⟨a, b | ababaaabba=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:
- Right-to-left recursive path with deg(a) = deg(e) = 0, a < e; deg(c) = deg(d) = 1, c < d; deg(b) = 2
Auxiliary generator: aab=c
Auxiliary generator: bacb=d
Auxiliary generator: bad=e

ae ⇒ ea
ea² ⇒ 1
dc ⇒ ea
cad ⇒ 1
d² ⇒ e²ac²ea
dad ⇒ ecace
da²d ⇒ cec
da³d ⇒ (eac)²a
cec² ⇒ da
ce(ac)² ⇒ ada²
cacec ⇒ a²d
c²eac ⇒ a³dea
c²d ⇒ a³decace
cacd ⇒ a²dacec
cecd ⇒ deac²ea
caced ⇒ a²dec²ea
c²a²d ⇒ a³d(eac)²a
ceca²d ⇒ da²cec
ceaca²d ⇒ ad(ac)²e
c²ead ⇒ a³de²ac²ea
cacead ⇒ a²de(ac)²e
ceca³d ⇒ daceaca
ceaca³d ⇒ ada³cec
ceaca⁴d ⇒ ada²ceaca
b ⇒ ec

# ab:ababaaabba=1 reversed:ae/cd/b aab=c,bacb=d,bad=e frequency:3/1,4/0,3/0 ae=ea eaa=1 dc=ea cad=1 dd=eeaccea dad=ecace daad=cec daaad=eaceaca cecc=da ceacac=adaa cacec=aad cceac=aaadea ccd=aaadecace cacd=aadacec cecd=deaccea caced=aadeccea ccaad=aaadeaceaca cecaad=daacec ceacaad=adacace ccead=aaadeeaccea cacead=aadeacace cecaaad=daceaca ceacaaad=adaaacec ceacaaaad=adaaceaca b=ec

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#1507 ⟨a, b | ababaaabba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)