#399 ababaaabba=babaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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