#115 bbaabbbbaa=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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