> n__cons(X1,X2)
   from(X) -> n__from(X)
   activate(n__cons(X1,X2)) -> cons(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    2nd#(cons(X,n__cons(Y,Z))) -> activate#(Y)
    from#(X) -> cons#(X,n__from(s(X)))
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    activate#(n__from(X)) -> from#(X)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [cons#](x0, x1) = x0,
     
     [from#](x0) = 4x0 + 0,
     
     [activate#](x0) = x0,
     
     [2nd#](x0) = x0 + -16,
     
     [n__from](x0) = 5x0 + 1,
     
     [s](x0) = 2x0 + -7,
     
     [cons](x0, x1) = x0 + x1 + -16,
     
     [n__cons](x0, x1) = 1x0 + x1 + -2
    orientation:
     2nd#(cons(X,n__cons(Y,Z))) = X + 1Y + Z + -2 >= Y = activate#(Y)
     
     from#(X) = 4X + 0 >= X = cons#(X,n__from(s(X)))
     
     activate#(n__cons(X1,X2)) = 1X1 + X2 + -2 >= X1 = cons#(X1,X2)
     
     activate#(n__from(X)) = 5X + 1 >= 4X + 0 = from#(X)
    problem:
     DPs:
      
     TRS:
      
    Qed