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 = 5] f(g(0,_0),s(0),g(0,_0)) -> f(g(0,_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->s(0)} and theta2 = {}.
We have r|p = f(g(0,_0),_0,g(0,_0)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(g(0,s(0)),s(0),g(0,s(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, 7 unfolded rules generated.
# Iteration 2: no loop detected, 68 unfolded rules generated.
# Iteration 3: no loop detected, 831 unfolded rules generated.
# Iteration 4: no loop detected, 12889 unfolded rules generated.
# Iteration 5: loop detected, 152234 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = f^#(0,s(0),_0) -> f^#(_0,double(_0),_0) is in U_IR^0.
Let p0 = [0].
We unfold the rule of L0 backwards at position p0
with the rule g(_0,_1) -> _0.
==> L1 = f^#(g(0,_0),s(0),g(0,_0)) -> f^#(g(0,_0),double(g(0,_0)),g(0,_0)) is in U_IR^1.
Let p1 = [1].
We unfold the rule of L1 forwards at position p1
with the rule double(_0) -> +(_0,_0).
==> L2 = f^#(g(0,_0),s(0),g(0,_0)) -> f^#(g(0,_0),+(g(0,_0),g(0,_0)),g(0,_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,_1) -> _1.
==> L3 = f^#(g(0,_0),s(0),g(0,_0)) -> f^#(g(0,_0),+(_0,g(0,_0)),g(0,_0)) is in U_IR^3.
Let p3 = [1, 1].
We unfold the rule of L3 forwards at position p3
with the rule g(_0,_1) -> _0.
==> L4 = f^#(g(0,_0),s(0),g(0,_0)) -> f^#(g(0,_0),+(_0,0),g(0,_0)) is in U_IR^4.
Let p4 = [1].
We unfold the rule of L4 forwards at position p4
with the rule +(_0,0) -> _0.
==> L5 = f^#(g(0,s(0)),s(0),g(0,s(0))) -> f^#(g(0,s(0)),s(0),g(0,s(0))) is in U_IR^5.

** END proof description **

Proof stopped at iteration 5
Number of unfolded rules generated by this proof = 166030
Number of unfolded rules generated by all the parallel proofs = 326949