#294 babbaaba=abba

Original presentation

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

Modified presentation

\( \left\langle a, b, c, d, e \;\middle|\; d c = e c,\; c = b a,\; d = c b c a,\; e = a b \right\rangle \)

Complete rewriting system

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

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