let R be the TRS under consideration

ap(ap(ap(g,_1),_2),ap(s,_3)) -> ap(ap(ap(g,_1),_2),ap(ap(_1,_2),0)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 1.0 is a position in r0
we have r0|p0 = ap(_1,_2)
ap(f,_4) -> _4 is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/f, _2/_4} is a mgu of r0|p0 and l'0

==> ap(ap(ap(g,f),_1),ap(s,_2)) -> ap(ap(ap(g,f),_1),ap(_1,0)) is in EU_R^1
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/s, _2/0}
let theta' = {}
we have r|p = ap(ap(ap(g,f),_1),ap(_1,0)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = ap(ap(ap(g,f),s),ap(s,0)) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=1, depth k=3
2 rule(s) generated