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