#069 abaabaabba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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