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 = 4] adx(cons(_0,n__zeros)) -> adx(cons(n__0,n__zeros))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->n__0}.
We have r|p = adx(cons(n__0,n__zeros)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = adx(cons(_0,n__zeros)) 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, 10 unfolded rules generated.
# Iteration 1: no loop detected, 20 unfolded rules generated.
# Iteration 2: no loop detected, 63 unfolded rules generated.
# Iteration 3: no loop detected, 327 unfolded rules generated.
# Iteration 4: loop detected, 2160 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = [adx^#(cons(_0,_1)) -> incr^#(cons(activate(_0),n__adx(activate(_1)))), incr^#(cons(_2,_3)) -> activate^#(_3), activate^#(n__adx(_4)) -> adx^#(_4)] is in U_IR^0.
We merge the first and the second rule of L0.
==> L1 = [adx^#(cons(_0,_1)) -> activate^#(n__adx(activate(_1))), activate^#(n__adx(_2)) -> adx^#(_2)] is in U_IR^1.
We merge the first and the second rule of L1.
==> L2 = adx^#(cons(_0,_1)) -> adx^#(activate(_1)) is in U_IR^2.
Let p2 = [0].
We unfold the rule of L2 forwards at position p2
with the rule activate(n__zeros) -> zeros.
==> L3 = adx^#(cons(_0,n__zeros)) -> adx^#(zeros) is in U_IR^3.
Let p3 = [0].
We unfold the rule of L3 forwards at position p3
with the rule zeros -> cons(n__0,n__zeros).
==> L4 = adx^#(cons(_0,n__zeros)) -> adx^#(cons(n__0,n__zeros)) is in U_IR^4.

** END proof description **

Proof stopped at iteration 4
Number of unfolded rules generated by this proof = 2580
Number of unfolded rules generated by all the parallel proofs = 4512