\newcommand{\QED}{\rule{2mm}{3mm}}
%\newcommand{\qed}{\mbox{$\Box$}}

\newcommand{\aplica}{\longrightarrow}              

\newcommand{\epi}{\fl{{\rm epi}}}
\newcommand{\fl}[1]{\  {\stackrel {#1} {\longrightarrow}}\ }
\newcommand{\cg}[1]{\mathrel{\sim_{#1}}}
\newcommand{\M}{{\cal M}}
\newcommand{\Ml}{{\cal S}^1}

\newcommand{\SB}{{\cal S}}
\newcommand{\T}{{\mathord{\cal T}}}
\newcommand{\Om}{\Omega}

\newcommand{\eqdef} {\ \stackrel{\rm def}{=\!\!=}\ }
\newcommand{\sss}   {\Longleftrightarrow}
\newcommand{\sssdef}{\ \stackrel{\rm def}{\Longleftrightarrow}\ }
\newcommand{\implica}{\mathrel{\Longrightarrow}}
\newcommand{\e}{,\ }
\newcommand{\teto}[1]{\lceil {#1} \rceil}
\newcommand{\chao}[1]{\lfloor {#1} \rfloor}
\newcommand{\set}[2]{{\{#1\mathrel{|}#2\}}}
\newcommand{\setbegin}[2]{{\{#1\mathrel{|}#2}}
\newcommand{\setend}{{\}}}

\newcommand{\per}[1]{\mathord{\mathop{\rm per}({#1})}}
\newcommand{\Pref}[1]{\mathord{\mathop{\rm Pref}({#1})}}
\newcommand{\Suf}[1]{\mathord{\mathop{\rm Suf}({#1})}}
\newcommand{\Fat}[1]{\mathord{\mathop{\rm Fat}({#1})}}

\newcommand{\encaixe}[2]{{#1}{\mathbin{\rightleftharpoons}}{#2}}
\newcommand{\bdir}[1]{\mathord{\mathop{\rm b_{R}}({#1})}}
\newcommand{\besq}[1]{\mathord{\mathop{\rm b_{L}}({#1})}}
\newcommand{\basis}[1]{\mathord{\mathop{\rm bas}({#1})}}

\newcommand{\gr}{\mathrel{{\cal R}}}
\newcommand{\gl}{\mathrel{{\cal L}}}
\newcommand{\gj}{\mathrel{{\cal J}}}
\newcommand{\gh}{\mathrel{{\cal H}}}
\newcommand{\gd}{\mathrel{{\cal D}}}
\newcommand{\grl}{\mathrel{{\cal R'}}}
\newcommand{\gll}{\mathrel{{\cal L'}}}
\newcommand{\gjl}{\mathrel{{\cal J'}}}
\newcommand{\ghl}{\mathrel{{\cal H'}}}
\newcommand{\gdl}{\mathrel{{\cal D'}}}
\newcommand{\ltgr} {\mathrel{<_{\cal R}}}
\newcommand{\leqgr}{\mathrel{\leq_{\cal R}}}
\newcommand{\ltgl} {\mathrel{<_{\cal L}}}
\newcommand{\leqgl}{\mathrel{\leq_{\cal L}}}
\newcommand{\ltgj} {\mathrel{<_{\cal J}}}
\newcommand{\leqgj}{\mathrel{\leq_{\cal J}}}
\newcommand{\rclass}[1]{{\rm R}_{#1}}
\newcommand{\lclass}[1]{{\rm L}_{#1}}
\newcommand{\jclass}[1]{{\rm J}_{#1}}
\newcommand{\hclass}[1]{{\rm H}_{#1}}
\newcommand{\dclass}[1]{{\rm D}_{#1}}
\newcommand{\rset}{{\frak R}}
\newcommand{\lset}{{\frak L}}
\newcommand{\grcac}[1]{\mathord{\mathop{{\rm cactus_{\gr}}}({#1})}}
\newcommand{\glcac}[1]{\mathord{\mathop{{\rm cactus_{\gl}}}({#1})}}
\newcommand{\rent}{$\gr$-entra\-da}
\newcommand{\rents}{$\gr$-entra\-das}
\newcommand{\lent}{$\gl$-entra\-da}
\newcommand{\lents}{$\gl$-entra\-das}
\newcommand{\ent}{$\gd$-entra\-da}
\newcommand{\ents}{$\gd$-entra\-das}
\newcommand{\sd}{se\-qüên\-cia de}
\newcommand{\ode}{ocor\-rên\-cia de \ent}
\newcommand{\odes}{ocor\-rên\-cias de \ents}
\newcommand{\sdodes}{\sd\ ocor\-rên\-cias de \ents}
\newcommand{\odt}{ocor\-rên\-cia de tran\-si\-ção}
\newcommand{\odts}{ocor\-rên\-cias de tran\-si\-ções}
\newcommand{\sdodts}{\sd\ ocor\-rên\-cias de tran\-si\-ções}
\newcommand{\sdts}{\sd\ tran\-si\-ções}
\newcommand{\cgreg}{$\cgAToS$-re\-gu\-lar}
\newcommand{\cgirreg}{$\cgAToS$-ir\-re\-gu\-lar}
\newcommand{\cgirregs}{$\cgAToS$-ir\-re\-gu\-la\-res}
\newcommand{\cgidemp}{$\cgAToS$-idem\-po\-ten\-te}

\newcommand{\ltr}{\mathrel{\prec}}
\newcommand{\leqr}{\mathrel{\preccurlyeq}}
\newcommand{\asuf}{\mathrel{\rm era_{\rm suff} }}
\newcommand{\apref}{\mathrel{\rm era_{\rm pref} }}
\newcommand{\Rdir}{\mathrel{\rm Rel_{\rm R} }}
\newcommand{\Resq}{\mathrel{\rm Rel_{\rm L} }}
\newcommand{\sufa}[2]{{\rm suff_{era}}\Parordenado{#1}{#2}}
\newcommand{\prefa}[2]{{\rm pref_{era}}\Parordenado{#1}{#2}}
\newcommand{\removedir}{\mathbin{-\!\!\!\!\shortparallel}}
\newcommand{\removeesq}{\mathbin{\shortparallel\!\!\!\!-}}
\newcommand{\tracedir}{\mathbin{\otimes_{\rm R}}}
\newcommand{\traceesq}{\mathbin{\otimes_{\rm L}}}
\newcommand{\trace}[1]{\otimes({#1})}
\newcommand{\irred}[1]{\mathord{\mathop{\rm irred}({#1})}}

\newcommand{\PI} {\mathord{\pi}}
\newcommand{\Pl} {\mathord{\pi'}}
\newcommand{\Sg} {\mathord{\Sigma}}
\newcommand{\Sl} {\mathord{\Sigma'}}
\newcommand{\Sll}{\mathord{\Sigma''}}
\newcommand{\CG} {\cg\Pl}

\newcommand{\mdc}[2]{\mathord{\mathop{\rm gcd}\Parordenado{#1}{#2}}}

\newcommand{\expande}{\mathrel{\Rightarrow}}
\newcommand{\expkt}[2]{\mathrel{\Rightarrow^{#1}_{#2}}}
\newcommand{\exps}[3]{{#1}: {#2} \Rightarrow {#3}}

\newcommand{\seq}[1]{\{{#1}_i\}}

\newcommand{\myAnd}{e}
\newcommand{\nm}{$n \geq 4$ \myAnd\ $m \geq 1$}
\newcommand{\nmnew}{$n \geq 3$ \myAnd\ $m \geq 1$}
\newcommand{\nmdelta}{$n=3$ \myAnd\ $m\geq1$}
\newcommand{\nmnewrest}{$n\geq1$ \myAnd\ $m\geq1$}
\newcommand{\nmrest}{$n\geq2$ \myAnd\ $m\geq1$}
\newcommand{\nmtwoone}{$n\geq2$ \myAnd\ $m=1$}
\newcommand{\nmtwotwo}{$n=2$ \myAnd\ $m\geq2$}
\newcommand{\nmtwo}{$n\geq2$ \myAnd\ $m\geq1$}
\newcommand{\nmgr}{$n=1$ \myAnd\ $m\geq1$}

\newcommand{\av}{de Luca \myAnd\ Varricchio}
\newcommand{\Av}{De Luca \myAnd\ Varricchio}
\newcommand{\mccam}{McCammond}
\newcommand{\guba}{Guba}
\newcommand{\jojo}{Brzozowski}
\newcommand{\kapo}{Ka\v{d}ourek \myAnd\ Pol{\'a}k}

\newcommand{\dbl}{de Burnside livre}
\newcommand{\dbls}{de Burnside livre satisfazendo}
\newcommand{\dbL}{de Burnside livres}
\newcommand{\dbLs}{de Burnside livres satisfazendo}
\newcommand{\cdbl}{gru\-pói\-de \dbl}
\newcommand{\cdbls}{gru\-pói\-de \dbls}
\newcommand{\gdbl}{grupo \dbl}
\newcommand{\gdbls}{grupo \dbls}
\newcommand{\mdbl}{mo\-nói\-de \dbl}
\newcommand{\mdbls}{mo\-nói\-de \dbls}
\newcommand{\sdbl}{semigrupo \dbl}
\newcommand{\sdbls}{semigrupo \dbls}
\newcommand{\csdbl}{gru\-pói\-des \dbL}
\newcommand{\gsdbl}{grupos \dbL}
\newcommand{\msdbl}{mo\-nói\-des \dbL}
\newcommand{\ssdbl}{semigrupos \dbL}

\newcommand{\tdm}{teorema dos marcadores}
\newcommand{\tdc}{teorema da caracterização}
\newcommand{\tdgm}{teorema dos grupos maximais}
\newcommand{\lds}{lema da substituição}
\newcommand{\lgr}{lema de Green}

\newcommand{\s}[1]{{\sigma_{#1}}}
\newcommand{\z}[1]{{\tau_{#1}}}

\newcommand{\N}{\mathbb{N}}     %{{\rm I\!N}}



\newcommand{\cat}[1]{\mathord{\mathcal{#1}}}
\newcommand{\catmult}{\mathop{\cdot}}
\newcommand{\concat}{\catmult}
\newcommand{\grafo}[1]{\mathord{\mathbf{#1}}}

\newcommand{\function}[2]{\mathord{#1}(#2)}
\newcommand{\functionarray}[2]{\mathord{#1}[#2]}
\newcommand{\subfunction}[2]{\mathord{{#1}_{#2}}}


\newcommand{\aresta}[1]{\subfunction{a}{{#1}}}  
\newcommand{\arestas}[1]{\function{E}{\grafo{#1}}}
\newcommand{\vertices}[1]{\function{V}{\grafo{#1}}}
\newcommand{\iniciosym}{\alpha}
\newcommand{\inicio}[1]{\function{\iniciosym}{#1}}
\newcommand{\terminosym}{\omega}
\newcommand{\termino}[1]{\function{\terminosym}{#1}}
\newcommand{\inicios}[2]{\function{\iniciosym_{#1}}{\grafo{#2}}}
\newcommand{\terminos}[2]{\function{\terminosym_{#1}}{\grafo{#2}}}
\newcommand{\iniciolsym}{\alpha'}
\newcommand{\iniciol}[1]{\function{\iniciolsym}{#1}}
\newcommand{\terminolsym}{\omega'}
\newcommand{\terminol}[1]{\function{\terminolsym}{#1}}
\newcommand{\iniciosl}[2]{\function{\iniciolsym_{#1}}{\grafo{#2}}}
\newcommand{\terminosl}[2]{\function{\terminolsym_{#1}}{\grafo{#2}}}
\newcommand{\normalizantesym}{\gamma}
\newcommand{\normalizante}[1]{\subfunction{\normalizantesym}{#1}}
\newcommand{\normalizacaosym}{\lambda}
\newcommand{\normalizacao}[1]{\function{\normalizacaosym}{#1}}
\newcommand{\inormalizacao}[1]{\function{\normalizacaosym^{-1}}{#1}}
\newcommand{\rotulosym}{\normalizacaosym}
\newcommand{\rotulo}[1]{\function{\rotulosym}{#1}}
\newcommand{\fumsym}{\varphi}
\newcommand{\fum}[1]{\function{\fumsym}{#1}}
\newcommand{\ifum}[1]{\function{\fumsym^{-1}}{#1}}
\newcommand{\frumsym}[1]{\mathord{\fumsym|_{#1}}}
\newcommand{\frum}[2]{\function{\frumsym{#1}}{#2}}
\newcommand{\fdoissym}{\delta}
\newcommand{\fdois}[1]{\function{\fdoissym}{#1}}
\newcommand{\ifdois}[1]{\function{\fdoissym^{-1}}{#1}}
\newcommand{\frdoissym}[1]{\mathord{\fdoissym|_{#1}}}
\newcommand{\frdois}[2]{\function{\frdoissym{#1}}{#2}}
\newcommand{\Rentsym}{\mathord{\epsilon_R}}
\newcommand{\Rent}[1]{\function{\Rentsym}{#1}}
\newcommand{\Lentsym}{\mathord{\epsilon_L}}
\newcommand{\Lent}[1]{\function{\Lentsym}{#1}}
\newcommand{\Obj}[1]{\function{\mathrm{Obj}}{\cat{#1}}}
\newcommand{\passeio}[1]{\subfunction{p}{{#1}}}
\newcommand{\passeioq}[1]{\subfunction{q}{{#1}}}  
\newcommand{\ocorrenciassym}[1]{\#_{{#1}}}
\newcommand{\ocorrencias}[2]{\function{\ocorrenciassym{#1}}{#2}}
\newcommand{\caracteristicasym}[1]{\chi_{{#1}}}
\newcommand{\caracteristica}[2]{\function{\caracteristicasym{#1}}{#2}}
\newcommand{\JB}[1]{\function{J}{#1}}
\newcommand{\MB}[1]{\function{M}{#1}}
\newcommand{\BB}[1]{\function{B}{#1}}
\newcommand{\GB}[1]{\function{\grafo{G}}{#1}}
\newcommand{\Jk}[1]{\subfunction{J}{#1}}
\newcommand{\Mk}[1]{\subfunction{M}{#1}}
\newcommand{\Bk}[1]{\subfunction{B}{#1}}
\newcommand{\Gk}[1]{\subfunction{\grafo{G}}{#1}}
\newcommand{\Comb}[2]{\binom{#1}{#2}}
\newcommand{\repsym}{\mathrm{rep}}
\newcommand{\rep}[1]{\function{\repsym}{#1}}


\newcommand{\identidade}[1]{\subfunction{1}{#1}}
\newcommand{\local}[2]{\subfunction{\cat{#1}}{#2}}

\newcommand{\x}{\,}
\newcommand{\tq}{\mathrel{|}}
\newcommand{\Par}[1]{({#1}^{n+m},{#1}^n)}
\newcommand{\ParOrdenado}[2]{({#1},{#2})}
\newcommand{\cgsint}[1]{\mathrel{\equiv_{#1}}}

\newcommand{\AToSsym}{\mathord{\widetilde{\mbox{ }}}}
\newcommand{\AToS}[1]{\mathord{\widetilde{{#1}}}}
\newcommand{\iAToS}[1]{\function{\AToSsym^{-1}}{#1}}
\newcommand{\cgAToS}{\sim}
\newcommand{\conteudosym}{c}
\newcommand{\conteudo}[1]{\function{\conteudosym}{#1}}
\newcommand{\AToKsym}{\sigma}
\newcommand{\AToK}[1]{\function{\AToKsym}{#1}}
\newcommand{\KToAsym}{\tau}
\newcommand{\KToA}[1]{\function{\KToAsym}{#1}}
\newcommand{\KToHsym}{\theta}
\newcommand{\KToH}[1]{\function{\KToHsym}{#1}}
\newcommand{\iKToH}[1]{\function{\KToHsym^{-1}}{#1}}
\newcommand{\KToBsym}{\mathord{\widehat{\ }}}
\newcommand{\iKToBsym}{(\KToBsym)^{-1}}
\newcommand{\KToB}[1]{\mathord{\widehat{#1}}}
\newcommand{\iKToB}[1]{\function{\KToBsym^{-1}}{#1}}
\newcommand{\cgKToB}{\cong}
\newcommand{\HToBsym}{\phi}
\newcommand{\HToB}[1]{\function{\HToBsym}{#1}}
\newcommand{\HToKsym}{\beta}
\newcommand{\HToK}[1]{\function{\HToKsym}{#1}}
\newcommand{\HToHsym}{\mathord{\KToHsym\circ\HToKsym}}
\newcommand{\HToH}[1]{\function{\HToHsym}{#1}}
\newcommand{\cgHToB}{\approx}

\newcommand{\radqsym}{\mathord{\eta}}
\newcommand{\radq}[1]{\subfunction{\radqsym}{#1}}
\newcommand{\ladqsym}{\mathord{\mu}}
\newcommand{\ladq}[1]{\subfunction{\ladqsym}{#1}}
\newcommand{\adeqsym}{\mathord{\psi}}
\newcommand{\adeq}[1]{\function{\adeqsym}{#1}}
\newcommand{\adeqrsym}{\mathord{\adeqsym^R}}
\newcommand{\adeqr}[1]{\function{\adeqrsym}{#1}}
\newcommand{\adeqlsym}{\mathord{\adeqsym^L}}
\newcommand{\adeql}[1]{\function{\adeqlsym}{#1}}

\newcommand{\cyr}{}
\newcommand{\noref}[1]{}
\newcommand{\defin}[2]{\emph{#1}\index{#2}}
\newcommand{\definition}[1]{\defin{#1}{#1}}

\newcommand{\range}{\mathinner{\ldotp\ldotp}}

%\newcommand{\SuffixTree}{ArvoreDosSufixos}
%\newcommand{\AddWord}{AdicionaPalavra}
%\newcommand{\Scan}{Soletra}



\newcommand{\Aarvore}{$A^+$-árvore}
\newcommand{\AarvoreRec}{$A^+$-árvore de reconhecimento}
\newcommand{\Bifurc}[1]{\mathord{\mathop{\rm Bifurc}({#1})}}
\newcommand{\Um}[1]{\mathord{\mathop{\rm Um}({#1})}}
\newcommand{\Primogsym}{{\textsc{Primog}}}
\newcommand{\Primog}[1]{\function{\Primogsym}{#1}}
\newcommand{\Irmaosym}{{\textsc{Irmão}}}
\newcommand{\Irmao}[1]{\function{\Irmaosym}{#1}}
\newcommand{\IrmaoA}[1]{\function{\Irmaosym}{#1}}
\newcommand{\Paisym}{{\textsc{Pai}}}
\newcommand{\Pai}[1]{\function{\Paisym}{#1}}
\newcommand{\PaiA}[1]{\function{\Paisym}{#1}}
\newcommand{\Raizsym}{{\textsc{Raiz}}}
\newcommand{\Raiz}[1]{\function{\Raizsym}{#1}}
\newcommand{\Rotulosym}{{\textsc{Ocorr}}}
\newcommand{\Rotulo}[1]{\function{\Rotulosym}{#1}}
\newcommand{\Comprimentosym}{{\textsc{Comp}}}
\newcommand{\Comprimento}[1]{\function{\Comprimentosym}{#1}}
\newcommand{\Sufixosym}{{\textsc{Sufixo}}}
\newcommand{\Sufixo}[1]{\function{\Sufixosym}{#1}}
\newcommand{\Soletrasym}{{\textsc{Soletra}}}
\newcommand{\Soletra}[1]{\function{\Soletrasym}{#1}}
\newcommand{\ReSoletrasym}{{\textsc{ReSoletra}}}
\newcommand{\ReSoletra}[1]{\function{\ReSoletrasym}{#1}}
\newcommand{\AdicionaPalavrasym}{{\textsc{AdicionaPalavra}}}
\newcommand{\AdicionaPalavra}[1]{\function{\AdicionaPalavrasym}{#1}}
\newcommand{\ArvoreDosSufixossym}{{\textsc{ÁrvoreDosSufixos}}}
\newcommand{\ArvoreDosSufixos}[1]{\function{\ArvoreDosSufixossym}{#1}}
\newcommand{\Palavrasym}{{\textsc{Palavra}}}
\newcommand{\Palavra}[1]{\function{\Palavrasym}{#1}}
\newcommand{\AdicionaSufixosym}{{\textsc{AdicionaSufixo}}}
\newcommand{\AdicionaSufixo}[1]{\function{\AdicionaSufixosym}{#1}}
\newcommand{\NovaCabecasym}{{\textsc{NovaCabeça}}}
\newcommand{\NovaCabeca}[1]{\function{\NovaCabecasym}{#1}}
\newcommand{\BuscaDePadraosym}{{\textsc{BuscaDePadrão}}}
\newcommand{\BuscaDePadrao}[1]{\function{\BuscaDePadraosym}{#1}}
\newcommand{\BuscaIngenuaDePadraosym}{{\textsc{BuscaIngênuaDePadrão}}}
\newcommand{\BuscaIngenuaDePadrao}[1]{\function{\BuscaIngenuaDePadraosym}{#1}}
\newcommand{\BuscaIngenuaDePadraoComErrossym}{{\textsc{BuscaIngênuaDePadrãoComErros}}}
\newcommand{\BuscaIngenuaDePadraoComErros}[1]{\function{\BuscaIngenuaDePadraoComErrossym}{#1}}
\newcommand{\BuscaDePadraoComErrossym}{{\textsc{BuscaDePadrão}}}
\newcommand{\BuscaDePadraoComErros}[1]{\function{\BuscaDePadraosym}{#1}}
\newcommand{\FatorComumsym}{{\textsc{FatorComum}}}
\newcommand{\FatorComum}[1]{\function{\FatorComumsym}{#1}}
\newcommand{\FatorComumIngenuosym}{{\textsc{FatorComumIngênuo}}}
\newcommand{\FatorComumIngenuo}[1]{\function{\FatorComumIngenuosym}{#1}}
\newcommand{\FatorComumQuadradosym}{{\textsc{FatorComumQuadrado}}}
\newcommand{\FatorComumQuadrado}[1]{\function{\FatorComumQuadradosym}{#1}}
\newcommand{\FatorComumCubicosym}{{\textsc{FatorComumCúbico}}}
\newcommand{\FatorComumCubico}[1]{\function{\FatorComumCubicosym}{#1}}
\newcommand{\ExtensaoComumsym}{{\textsc{ExtensãoComum}}}
\newcommand{\ExtensaoComum}[1]{\function{\ExtensaoComumsym}{#1}}
\newcommand{\PreExtensaoComumsym}{{\textsc{PreExtensãoComum}}}
\newcommand{\PreExtensaoComum}[1]{\function{\PreExtensaoComumsym}{#1}}
\newcommand{\VerticeFinalsym}{{\textsc{VérticeFinal}}}
\newcommand{\VerticeFinal}[1]{\function{\VerticeFinalsym}{#1}}


%% lca

\newcommand{\gT}{\grafo T}
\newcommand{\MACsym}{{\textsc{MAC}}}
\newcommand{\MAC}[2]{\mathop{\MACsym}({#1},{#2})}
\newcommand{\BuscaEmProfundidadesym}{{\textsc{BuscaEmProfundidade}}}
\newcommand{\fun}[3]{#1\,\colon\,\, #2 \to #3}   % fun      1:2->3
\newcommand{\Ancestraissym}{{\textsc{Ancestrais}}}
\newcommand{\Buscasym}{{\textsc{Busca}}}
\newcommand{\Busca}[1]{\mathord{\mathop{\Buscasym}({#1})}}
\newcommand{\lB}[1]{\mathord{\mathop{\Buscasym}[{#1}]}}
\newcommand{\Profsym}{{\textsc{Prof}}}
\newcommand{\lP}[1]{\mathord{\mathop{\Profsym}[{#1}]}}
\newcommand{\Descsym}{{\textsc{Desc}}}
\newcommand{\lD}[1]{\mathord{\mathop{\Descsym}[{#1}]}}
\newcommand{\Abansym}{{\textsc{Aban}}}
\newcommand{\lA}[1]{\mathord{\mathop{\Abansym}[{#1}]}}
\newcommand{\Vetorsym}{{\textsc{V}}}
\newcommand{\lV}[1]{\mathord{\mathop{\Vetorsym}[{#1}]}}
\newcommand{\Russosym}{{\textsc{Russo}}}
\newcommand{\lR}[1]{\mathord{\mathop{\Russosym}[{#1}]}}

\newcommand{\msym}{{\textsc{m}}}
\newcommand{\lm}{m}  %{\mathord{\mathop{\msym}}}
\newcommand{\bsym}{{\textsc{b}}}
\newcommand{\lb}{b} %{\mathord{\mathop{\bsym}}}

\newcommand{\MVCIntermediariosym}{{\textsc{MvcIntermediário}}}
\newcommand{\MVCIntermediario}[2]{\mathord{\mathop{\MVCIntermediariosym}({#1},{#2})}}
\newcommand{\PreMvc}[1]{\mathord{\mathop{\PreProcessamentoLinearsym}({#1})}}
\newcommand{\PaiAsym}{{\Paisym}}
\newcommand{\Dispersasym}{{\textsc{Dispersa}}}
\newcommand{\MVCsym}{{\textsc{MVC}}}
\newcommand{\MVC}[2]{\mathord{\mathop{\MVCsym}({#1},{#2})}}
\newcommand{\LogaritmosEPotenciassym}{{\textsc{LogaritmosEPotências}}}
\newcommand{\Logsym}{\textsc{Log}}
\newcommand{\Log}[1]{\mathord{\mathop{\Logsym}[{#1}]}}
\newcommand{\Expsym}{\textsc{Exp}}
\newcommand{\Exp}[1]{\mathord{\mathop{\rm Exp}[{#1}]}}
\newcommand{\PreProcessamentoIntermediariosym}{{\textsc{PréIntermediário}}}
\newcommand{\PosMinsym}{\textsc{PosMin}}
\newcommand{\PosMin}[2]{\mathord{\mathop{\PosMinsym}[{#1},{#2}]}}
\newcommand{\PapaLeguassym}{{\textsc{PapaLéguas}}}
\newcommand{\PapaLeguas}[2]{\mathord{\mathop{\PapaLeguassym}({#1},{#2})}}
\newcommand{\Quebrasym}{{\textsc{Quebra}}}
\newcommand{\Quebra}[2]{\mathord{\mathop{\Quebrasym}({#1},{#2})}}
\newcommand{\DIV}{\,\,\mathord{\mathop{\rm\bf div}\,\,}}
\newcommand{\Letrasym}{{\textsc{Letra}}}
\newcommand{\Letra}[1]{\mathord{\mathop{\Letrasym}[{#1}]}}
\newcommand{\Digitosym}{{\textsc{Dígito}}}
\newcommand{\Digito}[1]{\mathord{\mathop{\Digitosym}[{#1}]}}
\newcommand{\Variacaosym}{{\textsc{Variação}}}
\newcommand{\Variacao}[1]{\mathord{\mathop{\Variacaosym}[{#1}]}}
\newcommand{\ld}{{\tt d}}
\newcommand{\ls}{{\tt s}}
\newcommand{\Agrupasym}{{\textsc{Agrupa}}}
\newcommand{\Agrupa}[1]{\mathord{\mathop{\Agrupasym}({#1})}}
\newcommand{\FazCrachassym}{{\textsc{FazCrachás}}}
\newcommand{\FazCrachas}[2]{\mathord{\mathop{\FazCrachassym}({#1},{#2})}}
\newcommand{\Crachasym}{{\textsc{Crachá}}}
\newcommand{\Cracha}[1]{\mathord{\mathop{\Crachasym}[{#1}]}}
\newcommand{\MvcMonoBlocosym}{{\textsc{MvcInterno}}}
\newcommand{\MvcMonoBloco}[2]{\mathord{\mathop{\MvcMonoBlocosym}({#1},{#2})}}
\newcommand{\letra}{\mathord{\mathop{\rm letra}}}
\newcommand{\Russificasym}{{\textsc{Russifica}}}
\newcommand{\Russifica}[1]{\mathord{\mathop{\Russificasym}({#1})}}
\newcommand{\Tabelonasym}{{\textsc{Tabela}}}
\newcommand{\Tabelona}[2]{\mathord{\mathop{\Tabelonasym}({#1},{#2})}}
\newcommand{\PreProcessamentoLinearsym}{{\textsc{PréMvc}}}
\newcommand{\PreProcessamentosym}{{\textsc{PréMAC}}}
\newcommand{\AlgoritmoIngenuosym}{{\textsc{MacIngênuo}}}

\renewcommand{\N}{{\tt I\kern-.2em N \relax}}      % N        |N


%% diff
\newcommand{\Caixa}{\rule{2mm}{3mm}}

\newenvironment{demo}[1]                                      %      demo = ns
  {{\noindent\em #1\/}.}{\hfill\Caixa\vspace{3 mm}}
\newenvironment{semidemo}[1]                                  %  semidemo = ns
  {{\noindent\em #1\/}.}{\hfill\Caixa}
\newenvironment{superdemo}[1]                                 % superdemo = ns
  {{\vspace{3 mm}\noindent\em #1\/}.}{\hfill\Caixa\vspace{3 mm}}
\newenvironment{predemo}[1]                                   %   predemo = ns
  {{\vspace{3 mm}\noindent\em #1\/}.}{\hfill\Caixa}

\newtheorem{lem}{Lemma}    % numeracao global
\newtheorem{pro}[lem]{Proposition}
\newtheorem{cor}[lem]{Corollary}
\newtheorem{teo}[lem]{Theorem}

\newcommand{\num}[1]{\{\, #1 \,\}}               % num      { 1 }



%% Local Variables:
%% mode: latex
%% TeX-auto-save: t
%% TeX-master: "livro.tex"
%% TeX-parse-self: t
%% make-backup-files: t
%% End:
