Lengyel's period conjecture for two transfer games

Let $L(b;x_1,y_1;x_2,y_2)$ be the vector subtraction game with move set

$$\{(0,-b),(-x_1,y_1),(-x_2,y_2)\},$$

where $b,x_1,x_2\in\mathbb{N}^+$ and $y_1,y_2\in\mathbb{N}$. A period $(p,q)$ means that the game's pattern repeats under translation by $(p,0)$ and $(0,q)$.

Lengyel's conjecture. (a) If $b$ is odd and at least $3$, then $L(b;b,0;1,1)$ has period $(2b(b+1),2b)$. (b) For $b\geq 2$, $L(b;1,0;1,1)$ has period $(4b,2b)$.

These claims extend Lengyel's proved special cases for periods of vector subtraction games. The parser supplies no evidence that either assertion has been resolved, so they remain open.