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#043 baaabbabba=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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