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#025 abbababaaa=baabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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