Maximum length of a walk

Based on the diagram below prove a transition graph having a walk labeled w, it is said there is a walk w of length no more than=[ Λ+(1+Λ) |w| ] where Λ is the number of λ transitions in the graph.".  https://www.quora.com/Based-on-the-diagram-below-prove-a-transition-graph-having-a-walk-labeled-w-it-is-said-there-is-a-walk-w-of-length-no-more-than-%CE%9B+-1+%CE%9B-w-where-%CE%9B-is-the-number-of-%CE%BB-transitions-in-the-graph?__snids__=1441263194&__nsrc__=1&__filter__=all

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