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#234 baaababbaa=abbaaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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