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 = 2] P(_0,S(l(_1)),0,0,0,0,_2) -> P(_0,_0,0,0,0,0,0)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_0->S(l(_1)), _2->0} and theta2 = {}.
We have r|p = P(_0,_0,0,0,0,0,0) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = P(S(l(_1)),S(l(_1)),0,0,0,0,0) 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, 237 unfolded rules generated.
# Iteration 1: no loop detected, 6311 unfolded rules generated.
# Iteration 2: loop detected, 420451 unfolded rules generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = [P^#(_0,S(_1),0,0,0,0,_2) -> J2^#(_0,_1,_2), J2^#(_3,l(_4),_5) -> P^#(_3,J2(_3,_4,_5),0,0,0,0,0)] is in U_IR^0.
We merge the first and the second rule of L0.
==> L1 = P^#(_0,S(l(_1)),0,0,0,0,_2) -> P^#(_0,J2(_0,_1,_2),0,0,0,0,0) is in U_IR^1.
Let p1 = [1].
We unfold the rule of L1 forwards at position p1
with the rule J2(_0,_1,_2) -> _0.
==> L2 = P^#(S(l(_0)),S(l(_0)),0,0,0,0,0) -> P^#(S(l(_0)),S(l(_0)),0,0,0,0,0) is in U_IR^2.

** END proof description **

Proof stopped at iteration 2
Number of unfolded rules generated by this proof = 426999
Number of unfolded rules generated by all the parallel proofs = 426999