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#340 baabababaa=aaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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