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

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[21]
3.	bc ⇒ cb	[5]
4.	bd ⇒ db	[22]
5.	b³ ⇒ c	[2]
6.	ca²b²a ⇒ aca²b²	[31]
7.	daca² ⇒ a²b²adb	[29]
8.	cba²b²a ⇒ baca²b²	[32]
9.	dbaca² ⇒ ba²b²adb	[33]
10.	cb²a²b²a ⇒ b²aca²b²	[34]
11.	db²aca² ⇒ b²a²b²adb	[35]
12.	da²ca² ⇒ a²b²a²db	[28]
13.	ba²ca² ⇒ ca⁴b	[25]
14.	ba²b²a² ⇒ a⁴c	[36]
15.	b²a⁴ ⇒ a²ca²db²	[40]
16.	da³ca² ⇒ a²b²a³db	[42]
17.	ba³ca² ⇒ ca⁴cadb	[30]
18.	a⁴ca² ⇒ db	[23]
19.	ca²ba⁴ ⇒ (a²c)²ba²d	[43]
20.	ca²cba⁴ ⇒ (a²c)²b²a²db²	[47]
21.	ba²ba⁴ ⇒ a⁴cb²a²d	[46]
22.	ba²cba⁴ ⇒ a⁴c²a²db²	[45]

# ab:aaabbbaabba=1 cdb/a bbb=c,aabbaaaa=d magic:1 cd=1 dc=1 bc=cb bd=db bbb=c caabba=acaabb dacaa=aabbadb cbaabba=bacaabb dbacaa=baabbadb cbbaabba=bbacaabb dbbacaa=bbaabbadb daacaa=aabbaadb baacaa=caaaab baabbaa=aaaac bbaaaa=aacaadbb daaacaa=aabbaaadb baaacaa=caaaacadb aaaacaa=db caabaaaa=aacaacbaad caacbaaaa=aacaacbbaadbb baabaaaa=aaaacbbaad baacbaaaa=aaaaccaadbb

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

Σ	#	Presentation	Mapping
11	3114	⟨a, b \| aabbaabbbba=1⟩	φ(a) = b, φ(b) = a
11	3272	⟨a, b \| abbaaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3114

⟨a, b | aabbaabbbba=1⟩

φ(a) = b, φ(b) = a

3272

⟨a, b | abbaaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2984 ⟨a, b \| aaabbbaabab=1⟩
Next:	#2986 ⟨a, b \| aaabbbabaab=1⟩

#2985 ⟨a, b | aaabbbaabba=1⟩

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Properties

Rewriting system

Isomorphic instances