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#491 baabaabbba=abaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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