breq r$1$

s$00$

s$10$

acq r$1$

req r$2$

s$30$

acq r$2$

s$40$

rel r$2$

req r$2$

s$01$

rel r$1$

s$20$

s$11$

s$21$

s$31$

s$41$

rel r$2$

p$2$

acq r$2$

s$02$

s$12$

s$22$

s$32$

rel r$1$

req r$1$

s$03$

s$13$

$$23$

s$33$

acq r$1$

s$04$

s$14$

If p$2$ now requests r$1,$ the cycle closes and both processes become blocked in s$33.$ State s$33$ is a deadlock

aptions

state.

$1.$ Initially, in state s$00,$ no resources are allocated to either p$1$ or p$2.$

$2.$ When p$2$ is not using any resources, p$1$ can repeatedly request, acquire, and release both r$1$ and r$2$ in the specified order.

$3.$ Similarly, when p$1$ is not using any resources, p$2$ can repeatedly request, acquire, and release both r$2$ and r$1$ in the specified

order.

$4.$ When p$1$ and p$2$ execute concurrently, other states can be reached, each representing a different snapshot of requests and

allocations by the two processes.

$5.$ In state s$04,$ p$2$ is holding both r$2$ and r$1.$ p$1$ has not taken any action and thus has no edges to either resource.

$6.$ If p$1$ now requests r$1,$ p$1$ becomes blocked in state s$14$ because r$1$ is already held by p$2$ and cannot be acquired by p$1.$ No horizontal transition out of s$14$ exists.

$7.$ When p$2$ releases r$1,$ both processes are again unblocked in state s$12.$

$8.$ p$1$ can now acquire r$1$ and request r$2,$ becoming blocked again in s$32.$

$9.$ If p$2$ now requests r$1,$ the cycle closes and both processes become blocked in s$33.$ State s$33$ is a deadlock state.