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#272 ababababa=babaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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