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#054 bbaaabbaaa=abbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b^{2} &\rightarrow c \\ a c a^{2} &\rightarrow d \\ b c &\rightarrow c b \\ a d &\rightarrow d^{2} a \\ a c d^{2} a &\rightarrow d c a^{2} \\ c d^{8} a^{2} &\rightarrow d c a^{2} \\ c d^{4} a^{3} &\rightarrow d \\ c d^{10} a &\rightarrow d c d^{2} a \\ a c d^{3} &\rightarrow d c d^{2} a \\ c b d^{4} a^{3} &\rightarrow b d \\ c b d^{8} a^{2} &\rightarrow b d c a^{2} \\ c b d^{10} a &\rightarrow b d c d^{2} a \\ c d^{11} &\rightarrow d c d^{3} \\ c b d^{11} &\rightarrow b d c d^{3} \end{aligned} \)