⟨a, b | abbbabaaab=1⟩

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Monoids with two generators and one relation

Complete rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right recursive path with deg(d) = deg(e) = deg(c) = 0, d < e < c; deg(a) = 1; deg(b) = 2
Auxiliary generator: ab=c
Auxiliary generator: bbc=d
Auxiliary generator: daa=e

ce ⇒ ec
ec² ⇒ 1
eac²d ⇒ da
cac²d ⇒ ade
d²a ⇒ ac²dc³d
dea ⇒ ac²dc
ecad ⇒ ac²dc²
cda ⇒ eade
a²c²d ⇒ 1
da² ⇒ e
(ea)²d ⇒ a²c⁴dc²
eacad ⇒ daeac
eaeca ⇒ a²c²
(ca)²d ⇒ ade²ac
ecaead ⇒ ca²c⁴dc²
(eca)² ⇒ ca²c²
c²a² ⇒ aecae
a²cad ⇒ eac
eaca² ⇒ a²cae
ecaca² ⇒ ca²cae
b ⇒ ac²dc

# ab:abbbabaaab=1 dec/a/b ab=c,bbc=d,daa=e frequency:2/0,3/0,3/0 ce=ec ecc=1 eaccd=da caccd=ade dda=accdcccd dea=accdc ecad=accdcc cda=eade aaccd=1 daa=e eaead=aaccccdcc eacad=daeac eaeca=aacc cacad=adeeac ecaead=caaccccdcc ecaeca=caacc ccaa=aecae aacad=eac eacaa=aacae ecacaa=caacae b=accdc

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#1543 ⟨a, b | abbbabaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)