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