⟨a, b | aaabaabbbba=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:
- Left-to-right recursive path with deg(c) = deg(d) = deg(b) = 0, c < d < b; deg(a) = 1
Auxiliary generators:
1. bbbb=c
2. aaaabaa=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[20]
2.	dc ⇒ 1	[11]
3.	bc ⇒ cb	[5]
4.	bd ⇒ db	[24]
5.	b⁴ ⇒ c	[2]
6.	ba²ca ⇒ aba²c	[12]
7.	b³aba² ⇒ ca²cad	[29]
8.	ca⁴ ⇒ a²ba²b³	[27]
9.	da²ba² ⇒ a⁴db	[32]
10.	cba⁴ ⇒ (ba²)²b³	[30]
11.	d(ba²)² ⇒ ba⁴db	[25]
12.	cb²a⁴ ⇒ b(ba²)²b³	[35]
13.	db(ba²)² ⇒ b²a⁴db	[31]
14.	b³a⁴ ⇒ a²ca²db³	[33]
15.	b²(ba²)² ⇒ (ca²)²d	[37]
16.	da³ba² ⇒ a⁴bad	[7]
17.	dba³ba² ⇒ ba⁴bad	[34]
18.	db²a³ba² ⇒ b²a⁴bad	[38]
19.	b³a³ba² ⇒ ca²ca³d	[39]
20.	a⁴ba² ⇒ d	[3]

# ab:aaabaabbbba=1 cdb/a bbbb=c,aaaabaa=d magic:1 cd=1 dc=1 bc=cb bd=db bbbb=c baaca=abaac bbbabaa=caacad caaaa=aabaabbb daabaa=aaaadb cbaaaa=baabaabbb dbaabaa=baaaadb cbbaaaa=bbaabaabbb dbbaabaa=bbaaaadb bbbaaaa=aacaadbbb bbbaabaa=caacaad daaabaa=aaaabad dbaaabaa=baaaabad dbbaaabaa=bbaaaabad bbbaaabaa=caacaaad aaaabaa=d

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

Σ	#	Presentation	Mapping
11	2997	⟨a, b \| aaabbbbabba=1⟩	φ(a) = b, φ(b) = a
11	3049	⟨a, b \| aabaabbbbaa=1⟩	φ(a) = a, φ(b) = b
11	3152	⟨a, b \| aabbbbaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2997

⟨a, b | aaabbbbabba=1⟩

φ(a) = b, φ(b) = a

3049

⟨a, b | aabaabbbbaa=1⟩

φ(a) = a, φ(b) = b

3152

⟨a, b | aabbbbaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2925 ⟨a, b \| aaabaabbbab=1⟩
Next:	#2927 ⟨a, b \| aaababaaaab=1⟩

#2926 ⟨a, b | aaabaabbbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances