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 = 2] f(0) -> f(0)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = f(0) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(0) 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, 3 unfolded rules generated.
# Iteration 2: loop detected, 1 unfolded rule generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = f^#(s(0)) -> f^#(p(s(0))) is in U_IR^0.
Let p0 = epsilon.
We unfold the rule of L0 backwards at position p0
with the dependency pair f^#(0) -> f^#(s(0)).
==> L1 = f^#(0) -> f^#(p(s(0))) is in U_IR^1.
Let p1 = [0].
We unfold the rule of L1 forwards at position p1
with the rule p(s(0)) -> 0.
==> L2 = f^#(0) -> f^#(0) is in U_IR^2.

** END proof description **

Proof stopped at iteration 2
Number of unfolded rules generated by this proof = 7
Number of unfolded rules generated by all the parallel proofs = 7