#383 bababbbbba=aba
Original presentation
\( \left\langle a, b \;\middle|\; b a b a b^{5} a = a b a \right\rangle \)
Modified presentation
\( \left\langle a, b, c, d \;\middle|\; c^{2} d c = a c,\; c = b a,\; d = b^{4} \right\rangle \)
Complete rewriting system
Using recursive path order (RPOCmp) with \(c < d < a < b\):
\( \begin{aligned} b^{4} &\rightarrow d \\ b a &\rightarrow c \\ a c &\rightarrow c^{2} d c \\ b^{3} c &\rightarrow d a \\ b d &\rightarrow d b \\ b c^{2} &\rightarrow d c^{2} d c d c d c \\ d c^{2} d c d c d c d c &\rightarrow c^{2} \\ d c^{2} d c d c d c^{3} &\rightarrow c^{3} d c d c d c d c \end{aligned} \)