#367 baaababaaa=abaaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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