let R be the TRS under consideration

incr(cons(_1,_2)) -> activate(_2) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = epsilon is a position in l0
we have l0|p0 = incr(cons(_1,_2))
adx(cons(_3,_4)) -> incr(cons(_3,n__adx(activate(_4)))) is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/_3, _2/n__adx(activate(_4))} is a mgu of l0|p0 and r'0

==> adx(cons(_1,_2)) -> activate(n__adx(activate(_2))) 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 = cons(_1,_2)
zeros -> cons(0,n__zeros) is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/0, _2/n__zeros} is a mgu of l1|p1 and r'1

==> adx(zeros) -> activate(n__adx(activate(n__zeros))) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0 is a position in l2
we have l2|p2 = zeros
activate(n__zeros) -> zeros is in R
let r'2 be the right-hand side of this rule
theta2 = {} is a mgu of l2|p2 and r'2

==> adx(activate(n__zeros)) -> activate(n__adx(activate(n__zeros))) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = epsilon is a position in l3
we have l3|p3 = adx(activate(n__zeros))
activate(n__adx(_1)) -> adx(activate(_1)) is in R
let r'3 be the right-hand side of this rule
theta3 = {_1/n__zeros} is a mgu of l3|p3 and r'3

==> activate(n__adx(n__zeros)) -> activate(n__adx(activate(n__zeros))) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0.0 is a position in l4
we have l4|p4 = n__zeros
activate(_1) -> _1 is in R
let r'4 be the right-hand side of this rule
theta4 = {_1/n__zeros} is a mgu of l4|p4 and r'4

==> activate(n__adx(activate(n__zeros))) -> activate(n__adx(activate(n__zeros))) is in EU_R^5
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 = activate(n__adx(activate(n__zeros))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = activate(n__adx(activate(n__zeros))) is non-terminating w.r.t. R

Termination disproved by the backward process
proof stopped at iteration i=5, depth k=3
1434 rule(s) generated