MAYBE

Problem:
 app(app(app(if(),true()),xs),ys) -> xs
 app(app(app(if(),false()),xs),ys) -> ys
 app(app(sub(),x),0()) -> x
 app(app(sub(),app(s(),x)),app(s(),y)) -> app(app(sub(),x),y)
 app(app(gtr(),0()),y) -> false()
 app(app(gtr(),app(s(),x)),0()) -> true()
 app(app(gtr(),app(s(),x)),app(s(),y)) -> app(app(gtr(),x),y)
 app(app(d(),x),0()) -> true()
 app(app(d(),app(s(),x)),app(s(),y)) ->
 app(app(app(if(),app(app(gtr(),x),y)),false()),app(app(d(),app(s(),x)),app(app(sub(),y),x)))
 app(len(),nil()) -> 0()
 app(len(),app(app(cons(),x),xs)) -> app(s(),app(len(),xs))
 app(app(filter(),p),nil()) -> nil()
 app(app(filter(),p),app(app(cons(),x),xs)) ->
 app(app(app(if(),app(p,x)),app(app(cons(),x),app(app(filter(),p),xs))),app(app(filter(),p),xs))

Proof:
 Open