#020 aaabaabbaa=baaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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