⟨a, b | aaabbaba=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. bbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[10]
2.	dc ⇒ 1	[13]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[14]
5.	a⁴ ⇒ c	[2]
6.	cb² ⇒ baba³	[19]
7.	dbab ⇒ b²da	[15]
8.	abcb ⇒ babc	[22]
9.	cab² ⇒ (ab)²a³	[20]
10.	d(ab)² ⇒ ab²da	[18]
11.	ca²b² ⇒ a(ab)²a³	[24]
12.	da(ab)² ⇒ a²b²da	[17]
13.	a³b² ⇒ bcbda³	[27]
14.	a³bab ⇒ (cb)²d	[25]
15.	b²ab ⇒ d	[3]

# ab:aaabbaba=1 cda/b aaaa=c,bbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c cbb=babaaa dbab=bbda abcb=babc cabb=ababaaa dabab=abbda caabb=aababaaa daabab=aabbda aaabb=bcbdaaa aaabab=cbcbd bbab=d

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

Σ	#	Presentation	Mapping
8	334	⟨a, b \| ababbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

334

⟨a, b | ababbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#293 ⟨a, b \| aaabbaab=1⟩
Next:	#295 ⟨a, b \| aaabbabb=1⟩

#294 ⟨a, b | aaabbaba=1⟩

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Properties

Rewriting system

Isomorphic instances