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Regular Expression
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Input 1
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New
$hello$ $ hello $ .projection $I_{d,i} \rightarrow M_{d,i} M_{d,0}$, where all the \begin{itemize} \item $M$ is atomic and finitely generated; \item $M$ is cancellative; \item $(M, \le_L)$ and $(M, \le_R)$ are lattices; \item there exists an element $\Delta \in M$, called {\it Garside element}, such that the set $L(\Delta)= \{ x \in M; x\le_L \Delta\}$ generates $M$ and is equal to $R(\Delta)= \{ x\in M; x\le_R \Delta\}$. \end{itemize} Using the fact that is atomic and that $L(\Delta)= \{x \in M; x \le_L \Delta\} M \pi_L(a) \neq 1 a \neq 1 k \partial_L^k(a)=1 k$ be the
Substitution
$hello$ $ hello $ .projection $I_{d,i} \rightarrow M_{d,i} M_{d,0}$, where all the \begin{itemize} \item $M$ is atomic and finitely generated; \item $M$ is cancellative; \item $(M, \le_L)$ and $(M, \le_R)$ are lattices; \item there exists an element $\Delta \in M$, called {\it Garside element}, such that the set $L(\Delta)= \{ x \in M; x\le_L \Delta\}$ generates $M$ and is equal to $R(\Delta)= \{ x\in M; x\le_R \Delta\}$. \end{itemize} Using the fact that is atomic and that $L(\Delta)= \{x \in M; x \le_L \Delta\} M \pi_L(a) \neq 1 a \neq 1 k \partial_L^k(a)=1 k$ be the