#353 abaabbabaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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