#229 abbabbabaa=bababba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b c^{2} a &\rightarrow d \\ b a &\rightarrow c \\ a b c d &\rightarrow c^{2} b c \\ b c^{2} b c &\rightarrow c b c d \\ b c^{4} b c &\rightarrow d b c d \\ b c^{2} d b c d &\rightarrow c b c d c^{3} b c \\ b c^{3} b c d &\rightarrow c b c d c b c \\ b c^{4} d b c d &\rightarrow d b c d c^{3} b c \\ b c^{5} b c d &\rightarrow d b c d c b c \\ d b c d c a &\rightarrow b c^{4} d \\ c b c d c a &\rightarrow b c^{2} d \\ b c b c^{2} d &\rightarrow c b c d^{2} c a \\ b c^{2} b^{2} c^{2} d &\rightarrow c b c b c^{4} d \\ b c^{3} b c^{2} d &\rightarrow d b c d^{2} c a \\ b c^{4} b^{2} c^{2} d &\rightarrow d b c b c^{4} d \\ b c^{5} b c b c^{4} d &\rightarrow d b c d c b^{2} c^{2} d \\ b c^{4} d b c b c^{4} d &\rightarrow d b c d c^{3} b^{2} c^{2} d \\ b c^{3} b c b c^{4} d &\rightarrow c b c d c b^{2} c^{2} d \\ b c^{2} d b c b c^{4} d &\rightarrow c b c d c^{3} b^{2} c^{2} d \\ a b c b c^{4} d &\rightarrow c^{2} b^{2} c^{2} d \end{aligned} \)