#247 abaaabbaaa=baaaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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