⟨a, b | ababbbaaab=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) = 0, d < e; deg(c) = 1; deg(a) = 2; deg(b) = 3
Auxiliary generator: ab=c
Auxiliary generator: cbb=d
Auxiliary generator: daac=e

ce ⇒ 1
ec ⇒ 1
dac²d ⇒ ae(de)²
eaed ⇒ ac²dc
dea ⇒ aed
e²ac²d ⇒ da
ca(ed)² ⇒ ea(c²d)²c
cac²d ⇒ aede
cda ⇒ eac²d
a²c²d ⇒ 1
da² ⇒ e²
dac²aed ⇒ a(ed)²e²a
(ea)² ⇒ a²c³
e²ac²aed ⇒ daea
ca² ⇒ aeae³
cac²aed ⇒ aede²a
a²c²aed ⇒ ea
ea³ ⇒ a²c²ae³
b ⇒ ac²dc

# ab:ababbbaaab=1 de/c/a/b ab=c,cbb=d,daac=e frequency:2/0,3/1,4/0 ce=1 ec=1 daccd=aedede eaed=accdc dea=aed eeaccd=da caeded=eaccdccdc caccd=aede cda=eaccd aaccd=1 daa=ee daccaed=aededeea eaea=aaccc eeaccaed=daea caa=aeaeee caccaed=aedeea aaccaed=ea eaaa=aaccaeee b=accdc

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#1522 ⟨a, b | ababbbaaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)