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#194 baaabbaaba=aabbbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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