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#204 aabaaababa=baabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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