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#190 abaaabbaba=babaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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