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#077 aabbabbaba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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