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#391 bababaaba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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