(VAR x y xs fun)
(RULES
  app(f, 0) -> true
  app(f, 1) -> false
  app(f, app(s, x)) -> app(f, x)
  app(app(app(if, true), app(s, x)), app(s, y)) -> app(s, x)
  app(app(app(if, false), app(s, x)), app(s, y)) -> app(s, y)
  app(app(g, x), app(c, y)) -> app(c, app(app(g, x), y))
  app(app(g, x), app(c, y)) -> app(app(g, x), app(app(app(if, app(f, x)), app(c, app(app(g, app(s, x)), y))), app(c, y)))

  app(app(map,fun),nil) -> nil
  app(app(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs))

  app(app(filter,fun),nil) -> nil
  app(app(filter,fun),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(fun, x)),fun),x),xs)
  app(app(app(app(filter2,true),fun),x),xs) -> app(app(cons,x),app(app(filter,fun),xs))
  app(app(app(app(filter2,false),fun),x),xs) -> app(app(filter,fun),xs)

)