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#148 ababaabbba=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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