#501 baaaabbbaa=aaaabbba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b^{3} a^{2} = a^{4} b^{3} a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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