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
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [cons#](x0, x1) = 2,
    
    [from#](x0) = 4,
    
    [activate#](x0) = x0 + 5,
    
    [2nd#](x0) = x0 + 8,
    
    [n__from](x0) = 2x0,
    
    [s](x0) = x0 + 2,
    
    [from](x0) = 4x0 + 6,
    
    [activate](x0) = 3x0 + 8,
    
    [2nd](x0) = 1x0 + 13,
    
    [cons](x0, x1) = 3x0 + 1x1 + 5,
    
    [n__cons](x0, x1) = 2x0 + x1 + 4
   orientation:
    2nd#(cons(X,n__cons(Y,Z))) = 3X + 3Y + 1Z + 8 >= Y + 5 = activate#(Y)
    
    from#(X) = 4 >= 2 = cons#(X,n__from(s(X)))
    
    activate#(n__cons(X1,X2)) = 2X1 + X2 + 5 >= 2 = cons#(X1,X2)
    
    activate#(n__from(X)) = 2X + 5 >= 4 = from#(X)
    
    2nd(cons(X,n__cons(Y,Z))) = 4X + 4Y + 2Z + 13 >= 3Y + 8 = activate(Y)
    
    from(X) = 4X + 6 >= 3X + 5 = cons(X,n__from(s(X)))
    
    cons(X1,X2) = 3X1 + 1X2 + 5 >= 2X1 + X2 + 4 = n__cons(X1,X2)
    
    from(X) = 4X + 6 >= 2X = n__from(X)
    
    activate(n__cons(X1,X2)) = 5X1 + 3X2 + 8 >= 3X1 + 1X2 + 5 = cons(X1,X2)
    
    activate(n__from(X)) = 5X + 8 >= 4X + 6 = from(X)
    
    activate(X) = 3X + 8 >= X = X
   problem:
    DPs:
     
    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
   Qed