#426 bababaaaba=ababa

Original presentation

\( \left\langle a, b \;\middle|\; b a b a b a^{3} b a = a b a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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