#144 baaaaababa=abaaa
Original presentation
\( \left\langle a, b \;\middle|\; b a^{5} b a b a = a b a^{3} \right\rangle \)
Modified presentation
\( \left\langle a, b, c, d, e \;\middle|\; b c e a = d c a,\; c = a^{2},\; d = a b,\; e = c d^{2} \right\rangle \)
Complete rewriting system
Using recursive path order (RPOCmp) with \(d < e < c < a < b\):
\( \begin{aligned} b c e a &\rightarrow d c a \\ a b &\rightarrow d \\ a^{2} &\rightarrow c \\ c d^{2} &\rightarrow e \\ b c e c &\rightarrow d c^{2} \\ b c e d &\rightarrow d c d \\ a c &\rightarrow c a \\ a d c a &\rightarrow d c e a \\ c b &\rightarrow a d \\ b c e^{2} &\rightarrow d c e \\ a e &\rightarrow c a d^{2} \\ a d c^{2} &\rightarrow d c e c \\ a d c d &\rightarrow d c e d \\ a d c e &\rightarrow d c e^{2} \\ a d e &\rightarrow d c e d^{2} \\ c d c d &\rightarrow d c e^{2} d \\ c d c^{2} &\rightarrow d c e^{2} c \\ c d c e &\rightarrow d c e^{3} \\ c d c a &\rightarrow d c e^{2} a \\ d c e^{2} d^{2} &\rightarrow c d e \\ a d^{2} c e^{2} a &\rightarrow d c e d c a \\ a d^{2} c e^{2} c &\rightarrow d c e d c^{2} \\ a d^{2} c e^{3} &\rightarrow d c e d c e \\ a d^{2} c e^{2} d &\rightarrow d c e d c d \\ d c e^{2} d c a &\rightarrow e c e^{2} a \\ d c e^{2} d c^{2} &\rightarrow e c e^{2} c \\ d c e^{2} d c e &\rightarrow e c e^{3} \\ d c e^{2} d c d &\rightarrow e c e^{2} d \\ c^{2} d e &\rightarrow d c e^{4} d^{2} \\ c e c e^{2} a &\rightarrow d c e^{4} d c a \\ c e c e^{2} c &\rightarrow d c e^{4} d c^{2} \\ c e c e^{3} &\rightarrow d c e^{4} d c e \\ c e c e^{2} d &\rightarrow d c e^{4} d c d \\ d c e^{2} c d e &\rightarrow e c e^{4} d^{2} \\ d c e^{3} c e^{2} a &\rightarrow e c e^{4} d c a \\ d c e^{3} c e^{2} c &\rightarrow e c e^{4} d c^{2} \\ d c e^{3} c e^{3} &\rightarrow e c e^{4} d c e \\ d c e^{3} c e^{2} d &\rightarrow e c e^{4} d c d \\ d c e^{2} d e &\rightarrow e c e^{2} d^{2} \\ c d e c e^{2} a &\rightarrow e c e^{2} d c a \\ c d e c e^{2} c &\rightarrow e c e^{2} d c^{2} \\ c d e c e^{3} &\rightarrow e c e^{2} d c e \\ c d e c e^{2} d &\rightarrow e c e^{2} d c d \\ b d c e^{4} d c a &\rightarrow d c^{2} e^{2} a \\ b d c e^{4} d c^{2} &\rightarrow d c^{2} e^{2} c \\ b d c e^{4} d c e &\rightarrow d c^{2} e^{3} \\ b d c e^{4} d c d &\rightarrow d c^{2} e^{2} d \\ b d c e^{4} c d e &\rightarrow d c^{2} e^{4} d^{2} \\ b d c e^{5} c e^{2} a &\rightarrow d c^{2} e^{4} d c a \\ b d c e^{5} c e^{2} c &\rightarrow d c^{2} e^{4} d c^{2} \\ b d c e^{5} c e^{3} &\rightarrow d c^{2} e^{4} d c e \\ b d c e^{5} c e^{2} d &\rightarrow d c^{2} e^{4} d c d \\ b d c e^{4} d e &\rightarrow d c^{2} e^{2} d^{2} \\ b d c e^{4} d^{2} c e^{2} a &\rightarrow d c^{2} e^{2} d c a \\ b d c e^{4} d^{2} c e^{2} c &\rightarrow d c^{2} e^{2} d c^{2} \\ b d c e^{4} d^{2} c e^{3} &\rightarrow d c^{2} e^{2} d c e \\ b d c e^{4} d^{2} c e^{2} d &\rightarrow d c^{2} e^{2} d c d \end{aligned} \)