#363 aabaabbaba=babaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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