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#335 baaabbbaba=abaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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