#417 baaababbaa=aaaba
Original presentation
\( \left\langle a, b \;\middle|\; b a^{3} b a b^{2} a^{2} = a^{3} b a \right\rangle \)
Modified presentation
\( \left\langle a, b, c, d \;\middle|\; c a^{2} c d = a^{3} c,\; c = b a,\; d = b c a \right\rangle \)
Complete rewriting system
Using recursive path order (RPOCmp) with \(c < d < a < b\):
\( \begin{aligned} b a &\rightarrow c \\ b c a &\rightarrow d \\ c a^{2} c &\rightarrow d a c d \\ b c d a c d^{2} &\rightarrow d a^{2} c \\ a^{3} c &\rightarrow d a c d^{2} \\ b d a c d &\rightarrow d a c \\ a^{3} d a c d &\rightarrow d a c d^{2} a^{2} c \\ c a^{2} d a c d &\rightarrow d a c d a^{2} c \end{aligned} \)