#251 baabaabaa=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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