let R be the TRS under consideration

a__length(cons(_1,_2)) -> a__length(mark(_2)) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0 is a position in l0
we have l0|p0 = cons(_1,_2)
a__zeros -> cons(0,zeros) is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/0, _2/zeros} is a mgu of l0|p0 and r'0

==> a__length(a__zeros) -> a__length(mark(zeros)) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0 is a position in l1
we have l1|p1 = a__zeros
mark(zeros) -> a__zeros is in R
let r'1 be the right-hand side of this rule
theta1 = {} is a mgu of l1|p1 and r'1

==> a__length(mark(zeros)) -> a__length(mark(zeros)) is in EU_R^2
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = a__length(mark(zeros)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a__length(mark(zeros)) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=2, depth k=3
338 rule(s) generated