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\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\[\axjustifies\trans{\lambda}{\Nil}{\left(\Nil,\emptyset\right)}{\Nil}{\Nil}{\left(\Nil,\emptyset\right)}\using{\rlambdans}\]
\justifies{}\trans{\StmOutput}{\Nil}{\left(\texttt{""}:\Nil,\emptyset\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\routputns}\]
\justifies{}\trans{\StmPush~\texttt{""}:\StmOutput}{\Nil}{\left(\Nil,\emptyset\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}o"}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}o"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rexecns}\]
\justifies{}\trans{\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}o"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rgetns}\]
\justifies{}\trans{\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\texttt{"\textquotedblright{}\textquotedblright{}o"}:\texttt{""}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}
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"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rputns}\]
\justifies{}\trans{\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}o"}:\texttt{""}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}
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"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}
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"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmPut:\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\texttt{"\textquotedblright{}\textquotedblright{}
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"}:\texttt{""}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rputns}\]
\justifies{}\trans{\StmGet:\StmPut:\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{"input"}:\texttt{"\textquotedblright{}\textquotedblright{}
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"}:\texttt{""}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rgetns}\]
\justifies{}\trans{\StmPush~\texttt{"input"}:\StmGet:\StmPut:\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}
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"}:\texttt{""}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmCat:\StmPush~\texttt{"input"}:\StmGet:\StmPut:\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{"
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"}:\texttt{"\textquotedblright{}\textquotedblright{}"}:\texttt{""}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rcatns}\]
\justifies{}\trans{\StmPush~\texttt{"
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"}:\StmCat:\StmPush~\texttt{"input"}:\StmGet:\StmPut:\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}"}:\texttt{""}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmQuotify:\StmPush~\texttt{"
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\justifies{}\trans{\StmGet:\StmQuotify:\StmPush~\texttt{"
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