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] incr(cons(_0,n__incr(n__nats))) -> incr(cons(0,n__incr(n__nats)))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->0}.
We have r|p = incr(cons(0,n__incr(n__nats))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = incr(cons(_0,n__incr(n__nats))) 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, 3 unfolded rules generated.
# Iteration 1: no loop detected, 5 unfolded rules generated.
# Iteration 2: no loop detected, 24 unfolded rules generated.
# Iteration 3: loop detected, 13 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = [incr^#(cons(_0,_1)) -> activate^#(_1), activate^#(n__incr(_2)) -> incr^#(activate(_2))] is in U_IR^0.
We merge the first and the second rule of L0.
==> L1 = incr^#(cons(_0,n__incr(_1))) -> incr^#(activate(_1)) is in U_IR^1.
Let p1 = [0].
We unfold the rule of L1 forwards at position p1
with the rule activate(n__nats) -> nats.
==> L2 = incr^#(cons(_0,n__incr(n__nats))) -> incr^#(nats) is in U_IR^2.
Let p2 = [0].
We unfold the rule of L2 forwards at position p2
with the rule nats -> cons(0,n__incr(n__nats)).
==> L3 = incr^#(cons(_0,n__incr(n__nats))) -> incr^#(cons(0,n__incr(n__nats))) is in U_IR^3.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 45
Number of unfolded rules generated by all the parallel proofs = 45