(STRATEGY
    INNERMOST)

(VAR
    L X X1 X2 Y)
(DATATYPES
    A = µX.< 0, mark(X), true, false, nil, ok(X) >)
(SIGNATURES
    active :: [A] -> A
    inf :: [A] -> A
    take :: [A x A] -> A
    length :: [A] -> A
    proper :: [A] -> A
    eq :: [A x A] -> A
    s :: [A] -> A
    cons :: [A x A] -> A
    top :: [A] -> A)
(RULES
    active(eq(0(),0())) ->
      mark(true())
    active(eq(s(X),s(Y))) ->
      mark(eq(X,Y))
    active(eq(X,Y)) -> mark(false())
    active(inf(X)) -> mark(cons(X
                               ,inf(s(X))))
    active(take(0(),X)) ->
      mark(nil())
    active(take(s(X),cons(Y,L))) ->
      mark(cons(Y,take(X,L)))
    active(length(nil())) ->
      mark(0())
    active(length(cons(X,L))) ->
      mark(s(length(L)))
    active(inf(X)) -> inf(active(X))
    active(take(X1,X2)) ->
      take(active(X1),X2)
    active(take(X1,X2)) -> take(X1
                               ,active(X2))
    active(length(X)) ->
      length(active(X))
    inf(mark(X)) -> mark(inf(X))
    take(mark(X1),X2) ->
      mark(take(X1,X2))
    take(X1,mark(X2)) ->
      mark(take(X1,X2))
    length(mark(X)) ->
      mark(length(X))
    proper(eq(X1,X2)) ->
      eq(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(true()) -> ok(true())
    proper(s(X)) -> s(proper(X))
    proper(false()) -> ok(false())
    proper(inf(X)) -> inf(proper(X))
    proper(cons(X1,X2)) ->
      cons(proper(X1),proper(X2))
    proper(take(X1,X2)) ->
      take(proper(X1),proper(X2))
    proper(nil()) -> ok(nil())
    proper(length(X)) ->
      length(proper(X))
    eq(ok(X1),ok(X2)) -> ok(eq(X1
                              ,X2))
    s(ok(X)) -> ok(s(X))
    inf(ok(X)) -> ok(inf(X))
    cons(ok(X1),ok(X2)) ->
      ok(cons(X1,X2))
    take(ok(X1),ok(X2)) ->
      ok(take(X1,X2))
    length(ok(X)) -> ok(length(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))