#485 baaaababba=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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