Singular

Please note that there is a simple typo in f_2:
f_2=(l(3))*s(2)*c(1)+(l(3))*c(2)*s(1)+(l(2))*s(1)+(-b);

Hello,
for some time I've been trying the "reverse-kinematic-example" in the book (section 6, §3).
Unfortunately I don't get the solution the author has calculated in the book.
Could someone give me some hint for the corresponding singular code?
Below the code I tried so far:

[code]
ring R=(0,a,b,l(2),l(3)),(c(2),s(2),c(1),s(1)),lp;
poly f_1=l(3)*c(1)*c(2)-l(3)*s(1)*s(2)+l(2)*c(1)-a;
poly f_2=l(3)*c(1)*c(2)+l(3)*c(2)*s(1)+l(2)*s(1)-b;
poly f_3=c(1)^2+s(1)^2-1;
poly f_4=c(2)^2+s(2)^2-1;
ideal I = f_1, f_2, f_3, f_4;
option(redSB);
ideal G=std(I);
G;
[/code]

Many thanks,
MK