MAYBE

Problem:
 app(D(),t()) -> 1()
 app(D(),constant()) -> 0()
 app(D(),app(app(+(),x),y)) -> app(app(+(),app(D(),x)),app(D(),y))
 app(D(),app(app(*(),x),y)) -> app(app(+(),app(app(*(),y),app(D(),x))),app(app(*(),x),app(D(),y)))
 app(D(),app(app(-(),x),y)) -> app(app(-(),app(D(),x)),app(D(),y))
 app(D(),app(minus(),x)) -> app(minus(),app(D(),x))
 app(D(),app(app(div(),x),y)) ->
 app(app(-(),app(app(div(),app(D(),x)),y)),app(app(div(),app(app(*(),x),app(D(),y))),
                                               app(app(pow(),y),2())))
 app(D(),app(ln(),x)) -> app(app(div(),app(D(),x)),x)
 app(D(),app(app(pow(),x),y)) ->
 app(app(+(),app(app(*(),app(app(*(),y),app(app(pow(),x),app(app(-(),y),1())))),app(D(),x))),
     app(app(*(),app(app(*(),app(app(pow(),x),y)),app(ln(),x))),app(D(),y)))
 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)

Proof:
 Open