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#089 baabbaabba=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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