Let $L=\{win\{a,b{\}}^{**}||w{|}_a=2^{**}|w{|}_b\}$ where $|w{|}_a$ denotes the number of occurrences of $a$ in $w$ and $|w{|}_b$ denotes the number of occurrences of $b$ in $w.$

Provide a formal description of a Turing machine $M$ which decides $L.$

The transition function can be represented as a state diagram.