#207 aababbaaaa=baaaaba

Original presentation

\( \left\langle a, b \;\middle|\; a^{2} b a b^{2} a^{4} = b a^{4} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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