(VAR f k m n x xs )
(STRATEGY INNERMOST)
(RULES 
        app(app(eq, 0), 0) -> true
        app(app(eq, 0), app(s, m)) -> false
        app(app(eq, app(s, n)), 0) -> false
        app(app(eq, app(s, n)), app(s, m)) -> app(app(eq, n), m)
        app(app(le, 0), m) -> true
        app(app(le, app(s, n)), 0) -> false
        app(app(le, app(s, n)), app(s, m)) -> app(app(le, n), m)
        app(min, app(app(cons, 0), nil)) -> 0
        app(min, app(app(cons, app(s, n)), nil)) -> app(s, n)
        app(min, app(app(cons, n), app(app(cons, m), x))) -> app(app(if_min, app(app(le, n), m)), app(app(cons, n), app(app(cons, m), x)))
        app(app(if_min, true), app(app(cons, n), app(app(cons, m), x))) -> app(min, app(app(cons, n), x))
        app(app(if_min, false), app(app(cons, n), app(app(cons, m), x))) -> app(min, app(app(cons, m), x))
        app(app(app(replace, n), m), nil) -> nil
        app(app(app(replace, n), m), app(app(cons, k), x)) -> app(app(app(app(if_replace, app(app(eq, n), k)), n), m), app(app(cons, k), x))
        app(app(app(app(if_replace, true), n), m), app(app(cons, k), x)) -> app(app(cons, m), x)
        app(app(app(app(if_replace, false), n), m), app(app(cons, k), x)) -> app(app(cons, k), app(app(app(replace, n), m), x))
        app(sort, nil) -> nil
        app(sort, app(app(cons, n), x)) -> app(app(cons, app(min, app(app(cons, n), x))), app(sort, app(app(app(replace, app(min, app(app(cons, n), x))), n), x)))
        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)
        
)