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#274 baababaaba=abaaca

Original presentation

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

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; a d = c b a,\; c = b a^{5},\; d = b a b c \right\rangle \)

Complete rewriting system

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

\( \begin{aligned} b a b c &\rightarrow d \\ b a^{5} &\rightarrow c \\ c b a &\rightarrow a d \\ b a b a d &\rightarrow d b a \\ a d b c &\rightarrow c d \\ a d a^{4} &\rightarrow c^{2} \\ b a^{4} c d &\rightarrow c d b c \\ b a^{4} c^{2} &\rightarrow c d a^{4} \\ a d b a d &\rightarrow c d b a \\ c b c d &\rightarrow a d^{2} b c \\ c b c^{2} &\rightarrow a d^{2} a^{4} \\ c^{2} d b c &\rightarrow a d a^{3} c d \\ c^{2} d a^{4} &\rightarrow a d a^{3} c^{2} \\ b a^{4} c a d &\rightarrow c d a^{4} b a \\ c b c a d &\rightarrow a d^{2} a^{4} b a \\ c^{2} d b a d &\rightarrow a d a^{3} c d b a \end{aligned} \)