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(c,g(c),g(b)) -> f(c,g(c),g(b))
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(c,g(c),g(b)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(c,g(c),g(b)) 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, 3 unfolded rules generated.
# Iteration 2: no loop detected, 3 unfolded rules generated.
# Iteration 3: loop detected, 3 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = f^#(_0,g(_0),_1) -> f^#(_1,_1,_1) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 forwards at position p0
with the rule g(b) -> c.
==> L1 = f^#(_0,g(_0),g(b)) -> f^#(c,g(b),g(b)) is in U_IR^1.
Let p1 = [0].
The subterm at position p1 in the left-hand side of the rule of L1 unifies with
the subterm at position p1 in the right-hand side of the rule of L1.
==> L2 = f^#(c,g(c),g(b)) -> f^#(c,g(b),g(b)) is in U_IR^2.
Let p2 = [1, 0].
We unfold the rule of L2 forwards at position p2
with the rule b -> c.
==> L3 = f^#(c,g(c),g(b)) -> f^#(c,g(c),g(b)) is in U_IR^3.

** END proof description **

Proof stopped at iteration 3
Number of unfolded rules generated by this proof = 10
Number of unfolded rules generated by all the parallel proofs = 11