#095 babbabbbba=abba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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