#128 aaaabbabba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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