#224 babababbba=aba
Original presentation
\( \left\langle a, b \;\middle|\; b a b a b a b^{3} a = a b a \right\rangle \)
Modified presentation
\( \left\langle a, b, c, d \;\middle|\; c^{3} d = a c,\; c = b a,\; d = b^{2} c \right\rangle \)
Complete rewriting system
Using recursive path order (RPOCmp) with \(c < d < a < b\):
\( \begin{aligned} b^{2} c &\rightarrow d \\ b a &\rightarrow c \\ a c &\rightarrow c^{3} d \\ b c^{2} &\rightarrow d c^{2} d \\ d c^{2} d c d &\rightarrow c^{2} \\ b d c^{2} d &\rightarrow d c \\ d c^{2} d c^{3} &\rightarrow c^{4} d c d \\ b d c^{4} &\rightarrow d c^{3} d c d \end{aligned} \)