#153 baaaababaa=abaaba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b a b a^{2} = a b a^{2} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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