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

#	Rule	Proof
1.	dc ⇒ 1	[17]
2.	cd ⇒ 1	[9]
3.	ca ⇒ ac	[6]
4.	da ⇒ ad	[14]
5.	a⁷ ⇒ c	[2]
6.	b²c ⇒ a⁶bab	[19]
7.	babd ⇒ adb²	[15]
8.	bcba ⇒ cbab	[25]
9.	b²ac ⇒ a⁶(ba)²	[21]
10.	(ba)²d ⇒ adb²a	[16]
11.	b²a²c ⇒ a⁶baba²	[27]
12.	baba²d ⇒ adb²a²	[23]
13.	b²a³c ⇒ a⁶baba³	[30]
14.	baba³d ⇒ adb²a³	[29]
15.	b²a⁴c ⇒ a⁶baba⁴	[34]
16.	baba⁴d ⇒ adb²a⁴	[32]
17.	b²a⁵c ⇒ a⁶baba⁵	[37]
18.	baba⁵d ⇒ adb²a⁵	[36]
19.	b²a⁶ ⇒ a⁶dbcb	[40]
20.	baba⁶ ⇒ d(bc)²	[33]
21.	bab² ⇒ d	[3]

# ab:aaaaaababba=1 reversed:cda/b aaaaaaa=c,babb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaaaa=c bbc=aaaaaabab babd=adbb bcba=cbab bbac=aaaaaababa babad=adbba bbaac=aaaaaababaa babaad=adbbaa bbaaac=aaaaaababaaa babaaad=adbbaaa bbaaaac=aaaaaababaaaa babaaaad=adbbaaaa bbaaaaac=aaaaaababaaaaa babaaaaad=adbbaaaaa bbaaaaaa=aaaaaadbcb babaaaaaa=dbcbc babb=d

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

Σ	#	Presentation	Mapping
11	2821	⟨a, b \| aaaaababbaa=1⟩	φ(a) = a, φ(b) = b
11	2863	⟨a, b \| aaaababbaaa=1⟩	φ(a) = a, φ(b) = b
11	3269	⟨a, b \| abbaaaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2821

⟨a, b | aaaaababbaa=1⟩

φ(a) = a, φ(b) = b

2863

⟨a, b | aaaababbaaa=1⟩

φ(a) = a, φ(b) = b

3269

⟨a, b | abbaaaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2798 ⟨a, b \| aaaaaababab=1⟩
Next:	#2800 ⟨a, b \| aaaaaababbb=1⟩

#2799 ⟨a, b | aaaaaababba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances