#227 baaaabbba=aaaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b^{3} a = a^{4} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow a^{2} \\ a b^{3} &\rightarrow d \\ b a^{3} d a &\rightarrow a^{4} \\ a b^{2} a^{4} &\rightarrow d a^{3} d a \\ b a^{3} d^{2} &\rightarrow a^{3} d \\ a b^{2} a^{3} d &\rightarrow d a^{3} d^{2} \\ a b a^{3} d &\rightarrow d a^{3} d^{3} \\ a b a^{4} &\rightarrow d a^{3} d^{2} a \\ d a^{3} d^{4} &\rightarrow a^{4} d \\ d a^{3} d^{3} a &\rightarrow a^{5} \\ b a^{7} d &\rightarrow a^{6} d^{4} \\ b a^{8} &\rightarrow a^{6} d^{3} a \\ d a^{3} d^{2} a^{4} d &\rightarrow a^{7} d^{4} \\ d a^{3} d^{2} a^{5} &\rightarrow a^{7} d^{3} a \end{aligned} \)