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] f(_0,i(_0)) -> f(i(_0),i(i(_0)))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->i(_0)}.
We have r|p = f(i(_0),i(i(_0))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(_0,i(_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, 1 unfolded rule generated.
# Iteration 1: no loop detected, 1 unfolded rule generated.
# Iteration 2: no loop detected, 4 unfolded rules generated.
# Iteration 3: loop detected, 1 unfolded rule generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = f^#(_0,_0) -> f^#(i(_0),g(g(_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,i(_0)) -> f^#(_0,_0).
==> L1 = f^#(_0,i(_0)) -> f^#(i(_0),g(g(_0))) is in U_IR^1.
Let p1 = [1].
We unfold the rule of L1 forwards at position p1
with the rule g(_0) -> i(_0).
==> L2 = f^#(_0,i(_0)) -> f^#(i(_0),i(g(_0))) is in U_IR^2.
Let p2 = [1, 0].
We unfold the rule of L2 forwards at position p2
with the rule g(_0) -> i(_0).
==> L3 = f^#(_0,i(_0)) -> f^#(i(_0),i(i(_0))) is in U_IR^3.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 7
Number of unfolded rules generated by all the parallel proofs = 7