NO

Prover = TRS(tech=GUIDED_UNF, nb_unfoldings=unlimited, unfold_variables=true, strategy=LEFTMOST_NE)

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 3] quote1(n__cons(_0,n__from(_1))) -> quote1(n__cons(activate(_1),n__from(n__s(activate(_1)))))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->activate(_1), _1->n__s(activate(_1))}.
We have r|p = quote1(n__cons(activate(_1),n__from(n__s(activate(_1))))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = quote1(n__cons(_0,n__from(_1))) loops w.r.t. the analyzed TRS.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Searching for a loop by unfolding (unfolding of variable subterms: ON)...
# Iteration 0: no loop detected, 8 unfolded rules generated.
# Iteration 1: no loop detected, 33 unfolded rules generated.
# Iteration 2: no loop detected, 418 unfolded rules generated.
# Iteration 3: loop detected, 558 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = quote1^#(n__cons(_0,_1)) -> quote1^#(activate(_1)) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 forwards at position p0
with the rule activate(n__from(_0)) -> from(activate(_0)).
==> L1 = quote1^#(n__cons(_0,n__from(_1))) -> quote1^#(from(activate(_1))) is in U_IR^1.
Let p1 = [0].
We unfold the rule of L1 forwards at position p1
with the rule from(_0) -> cons(_0,n__from(n__s(_0))).
==> L2 = quote1^#(n__cons(_0,n__from(_1))) -> quote1^#(cons(activate(_1),n__from(n__s(activate(_1))))) is in U_IR^2.
Let p2 = [0].
We unfold the rule of L2 forwards at position p2
with the rule cons(_0,_1) -> n__cons(_0,_1).
==> L3 = quote1^#(n__cons(_0,n__from(_1))) -> quote1^#(n__cons(activate(_1),n__from(n__s(activate(_1))))) is in U_IR^3.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 1017
Number of unfolded rules generated by all the parallel proofs = 1930