#199 ababbababa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ c b c^{2} &\rightarrow e \\ c a &\rightarrow d \\ a e c &\rightarrow d c \\ b d c &\rightarrow c e c \\ c b c e &\rightarrow e b c^{2} \\ c b c d &\rightarrow e a \\ c d c &\rightarrow d e c \\ a e^{2} &\rightarrow d e \\ a e d &\rightarrow d^{2} \\ b d e &\rightarrow c e^{2} \\ b d^{2} &\rightarrow c e d \\ c^{2} e^{2} c &\rightarrow e a c \\ c d e &\rightarrow d e^{2} \\ c d^{2} &\rightarrow d e d \\ c b e a c &\rightarrow e^{3} c \\ c^{2} e^{3} &\rightarrow e a e \\ c^{2} e^{2} d &\rightarrow e a d \\ c b e a e &\rightarrow e^{4} \\ c b e a d &\rightarrow e^{3} d \\ c b e d c &\rightarrow e^{4} c \\ c b e d e &\rightarrow e^{5} \\ c b e d^{2} &\rightarrow e^{4} d \end{aligned} \)