#236 babaaaaaba=ababaa

Original presentation

\( \left\langle a, b \;\middle|\; b a b a^{5} b a = a b a b a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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