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#315 aaaabbaaba=baabaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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