#377 babaababaa=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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