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#142 baabaaaaba=aabaaba

Original presentation

\( \left\langle a, b \;\middle|\; b a^{2} b a^{4} b a = a^{2} b a^{2} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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