#376 abaabababa=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b c a &\rightarrow d \\ d a &\rightarrow c a c^{3} a \\ a b &\rightarrow c \\ b c^{2} &\rightarrow d b \\ d c &\rightarrow c a c^{4} \\ a d &\rightarrow c^{2} a \\ a c a c^{4} &\rightarrow c^{2} a c \\ a c a c^{3} a &\rightarrow c^{2} a^{2} \end{aligned} \)