#436 baabaaaaba=abaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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