#430 baabaabba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ a c &\rightarrow d \\ d c &\rightarrow e c \\ c d a b &\rightarrow e \\ b d &\rightarrow c^{2} \\ d^{2} a b &\rightarrow a e \\ d e &\rightarrow e^{2} \\ e a &\rightarrow c d^{2} \\ b e^{2} &\rightarrow c^{2} e \\ b e c &\rightarrow c^{3} \\ e d &\rightarrow c e^{2} c \\ a e^{3} &\rightarrow e^{3} c e \\ a e^{2} c &\rightarrow e^{3} c^{2} \\ c e^{2} c e &\rightarrow e^{3} \\ c e^{2} c^{2} &\rightarrow e^{2} c \\ c e^{5} &\rightarrow e^{4} c e \\ c e^{4} c &\rightarrow e^{4} c^{2} \end{aligned} \)