let R be the TRS under consideration

app(app(app(until,_1),_2),_3) -> app(app(app(if,app(_1,_3)),_3),app(app(app(until,_1),_2),app(_2,_3))) is in elim_R(R)
let l be the left-hand side and r be the right-hand side of this rule
let p = 1
let theta = {}
let theta' = {_1/_1, _2/_2, _3/app(_2,_3)}
we have r|p = app(app(app(until,_1),_2),app(_2,_3)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = app(app(app(until,_1),_2),_3) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=0, depth k=0
1 rule(s) generated