#487 abbaabbaba=babbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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