(STRATEGY
    INNERMOST)

(VAR
    l l1 l2 x y z)
(DATATYPES
    A = µX.< 0, s(X), nil, cons(X, X) >)
(SIGNATURES
    + :: [A x A] -> A
    * :: [A x A] -> A
    app :: [A x A] -> A
    sum :: [A] -> A
    prod :: [A] -> A)
(RULES
    +(x,0()) -> x
    +(0(),x) -> x
    +(s(x),s(y)) -> s(s(+(x,y)))
    +(+(x,y),z) -> +(x,+(y,z))
    *(x,0()) -> 0()
    *(0(),x) -> 0()
    *(s(x),s(y)) -> s(+(*(x,y)
                       ,+(x,y)))
    *(*(x,y),z) -> *(x,*(y,z))
    app(nil(),l) -> l
    app(cons(x,l1),l2) -> cons(x
                              ,app(l1,l2))
    sum(nil()) -> 0()
    sum(cons(x,l)) -> +(x,sum(l))
    sum(app(l1,l2)) -> +(sum(l1)
                        ,sum(l2))
    prod(nil()) -> s(0())
    prod(cons(x,l)) -> *(x,prod(l))
    prod(app(l1,l2)) -> *(prod(l1)
                         ,prod(l2)))