MAYBE

Problem:
 +(x,0()) -> x
 +(0(),x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 *(x,0()) -> 0()
 *(0(),x) -> 0()
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 sum(nil()) -> 0()
 sum(cons(x,l)) -> +(x,sum(l))
 prod(nil()) -> s(0())
 prod(cons(x,l)) -> *(x,prod(l))

Proof:
 Open