#114 aababbabaa=babaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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