let R be the TRS under consideration

U11(tt,_1) -> U12(tt,activate(_1)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 1 is a position in r0
we have r0|p0 = activate(_1)
activate(n__zeros) -> zeros is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/n__zeros} is a mgu of r0|p0 and l'0

==> U11(tt,n__zeros) -> U12(tt,zeros) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 1 is a position in l1
we have l1|p1 = n__zeros
activate(_1) -> _1 is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/n__zeros} is a mgu of l1|p1 and r'1

==> U11(tt,activate(n__zeros)) -> U12(tt,zeros) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = epsilon is a position in l2
we have l2|p2 = U11(tt,activate(n__zeros))
length(cons(_1,_2)) -> U11(tt,activate(_2)) is in R
let r'2 be the right-hand side of this rule
theta2 = {_2/n__zeros} is a mgu of l2|p2 and r'2

==> length(cons(_1,n__zeros)) -> U12(tt,zeros) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 0 is a position in l3
we have l3|p3 = cons(_1,n__zeros)
zeros -> cons(0,n__zeros) is in R
let r'3 be the right-hand side of this rule
theta3 = {_1/0} is a mgu of l3|p3 and r'3

==> length(zeros) -> U12(tt,zeros) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0 is a position in l4
we have l4|p4 = zeros
activate(_1) -> _1 is in R
let r'4 be the right-hand side of this rule
theta4 = {_1/zeros} is a mgu of l4|p4 and r'4

==> length(activate(zeros)) -> U12(tt,zeros) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = epsilon is a position in r5
we have r5|p5 = U12(tt,zeros)
U12(tt,_1) -> s(length(activate(_1))) is in R
let l'5 be the left-hand side of this rule
theta5 = {_1/zeros} is a mgu of r5|p5 and l'5

==> length(activate(zeros)) -> s(length(activate(zeros))) is in EU_R^6
let l be the left-hand side and r be the right-hand side of this rule
let p = 0
let theta = {}
let theta' = {}
we have r|p = length(activate(zeros)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = length(activate(zeros)) is non-terminating w.r.t. R

Termination disproved by the forward+backward process
proof stopped at iteration i=6, depth k=2
126 rule(s) generated