#189 ababaabbaa=baabaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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