(VAR f h i u v x xs y )
(RULES 
        app(app(eq, 0), 0) -> true
        app(app(eq, 0), app(s, x)) -> 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(or, true), y) -> true
        app(app(or, false), y) -> y
        app(app(union, empty), h) -> h
        app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
        app(app(app(app(reach, x), y), empty), h) -> false
        app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
        app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
        app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
        app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
        app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
        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)
        
)