(STRATEGY
    INNERMOST)

(VAR
    X X1 X2 Y)
(DATATYPES
    A = µX.< nats, mark(X), zeros, 0, ok(X) >)
(SIGNATURES
    active :: [A] -> A
    adx :: [A] -> A
    incr :: [A] -> A
    hd :: [A] -> A
    tl :: [A] -> A
    proper :: [A] -> A
    cons :: [A x A] -> A
    s :: [A] -> A
    top :: [A] -> A)
(RULES
    active(nats()) ->
      mark(adx(zeros()))
    active(zeros()) -> mark(cons(0()
                                ,zeros()))
    active(incr(cons(X,Y))) ->
      mark(cons(s(X),incr(Y)))
    active(adx(cons(X,Y))) ->
      mark(incr(cons(X,adx(Y))))
    active(hd(cons(X,Y))) -> mark(X)
    active(tl(cons(X,Y))) -> mark(Y)
    active(adx(X)) -> adx(active(X))
    active(incr(X)) ->
      incr(active(X))
    active(hd(X)) -> hd(active(X))
    active(tl(X)) -> tl(active(X))
    adx(mark(X)) -> mark(adx(X))
    incr(mark(X)) -> mark(incr(X))
    hd(mark(X)) -> mark(hd(X))
    tl(mark(X)) -> mark(tl(X))
    proper(nats()) -> ok(nats())
    proper(adx(X)) -> adx(proper(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) ->
      cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(incr(X)) ->
      incr(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(hd(X)) -> hd(proper(X))
    proper(tl(X)) -> tl(proper(X))
    adx(ok(X)) -> ok(adx(X))
    cons(ok(X1),ok(X2)) ->
      ok(cons(X1,X2))
    incr(ok(X)) -> ok(incr(X))
    s(ok(X)) -> ok(s(X))
    hd(ok(X)) -> ok(hd(X))
    tl(ok(X)) -> ok(tl(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))