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#151 ababaababa=bababaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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