#418 abaababbaa=babaaba
Original presentation
\( \left\langle a, b \;\middle|\; a b a^{2} b a b^{2} a^{2} = b a b a^{2} b a \right\rangle \)
Modified presentation
\( \left\langle a, b, c, d \;\middle|\; a c a c b c a = c^{2} a c,\; c = b a,\; d = b^{2} a^{2} \right\rangle \)
Complete rewriting system
Using recursive path order (RPOCmp) with \(a < d < b < c\):
\( \begin{aligned} c &\rightarrow b a \\ b^{2} a^{2} &\rightarrow d \\ b a b a^{2} b a &\rightarrow a b a^{2} b a d \\ b a b a^{3} b a^{2} b a d &\rightarrow a b a^{2} b a d b a^{2} b a \end{aligned} \)