(VAR N X X1 X2 Y Z )
(RULES 
        active(from(X)) -> mark(cons(X, from(s(X))))
        active(2ndspos(0, Z)) -> mark(rnil)
        active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
        active(2ndsneg(0, Z)) -> mark(rnil)
        active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z)))
        active(pi(X)) -> mark(2ndspos(X, from(0)))
        active(plus(0, Y)) -> mark(Y)
        active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
        active(times(0, Y)) -> mark(0)
        active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
        active(square(X)) -> mark(times(X, X))
        active(s(X)) -> s(active(X))
        active(posrecip(X)) -> posrecip(active(X))
        active(negrecip(X)) -> negrecip(active(X))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(rcons(X1, X2)) -> rcons(active(X1), X2)
        active(rcons(X1, X2)) -> rcons(X1, active(X2))
        active(from(X)) -> from(active(X))
        active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
        active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
        active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
        active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
        active(pi(X)) -> pi(active(X))
        active(plus(X1, X2)) -> plus(active(X1), X2)
        active(plus(X1, X2)) -> plus(X1, active(X2))
        active(times(X1, X2)) -> times(active(X1), X2)
        active(times(X1, X2)) -> times(X1, active(X2))
        active(square(X)) -> square(active(X))
        s(mark(X)) -> mark(s(X))
        posrecip(mark(X)) -> mark(posrecip(X))
        negrecip(mark(X)) -> mark(negrecip(X))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        rcons(mark(X1), X2) -> mark(rcons(X1, X2))
        rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
        from(mark(X)) -> mark(from(X))
        2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
        2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
        2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
        2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
        pi(mark(X)) -> mark(pi(X))
        plus(mark(X1), X2) -> mark(plus(X1, X2))
        plus(X1, mark(X2)) -> mark(plus(X1, X2))
        times(mark(X1), X2) -> mark(times(X1, X2))
        times(X1, mark(X2)) -> mark(times(X1, X2))
        square(mark(X)) -> mark(square(X))
        proper(0) -> ok(0)
        proper(s(X)) -> s(proper(X))
        proper(posrecip(X)) -> posrecip(proper(X))
        proper(negrecip(X)) -> negrecip(proper(X))
        proper(nil) -> ok(nil)
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(rnil) -> ok(rnil)
        proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
        proper(from(X)) -> from(proper(X))
        proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
        proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
        proper(pi(X)) -> pi(proper(X))
        proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
        proper(times(X1, X2)) -> times(proper(X1), proper(X2))
        proper(square(X)) -> square(proper(X))
        s(ok(X)) -> ok(s(X))
        posrecip(ok(X)) -> ok(posrecip(X))
        negrecip(ok(X)) -> ok(negrecip(X))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
        from(ok(X)) -> ok(from(X))
        2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
        2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
        pi(ok(X)) -> ok(pi(X))
        plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
        times(ok(X1), ok(X2)) -> ok(times(X1, X2))
        square(ok(X)) -> ok(square(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)