⟨a, b | aababbbaba=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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generator: aaa=c
Auxiliary generator: babbbab=d

cd ⇒ 1
dc ⇒ 1
ac ⇒ ca
ad ⇒ da
a³ ⇒ c
cbab² ⇒ b²abc
db²ab ⇒ bab²d
abcbab ⇒ babcba
cabab² ⇒ ab²abc
dab²ab ⇒ abab²d
a(ab)²cb ⇒ (cb)²abda²
ca²bab² ⇒ a²b²abc
da²b²ab ⇒ a²bab²d
ab³ab ⇒ b²abcbda
a²b²abcb ⇒ cb³aba²
a²bab³ ⇒ b³aba²
b³abcb ⇒ da²
abcb²abcb ⇒ ba(bc)²(ab)²da²

# ab:aababbbaba=1 cda/b aaa=c,babbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c cbabb=bbabc dbbab=babbd abcbab=babcba cababb=abbabc dabbab=ababbd aababcb=cbcbabdaa caababb=aabbabc daabbab=aababbd abbbab=bbabcbda aabbabcb=cbbbabaa aababbb=bbbabaa bbbabcb=daa abcbbabcb=babcbcababdaa

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#1433 ⟨a, b | aababbbaba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)