#206 abababbaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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