#283 baabbbaaba=aabbbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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