#023 baaabbbbba=aa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{3} b^{5} a = a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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