#325 abaaaababa=baaabaa

Original presentation

\( \left\langle a, b \;\middle|\; a b a^{4} b a b a = b a^{3} b a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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