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

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[6]
4.	ad ⇒ da	[18]
5.	a⁵ ⇒ c	[2]
6.	cb² ⇒ baba⁴	[24]
7.	dbab ⇒ b²da	[20]
8.	abcb ⇒ babc	[27]
9.	cab² ⇒ (ab)²a⁴	[25]
10.	d(ab)² ⇒ ab²da	[23]
11.	ca²b² ⇒ a(ab)²a⁴	[29]
12.	da(ab)² ⇒ a²b²da	[22]
13.	ca³b² ⇒ a³baba⁴	[32]
14.	da³bab ⇒ a³b²da	[30]
15.	a⁴b² ⇒ bcbda⁴	[34]
16.	a⁴bab ⇒ (cb)²d	[31]
17.	b²ab ⇒ d	[3]

# ab:aaaabbaba=1 cda/b aaaaa=c,bbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c cbb=babaaaa dbab=bbda abcb=babc cabb=ababaaaa dabab=abbda caabb=aababaaaa daabab=aabbda caaabb=aaababaaaa daaabab=aaabbda aaaabb=bcbdaaaa aaaabab=cbcbd bbab=d

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

Σ	#	Presentation	Mapping
9	643	⟨a, b \| aaabbabaa=1⟩	φ(a) = a, φ(b) = b
9	720	⟨a, b \| ababbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

643

⟨a, b | aaabbabaa=1⟩

φ(a) = a, φ(b) = b

720

⟨a, b | ababbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#620 ⟨a, b \| aaaabbaab=1⟩
Next:	#622 ⟨a, b \| aaaabbabb=1⟩

#621 ⟨a, b | aaaabbaba=1⟩

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Properties

Rewriting system

Isomorphic instances