$\operatorname{Path}\left(e_{1}, e_{2}, L\right)$
If $L=1$ then
If there is an operator 0 converting $e_{1}$ to $e_{2}$ then
return "'yes"'
Else
return "no'"
Endif
Else $(L>1)$
Enumerate all configurations $e^{\prime}$ using an $n$-bit counter
For each $e^{\prime}$ do the following:
Compute $x=\operatorname{Path}\left(e_{1}, \mathrm{e}^{\prime},\lceil L / 2\rceil\right)$
Delete all intermediate work, saving only the return value $x$
Path $\left(e_{1}, e_{2}, L\right)$
If $L=1$ then
If there is an operator $O$ converting $e_{1}$ to $e_{2}$ then
return ''yes''
Else
return 'no''
Endif
Else ( $L>1)$
Enumerate all configurations $e^{\prime}$ using an $n$-bit counter
For each $e^{\prime}$ do the following:
Compute $x=$ Path(e $x, e^{\prime}$, $\left.\lceil L / 2\rceil\right)$
Delete all intermediate work, saving only the return value $x$
Compute $y=$ Path(e', $e_{2}$, $\left.[L / 2\rceil\right)$
Delete all intermediate work, saving only the return value $y$
If both $x$ and $y$ are equal to ' 'yes'', then return ' yes'"
Endfor
If 'yes'' was not returned for any $e^{\prime}$ then
Return 'no' '
Endif
Endif
Compute $y=\operatorname{Path}\left(e^{\prime}, e_{2},\lceil L / 2\rceil\right)$
Delete all intermediate work, saving only the return value $y$
If both $x$ and $y$ are equal to " $y e s^{\prime \prime}$, then return "yes"
Endfor
If "'yes'" was not returned for any $e^{\prime}$ then
Return "no" '
Endif
Endif

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