#037 baaaabbbaa=aba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b^{3} a^{2} = a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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