#145 baababaaba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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