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#454 ababababaa=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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