Consider the following productions system where Working Memory $(WM)=\{-2\}$

Time left $0\mathrm{.}3$

List of Rules:

$($R$1)$ if $x$ in WM then add $x+1$ to WM$.$

$($R$2)$ if $x$ in WM and $x$ is odd then add $x+4$ to WM $.$

$($R$3)$ if $x$ in WM and $x$ is odd and $x>0$ then add $x-3$ to WM$.$

$($R$4)$ if $5$ in WM then print $"Hr".$

$($R$5)$ if $7$ in WM then print $"$OK$\text{'}$

Conflict Resolution:

$($a$)$ Ordering

$($O$1)R{1}^{3}R{2}^{3}R{3}^{3}R{4}^{3}R5$

$($O$2)R{5}^3{R}_4^3{R}_3=R_2=R1$

$($b$)$ Recency: rules more recently added take priority during conflict

$($c$)$ Refractoriness once: A rule that was selected in the previous cycle is excluded

$($d$)$ Specificity: rules with more specific antecedents$/$conditions are favored

We employ RoD in case we have one rule applicable to different data

i$.$e$.$ if there is one rule $R$ that is applicable to more than one data in WM$,$ then add R to the most recently added data to WM

Cycle No$.$

Applicable rules

Selected rule

Updated$-$WM

$1.$

$R\frac{1}{-}2$

R$1$

$\{-2,-1\}$

$2.$

R$1,$R$2$

R$2$

$\{-2,-1,3\}$