(STRATEGY
    INNERMOST)

(VAR
    M N X X1 X2 X3 Y)
(DATATYPES
    A = µX.< cons(X, X), 0, n__filter(X, X, X), s(X), n__sieve(X), n__nats(X) >)
(SIGNATURES
    filter :: [A x A x A] -> A
    sieve :: [A] -> A
    nats :: [A] -> A
    zprimes :: [] -> A
    activate :: [A] -> A)
(RULES
    filter(cons(X,Y),0(),M) ->
      cons(0()
          ,n__filter(activate(Y),M,M))
    filter(cons(X,Y),s(N),M) ->
      cons(X
          ,n__filter(activate(Y),N,M))
    sieve(cons(0(),Y)) -> cons(0()
                              ,n__sieve(activate(Y)))
    sieve(cons(s(N),Y)) -> cons(s(N)
                               ,n__sieve(filter(activate(Y)
                                               ,N
                                               ,N)))
    nats(N) -> cons(N,n__nats(s(N)))
    zprimes() ->
      sieve(nats(s(s(0()))))
    filter(X1,X2,X3) -> n__filter(X1
                                 ,X2
                                 ,X3)
    sieve(X) -> n__sieve(X)
    nats(X) -> n__nats(X)
    activate(n__filter(X1,X2,X3)) ->
      filter(X1,X2,X3)
    activate(n__sieve(X)) ->
      sieve(X)
    activate(n__nats(X)) -> nats(X)
    activate(X) -> X)