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#448 baabaaabba=abaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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