(VAR N X X1 X2 Y Z )
(RULES 
        a__from(X) -> cons(mark(X), from(s(X)))
        a__2ndspos(0, Z) -> rnil
        a__2ndspos(s(N), cons(X, Z)) -> a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
        a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
        a__2ndsneg(0, Z) -> rnil
        a__2ndsneg(s(N), cons(X, Z)) -> a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
        a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
        a__pi(X) -> a__2ndspos(mark(X), a__from(0))
        a__plus(0, Y) -> mark(Y)
        a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
        a__times(0, Y) -> 0
        a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
        a__square(X) -> a__times(mark(X), mark(X))
        mark(from(X)) -> a__from(mark(X))
        mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
        mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
        mark(pi(X)) -> a__pi(mark(X))
        mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
        mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
        mark(square(X)) -> a__square(mark(X))
        mark(0) -> 0
        mark(s(X)) -> s(mark(X))
        mark(posrecip(X)) -> posrecip(mark(X))
        mark(negrecip(X)) -> negrecip(mark(X))
        mark(nil) -> nil
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
        mark(rnil) -> rnil
        mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
        a__from(X) -> from(X)
        a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
        a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
        a__pi(X) -> pi(X)
        a__plus(X1, X2) -> plus(X1, X2)
        a__times(X1, X2) -> times(X1, X2)
        a__square(X) -> square(X)
        
)