#045 baabbaabaa=aabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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