⟨a, b | aaaaababbba=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. aaaaaa=c
2. babbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[15]
2.	cd ⇒ 1	[9]
3.	ca ⇒ ac	[6]
4.	da ⇒ ad	[13]
5.	a⁶ ⇒ c	[2]
6.	bcba ⇒ cbab	[26]
7.	baba⁵ ⇒ d(bc)²	[28]
8.	b³c ⇒ a⁵bab²	[18]
9.	bab²d ⇒ adb³	[16]
10.	b³ac ⇒ a⁵bab²a	[20]
11.	bab²ad ⇒ adb³a	[14]
12.	b³a²c ⇒ a⁵bab²a²	[30]
13.	bab²a²d ⇒ adb³a²	[22]
14.	b³a³c ⇒ a⁵bab²a³	[34]
15.	bab²a³d ⇒ adb³a³	[32]
16.	b³a⁴c ⇒ a⁵bab²a⁴	[37]
17.	bab²a⁴d ⇒ adb³a⁴	[36]
18.	b³a⁵ ⇒ a⁵db²cb	[40]
19.	bab²a⁵ ⇒ db(bc)²	[33]
20.	bab³ ⇒ d	[3]

# ab:aaaaababbba=1 reversed:cda/b aaaaaa=c,babbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaaa=c bcba=cbab babaaaaa=dbcbc bbbc=aaaaababb babbd=adbbb bbbac=aaaaababba babbad=adbbba bbbaac=aaaaababbaa babbaad=adbbbaa bbbaaac=aaaaababbaaa babbaaad=adbbbaaa bbbaaaac=aaaaababbaaaa babbaaaad=adbbbaaaa bbbaaaaa=aaaaadbbcb babbaaaaa=dbbcbc babbb=d

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

Σ	#	Presentation	Mapping
11	2867	⟨a, b \| aaaababbbaa=1⟩	φ(a) = a, φ(b) = b
11	2947	⟨a, b \| aaababbbaaa=1⟩	φ(a) = a, φ(b) = b
11	3295	⟨a, b \| abbbaaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2867

⟨a, b | aaaababbbaa=1⟩

φ(a) = a, φ(b) = b

2947

⟨a, b | aaababbbaaa=1⟩

φ(a) = a, φ(b) = b

3295

⟨a, b | abbbaaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2822 ⟨a, b \| aaaaababbab=1⟩
Next:	#2824 ⟨a, b \| aaaaababbbb=1⟩

#2823 ⟨a, b | aaaaababbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances