#059 abbabbbaba=babba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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