⟨a, b | aaabbbaaba=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(b) = 0, c < d < b; deg(a) = 1
Auxiliary generators:
1. bbb=c
2. aabaaaa=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[17]
2.	cd ⇒ 1	[18]
3.	cb ⇒ bc	[5]
4.	db ⇒ bd	[20]
5.	b³ ⇒ c	[2]
6.	aca²b ⇒ ca²ba	[23]
7.	a²bab² ⇒ daca²c	[24]
8.	a⁴c ⇒ b(ba²)²	[29]
9.	a²ba²d ⇒ bda⁴	[26]
10.	a⁴bc ⇒ b²(a²b)²	[30]
11.	(a²b)²d ⇒ bda⁴b	[28]
12.	a⁴b² ⇒ b²da²ca²	[32]
13.	(a²b)²b ⇒ d(a²c)²	[25]
14.	a²ba³d ⇒ daba⁴	[7]
15.	a²ba³bd ⇒ daba⁴b	[34]
16.	a²ba³b² ⇒ da(a²c)²	[35]
17.	a²ba⁴ ⇒ d	[3]

# ab:aaabbbaaba=1 reversed:cdb/a bbb=c,aabaaaa=d magic:1 dc=1 cd=1 cb=bc db=bd bbb=c acaab=caaba aababb=dacaac aaaac=bbaabaa aabaad=bdaaaa aaaabc=bbaabaab aabaabd=bdaaaab aaaabb=bbdaacaa aabaabb=daacaac aabaaad=dabaaaa aabaaabd=dabaaaab aabaaabb=daaacaac aabaaaa=d

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

Σ	#	Presentation	Mapping
10	1456	⟨a, b \| aabbabbbba=1⟩	φ(a) = b, φ(b) = a
10	1482	⟨a, b \| abaaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

1456

⟨a, b | aabbabbbba=1⟩

φ(a) = b, φ(b) = a

1482

⟨a, b | abaaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#1378 ⟨a, b \| aaabbbaaab=1⟩
Next:	#1380 ⟨a, b \| aaabbbaabb=1⟩

#1379 ⟨a, b | aaabbbaaba=1⟩

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Properties

Rewriting system

Isomorphic instances