#030 baabbaabba=abababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ a c^{3} &\rightarrow d^{2} c \\ c a b &\rightarrow d \\ b d^{2} c &\rightarrow c^{4} \\ c a c &\rightarrow d a \\ a c^{2} d &\rightarrow d^{3} \\ b d^{3} &\rightarrow c^{3} d \\ d a^{2} b &\rightarrow c a d \\ d a^{2} c &\rightarrow c a d a \\ d a c^{2} &\rightarrow c d^{2} c \\ d a c d &\rightarrow c d^{3} \\ c d^{2} c d &\rightarrow d^{4} \\ c d^{2} c^{2} &\rightarrow d^{3} c \\ d a d^{2} c^{2} &\rightarrow c a d^{3} c \\ d a d^{2} c d &\rightarrow c a d^{4} \\ a c d^{3} c &\rightarrow d^{4} c^{2} \\ a c d^{4} &\rightarrow d^{4} c d \\ c d^{5} c &\rightarrow d^{5} c^{2} \\ c d^{6} &\rightarrow d^{5} c d \\ d a d^{3} c &\rightarrow c d^{4} c^{2} \\ d a d^{4} &\rightarrow c d^{4} c d \\ a d^{5} c^{2} &\rightarrow d^{4} c d^{2} c \\ a d^{5} c d &\rightarrow d^{4} c d^{3} \\ a d^{8} c &\rightarrow d^{4} c d^{4} c^{2} \\ a d^{9} &\rightarrow d^{4} c d^{4} c d \end{aligned} \)