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 = 6] length(cons(_0,n__zeros)) -> length(cons(0,n__zeros))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->0}.
We have r|p = length(cons(0,n__zeros)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = length(cons(_0,n__zeros)) 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, 1 unfolded rule generated.
# Iteration 2: no loop detected, 1 unfolded rule generated.
# Iteration 3: no loop detected, 6 unfolded rules generated.
# Iteration 4: no loop detected, 36 unfolded rules generated.
# Iteration 5: no loop detected, 172 unfolded rules generated.
# Iteration 6: loop detected, 1 unfolded rule generated.
Here is the successful unfolding. Let IR be the TRS under analysis.
L0 = [length^#(cons(_0,_1)) -> U11^#(tt,activate(_1)), U11^#(tt,_2) -> U12^#(tt,activate(_2)), U12^#(tt,_3) -> length^#(activate(_3))] is in U_IR^0.
We merge the first and the second rule of L0.
==> L1 = [length^#(cons(_0,_1)) -> U12^#(tt,activate(activate(_1))), U12^#(tt,_2) -> length^#(activate(_2))] is in U_IR^1.
We merge the first and the second rule of L1.
==> L2 = length^#(cons(_0,_1)) -> length^#(activate(activate(activate(_1)))) is in U_IR^2.
Let p2 = [0].
We unfold the rule of L2 forwards at position p2
with the rule activate(_0) -> _0.
==> L3 = length^#(cons(_0,_1)) -> length^#(activate(activate(_1))) is in U_IR^3.
Let p3 = [0].
We unfold the rule of L3 forwards at position p3
with the rule activate(_0) -> _0.
==> L4 = length^#(cons(_0,_1)) -> length^#(activate(_1)) is in U_IR^4.
Let p4 = [0].
We unfold the rule of L4 forwards at position p4
with the rule activate(n__zeros) -> zeros.
==> L5 = length^#(cons(_0,n__zeros)) -> length^#(zeros) is in U_IR^5.
Let p5 = [0].
We unfold the rule of L5 forwards at position p5
with the rule zeros -> cons(0,n__zeros).
==> L6 = length^#(cons(_0,n__zeros)) -> length^#(cons(0,n__zeros)) is in U_IR^6.

** END proof description **

Proof stopped at iteration 6
Number of unfolded rules generated by this proof = 218
Number of unfolded rules generated by all the parallel proofs = 390