let R be the TRS under consideration

incr(cons(_1,_2)) -> activate(_2) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = epsilon is a position in r0
we have r0|p0 = activate(_2)
activate(n__adx(_3)) -> adx(_3) is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/n__adx(_3)} is a mgu of r0|p0 and l'0

==> incr(cons(_1,n__adx(_2))) -> adx(_2) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = epsilon is a position in r1
we have r1|p1 = adx(_2)
adx(cons(_3,_4)) -> incr(cons(activate(_3),n__adx(activate(_4)))) is in R
let l'1 be the left-hand side of this rule
theta1 = {_2/cons(_3,_4)} is a mgu of r1|p1 and l'1

==> incr(cons(_1,n__adx(cons(_2,_3)))) -> incr(cons(activate(_2),n__adx(activate(_3)))) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0.1.0 is a position in r2
we have r2|p2 = activate(_3)
activate(n__zeros) -> zeros is in R
let l'2 be the left-hand side of this rule
theta2 = {_3/n__zeros} is a mgu of r2|p2 and l'2

==> incr(cons(_1,n__adx(cons(_2,n__zeros)))) -> incr(cons(activate(_2),n__adx(zeros))) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0.1.0 is a position in r3
we have r3|p3 = zeros
zeros -> cons(n__0,n__zeros) is in R
let l'3 be the left-hand side of this rule
theta3 = {} is a mgu of r3|p3 and l'3

==> incr(cons(_1,n__adx(cons(_2,n__zeros)))) -> incr(cons(activate(_2),n__adx(cons(n__0,n__zeros)))) is in EU_R^4
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/activate(n__0), _2/n__0}
let theta' = {}
we have r|p = incr(cons(activate(_2),n__adx(cons(n__0,n__zeros)))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = incr(cons(activate(n__0),n__adx(cons(n__0,n__zeros)))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=4, depth k=4
2246 rule(s) generated