#366 aaababaaba=babaa

Original presentation

\( \left\langle a, b \;\middle|\; a^{3} b a b a^{2} b a = b a b a^{2} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; a^{3} c^{2} a c = c^{2} a,\; c = b a,\; d = a b a^{2} \right\rangle \)

Complete rewriting system

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

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