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#310 babaababa=abababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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