I hit that stumbling block as well. I handwaved it by saying “continue iterating until you have x(k,B) and x(k,G) such that f(xk,B)<0, f(xk,G)≥0, and f has no local maxima or local minima on the open interval (xk,B,xk,G)”, but that doesn’t work for the Weierstrass function, which will (I believe) never meet that criterion.
I hit that stumbling block as well. I handwaved it by saying “continue iterating until you have x(k,B) and x(k,G) such that f(xk,B)<0, f(xk,G)≥0, and f has no local maxima or local minima on the open interval (xk,B,xk,G)”, but that doesn’t work for the Weierstrass function, which will (I believe) never meet that criterion.