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#323 aaaaababba=babaaaa

Original presentation

\( \left\langle a, b \;\middle|\; a^{5} b a b^{2} a = b a b a^{4} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; c^{2} a d a = b a b c^{2},\; c = a^{2},\; d = b a b^{2} \right\rangle \)

Complete rewriting system

Using recursive path order (RPOCmp) with \(a < d < b < c\):

\( \begin{aligned} c &\rightarrow a^{2} \\ b a b^{2} &\rightarrow d \\ b a b a^{4} &\rightarrow a^{5} d a \\ b a b d &\rightarrow d a b^{2} \\ d a b a^{4} &\rightarrow a^{5} d a^{2} d a \end{aligned} \)