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(0,1,g(0,_0)) -> f(0,_0,g(0,_0))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_0->1} and theta2 = {}.
We have r|p = f(0,_0,g(0,_0)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(0,1,g(0,1)) 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, 2 unfolded rules generated.
# Iteration 1: no loop detected, 6 unfolded rules 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^#(0,1,_0) -> h^#(_0,_0), h^#(0,_1) -> f^#(0,_1,_1)] is in U_IR^0.
Let p0 = [0].
We unfold the second rule of L0 backwards at position p0
with the rule g(_0,_1) -> _0.
==> L1 = [f^#(0,1,_0) -> h^#(_0,_0), h^#(g(0,_1),_2) -> f^#(0,_2,_2)] is in U_IR^1.
We merge the first and the second rule of L1.
==> L2 = f^#(0,1,g(0,_0)) -> f^#(0,g(0,_0),g(0,_0)) is in U_IR^2.
Let p2 = [1].
We unfold the rule of L2 forwards at position p2
with the rule g(_0,_1) -> _1.
==> L3 = f^#(0,1,g(0,1)) -> f^#(0,1,g(0,1)) is in U_IR^3.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 13
Number of unfolded rules generated by all the parallel proofs = 13