MAYBE

Problem:
 a(a(divides(),0()),a(s(),y)) -> true()
 a(a(divides(),a(s(),x)),a(s(),y)) -> a(a(a(div2(),x),a(s(),y)),y)
 a(a(a(div2(),x),y),0()) -> a(a(divides(),x),y)
 a(a(a(div2(),0()),y),a(s(),z)) -> false()
 a(a(a(div2(),a(s(),x)),y),a(s(),z)) -> a(a(a(div2(),x),y),z)
 a(a(filter(),f),nil()) -> nil()
 a(a(filter(),f),a(a(cons(),x),xs)) -> a(a(a(if(),a(f,x)),x),a(a(filter(),f),xs))
 a(a(a(if(),true()),x),xs) -> a(a(cons(),x),xs)
 a(a(a(if(),false()),x),xs) -> xs
 a(a(not(),f),x) -> a(not2(),a(f,x))
 a(not2(),true()) -> false()
 a(not2(),false()) -> true()
 a(sieve(),nil()) -> nil()
 a(sieve(),a(a(cons(),x),xs)) ->
 a(a(cons(),x),a(sieve(),a(a(filter(),a(not(),a(divides(),x))),xs)))

Proof:
 Open