⟨a, b | aabbaaba=1⟩

Up:

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. bbaab=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.	ba²bc ⇒ a²bcb	[19]
7.	bcbd ⇒ adba²b	[29]
8.	bcba ⇒ ab²c	[26]
9.	ba²ba ⇒ cb²	[15]
10.	b²a² ⇒ a²dbcb	[27]
11.	bcb² ⇒ ad	[24]
12.	b²abc ⇒ dba(cb)²	[20]
13.	b²acbc ⇒ a²dba²(cb)²	[32]
14.	b(ba)² ⇒ dba²cb²	[16]
15.	b²acba ⇒ a²dbc²b²	[31]

# ab:aabbaaba=1 reversed:cda/b aaa=c,bbaab=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c baabc=aabcb bcbd=adbaab bcba=abbc baaba=cbb bbaa=aadbcb bcbb=ad bbabc=dbacbcb bbacbc=aadbaacbcb bbaba=dbaacbb bbacba=aadbccbb

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

Σ	#	Presentation	Mapping
8	324	⟨a, b \| abaaabba=1⟩	φ(a) = a, φ(b) = b
8	338	⟨a, b \| abbabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

324

⟨a, b | abaaabba=1⟩

φ(a) = a, φ(b) = b

338

⟨a, b | abbabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#310 ⟨a, b \| aababbba=1⟩
Next:	#313 ⟨a, b \| aabbaabb=1⟩

#312 ⟨a, b | aabbaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances