#048 abbababbba=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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