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#180 babababbba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b^{2} c &\rightarrow d \\ b a &\rightarrow c \\ a c^{2} &\rightarrow c^{3} d \\ b c^{3} &\rightarrow d c^{2} d \\ d c^{2} d^{2} &\rightarrow c^{3} \\ b d c^{2} d &\rightarrow d c^{2} \\ d c^{2} d c^{3} &\rightarrow c^{5} d^{2} \\ b d c^{5} &\rightarrow d c^{4} d^{2} \end{aligned} \)