let R be the TRS under consideration

length(cons(_1,_2)) -> length(activate(_2)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0 is a position in r0
we have r0|p0 = activate(_2)
activate(n__zeros) -> zeros is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/n__zeros} is a mgu of r0|p0 and l'0

==> length(cons(_1,n__zeros)) -> length(zeros) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0 is a position in r1
we have r1|p1 = zeros
zeros -> cons(0,n__zeros) is in R
let l'1 be the left-hand side of this rule
theta1 = {} is a mgu of r1|p1 and l'1

==> length(cons(_1,n__zeros)) -> length(cons(0,n__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 = {_1/0}
let theta' = {}
we have r|p = length(cons(0,n__zeros)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = length(cons(0,n__zeros)) is non-terminating w.r.t. R

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