#413 ababaabbaa=baababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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