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#055 baabaabbba=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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