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#498 bbaaabbaaa=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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