#042 baabababba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b d c^{3} &\rightarrow d c^{2} b c \\ a &\rightarrow b d c^{2} b c \\ c b d c^{2} b c &\rightarrow b d \\ b^{2} d c^{2} b c &\rightarrow c \\ b d c^{2} b^{2} d &\rightarrow d \\ b d c b d &\rightarrow d c^{3} \\ b d c^{2} b d &\rightarrow d c^{2} b^{2} d \\ b d b d &\rightarrow d c^{5} b c \\ c d &\rightarrow d c^{5} b c^{3} b c \\ b d^{2} &\rightarrow d c^{5} b c^{3} b^{2} d \end{aligned} \)