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#088 bbaaabbbba=abbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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