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#249 baaaabaaaa=aaaaaba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b a^{4} = a^{5} b a \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; d^{2} = a^{5} c,\; c = b a,\; d = c a^{3} \right\rangle \)

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ c a^{3} &\rightarrow d \\ a^{5} c &\rightarrow d^{2} \\ b d^{2} &\rightarrow d a c \\ c a^{2} d^{2} &\rightarrow d a^{4} c \\ c a d^{2} &\rightarrow d a^{3} c \\ c d^{2} &\rightarrow d a^{2} c \\ a^{5} d &\rightarrow d^{2} a^{3} \end{aligned} \)