#081 aabaababba=baabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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