#321 baabbaabaa=abaabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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