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#460 aabbaaabba=baabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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