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#291 baabbabbaa=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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