#474 bbaaabbaa=abba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b^{2} &\rightarrow c \\ b c &\rightarrow c b \\ a d &\rightarrow d^{2} a \\ a c d &\rightarrow c d^{4} a \\ a c a &\rightarrow c d^{2} a^{2} \\ c d^{6} a^{3} &\rightarrow d \\ c b d^{6} a^{3} &\rightarrow b d \\ a c^{2} d^{2} a^{2} &\rightarrow c d^{3} \\ c d^{8} a &\rightarrow d c a \\ c d^{9} &\rightarrow d c d \\ a c^{2} d^{3} &\rightarrow c d^{3} c a \\ c d^{8} c d^{2} a^{2} &\rightarrow d c^{2} d^{2} a^{2} \\ c d^{8} c d^{3} &\rightarrow d c^{2} d^{3} \\ c b d^{8} a &\rightarrow b d c a \\ c b d^{9} &\rightarrow b d c d \\ c b d^{8} c d^{2} a^{2} &\rightarrow b d c^{2} d^{2} a^{2} \\ c b d^{8} c d^{3} &\rightarrow b d c^{2} d^{3} \end{aligned} \)