#347 ababbbabba=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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