let R be the TRS under consideration

f(h(_1),_2) -> f(_2,f(_1,h(f(a,a)))) 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 = f(_2,f(_1,h(f(a,a))))
f(h(_3),_4) -> h(f(_4,f(_3,h(f(a,a))))) is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/h(_3), _4/f(_1,h(f(a,a)))} is a mgu of r0|p0 and l'0

==> f(h(_1),h(_2)) -> f(f(_1,h(f(a,a))),f(_2,h(f(a,a)))) 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 = f(_1,h(f(a,a)))
f(h(_3),_4) -> h(f(_4,f(_3,h(f(a,a))))) is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/h(_3), _4/h(f(a,a))} is a mgu of r1|p1 and l'1

==> f(h(h(_1)),h(_2)) -> f(h(f(h(f(a,a)),f(_1,h(f(a,a))))),f(_2,h(f(a,a)))) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0.0 is a position in r2
we have r2|p2 = f(h(f(a,a)),f(_1,h(f(a,a))))
f(h(_3),_4) -> h(f(_4,f(_3,h(f(a,a))))) is in R
let l'2 be the left-hand side of this rule
theta2 = {_3/f(a,a), _4/f(_1,h(f(a,a)))} is a mgu of r2|p2 and l'2

==> f(h(h(_1)),h(_2)) -> f(h(h(f(f(_1,h(f(a,a))),f(f(a,a),h(f(a,a)))))),f(_2,h(f(a,a)))) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 1 is a position in r3
we have r3|p3 = f(_2,h(f(a,a)))
f(h(_3),_4) -> h(f(_4,f(_3,h(f(a,a))))) is in R
let l'3 be the left-hand side of this rule
theta3 = {_2/h(_3), _4/h(f(a,a))} is a mgu of r3|p3 and l'3

==> f(h(h(_1)),h(h(_2))) -> f(h(h(f(f(_1,h(f(a,a))),f(f(a,a),h(f(a,a)))))),h(f(h(f(a,a)),f(_2,h(f(a,a)))))) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 1.0 is a position in r4
we have r4|p4 = f(h(f(a,a)),f(_2,h(f(a,a))))
f(h(_3),_4) -> h(f(_4,f(_3,h(f(a,a))))) is in R
let l'4 be the left-hand side of this rule
theta4 = {_3/f(a,a), _4/f(_2,h(f(a,a)))} is a mgu of r4|p4 and l'4

==> f(h(h(_1)),h(h(_2))) -> f(h(h(f(f(_1,h(f(a,a))),f(f(a,a),h(f(a,a)))))),h(h(f(f(_2,h(f(a,a))),f(f(a,a),h(f(a,a))))))) 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/f(f(_1,h(f(a,a))),f(f(a,a),h(f(a,a)))), _2/f(f(_2,h(f(a,a))),f(f(a,a),h(f(a,a))))}
we have r|p = f(h(h(f(f(_1,h(f(a,a))),f(f(a,a),h(f(a,a)))))),h(h(f(f(_2,h(f(a,a))),f(f(a,a),h(f(a,a))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(h(h(_1)),h(h(_2))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=5, depth k=7
44 rule(s) generated