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#418 abaababbaa=babaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow b a \\ b^{2} a^{2} &\rightarrow d \\ b a b a^{2} b a &\rightarrow a b a^{2} b a d \\ b a b a^{3} b a^{2} b a d &\rightarrow a b a^{2} b a d b a^{2} b a \end{aligned} \)