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#384 abaabaaaba=baabaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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