#412 abaababbaa=baabaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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