#003 babbabaaba=abba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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