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#277 baaaababaa=aaaba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b a b a^{2} = a^{3} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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