#313 abaabbaaaa=baaaba

Original presentation

\( \left\langle a, b \;\middle|\; a b a^{2} b^{2} a^{4} = b a^{3} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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