let R be the TRS under consideration

length1(_1) -> length(activate(_1)) 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(_1)
activate(_2) -> _2 is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/_2} is a mgu of r0|p0 and l'0

==> length1(_1) -> length(_1) 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 = _1
cons(_2,_3) -> n__cons(_2,_3) is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/cons(_2,_3)} is a mgu of r1|p1 and l'1

==> length1(cons(_1,_2)) -> length(n__cons(_1,_2)) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = epsilon is a position in r2
we have r2|p2 = length(n__cons(_1,_2))
length(n__cons(_3,_4)) -> s(length1(activate(_4))) is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/_3, _2/_4} is a mgu of r2|p2 and l'2

==> length1(cons(_1,_2)) -> length1(activate(_2)) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0 is a position in r3
we have r3|p3 = activate(_2)
activate(n__from(_3)) -> from(activate(_3)) is in R
let l'3 be the left-hand side of this rule
theta3 = {_2/n__from(_3)} is a mgu of r3|p3 and l'3

==> length1(cons(_1,n__from(_2))) -> length1(from(activate(_2))) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0 is a position in r4
we have r4|p4 = from(activate(_2))
from(_3) -> cons(_3,n__from(n__s(_3))) is in R
let l'4 be the left-hand side of this rule
theta4 = {_3/activate(_2)} is a mgu of r4|p4 and l'4

==> length1(cons(_1,n__from(_2))) -> length1(cons(activate(_2),n__from(n__s(activate(_2))))) 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' = {_1/activate(_2), _2/n__s(activate(_2))}
we have r|p = length1(cons(activate(_2),n__from(n__s(activate(_2))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = length1(cons(_1,n__from(_2))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=5, depth k=3
1699 rule(s) generated