⟨a, b | aaababbbaba=1⟩

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Monoids with two generators and one relation

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 generators:
1. aaaa=c
2. babbbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[16]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[20]
5.	a⁴ ⇒ c	[2]
6.	cbab² ⇒ b²abc	[24]
7.	db²ab ⇒ bab²d	[21]
8.	abcbab ⇒ babcba	[37]
9.	cabab² ⇒ ab²abc	[25]
10.	dab²ab ⇒ abab²d	[23]
11.	ca²bab² ⇒ a²b²abc	[29]
12.	da²b²ab ⇒ a²bab²d	[30]
13.	a³babcb ⇒ (cb)²abda³	[43]
14.	ca³bab² ⇒ a³b²abc	[34]
15.	da³b²ab ⇒ a³bab²d	[35]
16.	ab³ab ⇒ b²abcbda	[28]
17.	a³b²abcb ⇒ cb³aba³	[42]
18.	a³bab³ ⇒ b³aba³	[41]
19.	b³abcb ⇒ da³	[32]
20.	abcb²abcb ⇒ ba(bc)²(ab)²da³	[45]

# ab:aaababbbaba=1 cda/b aaaa=c,babbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c cbabb=bbabc dbbab=babbd abcbab=babcba cababb=abbabc dabbab=ababbd caababb=aabbabc daabbab=aababbd aaababcb=cbcbabdaaa caaababb=aaabbabc daaabbab=aaababbd abbbab=bbabcbda aaabbabcb=cbbbabaaa aaababbb=bbbabaaa bbbabcb=daaa abcbbabcb=babcbcababdaaa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
11	3087	⟨a, b \| aababbbabaa=1⟩	φ(a) = a, φ(b) = b
11	3299	⟨a, b \| abbbabaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3087

⟨a, b | aababbbabaa=1⟩

φ(a) = a, φ(b) = b

3299

⟨a, b | abbbabaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2948 ⟨a, b \| aaababbbaab=1⟩
Next:	#2950 ⟨a, b \| aaababbbabb=1⟩

#2949 ⟨a, b | aaababbbaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances