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#342 babaababba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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