⟨a, b | aabbbaabba=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:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. bbbaabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	ba²b²c ⇒ a²b²cb	[26]
7.	b²cbd ⇒ adba²b²	[27]
8.	ba²b²a ⇒ cb³	[15]
9.	b²cba ⇒ ab³c	[23]
10.	b³a² ⇒ a²db²cb	[33]
11.	b²cb²d ⇒ adb²a²b²	[32]
12.	b²cb²a ⇒ adbcb³c	[28]
13.	b²cb³ ⇒ ad	[21]
14.	b³ab²c ⇒ dba(cb²)²	[34]
15.	b³acb²c ⇒ a²db²a²cb²cb	[37]
16.	b(b²a)² ⇒ dba²bcb³	[16]
17.	b³acb²a ⇒ a²db²c²b³	[36]

# ab:aabbbaabba=1 reversed:cda/b aaa=c,bbbaabb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c baabbc=aabbcb bbcbd=adbaabb baabba=cbbb bbcba=abbbc bbbaa=aadbbcb bbcbbd=adbbaabb bbcbba=adbcbbbc bbcbbb=ad bbbabbc=dbacbbcbb bbbacbbc=aadbbaacbbcb bbbabba=dbaabcbbb bbbacbba=aadbbccbbb

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

Σ	#	Presentation	Mapping
10	1530	⟨a, b \| abbaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

1530

⟨a, b | abbaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#1460 ⟨a, b \| aabbbaabab=1⟩
Next:	#1463 ⟨a, b \| aabbbababa=1⟩

#1461 ⟨a, b | aabbbaabba=1⟩

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Properties

Rewriting system

Isomorphic instances