let R be the TRS under consideration

app(app(_1,0),_2) -> app(app(hd,app(app(map,_1),app(app(cons,0),nil))),_2) is in elim_R(R)
let l be the left-hand side and r be the right-hand side of this rule
let p = 0.1.1
let theta = {_1/cons, _2/nil}
let theta' = {}
we have r|p = app(app(cons,0),nil) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = app(app(cons,0),nil) 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