(VAR X X1 X2 X3 Y Z )
(RULES 
        active(and(true, X)) -> mark(X)
        active(and(false, Y)) -> mark(false)
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(add(0, X)) -> mark(X)
        active(add(s(X), Y)) -> mark(s(add(X, Y)))
        active(first(0, X)) -> mark(nil)
        active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
        active(from(X)) -> mark(cons(X, from(s(X))))
        active(and(X1, X2)) -> and(active(X1), X2)
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
        active(add(X1, X2)) -> add(active(X1), X2)
        active(first(X1, X2)) -> first(active(X1), X2)
        active(first(X1, X2)) -> first(X1, active(X2))
        and(mark(X1), X2) -> mark(and(X1, X2))
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
        add(mark(X1), X2) -> mark(add(X1, X2))
        first(mark(X1), X2) -> mark(first(X1, X2))
        first(X1, mark(X2)) -> mark(first(X1, X2))
        proper(and(X1, X2)) -> and(proper(X1), proper(X2))
        proper(true) -> ok(true)
        proper(false) -> ok(false)
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
        proper(add(X1, X2)) -> add(proper(X1), proper(X2))
        proper(0) -> ok(0)
        proper(s(X)) -> s(proper(X))
        proper(first(X1, X2)) -> first(proper(X1), proper(X2))
        proper(nil) -> ok(nil)
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(from(X)) -> from(proper(X))
        and(ok(X1), ok(X2)) -> ok(and(X1, X2))
        if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
        add(ok(X1), ok(X2)) -> ok(add(X1, X2))
        s(ok(X)) -> ok(s(X))
        first(ok(X1), ok(X2)) -> ok(first(X1, X2))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        from(ok(X)) -> ok(from(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)