#091 abaaabbaba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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