#317 bababbaaba=ababba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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