#209 abbaabbbaa=baabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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