YES

Problem:
 2nd(cons1(X,cons(Y,Z))) -> Y
 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(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)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   2nd(cons1(X,cons(Y,Z))) -> Y
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   from(X) -> cons(X,n__from(n__s(X)))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   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) = x0,
    
    [from#](x0) = 0,
    
    [activate#](x0) = x0,
    
    [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,
    
    [cons1](x0, x1) = x0 + 1/2x1,
    
    [cons](x0, x1) = x0 + 1/2x1 + 1
   orientation:
    2nd#(cons(X,X1)) = 2X + X1 + 2 >= X1 = activate#(X1)
    
    2nd#(cons(X,X1)) = 2X + X1 + 2 >= 2X + X1 = 2nd#(cons1(X,activate(X1)))
    
    activate#(n__from(X)) = 2X + 3 >= X = activate#(X)
    
    activate#(n__from(X)) = 2X + 3 >= 0 = from#(activate(X))
    
    activate#(n__s(X)) = X + 1/2 >= X = activate#(X)
    
    activate#(n__s(X)) = X + 1/2 >= X = s#(activate(X))
    
    2nd(cons1(X,cons(Y,Z))) = 2X + Y + 1/2Z + 1 >= Y = Y
    
    2nd(cons(X,X1)) = 2X + X1 + 2 >= 2X + X1 = 2nd(cons1(X,activate(X1)))
    
    from(X) = 2X + 3 >= 2X + 3 = cons(X,n__from(n__s(X)))
    
    from(X) = 2X + 3 >= 2X + 3 = n__from(X)
    
    s(X) = X + 1/2 >= X + 1/2 = n__s(X)
    
    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(cons1(X,cons(Y,Z))) -> Y
     2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
     from(X) -> cons(X,n__from(n__s(X)))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
   Qed