#015 baabaabbaa=abbaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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