#216 abbababbaa=bababba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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