Termination w.r.t. Q proof of TRS/higher-order/BirdBTreeMember.trs

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

app(app(lt, app(s, x)), app(s, y)) → app(app(lt, x), y)
app(app(lt, 0), app(s, y)) → true
app(app(lt, y), 0) → false
app(app(eq, x), x) → true
app(app(eq, app(s, x)), 0) → false
app(app(eq, 0), app(s, x)) → false
app(app(member, w), null) → false
app(app(member, w), app(app(app(fork, x), y), z)) → app(app(app(if, app(app(lt, w), y)), app(app(member, w), x)), app(app(app(if, app(app(eq, w), y)), true), app(app(member, w), z)))

Q is empty.

↳ QTRS

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

app(app(lt, app(s, x)), app(s, y)) → app(app(lt, x), y)
app(app(lt, 0), app(s, y)) → true
app(app(lt, y), 0) → false
app(app(eq, x), x) → true
app(app(eq, app(s, x)), 0) → false
app(app(eq, 0), app(s, x)) → false
app(app(member, w), null) → false
app(app(member, w), app(app(app(fork, x), y), z)) → app(app(app(if, app(app(lt, w), y)), app(app(member, w), x)), app(app(app(if, app(app(eq, w), y)), true), app(app(member, w), z)))

Q is empty.