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#119 bbaabbaa=abba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b^{2} &\rightarrow c \\ a c a &\rightarrow d \\ b c &\rightarrow c b \\ a d &\rightarrow d^{2} a \\ a c d &\rightarrow d c a \\ c d^{4} a &\rightarrow d c a \\ c d^{2} a^{2} &\rightarrow d \\ c d^{5} &\rightarrow d c d \\ c b d^{2} a^{2} &\rightarrow b d \\ c b d^{4} a &\rightarrow b d c a \\ c b d^{5} &\rightarrow b d c d \end{aligned} \)