#196 babbababba=abbabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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