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#200 ababaaabaa=baba

Original presentation

\( \left\langle a, b \;\middle|\; a b a b a^{3} b a^{2} = b a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow d \\ b a &\rightarrow d \\ a d^{2} a^{2} d a &\rightarrow d^{2} \\ b d^{2} &\rightarrow d^{3} a^{2} d a \\ a d^{2} a^{2} d^{3} &\rightarrow d^{4} a^{2} d a \end{aligned} \)