#071 baababbba=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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