YES
(VAR X Y Z X1 X2)
(RULES 
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
)

Proving termination of rewriting for Ex1_2_Luc02c_Z:

-> Dependency pairs:
nF_2nd(cons(X,n__cons(Y,Z))) -> nF_activate(Y)
nF_from(X) -> nF_cons(X,n__from(s(X)))
nF_activate(n__cons(X1,X2)) -> nF_cons(X1,X2)
nF_activate(n__from(X)) -> nF_from(X)

-> Proof of termination for Ex1_2_Luc02c_Z_1:
Termination proved: No cycles in dependency graph.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in DG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.