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#379 baaaabaaba=aabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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