#326 baaaabbaaa=aaaabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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