(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(le, 0), y) → true
app(app(le, app(s, x)), 0) → false
app(app(le, app(s, x)), app(s, y)) → app(app(le, x), y)
app(app(eq, 0), 0) → true
app(app(eq, 0), app(s, y)) → false
app(app(eq, app(s, x)), 0) → false
app(app(eq, app(s, x)), app(s, y)) → app(app(eq, x), y)
app(app(app(if, true), x), y) → x
app(app(app(if, false), x), y) → y
app(minsort, nil) → nil
app(minsort, app(app(cons, x), y)) → app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y))))
app(app(min, x), nil) → x
app(app(min, x), app(app(cons, y), z)) → app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z))
app(app(del, x), nil) → nil
app(app(del, x), app(app(cons, y), z)) → app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
Q is empty.