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#195 baabbababa=abbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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