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#405 aabaabbaaa=baaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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