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#217 babaaabba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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