#365 abaababbaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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