#496 abaaaababa=babaaa

Original presentation

\( \left\langle a, b \;\middle|\; a b a^{4} b a b a = b a b a^{3} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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