#299 babaababba=ababbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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