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#396 abaaaababa=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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