Termination w.r.t. Q of the given QTRS could not be shown:

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

ge(x, 0) → true
ge(0, s(y)) → false
ge(s(x), s(y)) → ge(x, y)
minus(x, 0) → x
minus(0, y) → 0
minus(s(x), s(y)) → minus(x, y)
id_inc(x) → x
id_inc(x) → s(x)
quot(x, y) → div(x, y, 0)
div(x, y, z) → if(ge(y, s(0)), ge(x, y), x, y, z)
if(false, b, x, y, z) → div_by_zero
if(true, false, x, y, z) → z
if(true, true, x, y, z) → div(minus(x, y), y, id_inc(z))

Q is empty.