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 = 1] ap(ap(ap(g,f),_0),ap(s,_1)) -> ap(ap(ap(g,f),_0),ap(_0,0))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_1->0, _0->s} and theta2 = {}.
We have r|p = ap(ap(ap(g,f),_0),ap(_0,0)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = ap(ap(ap(g,f),s),ap(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, 3 unfolded rules generated.
# Iteration 1: loop detected, 1 unfolded rule generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = ap^#(ap(ap(g,_0),_1),ap(s,_2)) -> ap^#(ap(ap(g,_0),_1),ap(ap(_0,_1),0)) is in U_IR^0.
Let p0 = [1, 0].
We unfold the rule of L0 forwards at position p0
with the rule ap(f,_0) -> _0.
==> L1 = ap^#(ap(ap(g,f),s),ap(s,0)) -> ap^#(ap(ap(g,f),s),ap(s,0)) is in U_IR^1.

** END proof description **

Proof stopped at iteration 1
Number of unfolded rules generated by this proof = 4
Number of unfolded rules generated by all the parallel proofs = 4