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#307 baabbbbbba=aa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{2} b^{6} a = a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b^{2} &\rightarrow c \\ a c^{3} &\rightarrow d \\ b c &\rightarrow c b \\ b a^{2} &\rightarrow c a d a \\ b a d &\rightarrow c a d^{2} \\ c a d^{3} &\rightarrow a d \\ c a d^{2} a &\rightarrow a^{2} \\ a c^{2} a d &\rightarrow d a d^{3} \\ a c^{2} a^{2} &\rightarrow d a d^{2} a \\ a c a d &\rightarrow d a d^{5} \\ a c a^{2} &\rightarrow d a d^{4} a \\ d a d^{7} &\rightarrow a^{2} d \\ d a d^{6} a &\rightarrow a^{3} \\ c a d a^{2} d &\rightarrow a^{2} d^{7} \\ c a d a^{3} &\rightarrow a^{2} d^{6} a \\ d a d^{5} a^{2} d &\rightarrow a^{3} d^{7} \\ d a d^{5} a^{3} &\rightarrow a^{3} d^{6} a \end{aligned} \)