MAYBE

Problem:
 app(app(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
 app(app(quot(),0()),app(s(),y)) -> 0()
 app(app(quot(),app(s(),x)),app(s(),y)) ->
 app(s(),app(app(quot(),app(app(minus(),x),y)),app(s(),y)))
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(plus(),app(app(minus(),x),app(s(),0()))),app(app(minus(),y),app(s(),app(s(),z)))) ->
 app(app(plus(),app(app(minus(),y),app(s(),app(s(),z)))),app(app(minus(),x),app(s(),0())))
 app(app(plus(),app(app(plus(),x),app(s(),0()))),app(app(plus(),y),app(s(),app(s(),z)))) ->
 app(app(plus(),app(app(plus(),y),app(s(),app(s(),z)))),app(app(plus(),x),app(s(),0())))
 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