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Double It $[10$ points$]$

Give a high$-$level description of a Turing Machine that decides the language

$L=\{win\{a,b,c{\}}^{**}$: the number $ofa\text{'}sinwis$ more than twice the number $ofb\text{'}s\}$

Note that a string with exactly two times as many a$\text{'}$s as b$\text{'}$s would not be accepted. You must include an explanation of why the TM halts in order to recieve full credit.