#138 aababbbaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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