#465 abbaababaa=baababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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