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#470 ababbabaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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