YES

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

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,n__cons(Y,Z))) -> activate#(Y)
   from#(X) -> cons#(X,n__from(n__s(X)))
   activate#(n__cons(X1,X2)) -> activate#(X1)
   activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
   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(cons(X,n__cons(Y,Z))) -> activate(Y)
   from(X) -> cons(X,n__from(n__s(X)))
   cons(X1,X2) -> n__cons(X1,X2)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s#](x0) = 0,
    
    [cons#](x0, x1) = 1/2,
    
    [from#](x0) = 1,
    
    [activate#](x0) = x0 + 1,
    
    [2nd#](x0) = 2x0,
    
    [s](x0) = x0 + 1/2,
    
    [n__from](x0) = 2x0 + 3,
    
    [n__s](x0) = x0 + 1/2,
    
    [from](x0) = 2x0 + 3,
    
    [activate](x0) = x0,
    
    [2nd](x0) = 2x0 + 1,
    
    [cons](x0, x1) = x0 + 1/2x1 + 1,
    
    [n__cons](x0, x1) = x0 + 1/2x1 + 1
   orientation:
    2nd#(cons(X,n__cons(Y,Z))) = 2X + Y + 1/2Z + 3 >= Y + 1 = activate#(Y)
    
    from#(X) = 1 >= 1/2 = cons#(X,n__from(n__s(X)))
    
    activate#(n__cons(X1,X2)) = X1 + 1/2X2 + 2 >= X1 + 1 = activate#(X1)
    
    activate#(n__cons(X1,X2)) = X1 + 1/2X2 + 2 >= 1/2 = cons#(activate(X1),X2)
    
    activate#(n__from(X)) = 2X + 4 >= X + 1 = activate#(X)
    
    activate#(n__from(X)) = 2X + 4 >= 1 = from#(activate(X))
    
    activate#(n__s(X)) = X + 3/2 >= X + 1 = activate#(X)
    
    activate#(n__s(X)) = X + 3/2 >= 0 = s#(activate(X))
    
    2nd(cons(X,n__cons(Y,Z))) = 2X + Y + 1/2Z + 4 >= Y = activate(Y)
    
    from(X) = 2X + 3 >= 2X + 3 = cons(X,n__from(n__s(X)))
    
    cons(X1,X2) = X1 + 1/2X2 + 1 >= X1 + 1/2X2 + 1 = n__cons(X1,X2)
    
    from(X) = 2X + 3 >= 2X + 3 = n__from(X)
    
    s(X) = X + 1/2 >= X + 1/2 = n__s(X)
    
    activate(n__cons(X1,X2)) = X1 + 1/2X2 + 1 >= X1 + 1/2X2 + 1 = cons(activate(X1),X2)
    
    activate(n__from(X)) = 2X + 3 >= 2X + 3 = from(activate(X))
    
    activate(n__s(X)) = X + 1/2 >= X + 1/2 = s(activate(X))
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
     from(X) -> cons(X,n__from(n__s(X)))
     cons(X1,X2) -> n__cons(X1,X2)
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
   Qed