#293 babaaaabba=ababa

Original presentation

\( \left\langle a, b \;\middle|\; b a b a^{4} b^{2} a = a b a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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