#395 baaababba=aa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{3} b a b^{2} a = a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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