(STRATEGY
    INNERMOST)

(VAR
    N X Y Z)
(DATATYPES
    A = µX.< cons(X, X), recip(X), s(X), 0, nil >)
(SIGNATURES
    terms :: [A] -> A
    sqr :: [A] -> A
    dbl :: [A] -> A
    add :: [A x A] -> A
    first :: [A x A] -> A
    half :: [A] -> A)
(RULES
    terms(N) -> cons(recip(sqr(N))
                    ,terms(s(N)))
    sqr(0()) -> 0()
    sqr(s(X)) -> s(add(sqr(X)
                      ,dbl(X)))
    dbl(0()) -> 0()
    dbl(s(X)) -> s(s(dbl(X)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) -> cons(Y
                                 ,first(X,Z))
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(X))) -> s(half(X))
    half(dbl(X)) -> X)