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#434 ababaaaba=babaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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