#490 babaabaaba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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