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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{\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{"input"}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}o"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rgetns}\]
\justifies{}\trans{\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}o"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmPut:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\texttt{"\textquotedblright{}\textquotedblright{}o"}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rputns}\]
\justifies{}\trans{\StmPush~\texttt{""}:\StmPut:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}o"}:\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"},\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rpushns}\]
\justifies{}\trans{\StmPush~\texttt{"\textquotedblright{}\textquotedblright{}o"}:\StmPush~\texttt{""}:\StmPut:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\Nil,\{\texttt{""}\mapsto\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"},\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:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{""}:\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"}:\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:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{"input"}:\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"}:\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:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"}:\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:\StmPush~\texttt{"input"}:\StmGet:\StmGet:\StmExec}{\Nil}{\left(\texttt{"\textquotedblright{}\textquotedblright{}\textquotedblright{}\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gh\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gt\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}o\textbackslash{}\textquotedblright{}+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}g\textbackslash{}\textquotedblright{}gq\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}gq++\textbackslash{}\textquotedblright{}p\textbackslash{}\textquotedblright{}g+\textbackslash{}\textquotedblright{}s\textbackslash{}\textquotedblright{}gp\textbackslash{}\textquotedblright{}\textbackslash{}\textquotedblright{}pgx\textquotedblright{}\textquotedblright{}p\textquotedblright{}p\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gh\textquotedblright{}g\textquotedblright{}g+\textquotedblright{}g\textquotedblright{}p\textquotedblright{}s\textquotedblright{}gt\textquotedblright{}s\textquotedblright{}p\textquotedblright{}s\textquotedblright{}g\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}o\textquotedblright{}+\textquotedblright{}s\textquotedblright{}gq\textquotedblright{}g\textquotedblright{}gq\textquotedblright{}p\textquotedblright{}gq++\textquotedblright{}p\textquotedblright{}g+\textquotedblright{}s\textquotedblright{}gp\textquotedblright{}\textquotedblright{}pgx"}:\texttt{"\textquotedblright{}\textquotedblright{}"}:\Nil,\{\texttt{"input"}\mapsto\texttt{""}\}\right)}{\Nil}{\texttt{""}:\Nil}{\left(\Nil,\emptyset\right)}\using{\rcatns}\]
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