(STRATEGY
    INNERMOST)

(VAR
    l l1 l2 x y z)
(DATATYPES
    A = µX.< #, 1(X), nil, cons(X, X) >)
(SIGNATURES
    0 :: [A] -> A
    + :: [A x A] -> A
    * :: [A x A] -> A
    app :: [A x A] -> A
    sum :: [A] -> A
    prod :: [A] -> A)
(RULES
    0(#()) -> #()
    +(x,#()) -> x
    +(#(),x) -> x
    +(0(x),0(y)) -> 0(+(x,y))
    +(0(x),1(y)) -> 1(+(x,y))
    +(1(x),0(y)) -> 1(+(x,y))
    +(1(x),1(y)) -> 0(+(+(x,y)
                       ,1(#())))
    +(+(x,y),z) -> +(x,+(y,z))
    *(#(),x) -> #()
    *(0(x),y) -> 0(*(x,y))
    *(1(x),y) -> +(0(*(x,y)),y)
    *(*(x,y),z) -> *(x,*(y,z))
    *(x,+(y,z)) -> +(*(x,y),*(x,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()) -> 1(#())
    prod(cons(x,l)) -> *(x,prod(l))
    prod(app(l1,l2)) -> *(prod(l1)
                         ,prod(l2)))