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#403 babaaaaaba=aaaababa

Original presentation

\( \left\langle a, b \;\middle|\; b a b a^{5} b a = a^{4} b a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b c a &\rightarrow d \\ d a^{3} c a &\rightarrow a^{3} c^{2} a \\ a b &\rightarrow c \\ b c^{2} &\rightarrow d b \\ a d &\rightarrow c^{2} a \\ d a^{3} c^{2} &\rightarrow a^{3} c^{3} \\ a^{4} c^{2} a &\rightarrow c^{2} a^{4} c a \\ a^{4} c^{3} &\rightarrow c^{2} a^{4} c^{2} \end{aligned} \)