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#408 babaababaa=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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