#337 baaaabbaa=abaaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} a^{2} &\rightarrow c \\ a b c^{2} &\rightarrow b c d c \\ c b^{2} &\rightarrow d \\ a c &\rightarrow c a \\ a b c d &\rightarrow b c d^{2} \\ c b c^{2} &\rightarrow b c d^{2} c \\ a d &\rightarrow c a b^{2} \\ c b c d &\rightarrow b c d^{3} \\ a b^{2} c d^{4} c &\rightarrow b c d b c d^{2} c \\ b c d^{2} b c d^{2} c &\rightarrow d c d^{4} c \\ a b^{2} c d^{5} &\rightarrow b c d b c d^{3} \\ a b^{2} c d^{4} b c d^{2} c &\rightarrow b c d^{2} c d^{4} c \\ c d c d^{4} c &\rightarrow b c d^{4} b c d^{2} c \\ b c d^{2} b c d^{3} &\rightarrow d c d^{5} \\ c b d c d^{4} c &\rightarrow d c d^{2} b c d^{2} c \\ b c d^{3} c d^{4} c &\rightarrow d c d^{4} b c d^{2} c \\ b c d^{3} c d^{5} &\rightarrow d c d^{4} b c d^{3} \\ a b^{2} c d^{4} b c d^{3} &\rightarrow b c d^{2} c d^{5} \\ c d c d^{5} &\rightarrow b c d^{4} b c d^{3} \\ c d c d^{4} b c d^{2} c &\rightarrow b c d^{5} c d^{4} c \\ c d c d^{4} b c d^{3} &\rightarrow b c d^{5} c d^{5} \\ c b d c d^{5} &\rightarrow d c d^{2} b c d^{3} \\ c b d c d^{4} b c d^{2} c &\rightarrow d c d^{3} c d^{4} c \\ c b d c d^{4} b c d^{3} &\rightarrow d c d^{3} c d^{5} \\ b c d^{3} c d^{4} b c d^{2} c &\rightarrow d c d^{5} c d^{4} c \\ b c d^{3} c d^{4} b c d^{3} &\rightarrow d c d^{5} c d^{5} \end{aligned} \)