\documentclass[envcountsect,runningheads,draft]{llncs} %  fails

\newcommand\hmmax{0}
\newcommand\bmmax{0}

\sloppy

\usepackage[nosumlimits,nointlimits,nonamelimits]{amsmath}
\usepackage{amssymb}

\usepackage[colorlinks,linkcolor={blue},citecolor={blue},urlcolor={red},breaklinks=true,final]{hyperref}

\renewcommand{\subsectionautorefname}{Section}%

\newcommand{\xTo}[1]{\,\xRightarrow{#1}\,}
%\newcommand{\lbs}[1]{\,\xRightarrow{#1}\,}
\newcommand{\dhat}[1]{\check{#1}}

\usepackage{lineno}
\linenumbers

\usepackage{etoolbox} %% <- for \cspreto, \csappto

%% Patch 'normal' math environments:  
\newcommand*\linenomathpatch[1]{%
  \cspreto{#1}{\linenomath}%
  \cspreto{#1*}{\linenomath}%
  \csappto{end#1}{\endlinenomath}%
  \csappto{end#1*}{\endlinenomath}%
}

\linenomathpatch{equation}
\linenomathpatch{gather}
\linenomathpatch{multline}
\linenomathpatch{align}
\linenomathpatch{alignat}
\linenomathpatch{flalign}

\usepackage[T1]{fontenc}
\usepackage[final]{graphicx}
\usepackage{color}
%\renewcommand\UrlFont{\color{blue}\rmfamily}
%\urlstyle{rm}
%

\usepackage{etoolbox}
\usepackage{needspace}

\usepackage{hypcap}
\setcounter{tocdepth}{2}

\spnewtheorem{thm}{Theorem}[section]{\bfseries}{\itshape}
\spnewtheorem{cor}[thm]{Corollary}{\bfseries}{\itshape}
\spnewtheorem{lem}[thm]{Lemma}{\bfseries}{\itshape}
\spnewtheorem{prop}[thm]{Proposition}{\bfseries}{\itshape}
\spnewtheorem{defn}[thm]{Definition}{\bfseries}{\upshape}
\spnewtheorem{rem}[thm]{Remark}{\bfseries}{\upshape}
\spnewtheorem{notation}[thm]{Notation}{\bfseries}{\upshape}
\spnewtheorem{expl}[thm]{Example}{\bfseries}{\upshape}
\spnewtheorem{assumption}[thm]{Assumption}{\bfseries}{\upshape}

\renewenvironment{theorem}{\begin{thm}}{\end{thm}}
\renewenvironment{corollary}{\begin{cor}}{\end{cor}}
\renewenvironment{lemma}{\begin{lem}}{\end{lem}}
\renewenvironment{proposition}{\begin{prop}}{\end{prop}}
\renewenvironment{definition}{\begin{defn}}{\end{defn}}
\renewenvironment{remark}{\begin{rem}}{\end{rem}}
\renewenvironment{example}{\begin{expl}}{\end{expl}}

%\renewcommand{\sectionautorefname}{Section}%
%\renewcommand{\subsectionautorefname}{Section}%

\let\vec\relax % 
\usepackage{accents}
\newcommand\thickbar[1]{\accentset{\rule{.55em}{.6pt}}{#1}}

\sloppy

\usepackage{wasysym} %Pouya: I added this package for auxillary compositions.
\usepackage{cancel}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{decorations}           % Required for all decorations
\usetikzlibrary{decorations.pathmorphing} % Specifically for 'zigzag'

\tikzset{
  commutative diagrams/.cd,
  arrow style = tikz,
  diagrams    = {>=stealth},
  row sep     = large, 
  column sep  = huge
}

\usepackage{textcomp}

\usepackage{enumitem} 
%\setlist{itemsep=0ex}
\setlist[itemize]{label={\small$\bullet$}}

\BeforeBeginEnvironment{align}{\noindent\ignorespaces}

\usepackage{todos}
\usepackage{proof}
\usepackage{xspace}
\usepackage{bm}

\input{catprog}

%\usepackage{pict2e}

%\DeclareRobustCommand{\pigpenA}{%
%  \begingroup\setlength{\untlength}{1em}%
%  \linethickness{.075em}%
%  \begin{picture}(1,.8)
%  \roundcap\roundjoin
%  \polyline(.2,.2)(.8,.2)(.8,.8)
%  \end{picture}%
%  \endgroup
%}

\newcommand{\lbs}[1]{
  \mathrel{%
    \tikz{
      \draw[double, double distance=.75pt, -{Stealth[inset=0pt, angle=75:4pt]}]
       	(0,.3) -- node[inner sep=0pt,above=1.75pt,midway] {\scriptsize$#1$} (.5,.3);
    }
  }
}

\newcommand{\pbk}{\arrow[dr, phantom, "\text{\tiny\pigpenA}", pos=0.05]}

\newcommand{\Fst}{\Pi_1} %{\oname{Fst}} 
\newcommand{\Snd}{\Pi_2} %{\oname{Snd}} 
\newcommand{\klstar}{\sharp}  			%% Kleisli star
\newcommand{\istar}{\dagger}  	
		
\newcommand{\mSv}{\mS_\val}
\newcommand{\mSc}{\mS_\com}
\newcommand{\mSl}{\mS_\lambda}

\newcommand{\Sigmas}{\Sigma^\star}

\newcommand{\ar}{\oname{ar}}

\newcommand{\oWh}{\oname{while}}
\newcommand{\oIf}{\oname{if}}
\newcommand{\oPut}{\oname{put}}
\newcommand{\oGet}{\oname{get}}
\newcommand{\oSeq}{\oname{seq}}

\newcommand{\app}{\,}
\usepackage{proof}
\newcommand{\inference}[2]{\infer{~#2~}{~#1~}}

\newcommand{\St}{\Gamma}

\newcommand{\exend}{\hfill{\rotatebox[origin=c]{45}{$\Box$}}}

\makeatletter
\let\dir@frac\frac
\newcommand{\inv@frac}[2]{\dir@frac{#2}{#1}}

\renewcommand{\frac}{\@ifstar{\inv@frac}{\dir@frac}}
\makeatother

%\renewcommand{\dar}{\kern1.2pt\operatorname{\downarrow}\kern1pt}

\newcommand{\G}{\St}
\newcommand{\D}{\Delta}

%\usepackage{txfonts}
%\usepackage{newtxtext,newtxmath}   
  
\newcommand{\mon}{\bullet}
\newcommand{\monto}{\mathrel{-}\joinrel\mathrel{\bullet}} %{\multimapdot}
\newcommand{\Pt}{V}

\newcommand{\dc}{\mspace{\medmuskip};\mspace{.5\medmuskip}}
\newcommand{\sep}{,\mspace{\medmuskip}}

\newcommand{\xCL}{\textbf{xCL}\xspace}  
\newcommand{\xTCL}{\textbf{xTCL}\xspace}  	
\newcommand{\Ty}{\mathsf{Ty}\xspace}
\newcommand{\Tr}{\mathsf{Tr}\xspace}
\newcommand{\arty}[2]{#1 \rightarrowtriangle #2}
\newcommand{\initob}{\textbf{0}}
\newcommand{\termob}{\textbf{1}}
\newcommand{\tcomp}{\textsf{comp}}
\newcommand{\unt}{\mathsf{unit}}
\newcommand{\true}{\mathsf{true}}
\newcommand{\false}{\mathsf{false}}	
\newcommand{\bool}{\mathsf{bool}}	
\newcommand{\fpc}{\mathsf{fix}}	
\newcommand{\casec}{\mathsf{if}}
\newcommand{\ndet}{\oplus} 					%{\;\ensuremath{\boldsymbol{\pmb{\oplus}}}\;}
\newcommand{\paral}{\parallel}			%{\;\ensuremath{\boldsymbol{\pmb{\mid\mid}}}\;}
\newcommand{\nDownarrow}{\cancel{\Downarrow}}
\newcommand{\paralv}{\mathrel{%
		\mathchoice{\PARV}{\PARV}{\scriptsize\PARV}{\tiny\PARV}
}}

\def\PARV{{%
		\setbox0\hbox{$\parallel$}%
		\rlap{\hbox to \wd0{\hss\rule[-.5ex]{.75em}{.12ex}\hss}}\box0
}}


\usepackage{ifdraft} 
\ifdraft{
%  \usepackage{showframe}
  \usepackage{showlabels} 
  \renewcommand{\showlabelfont}{\ttfamily\scriptsize}
  \usepackage[layout=footnote,draft]{fixme}

%  \usepackage[notcite,notref]{showkeys}
%  \renewcommand*\showkeyslabelformat[1]{%
%  \raisebox{1ex}{\raggedleft{\textit{\tiny #1}}}
}{
 \usepackage[layout=footnote,final]{fixme}
}

\FXRegisterAuthor{sg}{asg}{SG}	% Sergey
\FXRegisterAuthor{pp}{app}{PP}	% Pouya

\usepackage{savesym}

\savesymbol{degree}
\savesymbol{leftmoon}
\savesymbol{rightmoon}
\savesymbol{fullmoon}
\savesymbol{newmoon}
\savesymbol{diameter}
\savesymbol{emptyset}
\savesymbol{bigtimes}
%\savesymbol{blacktriangleright}
\savesymbol{triangleright}

\savesymbol{langle}
\savesymbol{rangle}

\usepackage[matha,mathx]{mathabx}

\restoresymbol{other}{langle}
\restoresymbol{other}{rangle}
\restoresymbol{other}{emptyset}
\restoresymbol{other}{triangleright}  

\usepackage{adjustbox}
% For size of diagrams.

% document specific
\newcommand{\val}{\mathsf{v}}
\newcommand{\com}{\mathsf{c}}
\newcommand{\nats}{\mathbb{N}}
\newcommand{\ints}{\mathbb{Z}}
\newcommand{\mS}{\mu\Sigma}
\newcommand{\bss}{\oname{bs}}
\renewcommand{\paragraph}[1]{\medskip\noindent{\bfseries\sffamily #1.}}
\renewcommand{\comp}{\cdot}
\newcommand{\dist}{\oname{dist}}
\newcommand{\ldist}{\oname{dist}'}
\newcommand{\zero}{\oname{o}}
\newcommand{\suc}{\oname{s}}
\newcommand{\init}{\oname{init}}
\newcommand{\primr}{\oname{primr}}

\newcommand{\peval}{\frak{p}}
\newcommand{\teval}{\frak{t}}
\newcommand{\neval}{\frak{n}}
\newcommand{\rcomp}{\mathbin{\raisebox{1pt}{\scalebox{.6}{$\RIGHTcircle$}}}}
\newcommand{\lcomp}{\mathbin{\raisebox{1pt}{\scalebox{.6}{$\LEFTcircle$}}}}
\newcommand{\fcomp}{\mathbin{\raisebox{1pt}{\scalebox{.6}{$\CIRCLE$}}}}%Pouya: I added these three.
\newcommand{\tsto}{\leftrightarrow}
\newcommand{\ba}{\Downarrow}
%\newcommand{\bba}{\pmb{\Downarrow}}
\newcommand{\ssim}{\mathrel{\pmb{\sim}}}
\newcommand{\hatssim }{\mathrel{\hat{\ssim}}}
\newcommand{\dhatssim }{\mathrel{\dhat{\ssim}}}
\newcommand{\klplus}{\boxplus}
\newcommand{\coit}{\mathsf{coit}}
\newcommand{\itt}{\mathsf{it}}
\newcommand{\eval}{\mathsf{eval}}
\newcommand{\refl}{\mathsf{refl}}
\newcommand{\trans}{\mathsf{trans}}
\newcommand{\preord}{\mathbf{PreOrd}}
\newcommand{\rel}{\mathbf{Rel}}
\newcommand{\gra}{\mathbf{Gra}}
\newcommand{\obj}{\mathbf{Obj}}


\newcommand{\bba}{
\mathrel{%
    \begin{tikzpicture}[baseline=-6pt]
      \draw[double, double distance=.75pt, -{Stealth[inset=0pt, angle=75:4pt]}] (0,.02) -- (0,-.28);
    \end{tikzpicture}%
  }%
}

\usepackage[final]{listings}

\lstset{
  language=Haskell
   %,xleftmargin=2.0cm
  , basicstyle=\small
  , commentstyle=\color{gray}
  , stringstyle=\itshape   % string literal style
  , keepspaces=true       % keeps spaces in text, useful for keeping indentation of code
  , numbers=none          % possible values are (none, left, right)
  , identifierstyle={\itshape}
  , flexiblecolumns={true}
  , showstringspaces={false}
   %,mathescape={true}
  , captionpos=b
  , deletekeywords={join,return,Eval,Left,Either,Right,id,either,Void,Functor,Monad}
%  , morekeywords={Free}
  , emphstyle=\slshape
  , literate={\\}{{$\lambda$}}1 {->}{{$\rightarrow$}}2
  , literate=
     {'}{$\,{}^\prime$\!}1
     {+s}{{$\,$}}1
     {\\}{{$\lambda$}}1
     {lnot}{$\lnot$}3
     {=>}{{$\Rightarrow$}}1
     {<=}{{$\leq$}}1
     {<<-}{{$\in$}}1
     {<<=}{{$\subseteq$}}1
     {>>=}{{$\gg\kern-1pt=$}}1
     {++}{{$\varoplus$}}2
     {|->}{{$\mapsto$}}1
     {->}{{$\rightarrow$}}1
     {->d}{{$\rightarrow_\delta$}}2
     {->b}{{$\rightarrow_\beta$}}2
     {->bd}{{$\rightarrow_{\beta\delta}^*$}}2
     {::=}{{$:=$}}2
     {:=}{{$\mapsto$}}1
     {alpha}{{$\alpha$}}1
     {UU}{{$\cup$}}1
     {All}{{${\forall}\!\!\!\!$}}1
}


\setcounter{totalnumber}{1} % No two figures in one page

\begin{document}\allowdisplaybreaks

\let\cedilla\c
\renewcommand{\c}{\colon}

%
\title{Weak Similarity for Strongly Separated HO-GSOS.}
%
%\titlerunning{Abbreviated paper title}
% If the paper title is too long for the running head, you can set
% an abbreviated paper title here
%
\author{Sergey Goncharov\inst{1}\orcidID{0000-0001-6924-8766} \and
Pouya Partow\inst{1}\orcidID{0009-0003-9652-9469}}
%
\authorrunning{S.~Goncharov, P.~Partow}
% First names are abbreviated in the running head.
% If there are more than two authors, 'et al.' is used.
%
\institute{University of Birmingham, UK\\
\email{\{s.goncharov,p.partow\}@bham.ac.uk}}
%
\maketitle              % typeset the header of the contribution
%
\begin{abstract}
	Hello simulation!
\end{abstract}
%
%
%

\end{document}














