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#176 bababbbba=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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