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__incr(_3)) -> incr(activate(_3)) is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/n__incr(_3)} is a mgu of r0|p0 and l'0

==> incr(cons(_1,n__incr(_2))) -> incr(activate(_2)) 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 = activate(_2)
activate(n__nats) -> nats is in R
let l'1 be the left-hand side of this rule
theta1 = {_2/n__nats} is a mgu of r1|p1 and l'1

==> incr(cons(_1,n__incr(n__nats))) -> incr(nats) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0 is a position in r2
we have r2|p2 = nats
nats -> cons(0,n__incr(n__nats)) is in R
let l'2 be the left-hand side of this rule
theta2 = {} is a mgu of r2|p2 and l'2

==> incr(cons(_1,n__incr(n__nats))) -> incr(cons(0,n__incr(n__nats))) is in EU_R^3
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 = incr(cons(0,n__incr(n__nats))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = incr(cons(0,n__incr(n__nats))) is non-terminating w.r.t. R

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