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#459 baaabaaaba=aabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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