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#301 abaabababa=babaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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