#116 abababaaba=bababaa

Original presentation

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

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; a c^{3} a c = c^{3} a,\; c = b a,\; d = a b a \right\rangle \)

Complete rewriting system

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

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